a some basic concepts in genetics revised

8/12/2019 A Some Basic Concepts in Genetics Revised

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2 Some basic concepts in genetics

Fred van Eeuwijk, Marcos Malosetti, Hans Jansen & Martin BoerWageningen, June 2011


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Phenotype, Genotype and Environment

Phenotype =

Function of

Genotype

Genes, QTLs

Environment

Is this a sufficient description?

Which genotype-to-phenotype (G2P) function transforms the genotype in

the phenotype (additive, multiplicative, crop growth model, network

model)?

What is a genotype (single/multi-locus, interactions within and between

loci)?

How does the environment enter the G2P function (GxE, environmentalcharacterization)?

What about intermediate omics-levels between genotype and phenotype?


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An ambitious definition

Task of statistical modeling in (plant)

genetics:

Predict phenotypic expression for from molecular marker variation, genomic information

and environmental inputs

for various types of (offspring) populations

across a range of environmental conditions for multiple traits

over developmental time


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Before QTL mapping

Recombination

Types of breeding populations

Phenotypic and genotypic values

Genetic variance, heritability

Genetic architecture


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Recombination in F2

Marker 1

Marker 2

Marker 1

Marker 2

Marker 1

Marker 2

Three-generation pedigree

Grandparents

Parent

Gametes

produced

by parent

Molecular marker =

short DNA segment

point on one of the chromosomes

= locus

(plural: loci)

Allele =

DNA variant

grandmaternal variant:grandpaternal variant:


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Recombination in F2

Marker 1

Marker 2

Marker 1

Marker 2

Marker 1

Marker 2


Grandparents

Parent

Gametes

produced

by parent

Marker 1

Marker 2

Frequencies of gametes

produced by parent

2

1 r

2

1 r

2

r

2

r

r= recombination frequency

probability that the grandparental origin of

the allele of marker 1 is different from the

grandparental origin of the allele of marker 2


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Recombination in F2 and DHs

Marker 1

Marker 2

Marker 1

Marker 2

Marker 1

Marker 2


Grandparents

Parent

Gametes

produced

by parent

Problem:

we cannot observe gametes

(haploid genotypes)

we observe combinations of gametes

(diploid genotypes)

Doubled haploids

obtained using anther/ovary culture

Marker 1

Marker 2


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Estimation of recombination frequency

JoinMap format

Doubledhaploid1

Doubledhaploid2

Doubledhaploid3

Doubledhaploid4

Marker 1 a b b a

Marker 2 a b a b

In a doubled-haploid population we have four different types of marker

data for any pair of markers:

type observed number probability

of doubled haploid

a-a naa paa=(1-r)/2

b-b nbb pbb= (1-r)/2

b-a nba pba= r/2

a-b nab

pab

=r/2

RRN

nnnn

abbabbaa

N

nnnnabbabbaa

N

nrnrnrnr

abbabbaa

nab

nba

nbb

naa

abbabbaa

rrC

rrnnnn

N

rrrrnnnn

N

nnnn

N

ppppnnnn

NL

abbabbaa

abbabbaa

abbabbaa

abbabbaa

1

1!!!!

!

11!!!!

!

!!!!

!

!!!!

!

21

21

2221

21

Likelihood:


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RRN rrCL 1Likelihood:

The maximum likelihood estimator of ris obtained by maximizing the likelihoodLwith regard to r.

Easier: take the natural logarithm of the likelihood rather than the likelihood itself.

rRrRNC ln1lnln Log-Likelihood:

Take derivative of log-likelihood and put result equal to zero:

rrrNR

rr

RrRNr

r

R

r

RN

1

1

1

10

Maximum likelihood estimator:N

Rr


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Fisher information: Expectation with regard toRof minus the second derivative of the log-likelihood

r

R

r

RN

r

1

1stderivative:

222

2

1 r

R

r

RN

r

2nd derivative:

rrN

rrN

r

Nr

r

NrN

rE

1

1

1

1

1 222

2

N

rrr

1

var

Variance: Inverse of Fisher information

The variance is zero if r = 0; thevariance attains a maximum of 1/(4N) if r = .


