1. Quantitative Genetics
Chapter 18
Quantitative Genetics
Continuous variation
April, 2005

3. 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.

6. 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.

7. 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

9. Measures of central tendency
Mode: most frequent class in sample
bimodal: two frequent classes
Mean: arithmetic average

10. Measures of dispersion
Variance of sample: average squared deviation from mean
Standard deviation

13. 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

14. R2=.82
R2=.99

15. 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:

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

19. 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

24. 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

26. H2: broad heritability s2p = total phenotypic variance in population
s2g = genetic variance
s2e = environmental variance
cov = covariance between genotypic and environmental effects
s2p = s2g + s2e + 2 cov ge
H2 tells what part of population’s variation is attributable to genotypic variation.

27. Estimating H2
Intercross homozygotes and measure variance within each heterozygous genotype. Average is s2e which can be subtracted from s2p to give s2g.
Statistically estimate from genetic similarities between relatives, particularly using difference in phenotypic correlation between monozygotic and dizygotic twins

28. 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

29. 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

31. 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

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