narelle kruger honours project

Simulation Analysis of Doubled Haploids in a Wheat Breeding Program

November 1999

N.L. Kruger

Research Report #5

Simulation Analysis of Doubled Haploids in a

Wheat Breeding Program

Narelle Lee Kruger

This report was submitted as a requirement of the subject AG421, for a Bachelor of

Agricultural Science (Plant Breeding) in the Faculty of Natural Resources, Agriculture and

Veterinary Science in the School of Land and Food, The University of Queensland,

November 1999.

Abstract

The Germplasm Enhancement Program (GEP) of the Australian Northern Wheat

Improvement Program (NWIP) is presently based on an S1 recurrent selection strategy.

The objective of the GEP is to ensure a continual supply of high yielding germplasm for the

pedigree programs in the NWIP. The GEP works on a four year breeding cycle. Years 1

and 2 are used for intermating, selection for the traits maturity and height, and seed

multiplication of the S1 families. Multi-environment Trials (METs) of the S1 families are

conducted in years 3 and 4 and selection is based on grain yield and grain protein

concentration data collected from these METs. There is interest in whether using doubled

haploid (DH) lines in the MET evaluation phase of the recurrent selection program, in

place of S1 families, could contribute to an increase in the rate of genetic improvement for

grain yield.

The objective of this project was to use computer simulation to investigate the applicability

of a DH strategy in the GEP for a range of genotype-environment system models which are

considered to be relevant to wheat improvement in the northern grains region of Australia.

This study considered the influence of models including additive and genotype-by-

environment (G×E) interaction effects. The computer simulation program QU-GENE,

developed at The University of Queensland, was used in this study. The advantages of the

computer simulation approach over alternative approaches based on either theoretical

analysis or experimental evaluation were: (1) that more complex genetic models could be

examined than were possible to examine using the theoretical approach, (2) larger

experiments with many more factors could be examined than would be feasible in an

experimental investigation, and (3) answers to researchable questions could be obtained in

a more timely manner than would be possible using either a theoretical or experimental

approach.

Five simulation experiments were conduct to compare the response to selection or genetic

gain when either S1 families or DH lines were used in the GEP. Experiment one involved

simulating the effective population size (Ne) for DH lines and S1 families, and comparing

these results to the theoretical predictions. The simulated results conformed well to the

results predicted from theory. For the same number of selected individuals, the S1 families

had a higher Ne than the DH lines and therefore the S1 family strategy was less likely to

lose favourable genes by random drift. The effect of linkage disequilibrium was assessed in

experiment two. Linkage disequilibrium was shown to have an influential role in the rates

of increase in the frequency of favourable genes in the GEP. The third experiment

compared the response to selection when identical numbers of S1 families and DH lines

were evaluated, for an additive genetic model without G×E interactions. The results

indicated that 250 DH lines had an advantage over 1000 S1 families in terms of rate of

response to selection. In the fourth experiment, intensity of selection was manipulated by

changing the number of families selected to proceed into the next cycle of selection.

Increasing the intensity of selection by selecting fewer families increased the rate of

response to selection in the short-term. However, selecting fewer families also decreased Ne

and consequently selecting too few families resulted in the loss of favourable genes from

the population due to the effects of random drift, resulting in a reduction in long-term

response to selection. As a trade-off, selecting 20 families greatly reduced the chance of

favourable genes from being lost from the population due to drift, without slowing the

response to selection significantly. Experiment five assessed the influence of introducing

complexity into the additive model by incorporating genotype-by-environment (G×E)

interactions. The advantage observed by the DH lines over S1 families for the additive

model was retained, and was also present when a MET based on one year for the DH lines

was conducted in comparison to two years for the S1 families.

Computer simulation analyses of the expected short-term and long-term responses to

selection for a range of additive genetic models suggests there are advantages of the DH

strategy when it is feasible to generate 250 or more DH lines for evaluation in the MET

phase of the GEP. This advantage was also observed with the presence of G×E interaction

in the model. These outcomes suggest that the use of DH lines in place of S1 families in the

GEP may be a feasible activity. As the production of DH lines becomes less expensive and

labour intensive, more DH lines will be able to be produced in a year and therefore greater

gains in selection will be potentially observed.

Declaration of Originality

This report describes the original work of the author, except where otherwise stated. It has

not been submitted previously as part of degree requirements at any other University.

Narelle Lee Kruger

Publications relevant to this thesis

Kruger NL, Podlich DW, Cooper M (1999) Comparison of S1 and doubled haploid

recurrent selection strategies by computer simulation with applications for the Germplasm

Enhancement Program of the Northern Wheat Improvement Program. In ‘Proceedings of

the Ninth Assembly Wheat Breeding Society of Australia.’ (Eds P Williamson, P Banks, I

Haak, J Thompson, A Campbell) pp.216-219. (Wheat Breeding Society of Australia:

Toowoomba)

Acknowledgements

I would like to thank the Grains Research and Development Corporation for the

Undergraduate Honours Scholarship Award and their support of this research project.

I would especially like to thank my project supervisor Dr Mark Cooper for his valuable

time, expertise, guidance, encouragement and dedication throughout the course of the

project.

I would also like to thank Dean Podlich for his expertise, advice, time and support.

Thankyou also to Mr Ian Phillips for helping with the use of ASREML and the support of

my fellow colleagues Dr Ian DeLacy, Ms Nicole Jensen, Mr Kevin Micallef and Mr Anura

Ratnasiri.

i

Table of Contents

List of Tables .............................................................................................................. iii

List of Figures..............................................................................................................iv

1. Introduction.........................................................................................1

2. Literature Review ...............................................................................4 2.1 Introduction ...........................................................................................4

2.2 Germplasm Enhancement Program ....................................................7

2.3 Doubled Haploids ................................................................................11

2.4 Genotype-by-environment Interaction ..............................................12

2.5 QU-GENE ............................................................................................13

2.6 Effective Population Size (Ne).............................................................15

2.7 Linkage Disequilibrium .......................................................................18

2.8 Study Focus ...........................................................................................20

3. Materials and Methods.....................................................................21

Experiment 1: Comparison of simulated and theoretical predictions of the effective population size (Ne) of S1 families and DH lines.................23

Experiment 2: Determining the effects of linkage disequilibrium

on gene frequency and response to selection ...............................................25

Experiment 3: Evaluating the response to selection of S1 families

and DH lines for an additive genetic model .................................................26

Experiment 4: Evaluating the impact of selection proportion on

response to selection for an additive genetic model.....................................26

Experiment 5: Evaluating the influence of G×E interaction

genetic models on response to selection.......................................................28

4. Results ................................................................................................31




ii






genetic models on response to selection.......................................................42

5. Discussion...........................................................................................45









genetic models on response to selection 52 Overall ..........................................................................................................54

6. Conclusion..........................................................................................56

7. The Future .........................................................................................57

8. References ..........................................................................................58

9. Appendices ..........................................................................................65 9.1 Appendix 1 ............................................................................................65

9.2 Appendix 2 ............................................................................................76

iii

List of Tables Table 1: Selected intensity (%) and corresponding standardised

selection differential (S), (within the brackets) from

Falconer and Mackay (1996), changes depending on

the number of families in the MET and the number of

families selected (selected proportion) from the MET. .............................27

Table 2: Input file for the QUGENE engine. This file represents

the G×E model 5 (Table 3). The genes 5-16 are removed

from this presentation for conciseness. GN represents the

gene number and E1 – E5 represent the five environment

types within the target population of environments. The

detail of the structure of this input file is explained by

Podlich and Cooper, (1997; 1998) .............................................................29

Table 3: Each model describes the number of genes interacting

with the five environment types and the level of G×E

interaction present as described by the ratio of the

genotype-by-environment interaction variance to

the genotypic variance (σ2GE:σ2

G)..............................................................30

iv

List of Figures

Figure 1a: Components and pathways of germplasm transfer

for yield improvement in the Australian Northern

Wheat Improvement Program: LRC-QDPI

represents the Queensland Department of Primary

Industries pedigree breeding programs located in

Toowoomba at the Leslie Research Centre; PBI-US

represents the University of Sydney pedigree

breeding programs located in Narrabri; GEP

represents the University of Queensland Germplasm

Enhancement Program (Cooper et al., 1999) ............................................8

Figure 1b: Outline of the Germplasm Enhancement Program

(GEP) 4 year cycle. Pictures show examples

of the activities and field experiments undertaken

at each stage of the cycle (Cooper et al., 1999) .........................................9

Figure 2: Schematic outline of the QU-GENE simulation

software. The central ellipse shows the engine and the

surrounding boxes show the application modules.

The GEPRSS module was used in this study

(Podlich and Cooper, 1997, 1998) ...........................................................14

Figure 3: Outline of the activities involved in the S1 and DH

breeding strategies over one cycle of the GEP. The

S1 activities are adapted from Fabrizius et al., (1996) ............................21

v

Figure 4: S1 families effective population size (Ne) calculated

theoretically (solid line) and the average of the simulation

runs (broken lines) for a range of values for the number

of S0 plants sampled (M) and the number of reserve

seed used for intermating per S0 plant sampled (m)................................31

Figure 5: Simulated S1 family effective population size (Ne)

variation, about the average of the simulation runs

(solid line) for a range of S0 plants sampled (M) and

the two extreme values of reserve seed used for

intermating per S0 plant sampled (m). (for intermediate

levels of m refer to Appendix 2)..............................................................32

Figure 6: Comparison of the DH simulated average (closed circles)

and DH theoretical (solid line) effective population size for

a range of S0 plants sampled ( 'M ) and when only one DH

plant was produced per S0 plant sampled ( 'm = 1) .................................32

Figure 7: Average of the simulated DH effective population

size (Ne) for a range of S0 plants sampled ( 'M ) and

DH plants produced per S0 plant sampled 'm .

A regression line is fitted to each 'm ......................................................33

Figure 8: Simulated S1 family effective population size (Ne) variation,

about the average of the simulation runs (solid line) for a range

of S0 plants sampled ( 'M ) and two extreme numbers of DH

plants produced per S0 plant sampled ( 'm ) (for intermediate

levels of 'm refer to Appendix ................................................................34

vi

Figure 9: The influence of linkage disequilibrium in the GEP with

S1 families, 20 genes under both an additive model and

G×E interaction (σ2GE:σ2

G = 2.89) model after five cycles

of selection. (a) frequency of each gene in the model

plotted for one generation of random mating per cycle

(b) gene frequency and value for each of the 20 genes

for one generation of random mating per cycle (c) frequency

of each gene in the model plotted for 10 generations of random

mating per cycle, and (d) gene frequency and value for each

of the 20 genes for 10 generations of random mating per cycle.............35

Figure 10: Comparison of the response to selection for S1 families

and DH lines with heritability 0.05, 20 genes and four

family sizes over 10 cycles of selection...................................................37

Figure 11: Comparison of the response to selection for S1

families and DH lines with heritability 0.05, 500

families and gene numbers over 10 cycles of selection...........................38


families and DH lines with 20 genes, two heritability

levels and two family sizes over 10 cycles of selection ..........................38

Figure 13: Comparison of the response to selection for 1000 S1

families to 100, 250, 500 and 1000 DH lines two

heritability levels and two gene numbers over 10 cycles of selection.....39


families (a,c,e) and DH lines (b,d,f) with a heritability

0.95, 20 genes and three levels of families selected over

10 cycles of selection...............................................................................41

vii

Figure 15: Comparison of response to selection of the G×E interaction

(σ2GE:σ2

G = 1.1: Table 3) model and the additive model

with constant heritability (0.95), genes (20) and two

levels of families selected (S) for four different family

sizes over 10 cycles of selection ..............................................................42

Figure 16: Comparison of response to selection of 1000 S1

families to two sizes of DH lines, 20 genes, two

heritability levels, two levels of G×E interaction

and both S1 families and DH lines having two years of METs...............43

Figure 17: Comparison of response to selection of 1000 S1

families to two sizes of DH lines, 20 genes, two

heritability levels, two levels of G×E interaction

and both S1 families and DH lines having two years of METs...............44

1

1. Introduction

The Germplasm Enhancement Program (GEP) is an S1 recurrent selection program. It

operates as a parent building component of the Northern Wheat Improvement Program

(NWIP) of Australia (Fabrizius et al., 1996). Recurrent selection programs are conducted to

achieve medium and long-term genetic improvement by increasing the frequency of

favourable genes and gene combinations. This is achieved by a combination of long-term

breeding strategies aimed at improvement of the genetic resource base, and short-term

breeding strategies aimed at exploiting the potential of the genetic resource base available

at a particular point in time. Hallauer (1981) argued that recurrent selection is the most

efficient breeding strategy for long-term genetic improvement and pedigree breeding is the

most efficient for short-term exploitation of genetic resources for the purpose of cultivar

development. This study focused on the issues relevant to the rate of genetic improvement

and long-term genetic improvement of a population, with applications to the GEP of the

NWIP. The response to selection can be evaluated in terms of the improvement in the mean

of a population subjected to selection and the rate of genetic improvement can be evaluated

by investigating response to selection over a series of cycles of selection.

Optimising the allocation of resources to activities within the GEP to achieve its role in the

NWIP is a complex problem. There is interest in whether a strategy using doubled haploid

(DH) lines (i.e. plants developed by a process where the haploid genome has been doubled)

can contribute to an increase in the rate of genetic improvement relative to that achieved by

the current S1 strategy. Some advantages of using DH lines in the GEP are: (1) the plants

are completely homozygous in one generation, whereas the S1 families are still segregating,

(2) the variation among DH lines is not influenced by dominance and they have twice as

much additive genetic variation partitioned among lines relative to S1 families, and (3)

selection of superior genotypes should be easier and more efficient. Some disadvantages of

using DH lines in the GEP are: (1) their production is more difficult and costly relative to

S1 families, and (2) with the current DH technology based on the wheat × maize crossing

system, they would add an extra year to the GEP cycle.

2

Breeding programs take many years to conduct and experimental comparisons of DH and

S1 family selection would be costly and time consuming. Further, it is questionable

whether experiments with sufficient power could be conducted to detect significant

differences between the breeding strategies within three cycles of the breeding program (i.e.

