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Chapter 18
Quantitative Genetics
Continuous variation
14 and 16 April, 2004
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 sample
bimodal: two frequent classes
Mean: arithmetic average
1
Mean  x   x i
N
Measures of dispersion
• Variance of sample: average squared
deviation from mean
2
1
s 
( xi  x)

N 1
2
• Standard deviation
s  variance  s
2
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
1
cov xy 
( xi  x)( yi  y )

N 1
cov xy
correlatio n  rxy 
sx s y
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:
y  bx  a
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
2
H:
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
H 
2
s
s
2
g
2
p

s
2
g
sg2  se2
H2 tells what part of
population’s variation is
attributable to
genotypic variation.
Estimating
2
H
•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
Meaning of
2
H
• 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
2
h:
narrow heritability
• Genetic variance can be divided into
additive genetic variance and dominance
variance
2
a
2
d
s
h  2
2
sa  s  se
2
• h2 is useful in determining whether there is
selectable genetic variation
– useful in plant and animal breeding
Assignment: Concept map, Solved
Problems 1-3, All Basic and
Challenging Problems.