Gene diversity measured by Gene diversity measured by

status numberstatus number

and other breeding conceptsand other breeding concepts

Dag Lindgren

Department of Forest Genetics and Plant Physiology

Swedish University of Agricultural Sciences

SE-901 83 Umeå, Sweden

Raleigh Jan 17, 2003

The art of breeding is combining a lot of things in a

good way!

Cost

Interactions

Technique

Gene diversity

Environments

Genetic parameters

Coancestry

InbreedingGain(BV)

To do that effectively, we must have quantitative concepts

and measures

To optimize, a quantitative measure must be defined and maximized!

Some concepts useful for quantitative genetics

Identical by descent (IBD) means that genes at the same locus are copies of the same original gene in some ancestor.

The chance that both homologous genes in the same zygote are identical by descent is called inbreeding (F) (or coefficient of inbreeding).

Self-coancestry: An individual's coancestry with itself is 0.5(1+F).

This can be realised e.g. by considering that coancestry in the previous generation becomes inbreeding in next, and then consider selfing.

Note that inbreeding and coancestry are relative to a situation with no inbreeding or relatedness.

If two individuals mate, their coancestry becomes the inbreeding of their offspring.

Coancestry (, f) between pair of individuals is the probability that genes, taken at random from each of the concerned individuals, are identical by descent (=coefficient of coancestry). A quantification of relatedness.  We will widen that concept!

 

Relative Coancestry (f,)

Unrelated 0

Half sibs 0.125

Full sibs 0.25

Parent-offspring 0.25

Cousin 0.0625

Itself (self-coancestry)

0.5 

Coancestries are probabilities, thus 0 f 1. Some examples

 

Gene pool means all genes in a population. It is convenient to consider genes at one locus. The gene pool is independent on how (or if) a population is organised in zygotes.

To get overall probability; average over all individual probabilities, f. Thus group coancestry could be called average coancestry.

f

Group coancestry

Let's put all homologous genes in a big pool and select two (at random with replacement). The probability that two are IBD is group coancestry. (, this term was introduced by Cockerham 1967).

Group coancestry

mother

sister

aunt

uncle

cousin

What is the average relatedness (group coancestry) of this ”family”?

Inbreeding and group coancestrySimulation of Swedish Norway spruce breeding program by POPSIM, BP=48, DPM, equal representation (2/parent)

0

0.02

0.04

0.06

0.08

0 2 4 6 8 10

Generations

Pro

ba

bil

ity

of

ide

nti

ty b

y d

es

ce

nt

f

Rosvall, Lindgren & Mullin 1999

Message: Group coancestry can often be regarded as a potential inbreeding, which becomes realized some generations later

Gene diversity!

• Evidently 1 - group coancestry is the probability that the genes are non-identical, thus diverse.

Group coancestry and gene diversity

• Group coancestry is the probability that two genes are IBD;

• Diversity means that things are different; • Gene Diversity means that genes are different.

GD = 1 - group coancestry is the probability that the genes are non-identical, thus diverse.

1GD

GD is Gene Diversity!

Group coancestry is a measure of gene diversity lost!

That seems to be something worth knowing!

This way of thinking sees all genes in the source (reference) populations as unique (“tagged”).

GD is similar to expected average heterozygosity (the chance that two genes are different).

Group coancestry based measures are (like inbreeding) relative to some reference population. For forest tree breeding the wild forest usually constitutes a good reference. The gene diversity of the wild forest is 1, and the group coancestry is the share of the initial gene diversity lost.

Monitor group coancestry in tree improvement operations! That says how much gene diversity has been lost since the initiation of the breeding program!

Status number

Status number is half the inverse of group coancestry

2

1SN

An attractive property of the status number is that it is the same as the census number for a population of unrelated, non-inbred trees.

Status Number

Status number is an effective number. It relates a real population to an ideal population. The ideal population consists of unrelated, non-inbred trees with the same probability of IBD.

Status number is an intuitively appealing way of presenting group coancestry, as it connects to the familiar concept of number (population size).

Seed orchard crops can be characterised by Status Number.I suggest this as a more useful and informative measure, than other concepts“effective population size of seed orchards”, which have been used.

Status Number and seed orchard crops

Lindgren and Mullin 1998

“Effective number of clones” could be useful for describing seed orchards. It is the status number of the seed orchard clones, considering a variable ramet number.

Kang et al. 2001

Sibling coefficient could be useful for characterizing seed orchards or seed orchard crops. It is a probabilistic description of fertility variations. “The chance that two genes in the offspring come from the same parent”. It carries the same information as CV for fertility, and is thus not needed, just more convenient.

Kang 2001

1)( 2

1

21

0

2

CVpNdxxfN

ii

SNGD

2

111

Gene diversity as a function of status number

Note that 1/2N is familiar in genetics!

Gene frequency

Generations

Gene frequency over generationsVariance effective numberStatus number

Status number versus variance effective number

Forest tree breeding and status number

are still very close to the founders thus close to the "wild forest“, a natural

reference point for evaluating impact of breeding

deal with few generations change strategy between generations structure population in sublines "own" and control the breeding population

The status number concept is more useful to forest tree breeders than other breeders or geneticists. Forest tree breeders :

Gene conservation is to keep status number high and group coancestry low

Genetic tree improvement is to combine a high gain and a reasonable status number

or

Genetic tree improvement is to balance gain and group coancestry

Conservation and improvement

Breeding value and gene diversity are both desirable; they have to be balanced!

The way to do it is: Maximise Group Merit!!!

Group merit

weighted average of Breeding Value and Gene Diversity

 

Weighting factor = “Penalty constant”; depends on specific circumstances

Group merit =

A seed orchard crop can be characterized by its group merit;

But as other factors, like inbreeding, are also important, I prefer to classify seed orchards and seed orchard crops by “benefit”;

but the semantics is open for discussion…

Group merit selection

Modifications of group merit selection can be used for designing seed orchards.

One modification is linear deployment. It applies to unrelated non inbred clones, and optimizes their contribution (=number of ramets) to an orchard.

Group merit selection

Selection of the genotypes, which maximises the group merit, using some predictor for Breeding Value and some weight for Gene Diversity.

Lindgren and Mullin 1997

Group merit selection

Group merit is not a sum of individual merits!

If the weight (penalty) can not be estimated?

Group merit selection is anyway better than any alternative resulting in the same status number.

Linear deployment Maximises gain at given Status number for a

seed orchard It is optimal to deploy clones linearly related to

their breeding valueN

um

ber

of

ram

ets

Breeding Value of Clone

Linear deployment

g0 (intercept) b (slope)

Lindgren and Matheson 1986

Linear deploymentWorks also with constraint (genetic

thinning of seed orchards)

Ram

ets

Breeding Value

Linear deployment

with constraint

I suggest linear deployment (or modifications) to be considered in currently planned P taeda seed orchards.

But in a decade, more advanced algorithms will be needed, because relatives will be frequent.

The math, relations and considerations become too difficult to solve mathematically and the optimizing algorithms become to difficult to program and master.

So, to optimize, we have to make use of existing optimizing programs, such as EXCEL solver.

The problem is just to set up how things relate, and to decide what is the best value of the parameters.

Long-term breeding

Annual Advance in Group merit

Wei and Lindgren 2001

Considers simultaneously three key factors

• Gain;

• Gene diversity;

• Time.

Long-term breeding criteria

Annual Advance in Group merit at a given annual budget

Danusevičius and Lindgren 2002

Considers simultaneously four key factors

• Gain;

• Gene diversity;

• Time;

• Cost.