12-15 years). Simulation allows a rapid and low cost assessment of the potential value of

using doubled haploids in the GEP. The aim of this study was to use computer simulation

methodology to compare the expected selection response for S1 and DH recurrent selection

strategies for a range of genetic models where the variables heritability, number of cycles,

number of families evaluated in METs, number of families selected and number of genes

contributing to the trait were manipulated. The genetic models investigated in this study

consider the influences of additive and additive-by-environment (G×E) interaction effects.

Response to selection in a recurrent selection program is a balance between directed

changes in gene frequency due to the effects of artificial selection imposed by the breeder

and random changes in gene frequency due to the effects of random drift. It has been

emphasised by Hospital and Chevalet (1996) that the joint effects of selection, linkage and

drift must be considered in any evaluation of selection response. Both changes in gene

frequency due to the effects of selection and drift are influenced by the number of lines

selected and the resulting selection intensity applied by the breeder. Therefore, in this study

factors that influenced response to selection (i.e. heritability, selection intensity and number

of families/lines evaluated) and random drift (i.e. effective population size) were examined

for their influence on selection response within the GEP. The effective population size (Ne)

of DH populations is not well documented in the literature. Simulations were run to

determine the factors that influenced Ne of DH lines in the GEP and to determine whether

the simulated variation for Ne could be explained using the theoretical prediction equations

derived from the work of Comstock (1996).

Linkage disequilibrium is an important consideration in the GEP as the base population was

generated from a small number of parents. Linkage disequilibrium can cause the genetic

variability of a population to either be inflated or depressed, depending on the linkage phase

relationships (coupling or repulsion) among the loci influencing the traits to be manipulated

3

by selection. This in turn affects the heritability of the trait being selected for and therefore

the population’s response to selection.

The computer simulation platform QU-GENE, developed at The University of Queensland

(Podlich and Cooper, 1998) was used to conduct the simulations. One of the application

modules available within QU-GENE is the GEPRSS (Germplasm Enhancement Program

Recurrent Selection Strategy; Podlich and Cooper, 1997). The GEPRSS module was

modified, and an option added so that the user could choose between the current S1 or DH

strategy. This gives the breeder the choice of whether or not they would like to incorporate

doubled haploids into the program in place of the S1 families.

This report has been structured into five sections:

(1) Literature review (section 2): Within this section the relevant literature has been

investigated and a background to the project presented,

(2) Materials and methods (section 3): The objective of this section was to outline the

components of the different genetic models used in the computer simulations, the

experiments undertaken were (i) comparison of simulated and theoretical

predictions of the effective population size (Ne) of S1 families and DH lines, (ii)

determining the effects of linkage disequilibrium on gene frequency and response

to selection, (iii) evaluating the response to selection of S1 families and DH lines

for an additive genetic model, (iv) evaluating the impact of selection proportion on

response to selection for an additive genetic model, (v) evaluating the influence of

G×E interaction genetic models on response to selection.

(3) Results (section 4): This section presents the analysis of the results of the

simulation experiments and the graphical representations of the important results

of the computer simulations,

(4) Discussion (section 5): Presented in this section is an interpretation of the results of

the simulation experiments, and what these results mean for the GEP,

(5) Conclusion (section 6): This section draws together the important points that

resulted from conducting the simulation study,

(6) The future (section 7): Additional investigations to be run in the future are outlined

in this section.

4

2. Literature review

2.1 Introduction

One of the main objectives of a breeding program is to produce a range of cultivars

superior to those that already exist. This objective can be quantified by monitoring the

response to selection of a breeding population over cycles of selection. Any change in the

mean genetic value of a population due to the influence of selective forces is termed the

response to selection (R) or genetic gain. This can be quantified as the difference of the

mean phenotypic value between the offspring of the selected parents and the whole of the

parental generation before selection (Falconer and Mackay, 1996). Response to selection

can be predicted from knowledge of the heritability of the traits subjected to selection, and

the selection pressure applied using the following formula

2 2pR h S ih σ= = , (1)

where h2 is heritability, which can be obtained from genetic experiments conducted for

generations prior to selection, S is the selection differential, i is the standardised selection

differential and σp is the standard error of the phenotypic values of the individuals

(selection units). The selection differential is the mean phenotypic value of the individuals

selected as parents, expressed as a deviation from the population mean. The selection

differential is not known until the parents are selected. However, the expected value of the

standardised selection differential can be predicted assuming that the distribution of

phenotypic values of the individuals to be subjected to selection is normal.

The prediction of response however is only valid for one generation of selection as the

response depends on the heritability of the character in the generation from which the

parents are selected. The heritability of the character is expected to change between

generations of selection for two reasons. First, any response to selection will cause the gene

frequencies to change, on which the heritability depends, and secondly, the selection of

parents reduces the variance and the heritability (Falconer and Mackay, 1996).

5

The response to selection equation is therefore important to plant breeders as it quantifies

the genetic gain achievable in any cycle of selection. The basic principle of any plant

breeding program is the continuous improvement of the target species. It is the plant

breeder’s role to control the intensity and speed of this improvement by changing the

genetic structure of a population (Williams, 1964). By understanding the underlying

concepts of the components of the response to selection equation, and the effect that

manipulating them has on the response to selection, breeders can increase the genetic gain

expected from a cycle of selection.

Equation (1) is a basic prediction equation which applies to the mass selection of

individuals in a random mating base population. Most breeding programs however apply

different forms of selection to a population. The general equation can be extended to

accommodate the features of the different selection methods. Of relevance to this study is

the prediction equation for S1 recurrent selection in the GEP, which is

( )

2'

2 212' 4 2 21

' 4

Ac

AE DEeA D

kcG

rt t

σσ σσ σ σ

=+

+ + +

, (2)

where Gc is the expected gain per cycle, k is the standardised selection differential applied

to S1 families, c is the parental control, 2'Aσ is the additive genetic variance plus a

component that is mainly a function of degree of dominance, 2eσ is the environmental

(error) component of variance, r is the number of replications per environment, t is the

number of environments, 2'AEσ and 2

DEσ are the additive-by-environmental and

dominance-by-environmental interactions variance, and 2Dσ is the dominance genetic

variance (Fehr, 1987). The parental control factor (c) is 1 for selfed families, as used in the

GEP. By changing different variables in the QU-GENE GEPRSS module, the components

of the prediction equation can be manipulated which allows simulation investigations of

different selection strategies for the GEP.

6

If no artificial or natural selection pressures are placed on a population, there is no expected

response to selection, therefore any changes in gene frequency and population mean will be

a result of the effects of random drift, when the effects of mutation and migration are

neglected. A rapid response to selection is necessary in the short-term so that breeders can

find a cultivar that is better than what is currently being used. Long-term selection, from the

perspective of a breeding program, is more concerned about maintaining the genetic

diversity within a population for periods of at least 40 years, while maintaining genetic

advance from selection. However, the maintenance of genetic variation must be balanced

with reductions in genetic variation due to the positive effects of selection. If the response

to selection plateaus then it is possible all of the genetic diversity has been lost from the

population. If this occurs early in a breeding program, new germplasm may need to be

introduced into the program. Alternatively, countering forces from natural selection or

mutation may be balancing the effects of the artificial selection. If such countering forces

are present an alternative breeding strategy may have to be considered. This may also

involve introducing new sources of genetic variation and/or increasing the artificial

selection pressures applied. The overall aim of a breeding program is to maintain its long-

term response to selection while also achieving new cultivar development through short-

term response to selection.

The goal of recurrent selection is to maintain the variability of a population for one or more

quantitative characters, with minimal reduction of genetic diversity in the long-term to

allow for continued genetic gain (Hallauer, 1981; Strahwald and Geiger, 1988; Carver and

Bruns, 1993; De Koyer et al., 1999). Recurrent selection maintains heterozygosity of loci

and promotes crossing over within gene blocks, which has the potential to release large

amounts of genetic variance and contribute positively to maximising genetic gain.

Recurrent selection is most commonly associated with breeding of allogamous (cross-

pollinating) species (e.g. maize, Hallauer and Miranda (1988)). A recent review of genetic

gains (Carver and Bruns, 1993) for grain yield and quality for autogamous (self-pollinating)

species indicates that recurrent selection has been equally, if not more effective than

traditional breeding methods, such as the pedigree strategy.

7

By testing homozygous lines (DH) rather than heterozygous families (S1), selection

efficiency can be increased in a recurrent selection breeding scheme (Griffing, 1975;

Baenzinger et al., 1984). Knowledge of expected genetic gain by selection has proved to be

useful for choosing the most efficient selection method. Before starting a long-term

recurrent selection program the breeder needs to know whether the progress is likely to be

high enough throughout the recurrent cycles of selection (Charmet et al., 1993).

Findings of Carver and Bruns (1993) and De Koyer et al. (1999) indicate that the genetic

gain is often highest in the first cycle of selection when genetic variance (σ2G) is usually

greatest. Selection and genetic drift will ultimately cause a decrease in σ2G in later cycles of

selection when a larger proportion of the favourable alleles of genes are fixed or lost. This

results in a decrease in genetic diversity, which may or may not be significant or sufficient

enough to affect the long-term response to selection.

To improve selection efficiency, a breeder wants to be able to select in their population a

particular phenotype that accurately reflects the true-breeding genotype. This is where the

use of DH lines in breeding programs can greatly enhance selection efficiency. In general,

the probability of selecting a particular phenotype in a conventional F2 population is (¼)n

for recessive, and (¾)n for dominant genes, where n is the number of loci segregating. This

compares to (½)n for both recessive and dominant genes in a DH population. For example

in phenotypic selection for three recessive genes, (½)3 =1/8 of the DH plants would be

selected and expected to breed true in the DH population, compared to (¼)3 =1/64 of the F2

population. For dominant genes, 1/8 of the DH population would breed true for the desired

trait, whereas 27/64 of the F2 population will have to be selected to ensure the inclusion of

the desired 1/64 true-breeding lines (Baenzinger et al., 1984).

2.2 Germplasm Enhancement Program

The main breeding objective of the Germplasm Enhancement Program (GEP) is to combine

high yielding germplasm, from selected sources around the world, with high quality

Australian wheats, and maintain a long-term population improvement strategy that will

8

provide a source of high yielding and high quality wheat germplasm to the pedigree

breeding programs run by the Leslie Research Centre (LRC) at Toowoomba and the Plant

Breeding Institute of the University of Sydney (PBI-US) at Narrabri, of the northern grains

region of Australia (Figure 1a) (Cooper et al., 1999).

The current strategy used in the GEP program is a modified S1 recurrent selection strategy.

It works on a four-year cycle within the general recurrent selecting framework (Figure 1b).

Years 1 and 2 are used for intermating, selection for the traits maturity and height, and seed

multiplication of the S1 families. Multi-environment Trials (METs) of the S1 families are

conducted in years 3 and 4 and selection is based on grain yield and grain protein

concentration. It is expected that this improvement strategy can provide a gradual increase

of favourable allelic frequencies and thus increase the mean of a population for the selected

traits (Fabrizius et al., 1996).

Figure 1a: Components and pathways of germplasm transfer for yield improvement in the

Australian Northern Wheat Improvement Program: LRC-QDPI represents the Queensland

Department of Primary Industries pedigree breeding programs located in Toowoomba at the Leslie

Research Centre; PBI-US represents the University of Sydney pedigree breeding programs located

in Narrabri; GEP represents the University of Queensland Germplasm Enhancement Program

(Cooper et al., 1999).

Cultivar

LRC-QDPIToowoomba

PBI-USNarrabri

Germplasm EnhancementProgram GEP-UQ

Overseas GermplasmResearch Programs

Parents Parents

9

Year Activity

1

2

3

4

Random intermating

10,000 S0 plants Select 2,000

(height, maturity)

2,000 S1 families Select 1,000

(height, maturity, rust)

MET (5 sites) 1,000 S1 families

MET (5 sites) 1,000 S1 families

Select 20-30 (yield & protein)

LRC-QDPI

PBI-US CIMMYT

Figure 1b: Outline of the Germplasm Enhancement Program (GEP) 4 year cycle. Pictures show examples

of the activities and field experiments undertaken at each stage of the cycle (Cooper et al., 1999).

10

Genotype-by-environment (G×E) interactions have a large impact on response to selection

for grain yield of wheat in the Australian target production environments, particularly

G×S×Y (genotype-by-site-by-year) interactions (Basford and Cooper, 1998). The focus on

G×E interactions arises because the interactions introduce uncertainty into the process of

selection among genotypes, especially when selection is based on their phenotypic

performance in a relatively small sample of environments taken from the target population

of environments (Cooper and DeLacy, 1994), as occurs in the case of the GEP. The GEP

therefore utilises two years of METs to accommodate for the G×S×Y interactions that are

encountered, in order to improve S1 family mean heritability and thus help make selection

more efficient. The traditional S1 selection strategy works on a three year cycle, using only

one year of METs. The first two years involve similar steps to those conducted for the GEP.

The traditional S1 selection strategy has been applied in maize breeding for target

environment populations where G×S×Y interactions are not sufficiently large as to warrant

two years of METs (Hallauer and Miranda, 1988). However, for yield of wheat in the

northern grains region the large G×S×Y interactions require at least two years of METs

(Brennan et al., 1981; Cooper et al., 1996). Hence the modification of the S1 recurrent

selection strategy for the GEP involves an additional year of multi-environment testing of

the S1 families.

Following theoretical considerations relevant to the partitioning of additive genetic

variation for quantitative traits and the contributions of this variation to selection response

it has been argued that the inclusion of doubled haploids into the GEP strategy in place of

S1 families can increase the rate of genetic improvement achieved by the GEP. Therefore,

this project was developed to evaluate whether there is an increase in response to selection

in the program contributed by the use of DH lines in place of S1 families. Limitations on

the availability of resources, particularly labour costs and time, will influence the feasibility

of the production of DH lines for use in the GEP. At present approximately 300 DH lines

could be produced by one dedicated person with the available resources for use in the GEP.

As the ability to produce more DH improves (e.g. through increasing skilled labour

availability, decreasing time and cost to produce the DH lines) the relative merits of DH

line selection increases (Strahwald and Geiger, 1988).

