13 - 18 April, 2005

Chapter 18

Quantitative Genetics

Continuous variation

Overview• In nature, variation in most phenotypic

characters is continuous.• Such quantitative variation is studied with

statistical techniques.• Continuous variation may be the result of

segregation of interacting alleles at several loci with cumulative effect on phenotype.

• Environmental interaction with genotype contributes to phenotypic variance.

• Heritability is a population trait, not an individual one.

Quantitative genetics•Genetics of continuously varying characters

•Attempts to determine genetic variation contributing to character

–number of loci with segregating alleles–how genes interact with one another and the environment (norm of reaction)–How do loci interact (dominance, epistasis, etc)–possible maternal effects

•Often requires statistical analysis

•Quantitative traits: small variation between genotypes, large variation within genotype.

Statistical measures

•Statistical distribution: description of set of quantitative measurements

–graphical representation: e.g, histogram–distribution function: continuous curve

•Mean: measure of central tendency (average)–mode: most frequent observation

•Variance: measure of dispersion about mean

•Correlation: relationship between two measured quantities

Measures of central tendency

Mode: most frequent class in samplebimodal: two frequent classes

Mean: arithmetic average

€

Mean = x =1

Nx i∑

Measures of dispersion

• Variance of sample: average squared deviation from mean

• Standard deviation

22 )(1

1xx

Ns i −−

= ∑

2variance ss ==

Measures of relationship (1)

• Correlation coefficient: relation between two variables, x and y– calculated from covariance of sample and

standard deviations of x and y

yxxy

ii

ss

xyr

yyxxN

xy

covncorrelatio

))((1

1cov

==

−−−

= ∑

R2=.82

R2=.99

Measures of relationship (2)

• Correlation is estimate of precision of relation between two variables; can not be used to predict value of one given the other.

• Regression describes relationship between two variables and allows their prediction. linear regression:

abxy +=

Although most quantitative traits are polyfactorial, variation at a single locus can behave quantitatively.

Norm of reaction• The relationship between environment and

phenotype for a given genotype• Studied by subjecting homozygous lines to

different environments– replicated (e.g., cloned) genotypes– inbred lines (e.g., from repeated sib mating)– use of dominant markers and crossover

suppressors to make lines homozygous for particular chromosomes

• Studies indicate that phenotypic differences between genotypes are small

Heritability

• Important to know whether genes contribute to phenotypic variation of quantitative character

• Heritability is a population trait, not property of individual

• Not same as familial trait shared by members of a family

• Characters are heritable only if similarity arises from shared genotypes– estimated from phenotypic similarity of relatives

– estimated by cosegregation of gene markers

– difficult to estimate in humans

H2: broad heritability

s2p = total phenotypic variance in population

s2g = genetic variance

s2e = environmental variance

cov = covariance between genotypic and environmental effects

s2p = s2

g + s2e + 2 cov ge

22

2

2

22

eg

g

p

g

ss

s

s

sH

+==

H2 tells what part of population’s variation is attributable to genotypic variation.

•Intercross homozygotes and measure variance within each heterozygous genotype. Average is s2

e which can be subtracted from s2

p to give s2g.

•Statistically estimate from genetic similarities between relatives, particularly using difference in phenotypic correlation between monozygotic and dizygotic twins

Estimating H2

Meaning of H2

• It is a population parameter, with no application to particular individuals

• H2 > 0 means that genetic variance is present

• H2 = 0 means that there is no genetic variation; genes may still be relevant to trait (as in development)

• Value of H2 provides limited prediction about effect of environmental modification

• H2 is specific to environmental conditions under which it is measured

Locating genes

•Difficult to identify genes for quantitative characters

•Candidate gene: from prior biochemical or developmental knowledge

•Quantitative trait loci (QTL) may be located to regions of chromosomes by cosegregation with marker genes

•Dominance and epistasis may be involved

h2: narrow heritability• Genetic variance can be divided into

additive genetic variance and dominance variance

• h2 is useful in determining whether there is selectable genetic variation– useful in plant and animal breeding

222

22

eda

a

sss

sh

++=

Assignment: Concept map, Solved Problems 1-3, All Basic and Challenging Problems.