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Testing for linkage

RRN rrCL 1 Maximum likelihood:

Likelihood under assumption of no linkage (r= ):

N

RRN

C

CL

21

21

21

Likelihood ratio:

N

RRN

N

RRN

rr

C

rrCLR

21

21

1

1

10log(LR) is called the LOD score for linkage.

Geneticists speak: a LOD of 3 means that the observed value of the recombination frequency is

1000 times as likely as the value .

2ln(LR) follows (approximately) a chi-square distribution with 1 degree of freedom


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Some population types


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F2


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Back cross


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Population types

Recombinant inbred lines

Per locus:

every generation the proportion of

heterozygotes is halved

...2,1g2

1)g(He

1g

008.02

1)8(

7

He

a h b

a

h

b


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Population types

Recombinant inbred lines

Number of recombinant individuals:

Nrr

R

21

2

intensity of recombination2 if r is small

Estimate of the recombination frequency:

RNRr 2

By the process of repeated selfing we obtain

(nearly) twice as many recombinations as in

a single meiosis.

We are able to produce denser maps


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Accumulated recombination history

BC and DH populations have less accumulated

recombination than RILs and for that reason mapping inRILs can be more accurate

The accumulated recombination history of a population

determines how accurate QTLs can be mapped & the

power to identify QTLs Another factor determining the power to pick up QTLs is

the number of different genetic effects that can be picked

up at a particular locus

Additive + Dominance effects in F2 (Advanced Intercross Lines) Additive effects in DHs and RILs

What about BCs?


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Accumulated recombination history for complex populations?


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Transforming genotype into phenotype (multi-locus)

Genes segregating in populations affect

phenotypic distribution of trait

For quantitative (complex) trait there are many

genes, whose effect in addition may depend on

the environment (gene by environmentinteraction)

Linear model

P = G + E + GxE + error (field trials in plant genetics)

Variance decomposition

Vp= VG+ VE+ VGxE+ Verror


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Genetic effects (Table 4.3 Lynch & Walsh)

Additive and dominance effects for alleles

Intrinsic property of allele, but may differ with genetic background(population)

Average (additive) effect due to substitution of alleles

Property of alleles in a particular population, function of intrinsic

additive and dominance effects & genotype frequencies Breeding value

Property of individual in particular reference population, sum of

average effects of an individuals alleles

Additive genetic variance

Variance of breeding values of individuals in particular population

Mean and genetic variance for trait under single gene in HW


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Mean and genetic variance for trait under single gene in HW

Additive and dominance variance (single and multiple genes)

For multiple non interactive genes:

Average substitution effect

Wu, Ma & Casella, 1.7


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Genotypic values and frequencies for 2 genes in F2


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Back cross


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Two locus epistatic model (F2)


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Genotypic values and frequencies for two locus epistatic model (F2)


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Broad sense heritability

General

H2= VG/[VG+ VE+ VGxE+ Verror]

In plant breeding heritability comparison are

made between genotypes within environments

(eliminate VEfrom total variation)

For homozygous population types (DH, RIL) H2

can be manipulated by increasing number of

environments and replicates within environmentsat which genotypes are evaluated

H2= VG/[VG+ VGxE/nE+ Verror/nEnr]


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Narrow sense heritability

What is the use of broad and narrow sense heritability?


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Estimating genetic variances and heritabilities in practice

Create a set of crosses following specific mating

designs and grow the offspring populations (forexample: back cross, F2, RIL, DH, etc) in field

experiments using appropriate experimental

design to minimize environmental disturbances in

the estimation of quantitative genetic parameters. Example: Grow Parent 1 (P1), Parent 2 (P2), F1

and F2together in a trial

Then


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Genetic architecture of quantitative trait

Fairly large number of loci (50 or more) Additive, dominance, epistatic action & interaction

with environment

Magnitude of effects at different loci can vary

considerably

Same gene may act at different phenotypic traits:

pleiotropy

Genes for a trait are distributed over the genomeat random or following particular pattern


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Estimation of gene number

Assume two contrasting parental lines,

homozygous and one containing all + alleles, andother allalleles, meunlinked effective genes

with the same effect (a), purely additive


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Summary

Recombination

Genotypic and average allele effect due to substitution Genetic, environmental, GxE variances

Broad sense and narrow sense heritability

Estimating number of genes underlying a trait

a some basic concepts in genetics revised

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