11

2.3 Doubled Haploids

Doubled haploids are plants for which the haploid genome has been doubled. There are a

variety of methods available for producing DH lines in wheat:

(1) anther culture (Ouyang et al., 1973; Henry and de Buyser, 1981), and

(2) chromosome elimination

a) wheat × maize method (Laurie and Bennett, 1986, 1988)

b) Hordeum bulbosum method (Barclay, 1975; Sitch and Snape, 1986)

Jensen and Kammholz (1998), modified the wheat × maize method, which is the DH line

production method currently used at the Leslie Research Centre (LRC). In wheat, selected

wheat plants are emasculated and crossed as females with maize pollen to produce a

haploid wheat embryo. The haploid embryo is progressed to a haploid plant in tissue

culture. The young haploid plant from this embryo undergoes a colchicine treatment that

causes the chromosomes to double, resulting in a doubled haploid (diploid: in the case of

wheat as it is an allohexaploid referring to an amphidiploid) plant.

Plant breeders have long been interested in the use of DH lines in breeding programs, as

there are several advantages with using them;

(1) a DH line exhibits twice as much additive genetic variation among lines as that for

S1 families used in an S1 recurrent selection program. DH lines do not express

dominance variation or segregation within lines, resulting in easier and more

efficient selection (Griffing, 1975; Baenziger et al., 1984; Wricke et al., 1986;

Snape, 1989), and

(2) the selection efficiency among completely inbred DH lines is increased as

homozygosity is reached in one generation (equivalent to F∞ selfing generations),

instead of being close to homozygosity after 5-6 generations of self-pollination,

(Baenziger et al., 1984; Wricke and Weber, 1986; Witherspoon and Wernsman,

1989).

The adoption of this new technology however has been slow due to several disadvantages;

(1) production of them is difficult and quite costly, and

12

(2) if they were to be used in the GEP, and to keep the GEP as a four year cycle, the

first year of multi-environment trials would be lost due to the extra time taken to

produce the DH lines relative to the S1 families, therefore the DH lines would only

undergo one year of METs.

Due to DH being completely homozygous in one generation, they allow for only one

crossover opportunity, which is desirable if a line contains a superior combination of genes,

as those genes will be fixed permanently. However with the S1 families, recombination can

occur in every generation, therefore both increasing the chances of finding a good

combination of genes, but also allowing a chance to lose that combination of genes. The

effects of recombination lessens with each progressive generation of selfing (Baenziger et

al., 1984; Knox et al., 1998).

2.4 Genotype-by-environment Interaction

Genotype-by-environment (G×E) interactions can result in changes in rank among

genotypes in different environmental conditions (Haldane, 1947; Comstock and Moll,

1963). When cultivars are compared in different environments, their performance relative

to each other may not be the same. One cultivar may have the highest yield in some

environments and a second cultivar may excel in others. G×E interaction is a major

problem in the study of quantitative traits as it complicates the interpretation of genetic

experiments and undermines the repeatability of experimental results, which consequently

makes predictions difficult and reduces the efficiency of selection (Kearsey and Pooni,

1996).

To emphasise the different influences of G×E interaction on the efficiency of selection they

are sometimes categorised into interactions due to:

(1) heterogeneity of genetic variance among environments (Robertson, 1959), i.e. the

ranking of the genotypes does not differ between environments, only the

magnitude of the difference between the genotypes in each environment changes,

13

therefore the same genotypes are selected regardless of environment and prediction

of response to selection is not complicated by changes in rank of genotypes, or

(2) lack of genetic correlation among environments (Robertson, 1959), i.e. this source

of interaction can result in cross-over interactions, where reranking of the

genotypes occurs and a genotype that performs well in one environment, does not

perform well in other environments, this form of G×E interaction complicates the

selection decisions in a breeding program.

The analysis of variance (ANOVA) has been used to partition total phenotypic variation

into components due to genotype, G×E interaction and error (Brennan and Byth, 1979;

DeLacy et al., 1990). The relative sizes of the variance components are frequently used to

quantify the magnitude of G×E interactions. The influence of G×E interaction in a breeding

program is a problem when the ratio of the G×E interaction to genotypic variance

(σ2GE:σ2

G) is high (Cooper and DeLacy, 1994).

Genotype-by-environment interactions for the grain yield of wheat are large in the northern

grains region and these commonly change the rank of genotypes. These interactions have a

major influence on selection decisions, and therefore response to selection in the GEP.

With the GEP being a recurrent selection program, continual long-term improvement can

only occur if the breeders are able to efficiently select the superior genotypes, for the target

environmental conditions.

2.5 QU-GENE

QU-GENE (QUantitative-GENEtics) is a computer simulation platform developed for the

quantitative analysis of genetic models. The QU-GENE software platform was developed

with a modular structure (Figure 2) and consists of two major component levels;

(1) the genotype-environment system engine (QUGENE), which is used to define the

genetic models to be examined, and

14

(2) the application modules that examine properties of the genotype-environment

system by investigating, analysing or manipulating a population of genotypes for a

target population of environments created from the QUGENE engine (Podlich and

Cooper, 1997, 1998). For the purposes of this study the GEPRSS application

module is used in combination with the engine.

Figure 2: Schematic outline of the QU-GENE simulation software. The central ellipse shows the

engine and the surrounding boxes show the application modules. The GEPRSS module was used in

this study (Podlich and Cooper, 1997, 1998).

QU-GENE enables investigation of the impact of resource allocation decisions within the

breeding program, e.g. variables population size and selection decisions influence how the

resources will be allocated (Fabrizius et al., 1996). QU-GENE has also been used to model

breeding programs in previous simulation experiments (Podlich et al., 1999; Podlich and

Cooper, 1999). Strahwald and Geiger (1988) have previously published work involving the

use of computer simulation to study the efficiency of DH in a barley recurrent selection

program.

15

2.6 Effective Population Size (Ne)

The effective population size (Ne) of a breeding strategy is an important part of any

recurrent selection breeding program. It needs to be determined to quantify the potential

influence of random drift, and balanced with intense selection so that the maximum

response to selection from the available resources can be realised. If the Ne is too small then

favourable genes may be lost from the population through random genetic drift. When drift

occurs the response to selection can never reach its full potential. Therefore, it is important

to understand the effects of drift, which can be determined and quantified in terms of the

effective population size.

Quantifying the effect of random drift in a population requires knowledge of the variability

in changes of gene frequency between repeated runs of the same breeding strategy. This is

defined theoretically in terms of the idealised population (Falconer and Mackay, 1996).

However, populations do not always conform to that of an idealised population (random

mating, monoecious population in which there is no selection, there are N individuals that

reach reproductive age and function as parents, and only one offspring is produced per

mating). One way to deal with deviations from the idealised breeding structure is to express

the situation of a breeding program in terms of the effective number of breeding

individuals, or the effective population size (Ne). This is the number of individuals that

would give rise to the observed sampling variance for gene frequencies, or rate of

inbreeding, if they bred in the manner of the idealised population (Comstock, 1996;

Falconer and Mackay, 1996). The effective population size is therefore a relative measure

of the number of parents used to form a breeding population. It does not represent the

number of individuals from a population that are tested in a recurrent selection program and

is dependent on the level of inbreeding of the parents that are mated and the number of

gametes contributed to the next generation (Hallauer and Miranda, 1988).

Genetic drift is a consequence of sampling in a finite population of small Ne. This is a

disadvantage to any breeding program as genetic diversity needs to be maintained within a

breeding population. Small values of Ne can result from applying intense selection pressure.

16

Following the theoretical development by Comstock (1996) the standard procedure for

calculating Ne is quantified by the equation

( )12

11e n

n

MN

fm−

=

+ +

, (3)

where considered in terms of the GEP, M is the number of S0 plants sampled, 1nf − is the

coefficient of inbreeding after n-1 generations of inbreeding, n is the number of successive

generations and m is the number of reserve seed used for intermating per S0 plant sampled.

In the above equation, whenever n and/or m are large enough to make ( )12

n

m small relative

to ( )11 nf −+ then:

( )11en

MNf −

≈+

. (4)

The theoretical Ne for the S1 recurrent selection strategy used in the GEP is derived from

equation (3) by noting that 1nf − = 0 and n = 1. These values are substituted into equation (3)

and following rearrangement this becomes

( )

+=

mmMNe

212 . (5)

This equation is a special case for S1 families, derived from the standard procedure for

calculating Ne when selecting among families produced by self-fertilisation.

When calculating the Ne of doubled haploids, equation (3) is also used. DH lines are

completely inbred in one generation, therefore fn-1 = 1. If we assume that this is equivalent

to n being large then following equation (4) this results in the theoretical Ne of DH being

'2e

MN = , (6)

17

where 'M is the number of S0 plants sampled in the case of the GEP. This equation is

expected as only one parent is contributing gametes to the next generation and not two

parents which occurs with cross, and self pollination (depending on the level of inbreeding

in the base population), where two sets contribute. Therefore to determine the Ne for DH

the number of S0 plants sampled ( 'M ) is divided by 2 (Equation 6).

Of practical importance to plant breeders is the amount by which the probabilities of

fixation of favourable alleles are increased by selection. Kimura (1957) considered the case

where a gene has two alleles, relative fitness of the single locus genotypes are constant

through time, any level of dominance except overdominance and effective population size

constant through time. He derived the following equation, which has been shown to be a

close approximation for the probability of the fixation of a favourable allele as

( )

( )

02 2 1 2

01

2 2 1 2

0

( )

e

e

pN sx h x h

N sx h x h

e dxP fixation

e dx

− + −

− + −

=∫

∫, (7)

where p0 is the initial frequency of the favourable allele, Ne is the effective population size

as defined above, s is the selection coefficient (a selection proportion), x is the continuous

variable being measure (gene frequency) ranging from 0→1, and h is level of dominance

coefficient.

When there is no selection (s = 0) then equation (7) reduces to P(fixation) = p. It also must

be noted that P(fixation) is a function of the product Nes, and not Ne and s as separate

values. It is much easier to derive a numerical evaluation of P(fixation) when h = ½, as this

corresponds to an additive model. When h = ½, and x is defined in relation to the initial

gene frequency ( 0p ) rather than as a continuous function then equation (7) reduces to

02

2

1( )

1

e

e

N sp

N s

eP fixation

e

−

−

− = −

. (8)

18

Equations (7) and (8) are important to breeders as they provide a quantifiable basis for

determining the influence that the population sizes and selection coefficient values used in

breeding programs have on the probability of fixing favourable genes. From equation (8) it

can be seen that with an additive model there is a relationship between Ne and the selection

coefficient that determines the chances of fixing or losing favourable alleles (Comstock,

1996).

2.7 Linkage Disequilibrium

Linkage disequilibrium is an important factor in the GEP as the starting population is

obtained from the random intermating of 10 initial parents (Fabrizius et al., 1996), a

relatively small number. In one generation of random mating recombination occurs,

however there is a chance that either undesirable or desirable genes may be linked to

desirable genes. When genes are linked, selection for the desirable gene will also result in

indirect selection of the linked gene, increasing its frequency in the population. This form

of indirect selection is unwanted if an undesirable gene is linked to a desirable gene being

selected for as it will decrease the potential response to selection of the population.

Linkage disequilibrium between loci can originate through selection, migration, mutation

and random drift (Lynch and Walsh, 1998). Two alleles at two loci (A allele or a allele at

locus 1 and B allele or b allele at locus 2) can be linked in a coupling abAB or repulsion

aBAb

phase. A population is in linkage disequilibrium when the frequency of gametes with genes

in coupling is not equal to the frequency of gametes with genes in repulsion (Fehr, 1987). It

is most common in populations derived from two inbred parents with contrasting

phenotypes (e.g. one parent is tall (AABB), while the other parent is short (aabb)). Linkage

disequilibrium can influence heritability estimates by causing an upward bias (increase) or

downward bias (decrease) in the estimates of additive (σ2A) and non-additive (dominance

(σ2D)) genetic variation (Fehr, 1987; Hallauer and Miranda, 1988).

19

Groups of genes that are linked, and tend to be transmitted intact from one generation to the

next, are referred to as linkage blocks. Linkage can influence estimates of genetic variance

for quantitative characters. For achievement of linkage equilibrium in a population, the

opportunity must be provided for genetic recombination within heterozygous individuals.

This requires repeated generations of intermating or selfing of heterozygous individuals.

Recombination is an event that occurs during meiosis, which causes new combinations of

genes to occur, and helps break up linkage blocks and reduce the linkage disequilibrium

effect. The length of linkage blocks that are retained in a breeding population is influenced

by the number of parents used to develop the population, the number of generations of

intermating before selfing is initiated and the number of selfing generations conducted after

intermating is completed (Fehr, 1987).

In the GEP the number of parents that form the starting population is relatively small, there

is only one generation of random mating before selfing starts followed by one generation of

selfing for the intermating units used within the GEP modified S1 family strategy. All these

factors contribute to a relatively low frequency of recombination events and a high level of

linkage disequilibrium in the GEP. It is expected that the level of linkage disequilibrium in

the DH strategy will be greater than that of the S1 families (Powell et al., 1992), as the S1

families, unlike DH lines, have a further opportunity to recombine during selfing after the

intermating of the selected lines.

The reduction in additive genetic variance due to gametic linkage disequilibrium caused by

selection, is known as the Bulmer effect (Bulmer, 1971, 1980; Falconer and Mackay,

1996). The changes of the additive genetic variance affect variances, covariances and

heritability, with these parameters requiring re-estimation at each cycle during recurrent

selection (Charmet et al., 1993). The change in these parameters means that the response to

selection will also be altered. To predict long-term response to selection the effects of

linkage disequilibrium and genetic drift on additive variance need to be considered

simultaneously (Wei et al., 1996).

20

2.8 Study focus

The literature outlined above covers the necessary background that needs to be considered

when evaluating the response to selection of a breeding program. The computer simulations

will be conducted using the computer program QU-GENE, to evaluate the response to

selection for both S1 families and DH lines by analysing the impact of effective population

sizes, selection intensity, linkage disequilibrium and genotype-by-environment interactions.

21

3. Materials and Methods

The QU-GENE simulation platform (Podlich and Cooper, 1998) was used to conduct the

simulation experiments. The application module, GEPRSS, representing the GEP had

already been developed prior to the commencement of this project (Podlich and Cooper,

1997). In the GEPRSS module both the S1 family and DH strategies were implemented as

options. An outline of the way in which two breeding strategies were modelled in the

GEPRSS module is presented in Figure 3.

Year Activity (S1) Activity (DH)

Figure 3: Outline of the activities involved in the S1 and DH breeding strategies over one cycle of

the GEP. The S1 activities are adapted from Fabrizius et al., (1996).

To quantify rate of response to selection and long-term selection response each breeding

strategy was run for 10 cycles, which is equivalent to 40 years of the S1 strategy and 50

years of the DH strategy. On a time scale of 40 years the two strategies can alternatively be

compared after 10 cycles of selection for S1 families and after 8 cycles of selection for DH

lines. Response to selection was calculated as the genotypic value of selected individuals

expressed as a percentage of the target genotype, where the target genotype was defined to

1 Random intermating

2 10,000 S0 plants Sample 2,000

3

2,000 S1 familiesSample 1,000

4

MET (5 sites) S1 evaluation

MET (5 sites) S1 evaluation.

5

Generate doubled haploid plants

MET (5 sites) DH evaluation. Select.

Production of DH lines Seed increase

MET (5 sites) DH evaluation

22

be the genotype containing all of the favourable alleles. The mean response to selection was

estimated as the average response obtained for 100 runs of the simulation experiment. This

methodology was used by Podlich et al. (1998) to normalise response to selection for

comparisons between genetic models.

Analyses of variance were conducted on the results of the experiments using the ASREML

software (Gilmour et al., 1999).

Important points with regard to the simulations:

(1) Heritability in the GEPRSS module is calculated on a plot mean basis, however in

the QUGENE engine it is assigned on a single plant basis in the base population.

For the MET evaluation phase of the cycle the between plot experimental variance

was set to be two times that of the within plot variance (Podlich et al., 1998),

(2) All experiments were conducted with 20 families being selected from the METs to

go into the next cycle of selection, unless otherwise stated,

(3) When the term families are used in the experiments it refers to both S1 families

and DH lines i.e. families and lines throughout the report are used interchangeably

for DH lines to simplify presentation of results.

Five simulation experiments were conducted to evaluate different aspects of response to

selection in the GEP. These were:

(1) Comparison of simulated and theoretical predictions of the effective population

size (Ne) of S1 families and DH lines (Experiment 1),

(2) Determining the effects of linkage disequilibrium on gene frequency and response

to selection (Experiment 2),

(3) Evaluating the response to selection of S1 families and DH lines for an additive

genetic model (Experiment 3),

(4) Evaluating the impact of selection proportion on response to selection for an

additive genetic model (Experiment 4),

(5) Evaluating the influence of G×E interaction genetic models on response to

selection (Experiment 5).

The treatments incorporated for each simulation experiment and their objectives are

explained below.

23

Experiment 1: Comparison of simulated and theoretical predictions of the effective

population size (Ne) of S1 families and DH lines

The objective of running the effective population size experiments was to determine

whether the S1 families or DH lines strategies in the GEP reached a critical point where

favourable genes were being lost due to the effects of genetic drift. A secondary objective

was to compare the simulation results of the Ne with the theoretical predictions, that were

given in the literature review section of this thesis. Doubled haploid effective population

equations only exist at a restricted level (e.g. for the case of one DH plant per S0 plant

selected), therefore it was of interest to see what the simulated Ne results were when more

DH plants were produced per S0 plant.

The effective population size was simulated using the S1 and DH strategy additive model

input files to see whether they conformed to the theoretical predictions. The following

parameters were considered:

(1) heritability (one level: 1.00)

(2) number of genes contributing to the trait (one level: 50)

(3) starting gene frequency (one level: 0.5)

(4) number of families used in the METs (five levels: 100, 250, 500, 750, 1000)

(5) number of families selected (no selection was imposed, therefore this value was

equal to the number of families being evaluated in the MET)

Refer to Appendix 1 Table A1.1 for QUGENE engine input file.

To test for the effective population size two more parameters were altered under each

option. The parameters changed in the theoretical equation (5) for the S1 families were:

(1) number of S0 plants sampled (equivalent to number of S1 families) ( M ): 5, 10,

15, 20, 25, 30, 40, 50, 100, 150, 200

(2) number of reserve seeds per S0 plant (m): 1, 2, 3, 4, 5, 10, 100.

M and m are both components of the theoretical equations, allowing the simulations and the

theoretical predictions to be compared. This enabled investigation of the effective

population size of the S1 strategy in the GEP at a range of numbers of families evaluated in

24

the MET and the number of reserve seed used in random mating to create the base

population for each cycle of selection.

The approach to determine the effective population size of the DH strategy was slightly

different to that used for the S1 families. The parameters changed in the input file to

determine the Ne of DH lines were:

(1) number of S0 plants sampled ( 'M ): 5, 10, 15, 20, 25, 30, 40, 50, 100, 150, 200

(2) number of DH produced per S0 plant ( 'm ): 1, 2, 3, 4, 5, 10.

Only 'M however, is present in the theoretical equation (6) to determine the Ne of DH

lines. There is presently no theoretical equation derived to determine the Ne of DH when

more than one DH plant is produced per S0 plant (i.e. when 'm >1). Simulations were still

conducted with values of 'm greater than one so that the response of Ne due to changes in

'm could be evaluated.

The effective population size was calculated for each of the 50 genes not under the

influence of selection in the QU-GENE simulations following the procedure outlined in

example 4.1 (p.70) in Falconer and Mackay (1996). The inbreeding coefficient (F) for each

gene was calculated from the variation among 100 runs using the following formula

2qF

pqσ

= , (9)

where 2qσ is the variance of gene frequencies among runs, p mean gene frequency of a

particular allele at a locus among runs, and q mean gene frequency of all other alleles at

that locus among runs. Using this procedure each gene gave an independent estimate of F.

From this estimate, the rate of inbreeding (∆F) can be calculated by rearranging the

following equation

( )1

1 1 ttF F∆ = − − , (10)

where t is the generation number. The effective population size of each of the fifty genes

was then calculated from ∆F with the following equation

12eN

F=

∆. (11)

25

An estimate of the variation of Ne was obtained by estimating the effective population size

for each gene, and the variation amongst these genes.

Experiment 2: Determining the effects of linkage disequilibrium on gene frequency and

response to selection

A study was conducted to determine the impact of linkage disequilibrium on the frequency

of genes in the GEP after 5 cycles of selection. This study was only conducted on S1

families. Both additive and a complex G×E interaction model were assessed and compared.

Genetic models based on twenty genes were considered. The effects of the genes were

scaled to generate major or minor genes. The favourable alleles for all 20 genes

commenced at a gene frequency of 0.2. Therefore, any positive effects of selection were

expected to increase the gene frequencies above the starting value of 0.2. The following

parameters were considered in both the additive and G×E interaction models:




(4) number of families used in the METs (one level: 250)

(5) number of families selected (one level: 10)

Refer to Appendix 1 Table A1.2 for QUGENE engine input file.

To reduce the effects of linkage disequilibrium in the recurrent selection strategy, ten

generations of random mating were incorporated into the S1 program. The random matings

were conducted from the S0 plants for each cycle of selection. The rate of change of the

favourable alleles for each gene was monitored for the cases with and without the extra

generations of random mating, of particular interest was whether the presence of linkage

disequilibrium influenced the rate of change in gene frequency of the favourable alleles. In

the absence of any effects of linkage disequilibrium the rate of change in the frequencies of

the alleles was expected to be proportional to the size of the gene effects, and independent

of the number of generations of random mating. However, when linkage disequilibrium

was present, i.e. as was expected without the additional generations of random mating, the

26

rate of change in the frequencies of the alleles could be influenced by the size of the gene

effects and the degree of linkage disequilibrium.

Experiment 3: Evaluating the response to selection of S1 families and DH lines for an

additive genetic model

This experiment was conducted to determine whether using DH lines resulted in a faster

response to selection relative to the S1 families for a range of heritabilities, number of

genes contributing to the attribute, number of families evaluated in the MET and the

number of families selected from the MET to progress into the next cycle of selection.

Theoretical considerations suggest that a higher rate of response would be observed when

DH lines were used in the place of S1 families in the GEP.

Using a completely additive genetic model (i.e. no epistasis, no genotype-by-environment

interaction and no linkage) the following parameters were altered providing a range of

genetic model scenarios:

(1) heritability (five levels: 0.05, 0.25, 0.50, 0.75, 0.95)

(2) number of genes contributing to the trait (four levels: 5, 10, 20, 100)



(5) number of selected families (one level: 20)

Refer to Appendix 1 Table A1.3 to Table A1.6 for the relevant QUGENE engine input file.

Experiment 4: Evaluating the impact of selection proportion on response to selection for

an additive genetic model

The number of families selected from one cycle of selection to be progressed through the

next cycle of selection is an important factor in the GEP. If too few families are selected

(high selection intensity) random drift may result and valuable genes may be lost from this

population. On the other hand if too many families are selected (low selection intensity)

27

then too many undesirable genes will be retained in the population and the response to

selection will be slowed down. The GEP currently selects 20 families based on the results

of the MET. This experiment was conducted to determine whether this figure provided a

suitable balance between selection intensity and effective population size.

Table 1: Selected intensity (%) and corresponding standardised selection differential (S), (within

the brackets) from Falconer and Mackay (1996), changes depending on the number of families in

the MET and the number of families selected (selected proportion) from the MET.

Number of families in MET Number of

families selected 250 500 750 1000

5 2% (2.054) 1% (2.326) 0.67% (2.4705) 0.5% (2.576)

10 4% (1.751) 2% (2.054) 1.3% (2.227) 1% (2.326)

15 6% (1.555) 3% (1.881) 2% (2.054) 1.5% (2.1705)

20 8% (1.405) 4% (1.751) 2.67% (1.945) 2% (2.054)

25 10% (1.282) 5% (1.645) 3.33% (1.8255) 2.5% (1.960)

30 12% (1.175) 6% (1.555) 4% (1.751) 3% (1.881)

Table 1 documents the number of families in a MET and the selection proportions applied

and shows that as the selected proportion increases, the standardised selection differential

and selection intensity decreases. To explore the effect that different selection proportions

can have on the response to selection, simulations were run for both S1 families and DH

lines where the following parameters were used:


(2) number of genes contributing to the trait (four levels: 5, 10, 20, 100)



(5) number of selected families (six levels: 5, 10, 15, 20, 25, 30)

28

Experiment 5: Evaluating the influence of G××××E interaction genetic models on response

to selection

Genotype-by-environment interaction was included in the genetic model to determine

whether the responses to selection and advantages of the DH lines over S1 families, that

were observed for the additive model, would be retained in the presence of G×E

interactions. It was also incorporated as G×E interaction has a major influence on the

selection of genotypes in Australian environments, and the simulations would be

incomplete if it was not considered as a factor in the genetic model. Two major experiments

were undertaken to fulfil two objectives. The first, to assess the response to selection when

two years of METs were conducted for both the DH lines and S1 families. Secondly, to

assess response to selection when only the DH lines are conducted with one year of METs.

It was expected that the DH line advantage would be retained when two years of METs

were conducted, however it was uncertain whether this would be retained with the scenario

where one year of METs was used.

To introduce G×E interaction into the additive model, five environment types were added

into the QU-GENE engine input file. The inputs into the genotype-environment system can

be manipulated so that genes can have different effects in different environments, thus

generating G×E interactions. In the input (Table 2), a value of 0 means that a gene has no

effect in that environment, a value of 1 means that a gene has the effects defined by the

m,a,d genetic model, and –1 means that a gene has a cross-over genetic effect in that

environment. These different gene effects are outlined in bold (Table 2) for each of the five

environments (E1 – E5). Refer to appendix 1 for all of the input files.

Five G×E interaction models were produced to create different levels of G×E interaction

(Table 3). There were 20 genes contributing to the attribute subjected to selection in each of

the simulations. The genes in this experiment were interacting with five environment types.

29

Table 2: Input file for the QUGENE engine. This file represents the G×E model 5 (Table 3). The

genes 5-16 are removed from this presentation for conciseness. GN represents the gene number and

E1 – E5 represent the five environment types within the target population of environments. The

detail of the structure of this input file is explained by Podlich and Cooper, (1997; 1998).

S ! Pollination Type

N ! Random Seed

100 200 300

Y N N ! Linkage, Epistasis, Random GxE

1 ! Gene Sampling type (1=fixed, 2=random)

10 ! no. of runs to calc var comp

(BP,Progeny, Genes, Attributes, Environment Types, Sample Environments)

5000 10 22 2 5 1

0.4 0.3 0.15 0.1 0.05 ! Environment Frequency

1 1 1 1 1 ! GxE multipliers

0.95 1 ! Heritability for each Attribute

GN M A D AT L LN K E1 E2 E3 E4 E5 P

1 0.100 0.050 0.000 1 1 1 0 1 0 -1 1 1 0.2

2 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 1 0 0.2

3 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 -1 1 0.2

4 0.100 0.050 0.000 1 1 0.5 0 1 -1 0 1 1 0.2

" " " " " " " "

17 0.100 0.050 0.000 1 1 0.5 0 1 0 1 1 -1 0.2

18 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 -1 1 0.2

19 0.100 0.050 0.000 1 1 0.5 0 1 0 -1 1 -1 0.2

20 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 -1 1 0.2

21 0.50 -0.500 -0.490 2 1 2 0 1 1 1 1 1 0

22 0.50 -0.500 -0.490 2 1 0.5 0 1 1 1 1 1 1

N ! Mating Type

1 ! Selection type

********************************************************************

R ! Mating (Random Mating)

10 5 0.2 ! Generations, Generations before selection, Select Pressure

M ! Mating (Mixture)

0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure

N ! No Further Mating

30

To explore these models, simulations were run for both S1 families and DH lines where the

following parameters were used:

(1) heritability (three levels: 0.05, 0.25, 0.95)



(4) number of families used in the METs (four levels: 250, 500, 750, 1000)

(5) number of selected families (three levels: 10, 20, 30)

(6) level of G×E interaction (five levels: models 1, 2, 3, 4, 5); Table 3

Refer to Appendix 1 Table A1.7 to Table A1.11 for the relevant QUGENE engine input

files.

Table 3: Each model describes the number of genes interacting with the five environment types and

the level of G×E interaction present as described by the ratio of the genotype-by-environment

interaction variance to the genotypic variance (σ2GE:σ2

G).

Model number Number of genes

interacting

(σ2GE:σ2

G)

1 10 0.4

2 10 0.6

3 15 0.8

4 15 1.1

5 20 2.89

31

4. Results



The simulated effective population size (Ne) of the S1 family strategy corresponded well

with the predictions based on theoretical equation (5) (Figure 4). As the number of S1

families selected (M) increases, Ne increases. Ne also increases as the number of reserve

seed used for intermating per S0 plant sampled (m) increases.

Number of S0 plants sampled (M)0 50 100 150 200

Effe

ctiv

e po

pula

tion

size

(Ne)

0

50

100

150

200

250

m=1m=2m=3m=4m=5m=10m=100

The variability of Ne for two levels of m (1 (Figure 5a), 100 (Figure 5b)) is indicated by the

scatter points about the mean (solid line) for each value of M. The variability of Ne about

the mean increases as the number of S0 plants sampled increases. This effect was observed

for all levels of m (Appendix 2).

Figure 4: S1 families effective population size (Ne) calculated theoretically (solid line)

and the average of the simulation runs (broken lines) for a range of values for the number

of S0 plants sampled (M) and the number of reserve seed used for intermating per S0 plant

sampled (m).

32

(a) m = 1

Number of S0 plants sampled (M)

0 50 100 150 200

Effe

ctiv

e po

pula

tion

size

(Ne)

0

50

100

150

200

250

300(b) m = 100


0 50 100 150 200

Effe

ctiv

e po

pula

tion

size

(Ne)

0

50

100

150

200

250

300

Like the S1 family Ne, for the DH lines, as the number of S0 plants sampled ( 'M )

increases, Ne increases (Figure 6). The simulated results and theoretical predictions show

good correspondence.

Number of S0 plants sampled (M')

0 50 100 150 200 250

Effe

ctiv

e pp

ulat

ion

size

(Ne)

0

20

40

60

80

100

120

m' = 1

Figure 7 indicates how the simulated Ne increases as the number of DH plants produced per

S0 plant ( 'M ) increased. Theoretical equations were derived only for the situation when

Figure 5: Simulated S1 family effective population size (Ne) variation, about the average

of the simulation runs (solid line) for a range of S0 plants sampled (M) and the two

extreme values of reserve seed used for intermating per S0 plant sampled (m). (for

intermediate levels of m refer to Appendix 2)

Figure 6: Comparison of the DH simulated average (closed circles) and DH

theoretical (solid line) effective population size for a range of S0 plants

sampled ( 'M ) and when only one DH plant was produced per S0 plant

sampled ( 'm = 1).

33

'm = 1, however, also plotted were the simulated Ne for four levels of 'm > 1. Like the S1

strategy, as the number of DH plants produced per S0 plant ( 'm ) increased the Ne also

increased. This increase was less than that observed for increasing m in the case of the S1

family strategy (Figure 4).


0 50 100 150 200

Effe

ctiv

e po

pula

tion

size

(Ne)

0

20

40

60

80

100

120

140

160

180

200

m' = 1m' = 2m' = 3m' = 4m' = 5m' = 10

The variability of the DH lines Ne for each 'M for the simulated data is shown for two

levels of 'm (1 (Figure 8a), 10 (Figure 8b)). The variation of the Ne is indicated by the

scatter points about the mean (solid line) for each value of 'M . The variability about the

mean increases as the number of S0 plants sampled increases. This effect was observed for

all levels of 'm (Appendix 2).

Figure 7: Average of the simulated DH effective population size (Ne) for

a range of S0 plants sampled ( 'M ) and DH plants produced per S0 plant

sampled 'm . A regression line is fitted to each 'm .

34

(a) m'=1


0 50 100 150 200

Effe

ctiv

e po

pula

tion

size

(Ne)

0

20

40

60

80

100

120

140

160

180

200

220

240

(b) m'=10


0 50 100 150 200

Effe

ctiv

e po

pula

tion

size

(Ne)

0

20

40

60

80

100

120

140

160

180

200

220

240



The results from the linkage disequilibrium experiment focus on cycle five of the GEP,

where the S1 family strategy was used. The genes were scaled to have a distribution of

effects ranging from 1.2% to 10% of the total trait value. Both an additive model and G×E

interaction (σ2GE:σ2

G = 2.89) model were considered. All genes commenced with a gene

frequency of 0.2. Therefore, any increase in the frequency above 0.2 is a consequence of

selection. The smaller the increase in frequency towards a frequency of 1.0, the less

effective was the influence of selection on changing gene frequency. It can be seen from

Figure 9a,c that for most genes selection was effective in increasing the frequency of the

favourable allele, and after five cycles of selection the genes ended up with different gene

frequencies for both the additive and the G×E interaction models.

Figure 8: Simulated S1 family effective population size (Ne) variation, about the average

of the simulation runs (solid line) for a range of S0 plants sampled ( 'M ) and two

extreme numbers of DH plants produced per S0 plant sampled ( 'm ) (for intermediate

levels of 'm refer to Appendix 2)

35

(a) Gene frequency of 20 genes,

with one cycle of random mating

Gene number

0 5 10 15 20 25

Gen

e fre

quen

cy

0.0

0.2

0.4

0.6

0.8

1.0

AdditiveGxE

(b) Gene value and frequency for 20 genes,

with one cycle of random mating

Value of gene

0.00 0.02 0.04 0.06 0.08 0.10

Gen

e fre

quen

cy

0.0

0.2

0.4

0.6

0.8

1.0

1.2

(c) Gene frequency of 20 genes,

with 10 generations of random mating

Gene number

0 5 10 15 20 25

Gen

e fre

quen

cy

0.0

0.2

0.4

0.6

0.8

1.0

(d) Gene value and frequency for 20 genes,

with 10 generations of random mating per cycle

Value of gene

0.00 0.02 0.04 0.06 0.08 0.10

Gen

e fre

quen

cy

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Additive

GxE

AdditiveGxE

Additive

GxE

After five cycles of selection, genes with a relatively low value could have either a low or

high frequency of occurrence in the population (Figure 9b). When the genes are influenced

by the effects of G×E interaction their frequency in the population was generally less then

when there was no G×E interaction effect. There is a lack of a consistent relationship

between the magnitude of the effect of a gene and its frequency following five cycles of

selection for the case where no generations of additional random intermating were

undertaken (Figure 9b). Therefore, genes with similar value, in terms of the way that they

Figure 9: The influence of linkage disequilibrium in the GEP with S1 families, 20 genes

under both an additive model and G×E interaction (σ2GE:σ2

G = 2.89) model after five cycles of

selection. (a) frequency of each gene in the model plotted for one generation of random

mating per cycle (b) gene frequency and value for each of the 20 genes for one generation of

random mating per cycle (c) frequency of each gene in the model plotted for 10 generations of

random mating per cycle, and (d) gene frequency and value for each of the 20 genes for 10

generations of random mating per cycle.

36

contributed to the trait, can have dissimilar gene frequencies. It is hypothesised that this is

predominantly a consequence of linkage disequilibrium. To reduce the effects of linkage

disequilibrium, ten generations of random intermating following each cycle of selection

were added into the simulation (Figure 9d). With the inclusion of the additional generations

of random mating after each cycle of selection, the frequency of the genes was found to be

approximately proportional to the value of the gene after five cycles of selection. As

expected, a pattern was observed after selection whereby genes with low value had a lower

frequency in the population relative to genes with a higher value. The genes in the additive

model still had a higher frequency that was the case for the G×E interaction model genes.

This was expected due to the added complications of selection due to G×E interaction.

There also appears to be a point (approximately a gene value of 0.055) on Figures 9b,d

where the value of the gene is high enough that linkage disequilibrium had little or no effect

on the frequency of these genes after five cycles of selection, as genes with affects of this

magnitude or greater have comparable gene frequencies.



The analysis of variance on the additive model simulation output data indicated significant

interactions between the two breeding strategies (DH lines and S1 families) and cycles,

heritability, number of families tested in the MET and number of genes. Greater levels of

selection response were associated with higher levels of heritability, larger numbers of

families, smaller numbers of genes and increasing numbers of cycles. On average,

including all runs and cycles, the DH strategy had a 13% mean improvement over the S1

family strategy. The following results represent a comparison between the DH and S1

strategies for the changes in response to selection when the number of families, number of

genes and heritability, in each of the strategies were changed.

As the number of families evaluated in the MET increased (with heritability 0.05, 20 genes,

and selecting 20 families), there was stronger selection pressure placed on the population

37

(Table 1) resulting in an increase in the rate of genetic progress (Figure 10a,b,c,d). The

simulation therefore indicates that the DH strategy provided a greater response to selection

relative to the S1 strategy over all family sizes and cycles considered.

(a) 250 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

(d) 1000 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

(c) 750 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

(b) 500 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

At a low heritability (0.05) and a medium family size (500), as the number of genes

increased it took longer to achieve a large response to selection (Figure 11a,b,c,d).

However, the DH strategy had a faster rate of progress relative to the S1 strategy over all of

the gene levels and cycles. With 20 genes contributing toward the attribute under selection

(a potentially realistic value for some traits targeted by the GEP) the DH strategy reached

100% of the target genotype after seven cycles of selection (Figure 11c), while the S1

strategy only reached approximately 90% after 10 cycles.

Figure 10: Comparison of the response to selection for S1 families and DH

lines with heritability 0.05, 20 genes and four family sizes over 10 cycles of

selection.

38

(a) 5 genes

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

(d) 100 genes

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

(c) 20 genes

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

(b) 10 genes

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

S1DH

S1DH

(a) 0.05 heritability, 250 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

(d) 0.95 heritability, 1000 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

(c) 0.95 heritability, 250 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH

(b) 0.05 heritability, 1000 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

S1DH


lines with heritability 0.05, 500 families and gene numbers over 10 cycles of

selection.


lines with 20 genes, two heritability levels and two family sizes over 10 cycles

of selection.

39

Figure 12 shows the effects of two different heritability levels for low (250) and high

(1000) numbers of families when 20 genes are contributing towards the attribute under

selection. At the low heritability of 0.05 (Figure 12a,b) both family sizes have a slower

response to selection than when the heritability is high (0.95) (Figure 12c,d). When the

heritability is high, the 1000 families had a faster response to selection than when 250

families were used (Figure 12c,d). The DH strategy was again superior to the S1 strategy

across the levels of heritability examined. The change in the level of heritability however

did not have a great effect on response to selection when using an additive model.

The impact of the use of different numbers of DH lines in the GEP was assessed relative to

1000 S1 families by comparing the response to selection at two heritability levels (0.05 and

0.95) and two gene numbers (20 and 100). Over all the combinations examined the rate of

progress for 100 DH families was similar to the rate of progress observed for 1000 S1

families (Figure 13a,b,c,d). When the number of DH families was greater than or equal to

250, they gave a greater response to selection than that observed for 1000 S1 families. The

genetic models based on a larger number of genes resulted in the rate of progress being

slower (Figure 13b,d) than the models based on lower gene number (Figure 13a,c).

(a) heritability 0.25, 20 genes

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

(c) heritability 0.95, 20 genes

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

1000 S1100 DH250 DH500 DH1000 DH

(d) heritability 0.95, 100 genes

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

(b) heritability 0.25, 100 genes

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

1000 S1100 DH250 DH500 DH1000 DH

1000 S1100 DH250 DH500 DH1000 DH

1000 S1100 DH250 DH500 DH1000 DH

Figure 13: Comparison of the response to selection for 1000 S1 families to 100,

250, 500 and 1000 DH lines two heritability levels and two gene numbers over

10 cycles of selection.

40

The Bulmer effect was observed in the additive model simulations and was visualised as a

rapid decrease in heritability in the early cycles of selection. This effect can be observed on

Figure 13 as a greater and more rapid increase in response to selection for the first two

cycles of selection compared to the subsequent cycles of selection.



The impact of changing the number of families selected was examined with a heritability of

0.95, 20 genes, three different family sizes (250, 500, 1000) and three different numbers of

selected families (5, 20, 30) for S1 families and DH lines separately.

When five families were selected in the S1 strategy (Figure 14a) the rate of response to

selection was faster than that observed when 20 (Figure 14c) or 30 (Figure 14e) families

were selected. However, when five families were selected the long-term selection response

plateaued before it reached 100% of the target genotype (Figure 14a). This plateau did not

occur at less than 100% of the target genotype for either 20 or 30 families selected (Figure

14c,e). The same overall response was also observed using the DH strategy (Figure

14b,d,f). The DH response to selection was much faster than that observed for the S1

strategy at all levels of families selected. 1000 families in both the S1 and DH strategy had

the fastest short-term response to selection.

The sub-optimal long-term responses to selection that were observed when five S1 and DH

families were selected (Figure 14a,b) is a consequence of loss of favourable alleles for

some of the genes due to the effects of random drift. Thus, while the intense selection that

resulted when five families were selected gave a rapid short-term rate of genetic progress,

the small effective populations required to achieve the high selection intensity placed limits

on the long-term response to selection. The practice of selecting 20 S1 families, which is

currently used in the GEP, did not appear to place severe limits on the expected long-term

response to selection (Figure 14c).

41

(a) 5 S1 families selected

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

(f) 30 DH lines selected

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

250 DH500 DH1000 DH

(d) 20 DH lines selected

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

(b) 5 DH lines selected

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

(c) 20 S1 families selected

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

250 S1500 S11000 S1

(e) 30 S1 families selected

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

250 S1500 S11000 S1

250 DH500 DH1000 DH

250 DH500 DH1000 DH

250 S1500 S11000 S1

The rate of response to selection was examined further for the S1 strategy for both an

additive and G×E interaction model (Model 4 Table 3; σ2GE:σ2

G = 1.1) with a heritability

0.95 and 20 genes, with two levels of families selected (10, 30), and at four different family

sizes (250, 500, 750, 1000) (Figure 15). For each of the four family sizes the G×E

interaction model (circular symbols) had a faster response to selection than the additive

model (triangular symbols) in the short to medium-term (Figure 15ab,c,d). Selecting 10

families also gave a greater response to selection then selecting 30 families for both the

additive and G×E interaction models. The rate of response to selection was increased from

that observed when 250 families were evaluated in the model (Figure 15a) to when 1000

Figure 14: Comparison of the response to selection for S1 families (a,c,e) and DH

lines (b,d,f) with a heritability 0.95, 20 genes and three levels of families selected

over 10 cycles of selection.

42

families were evaluated (Figure 15d). The effects of G×E interaction on response to

selection were examined further in simulation experiment five. (a) 250 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

GxE 10 SGxE 30 SAdd 10 SAdd 30 S

(b) 500 families

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

(d) 1000 families

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

(c) 750 families

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100





to selection

The analysis of variance of the G×E interaction simulation output data indicated significant

interactions between the S1 (2 years of MET), DH (1 year of MET) and DH (2 years of

MET) breeding strategies and level of G×E interaction, cycles, selected proportion and

number of families. On average, including all runs and cycles, the DH (2 MET) had a 12%

increase in mean performance compared to the S1 (2 MET) and a 2% increase in mean

performance over DH (1 MET). DH (1 MET) also had on average a 9% increase in mean

performance compared to the S1 (2 MET). The studies conducted in simulation experiment

three indicated that 100 families were not required in this model as that family size was too

small for the DH lines to have a greater response than 1000 S1 families.

Figure 15: Comparison of response to selection of the G×E interaction

(σ2GE:σ2

G = 1.1: Table 3) model and the additive model with constant heritability

(0.95), genes (20) and two levels of families selected (S) for four different family

sizes over 10 cycles of selection.

43

With two years of MET testing for both strategies, 250 DH lines have an advantage over

1000 S1 families at both high and low levels of heritability and for all levels of G×E

interaction considered (Figure 16a,b,c,d). A faster response to selection was observed at the

higher level of heritability (Figure 16b,d) compared to the lower heritability (Figure 16a,c).

(c) heritability 0.05 h2, σ2GE:σ2

G = 2.89

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

(a) heritability 0.05, σ2GE:σ2

G = 0.8

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

(b) heritability 0.95, σ2GE:σ2

G = 0.8

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

1000 S1 (2 MET)250 DH (2 MET)1000 DH (2 MET)

(d) heritability 0.95, σ2GE:σ2

G = 2.89

Cycle

0 2 4 6 8 10

Perfo

rman

ce (%

targ

et g

enot

ype)

0

20

40

60

80

100

1000 S1 (2 MET)250 DH (2 MET)1000 DH (2 MET)

1000 S1 (2 MET)250 DH (2 MET)1000 DH (2 MET)

1000 S1 (2 MET)250 DH (2 MET)1000 DH (2 MET)

To compare a four year DH strategy to the four year S1 cycle, simulations were also run

where the DH breeding strategy was conducted for one year of METs while S1 families

remained at two years of METs (Figure 17a,b,c,d). The advantage of 250 DH lines over

1000 S1 families was retained, but the magnitude of the advantage reduced, when only one

year of METs was run. At a heritability of 0.95 the response to selection was faster then

when the heritability was 0.05, however the DH advantage was lost after 8 cycles of

selection and 1000 S1 families had a slightly greater response to selection in the long-term

(Figure 17b,d).

Figure 16: Comparison of response to selection of 1000 S1 families to two sizes

of DH lines, 20 genes, two heritability levels, two levels of G×E interaction and

both S1 families and DH lines having two years of METs.

44

(b) heritability 0.95, σ2GE:σ2

G = 0.8

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

1000 S1 (2 MET)250 DH (1 MET)1000 DH (1 MET)

(d) heritability 0.95, σ2GE:σ2

G = 2.89

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

1000 S1 (2 MET)250 DH (1 MET)1000 DH (1 MET)

(a) heritability 0.05, σ2GE:σ2

G = 0.8

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

(c) heritability 0.05, σ2GE:σ2

G = 2.89

Cycle

0 2 4 6 8 10

Per

form

ance

(% ta

rget

gen

otyp

e)

0

20

40

60

80

100

1000 S1 (2 MET)250 DH (1 MET)1000 DH (1 MET)

1000 S1 (2 MET)250 DH (1 MET)1000 DH (1 MET)

Figure 17: Comparison of response to selection of 1000 S1 families to two sizes

of DH lines, 20 genes, two heritability levels, two levels of G×E interaction and

both S1 families and DH lines having two years of METs.

45

5. Discussion



The effective population size simulations were conducted to ensure that the Ne of both the

DH lines and S1 families was large enough that favourable alleles in the population did not

have a high probability of loss through random drift. However, if the Ne is too large the

response to selection will be slowed due to a reduction in selection pressure and the greater

tendency to retain the undesirable alleles in the population. In both the S1 and DH strategy

as the number of S0 plants sampled increased, the effective population size increased. This

is especially important in the DH strategy, as the Ne is smaller than when S1 families are

used. If a breeder was concerned about the Ne size being small with DH lines it is therefore

feasible to increase Ne in this recurrent selection strategy by sampling more than one DH

line from the selected S0 plants. Therefore, there are opportunities to manipulate the

effective population size with DH lines within the GEP if it became an issue. Previous

experiments however have indicated that the Ne is not so low as to have a major influence

on the response to selection relative to the effects of selection, even with relatively intense

selection, as long as the Ne is maintained above a value of 10.

An effective population size with a balance between the random drift and slowed response

to selection scenarios can be accommodated by selecting between 10 and 20 S1 or DH

families per cycle of selection. When the selected proportion was less than 5, there was

strong evidence that significant numbers of genes were lost due to random drift, if it was

greater than 20, the response to selection was slowed considerably.

An increase in the variability around the mean Ne as M (number of S1 families) or 'M

(number of DH lines) increased was a result of random fluctuations in gene frequency. This

variation was greater for those genes that were not under the influence of selection. This

indicates that the observed Ne has the ability to fluctuate dramatically as the selection

intensity decreases. For those genes under the influence of selection there is less scope for

46

undesirable loss of genes by chance. This was quantified in equation (8). As the effective

population size multiplied by the selection coefficient (Nes) increases the probability of the

favourable alleles being fixed in the population approaches one and the probability of loss

of the favourable alleles approaches zero.



The impact of linkage disequilibrium in the GEP was demonstrated in experiment 2 by

showing that low value genes could have a low or high frequency in the population after

five cycles of selection when there was only one generation of random mating between

cycles of selection. The need to consider the effects of linkage disequilibrium in this study

was alerted by the observation that in some of the simulations conducted with the presence

of G×E interaction effects in the genetic model (experiment 4 and 5), a faster response to

selection was being produced compared to the additive model (Figure 15). This result was

produced because in the additive model all of the genes contributing to the attribute had

small and equal effects, i.e. there were no major genes that were selected for initially to

increase the response to selection. However, with the G×E interaction model the genes had

different effects in different environments. The consequence of this was that there were

major and minor genes within the target population of environments. This resulted in the

major genes being fixed quickly, resulting in an increase in their frequency and therefore a

rapid response to selection. The fate of the minor genes was a consequence of the effects of

selection and linkage disequilibrium.

When the effects of genes in the additive model were scaled to be proportional in relative

effects in the same way as for the G×E interaction model it was possible to compare the

effects of linkage disequilibrium and selection for both the additive and G×E interaction

model. By cycle five, the favourable alleles of the genes in the G×E interaction model had

increased to a smaller gene frequency in the population than in the additive model. This

was due to G×E interaction adding a level of complexity into the selection procedure that

47

was not present with the additive model, resulting in selection being less efficient relative

to the additive model.

To observe the effects of linkage disequilibrium, in the additive model the genes were given

the same value as the genes in the G×E interaction model. The effect of linkage

disequilibrium was evident in the simulations even after five cycles of recurrent selection,

as selection for the major genes results in any associated minor genes also being selected.

In some cases the frequency of these minor genes in the population increased to a level

above that which would be expected in the population in the absence of linkage

disequilibrium. A number of the minor genes were ‘pulled’ to gene frequencies higher than

what would be expected due to linkage disequilibrium associations with important major

genes that were being selected for in early cycles. This causes the genotypic variance of the

population and response to selection to decrease after the first few cycles of selection. This

effect is known as the Bulmer effect.

Introducing ten generations of random mating into the S1 strategy reduced the effects of

linkage disequilibrium after each cycle of selection. Random mating allows the genes in the

population to recombine, resulting in new gene combinations, and an approach towards

linkage equilibrium. Therefore, when selection is applied to the major genes there is less

chance that there is indirect selection for minor genes. When the random mating is

introduced a pattern emerges, as the value of the gene increases, its frequency in the

population increases at a greater rate (Figure 9d). There is however a major disadvantage

with adding additional generations of random mating into the GEP, it means that every

cycle of selection will be longer. This limits the scope to use further generations of random

mating. The use of 10 generations of random mating is not feasible for any selection

program, as the genetic gain per year would be greatly reduced, reducing the benefits from

the recurrent selection program.

If the same simulations were run with the DH strategy it would be expected that the linkage

disequilibrium effect would be greater as there are less chances for recombination within

each cycle of selection (Powell et al., 1992). Relative to the case for S1 families. This issue

will be the subject of further investigations.

48



The results of the experiment three simulations indicated that for the additive models

considered, the DH strategy achieved higher levels of response than the S1 strategy. This

advantage was retained across all levels of family numbers evaluated, gene numbers and

heritability examined. The use of DH lines therefore in this or possibly any wheat breeding

programs gives breeders optimism in achieving commercial cultivars more quickly,

especially since DH are all ready completely homozygous and ready for commercial use as

soon as they are made. S1 families require additional years of self-pollination and selection

to become a homozygote for use as pure line wheat cultivars.

As the number of families evaluated in the METs increased there was an increase in the

response to selection. When 250 families were evaluated, with 20 families selected to go to

the next cycle, the selection intensity is 8%, a fairly weak selection intensity value. Because

in this scenario a relatively large proportion of the population was contributing genes to the

next cycle of selection, families that just make it in to the selected group are likely to

possess both desirable genes being selected for, and undesirable genes. This can be avoided

to some extent by increasing the selection intensity. This can be achieved by increasing the

number of families tested, selecting less families, or a combination of both. With the

combination of 1000 S1 families evaluated in the MET and 20 families selected, the

selection intensity is 2%. Therefore, it is more likely that a higher frequency of plants with

the desirable genes are in the selected group and fewer undesirable genes will be present.

Therefore, the response to selection is more likely to be faster as a higher frequency of the

desirable genes are passed from one generation to the next in the population.

DH lines once again had a greater response to selection than the S1 families as superior

genotypes could be more easily identified compared to the S1 families. The use of DH lines

therefore gives a breeder the ability to decrease the number of families used in the MET

without decreasing the genetic diversity present. 1000 S1 families is the largest number that

can be conducted in two years of METs at five locations each year with the current level of

resources available to the GEP. At the low heritability level considered (0.05), after 10

49

cycles of selection with 1000 S1 families, the population was nearly 100% of the target

genotype. Therefore, this shows how small numbers of DH lines are likely to give rise to

very valuable lines, as even with a low number of DH lines, the breeder can easily select

valuable lines in DH populations exhibiting the same genetic variability (Picard et al.

1988).

The number of genes contributing to the trait under selection was altered, as it is not known

how many genes influence the expression of a quantitative trait (e.g. yield). The number of

genes contributing to a trait influences the response to selection, as the more genes there are

to select for the harder it is to find a genotype with all of the favourable genes present. In

the additive model considered the genes contributing to a trait all have a small and equal

effect. To increase the response to selection all the genes need to increase their frequency

together. The five gene model gave a faster response to selection than the models based on

a larger number of genes as there were fewer genes that required selecting for. The ability

to efficiently select for all the genes decreases as the number of genes increases, therefore

resulting in a lower response to selection. The fact that the DH lines have twice as much

additive genetic variance among the lines compared to S1 families, makes selection for a

particular genotype more efficient and therefore results in a faster response to selection. A

larger DH population is required to have a reasonable chance of selecting desirable

recombinant genotypes as the number of genes controlling the trait becomes larger. Inagaki

et al., (1998) came to the same conclusion when they indicated that a larger DH population

is required to increase the probability of selecting desirable genotypes in crosses containing

larger genetic variation.

Heritability was assigned on a single plant basis in the base population, however this does

not accurately reflect the heritability on a family mean basis. For selection on a family

mean basis the family mean heritability can be increased by sampling larger numbers of

individuals from the families and employing greater replication across environments. The

family mean heritability was assessed in the simulations as it is one of the components in

the response to selection equation, and therefore its magnitude influences the realised

response to selection. As the heritability increases to one, the phenotype (what you can see

or measure) of a plant more accurately reflects the genotype (underlying genetic

50

framework) of the plant. The higher the heritability, the easier it is to select for genes based

on the phenotypes of particular plants, and the greater the response to selection will be. As

the heritability decreases, the influence of the environment on the phenotype increases, and

the phenotype less accurately reflects the genotype, this results in undesirable genes being

selected for more frequently and a slower response to selection. In the additive model the

heritability did not have a dramatic influence on the response to selection as there were no

complex G×E interactions influencing selection. Once again DH lines gave a greater

response to selection than S1 families due to the higher proportion of additive genetic

variation among the selection units.

A useful way of comparing the use of DH lines in the GEP under any genetic model is to

compare the number of families that can easily be produced using S1 families (target =

1000 families) and compare the response to selection to variable numbers of DH lines (e.g.

100, 250, 500, 1000). A target of 1000 S1 families is feasible for the resources available to

the GEP. In contrast DH lines are more costly to produce, with 300 DH families considered

to be a relatively large number. Generally the rate of progress for 100 DH families was

similar to the rate of progress observed for 1000 S1 families (Figure 13a-d), this was

especially so at the lower levels of heritability. When the number of DH lines was 250 or

greater, a much greater response to selection was observed than that for 1000 S1 families.

As there was no advantage of 100 DH lines over 1000 S1 families, 100 families were not

considered in the subsequent experimental simulations.

With the additive model and a high heritability, in the base population of the GEP a large

amount of additive genetic variation was present. This large genetic variation decreased

significantly after the first cycle of selection due to the presence of linkage disequilibrium

(Bulmer effect), the effects of selection and the effects of random drift. Selection therefore

reduced the genetic variance and the heritability of the progeny of the first selection cycle.

There is further but progressively smaller, reduction in subsequent generations. This

response was also observed in the simulation study of Hospital and Chevalet (1996) where

the genetic variance decreased towards zero as the number of generations increased. They

also emphasised that the joint effects of selection, linkage and drift must be considered in

any evaluation of selection response.

51



It is important in a breeding program to minimise the reduction of genetic diversity while

maintaining genetic progress when selecting plants to go into the next cycle of selection. If

the number of families selected from the METs is too small, important genes may be lost

through genetic drift. If the number of families selected is too large, response to selection

will be reduced as undesirable genes are not rapidly selected out through selection. The

number of families selected (selection proportion) was altered to determine what proportion

of families should be selected in the GEP to provide a balance between these two

constraints. Selecting five families resulted in a rapid response to selection in the early

cycles of selection, however the population mean plateaued before it reached the 100% of

the target genotype, as desirable genes were lost from the population due to the effects of

random drift. This indicates that at this selection proportion, drift is a more important factor

than selection for reducing the genetic diversity within this population (De Koyer et al.,

1999). Currently the GEP adopts a selection proportion of 20 families out of approximately

800-1000 tested. This value ensures that relatively few genes are lost due to random drift, a

high selection intensity is imposed, and that the response to selection isn’t reduced, due to

selecting undesirable individuals as was observed when 30 individuals were selected.

The DH strategy gave a much greater response to selection at each of the selection

proportions, as plants with superior combination of genes were more efficiently selected

than for the S1 strategy. This was due to the increase in additive genetic variance among the

DH line selection units relative to the S1 families. If the evaluation of 250 DH lines was to

be incorporated into the GEP, then selecting 20 lines also represents a reasonable balance

between random drift and selection intensity. If five DH lines were selected, the maximum

expected performance would be approximately 85% of the target genotype which would be

reached at cycle 5. With a selection proportion based on 20 DH lines, the population would

reach 98% of the target genotype at 7 cycles. The S1 strategy still had not plateaued after

10 cycles of selection. This indicates the strong advantage that DH lines could add to the

current GEP.

52

With the inclusion of G×E interaction in the genetic model, the genes contributing to the

trait have different effects in different environments. In the selection proportion simulation

(experiment 4) containing G×E interaction, a greater response to selection was observed for

the G×E interaction model, than that for the additive model in the early cycles of selection.

This was not anticipated, as the presence of G×E interaction was expected to slow the

response to selection due to the added complexity when selecting families. The reason for

this increase in response for the G×E interaction model was because the genes with a major

effect on the trait were more rapidly selected for in early cycles of selection. Additionally,

some of the lower value genes were associated with the major genes due to linkage

disequilibrium. Therefore, when selecting the higher value genes, the lower value genes

were also being selected indirectly, further contributing to selection response and the rapid

increase in response to selection. The effect of linkage disequilibrium was not prominent in

the simple additive model when all of the genes have the same effect or value. However,

when genes of varying magnitude of effect were included in the additive model the effects

of linkage disequilibrium were observed. These results suggest that linkage disequilibrium

may be having a greater effect on selection response in the GEP than was at first thought.

This issue requires further investigation.


to selection

The G×E interaction simulations were one of the most important simulations conducted in

this project. The additive model consists of many assumptions that don’t hold in reality.

The absence of G×E interaction is one of these assumptions. However, G×E interaction is

one of the most influential factors affecting selection efficiency in the GEP. It was therefore

necessary to investigate the relative efficiency of the DH and S1 breeding strategies for a

wider range of genotype-environment systems than was considered for the additive model.

To observe the effects of G×E interaction and heritability on response to selection, a

comparison can be made between the G×E interaction model and the additive model by

53

focusing on Figures 13c (additive) and 16b (G×E interaction). Both of these figures

consider a heritability of 0.95, have 20 genes contributing towards the trait and are based on

selection of 20 families. The two graphs are similar, however Figure 16b has a slighter

slower response to selection due to the presence of a small G×E interaction effect. The

response to selection is even slower when the amount of G×E interaction influencing

selection efficiency increases (Figure 16d), especially when the heritability is low. As

heritability decreases, the environment has a greater effect on the expression of the

genotype, therefore the ability to select a particular genotype, based on its phenotype,

decreases and response to selection decreases. As G×E interaction increases, the

environmental effect increases causing genotype rankings to change under different

environmental conditions. This influences selection as breeders may be selecting for genes

that are only superior because of the impact the specific environments sampled, rather than

for gene combinations that are superior across environments within the target population of

environments.

In the presence of G×E interaction the DH lines did retain the advantage of having a faster

response to selection. When the DH strategy was applied with a MET based on two years

there was on average a 12% increase in mean performance over the S1 strategy. When

conducting METs, if the use of DH lines meant that the number of families being evaluated

decreased, the resources saved would be able to be put into sampling the target population

of environments more adequately.

Using the currently available wheat × maize crossing technology the production of DH

lines is a resource expensive process that adds a year on to the current four year cycle

achievable when using S1 families. To maintain a strict four year cycle, only one year of

METs would be feasible for the DH strategy. A reduction in the response to selection was

observed when only one year of METs were conducted for the DH lines. Genotype-by-

year-by-location (G×Y×L) interaction is the major component of G×E interaction

influencing selection for yield in the GEP. Conducting only one year of METs results in

inadequate sampling of the G×Y and G×Y×L interaction components, resulting in a

potential bias in the ranking of the genotypes. Therefore, a decrease in response to selection

54

was expected with the DH strategy and one year of METs. However, a drop of only 2% in

mean performance on average was observed when one year of METs were conducted

compared to two years for the DH strategy, and one year of METs for the DH strategy still

had a 9% increase in mean performance on average over the S1 strategy with two years of

METs. Twice as much additive genetic variance being partitioned among DH lines relative

to S1 families has provided some compensation for the reduction in MET testing. Methods

decreasing the time required to produce doubled haploids could enable the DH strategy to

be conducted as a four year cycle. This would be an advantage to the conduct of the GEP

based on DH lines.

Overall

From this experiment and others (Gallais, 1988; 1989; 1990) DH lines have shown that

they are the most efficient breeding method in the recurrent selection strategies studied.

Compared to other breeding methods (single-seed descent and pedigree selection) the use

of DH lines in breeding programs can also save time in obtaining recombinant inbred lines

ready for yield evaluation (Inagaki et al., 1998). The advantage of the DH lines over the S1

families is largely due to there being twice as much additive genetic variance being

partitioned among DH lines relative to S1 families, this makes selection a lot easier in the

field as the plants within a DH plot (one DH line) are all genetically identical, and

differences only occur due to environmental effects, therefore differences between the DH

lines are much easier to detect. With the S1 families there is genetic variation within plots

and between plots as they are not completely homozygous, making selection more difficult

and less efficient.

Across all of the genetic models examined so far the use of DH lines in the GEP breeding

program looks promising. Due to the expense and time involved in producing DH lines, it

may not be feasible for the GEP to be completely dependent on DH lines. Foroughi-Wehr

and Wenzel (1990) proposed the use of alternating steps of DH lines in combination with

other breeding strategies (such as S1 families) in a recurrent selection program, for

programs combining exotic germplasm with adapted germplasm or when combining

55

unrelated genotypes. The results of this study strongly indicate that DH lines may be a

useful tool within a breeding program and as the production of DH plants becomes easier,

this method will become efficient as an option in a recurrent selection strategy (Picard et

al., 1988).

The incorporation of DH into a breeding strategy may result in the release of commercial

lines earlier than from the conventional pedigree program. If a breeder can develop a

cultivar superior to what is already being commercially grown one year earlier than

expected, it can be worth millions of dollars to the target industry. In 1993, Cooper and

Woodruff (1993) put the net present value of saving five years on a wheat breeding

program at $29,784,882 with a 5% discount rate. A more recent study in rice (Pandey and

Rajatasereekul, 1999) put the net present value from reducing a breeding cycle by one year

with a discount rate of 5%, as worth $19 million, and saving five years, as worth $105.1

million.

The results of this study emphasises the power computer simulation technology has

provided to determine the efficiency of two complex breeding programs. Some of these

results may also be obtained through theoretical prediction equations. However, many

assumptions are required to make the equations tractable, limiting their use in practice. The

use of computer modelling allows these assumptions to be relaxed and a more realistic

answer to be obtained. The results could also be obtained through field experimental work.

However, the scope of such work would be severely limited. In the simulations examined in

this study over 600 different genetic models were considered, each being run for 40-50

years. If all of the field experiments could be run at once, it would still take many lifetimes

to conduct and then analyse the results. Apart from this, the resources are not available to

conduct a study of this magnitude. Therefore, the computer simulation methodology used in

this investigation has allowed an insight into the GEP strategy that would otherwise not

have been possible.

56

6. Conclusions

Based on the results of this study the utilisation of the DH strategy in the GEP provided a

significant increase in response to selection compared to the S1 strategy. This advantage

was observed over a range of heritabilities, number of genes, number of families evaluated

in METs, number of families selected, levels of G×E interactions and the number of METs

conducted in the GEP. Therefore, this provides a solid foundation for considering the use of

DH lines in place of S1 families in the GEP. The major problem that still remains is the

expense of producing DH lines and the time taken to produce them. However, new

strategies for producing DH lines are being continually investigated and as this field of

research progresses, their use in the GEP or any breeding program should be considered.

The inclusion of DH lines into the GEP in place of the S1 families is an option that will be

acknowledged at the next assessment and resource allocation meeting of the GEP group.

An optimisation of the DH strategy and full-scale cost analysis will be conducted to

determine the amount of resource required for this strategy compared to what is presently

utilised. With any kind of breeding program, funding and resource allocation will influence

their inclusion into the program, and as DH line production efficiency increases, their

addition into the program looks more feasible.

57

7. The future

Future studies will be conducted to determine the effects of adding another level of

complexity, dominance, into the additive and G×E interaction models. Experiments 4 and 5

will be repeated with models containing both partial and complete dominance in place of

the additive model. The presence of dominance is not expected to affect the DH line

response to selection, however the response to selection of the S1 families is expected to

slower due to the difficulty involved in distinguishing between homozygous and

heterozygous individuals. A problem not encountered with the additive model. An

important issue that will also be considered is the effect of linkage disequilibrium in the DH

populations and the influence it will have on the response to selection.

Further studies will also be conducted to determine the effects of another level of

complexity, epistasis. This will be investigated to determine if the DH lines still retain their

advantage at relatively low family numbers compared to the S1 families. Optimisation

studies will also be conducted to determine under a fixed resources schemes, what DH

family size will give the greatest efficiency in the GEP, and to determine if this efficiency is

greater than that which can be achieved using the S1 families, and whether DH should be

utilised in the GEP.

58

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65

9. Appendices 9.1 Appendix 1

Table A1.1: Input file for the QUGENE engine. This file represents the Effective Population size

input file. The genes 11-50 are removed from this presentation for conciseness. The detail of the

structure of this input file is explained by Podlich and Cooper, 1997; 1998.

S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 1 (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 57 3 1 1 1.0 ! Environment Frequency 1 ! GxE multipliers 0.95 1 1 ! Heritability for each Attribute GN M A D AT L LN K E1 P 1 0.100 0.050 0.000 1 1 1 0 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 0.2 6 0.100 0.050 0.000 3 1 1 0 1 0.5 7 0.100 0.050 0.000 3 1 0.5 0 1 0.5 8 0.100 0.050 0.000 3 1 0.5 0 1 0.5 9 0.100 0.050 0.000 3 1 0.5 0 1 0.5 10 0.100 0.050 0.000 3 1 0.5 0 1 0.5 “ “ “ “ “ “ “ “ “ “ “ “ 51 0.100 0.050 0.000 3 1 0.5 0 1 0.5 52 0.100 0.050 0.000 3 1 1 0 1 0.5 53 0.100 0.050 0.000 3 1 0.5 0 1 0.5 54 0.100 0.050 0.000 3 1 0.5 0 1 0.5 55 0.100 0.050 0.000 3 1 0.5 0 1 0.5 56 0.50 -0.500 -0.490 2 1 2 0 1 0 57 0.50 -0.500 -0.490 2 1 0.5 0 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

66

Table A1.2: Input file for the QUGENE engine. This file represents Linkage disequilibrium

input file. The detail of the structure of this input file is explained by Podlich and Cooper, 1997;

1998.

S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 1 (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 22 2 1 1 1.0 ! Environment Frequency 1 ! GxE multipliers 0.95 1 ! Heritability for each Attribute GN M A D AT L LN K E1 P 1 0.100 0.02 0.000 1 1 1 0 1 0.2 2 0.100 0.0325 0.000 1 1 0.5 0 1 0.2 3 0.100 0.01 0.000 1 1 0.5 0 1 0.2 4 0.100 0.0125 0.000 1 1 0.5 0 1 0.2 5 0.100 0.015 0.000 1 1 0.5 0 1 0.2 6 0.100 0.0425 0.000 1 1 1 0 1 0.2 7 0.100 0.005 0.000 1 1 0.5 0 1 0.2 8 0.100 0.0375 0.000 1 1 0.5 0 1 0.2 9 0.100 0.03 0.000 1 1 0.5 0 1 0.2 10 0.100 0.0325 0.000 1 1 0.5 0 1 0.2 11 0.100 0.0325 0.000 1 1 1 0 1 0.2 12 0.100 0.015 0.000 1 1 0.5 0 1 0.2 13 0.100 0.02 0.000 1 1 0.5 0 1 0.2 14 0.100 0.005 0.000 1 1 0.5 0 1 0.2 15 0.100 0.0225 0.000 1 1 0.5 0 1 0.2 16 0.100 0.0125 0.000 1 1 1 0 1 0.2 17 0.100 0.03 0.000 1 1 0.5 0 1 0.2 18 0.100 0.01 0.000 1 1 0.5 0 1 0.2 19 0.100 0.015 0.000 1 1 0.5 0 1 0.2 20 0.100 0.025 0.000 1 1 0.5 0 1 0.2 21 0.50 -0.500 -0.490 2 1 2 0 1 0 22 0.50 -0.500 -0.490 2 1 0.5 0 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

67

Table A1.3: Input file for the QUGENE engine. This file represents the additive model input file

with 5 genes (there are five different 5 gene files, each with a different heritability: 0.05, 0.25, 0.5

,0.75, 0.95 the heritability is in bold and changes for each file. The detail of the structure of this

input file is explained by Podlich and Cooper, 1997; 1998.

S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 1 (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 7 2 1 1 1.0 ! Environment Frequency 1 ! GxE multipliers 0.05 1 ! Heritability for each Attribute GN M A D AT L LN K E1 P 1 0.100 0.050 0.000 1 1 1 0 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 0.2 6 0.50 -0.500 -0.490 2 1 2 0 1 0 7 0.50 -0.500 -0.490 2 1 0.5 0 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

68





S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 1 (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 12 2 1 1 1.0 ! Environment Frequency 1 ! GxE multipliers 0.05 1 ! Heritability for each Attribute GN M A D AT L LN K E1 P 1 0.100 0.050 0.000 1 1 1 0 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 0.2 6 0.100 0.050 0.000 1 1 1 0 1 0.2 7 0.100 0.050 0.000 1 1 0.5 0 1 0.2 8 0.100 0.050 0.000 1 1 0.5 0 1 0.2 9 0.100 0.050 0.000 1 1 0.5 0 1 0.2 10 0.100 0.050 0.000 1 1 0.5 0 1 0.2 11 0.50 -0.500 -0.490 2 1 2 0 1 0 12 0.50 -0.500 -0.490 2 1 0.5 0 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

69

Table A1.5: Input file for the QUGENE engine. This file represents the additive model input

file with 20 genes (there are five different 5 gene files, each with a different heritability:

0.05, 0.25, 0.5 ,0.75, 0.95 the heritability is in bold and changes for each file. The detail of

the structure of this input file is explained by Podlich and Cooper, 1997; 1998.

S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 1 (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 22 2 1 1 1.0 ! Environment Frequency 1 ! GxE multipliers 0.05 1 ! Heritability for each Attribute GN M A D AT L LN K E1 P 1 0.100 0.050 0.000 1 1 1 0 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 0.2 6 0.100 0.050 0.000 1 1 1 0 1 0.2 7 0.100 0.050 0.000 1 1 0.5 0 1 0.2 8 0.100 0.050 0.000 1 1 0.5 0 1 0.2 9 0.100 0.050 0.000 1 1 0.5 0 1 0.2 10 0.100 0.050 0.000 1 1 0.5 0 1 0.2 11 0.100 0.050 0.000 1 1 1 0 1 0.2 12 0.100 0.050 0.000 1 1 0.5 0 1 0.2 13 0.100 0.050 0.000 1 1 0.5 0 1 0.2 14 0.100 0.050 0.000 1 1 0.5 0 1 0.2 15 0.100 0.050 0.000 1 1 0.5 0 1 0.2 16 0.100 0.050 0.000 1 1 1 0 1 0.2 17 0.100 0.050 0.000 1 1 0.5 0 1 0.2 18 0.100 0.050 0.000 1 1 0.5 0 1 0.2 19 0.100 0.050 0.000 1 1 0.5 0 1 0.2 20 0.100 0.050 0.000 1 1 0.5 0 1 0.2 21 0.50 -0.500 -0.490 2 1 2 0 1 0 22 0.50 -0.500 -0.490 2 1 0.5 0 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

70





S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 1 (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 102 2 1 1 1.0 ! Environment Frequency 1 ! GxE multipliers 0.05 1 ! Heritability for each Attribute GN M A D AT L LN K E1 P 1 0.100 0.050 0.000 1 1 1 0 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 0.2 6 0.100 0.050 0.000 1 1 1 0 1 0.2 7 0.100 0.050 0.000 1 1 0.5 0 1 0.2 8 0.100 0.050 0.000 1 1 0.5 0 1 0.2 9 0.100 0.050 0.000 1 1 0.5 0 1 0.2 10 0.100 0.050 0.000 1 1 0.5 0 1 0.2 11 0.100 0.050 0.000 1 1 1 0 1 0.2 12 0.100 0.050 0.000 1 1 0.5 0 1 0.2 13 0.100 0.050 0.000 1 1 0.5 0 1 0.2 14 0.100 0.050 0.000 1 1 0.5 0 1 0.2 15 0.100 0.050 0.000 1 1 0.5 0 1 0.2 16 0.100 0.050 0.000 1 1 1 0 1 0.2 17 0.100 0.050 0.000 1 1 0.5 0 1 0.2 18 0.100 0.050 0.000 1 1 0.5 0 1 0.2 19 0.100 0.050 0.000 1 1 0.5 0 1 0.2 20 0.100 0.050 0.000 1 1 0.5 0 1 0.2 " " " " " " " " " " " " " " " 97 0.100 0.050 0.000 1 1 0.5 0 1 0.2 98 0.100 0.050 0.000 1 1 0.5 0 1 0.2 99 0.100 0.050 0.000 1 1 0.5 0 1 0.2 100 0.100 0.050 0.000 1 1 0.5 0 1 0.2 101 0.50 -0.500 -0.490 2 1 2 0 1 0 102 0.50 -0.500 -0.490 2 1 0.5 0 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

71

Table A1.7: Input file for the QUGENE engine. This file represents the G×E model 1 (Table 3).

GN represents the gene number and E1 – E5 represent the five environments. The detail of the


S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 10 ! no. of runs to calc var comp (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 22 2 5 1 0.4 0.3 0.15 0.1 0.05 ! Environment Frequency 1 1 1 1 1 ! GxE multipliers 0.95 1 ! Heritability for each Attribute GN M A D AT L LN K E1 E2 E3 E4 E5 P 1 0.100 0.050 0.000 1 1 1 0 1 1 1 1 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 6 0.100 0.050 0.000 1 1 1 0 1 1 1 1 1 0.2 7 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 8 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 9 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 10 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 11 0.100 0.050 0.000 1 1 1 0 1 1 1 1 0 0.2 12 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 1 1 0.2 13 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 1 0.2 14 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 1 1 0.2 15 0.100 0.050 0.000 1 1 0.5 0 1 1 1 -1 0 0.2 16 0.100 0.050 0.000 1 1 1 0 1 -1 0 1 1 0.2 17 0.100 0.050 0.000 1 1 0.5 0 1 0 1 1 -1 0.2 18 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 1 1 0.2 19 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 1 0.2 20 0.100 0.050 0.000 1 1 0.5 0 1 1 1 -1 1 0.2 21 0.50 -0.500 -0.490 2 1 2 0 1 1 1 1 1 0 22 0.50 -0.500 -0.490 2 1 0.5 0 1 1 1 1 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

72




S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 10 ! no. of runs to calc var comp (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 22 2 5 1 0.4 0.3 0.15 0.1 0.05 ! Environment Frequency 1 1 1 1 1 ! GxE multipliers 0.95 1 ! Heritability for each Attribute GN M A D AT L LN K E1 E2 E3 E4 E5 P 1 0.100 0.050 0.000 1 1 1 0 1 1 1 1 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 6 0.100 0.050 0.000 1 1 1 0 1 1 1 1 1 0.2 7 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 8 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 9 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 10 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 11 0.100 0.050 0.000 1 1 1 0 1 1 -1 1 0 0.2 12 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 0 1 0.2 13 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 -1 0.2 14 0.100 0.050 0.000 1 1 0.5 0 1 -1 -1 1 1 0.2 15 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 0 0.2 16 0.100 0.050 0.000 1 1 1 0 1 -1 0 1 1 0.2 17 0.100 0.050 0.000 1 1 0.5 0 1 0 1 1 -1 0.2 18 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 -1 1 0.2 19 0.100 0.050 0.000 1 1 0.5 0 1 0 -1 1 -1 0.2 20 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 -1 1 0.2 21 0.50 -0.500 -0.490 2 1 2 0 1 1 1 1 1 0 22 0.50 -0.500 -0.490 2 1 0.5 0 1 1 1 1 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

73




S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 10 ! no. of runs to calc var comp (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 22 2 5 1 0.4 0.3 0.15 0.1 0.05 ! Environment Frequency 1 1 1 1 1 ! GxE multipliers 0.95 1 ! Heritability for each Attribute GN M A D AT L LN K E1 E2 E3 E4 E5 P 1 0.100 0.050 0.000 1 1 1 0 1 1 1 1 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 1 0 0.2 6 0.100 0.050 0.000 1 1 1 0 1 1 1 1 1 0.2 7 0.100 0.050 0.000 1 1 0.5 0 1 1 1 -1 1 0.2 8 0.100 0.050 0.000 1 1 0.5 0 1 0 1 0 1 0.2 9 0.100 0.050 0.000 1 1 0.5 0 1 1 1 -1 1 0.2 10 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 1 1 0.2 11 0.100 0.050 0.000 1 1 1 0 1 1 1 1 0 0.2 12 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 1 1 0.2 13 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 1 0.2 14 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 1 1 0.2 15 0.100 0.050 0.000 1 1 0.5 0 1 1 1 -1 0 0.2 16 0.100 0.050 0.000 1 1 1 0 1 -1 0 1 1 0.2 17 0.100 0.050 0.000 1 1 0.5 0 1 0 1 1 -1 0.2 18 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 1 1 0.2 19 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 1 0.2 20 0.100 0.050 0.000 1 1 0.5 0 1 1 1 -1 1 0.2 21 0.50 -0.500 -0.490 2 1 2 0 1 1 1 1 1 0 22 0.50 -0.500 -0.490 2 1 0.5 0 1 1 1 1 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

74




S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 10 ! no. of runs to calc var comp (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 22 2 5 1 0.4 0.3 0.15 0.1 0.05 ! Environment Frequency 1 1 1 1 1 ! GxE multipliers 0.95 1 ! Heritability for each Attribute GN M A D AT L LN K E1 E2 E3 E4 E5 P 1 0.100 0.050 0.000 1 1 1 0 1 1 1 1 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 1 1 1 1 0.2 6 0.100 0.050 0.000 1 1 1 0 1 1 0 1 1 0.2 7 0.100 0.050 0.000 1 1 0.5 0 1 -1 -1 1 1 0.2 8 0.100 0.050 0.000 1 1 0.5 0 1 1 0 1 -1 0.2 9 0.100 0.050 0.000 1 1 0.5 0 1 0 1 1 -1 0.2 10 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 1 0 0.2 11 0.100 0.050 0.000 1 1 1 0 1 1 -1 1 0 0.2 12 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 0 1 0.2 13 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 -1 0.2 14 0.100 0.050 0.000 1 1 0.5 0 1 -1 -1 1 1 0.2 15 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 0 0.2 16 0.100 0.050 0.000 1 1 1 0 1 -1 0 1 1 0.2 17 0.100 0.050 0.000 1 1 0.5 0 1 0 1 1 -1 0.2 18 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 -1 1 0.2 19 0.100 0.050 0.000 1 1 0.5 0 1 0 -1 1 -1 0.2 20 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 -1 1 0.2 21 0.50 -0.500 -0.490 2 1 2 0 1 1 1 1 1 0 22 0.50 -0.500 -0.490 2 1 0.5 0 1 1 1 1 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

75




S ! Pollination Type N ! Random Seed 100 200 300 Y N N ! Linkage, Epistasis, Random GxE 1 ! Gene Sampling type (1=fixed, 2=random) 10 ! no. of runs to calc var comp (BP,Progeny, Genes, Attributes, Environment Types, Sample Environments) 5000 10 22 2 5 1 0.4 0.3 0.15 0.1 0.05 ! Environment Frequency 1 1 1 1 1 ! GxE multipliers 0.95 1 ! Heritability for each Attribute GN M A D AT L LN K E1 E2 E3 E4 E5 P 1 0.100 0.050 0.000 1 1 1 0 1 0 -1 1 1 0.2 2 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 1 0 0.2 3 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 -1 1 0.2 4 0.100 0.050 0.000 1 1 0.5 0 1 -1 0 1 1 0.2 5 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 0 1 0.2 6 0.100 0.050 0.000 1 1 1 0 1 1 0 1 1 0.2 7 0.100 0.050 0.000 1 1 0.5 0 1 -1 -1 1 1 0.2 8 0.100 0.050 0.000 1 1 0.5 0 1 1 0 1 -1 0.2 9 0.100 0.050 0.000 1 1 0.5 0 1 0 1 1 -1 0.2 10 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 1 0 0.2 11 0.100 0.050 0.000 1 1 1 0 1 1 -1 1 0 0.2 12 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 0 1 0.2 13 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 -1 0.2 14 0.100 0.050 0.000 1 1 0.5 0 1 -1 -1 1 1 0.2 15 0.100 0.050 0.000 1 1 0.5 0 1 0 1 -1 0 0.2 16 0.100 0.050 0.000 1 1 1 0 1 -1 0 1 1 0.2 17 0.100 0.050 0.000 1 1 0.5 0 1 0 1 1 -1 0.2 18 0.100 0.050 0.000 1 1 0.5 0 1 -1 1 -1 1 0.2 19 0.100 0.050 0.000 1 1 0.5 0 1 0 -1 1 -1 0.2 20 0.100 0.050 0.000 1 1 0.5 0 1 1 -1 -1 1 0.2 21 0.50 -0.500 -0.490 2 1 2 0 1 1 1 1 1 0 22 0.50 -0.500 -0.490 2 1 0.5 0 1 1 1 1 1 1 N ! Mating Type 1 ! Selection type ******************************************************************** R ! Mating (Random Mating) 10 5 0.2 ! Generations, Generations before selection, Select Pressure M ! Mating (Mixture) 0.8 0.2 10 5 0.2 ! Proportions (RM/S), Gen, Gen before Sel, Sel Pressure N ! No Further Mating

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9.2 Appendix 2 m = 2


0 50 100 150 200

Effe

ctiv

e po

pula

tion

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(Ne)

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m = 1


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ctiv

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m = 3


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ctiv

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m = 4


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ctiv

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m = 5


0 50 100 150 200

Effe

ctiv

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(Ne)

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m = 10


0 50 100 150 200

Effe

ctiv

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m = 100


0 50 100 150 200

Effe

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e po

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tion

size

(Ne)

0

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Figure A2.1: Simulated S1 family effective population size (Ne) variation about the

average (solid line) for all numbers of reserve seed (m).

77

m'=1


0 50 100 150 200

Effe

ctiv

e po

pula

tion

size

(Ne)

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m'=10


0 50 100 150 200

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(Ne)

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m'=5


0 50 100 150 200

Effe

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m'=2


0 50 100 150 200

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m'=4


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m'=3


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Figure A2.2: Simulated DH line effective population size (Ne) variation about the

average (solid line) for all numbers of reserve seed ( 'm ).

narelle kruger honours project

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