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Chapter 8
Quantitative Genetics
Polygenic Inheritance: when a number of different pairs
of alleles at several loci are important for expression
of a trait. Such traits are typically quantitative in
nature, not qualitative.
Quantitative Genetics: study of traits that show
continuous variation and are due to the combined
effects of many different loci, as well as the
environment.
Some Quantitative Traits in Humans
Fig 8.1
Mendelian Genetics can Explain Quantitative Traits
Figure 8.2
East’s Data confirming the Predictions of Mendelian Genetics
Fig 8.3
What is the cause of this phenotypic variation in height?
For an individual:
Phenotype = genotype + environment
P=G+E
For a population, measure phenotypic variance:
VP = VG + VE
Heritability: the fraction of the total variance in
a trait that is due to variance explained by
genotypes.
In the broad sense (using clones, full-sibs)
heritability = VG/VP = VG/(VG + VE)
Estimating Heritability from Parents and Offspring
Offspring do not
Offspring moderately
Offspring strongly
resemble parents
resemble parents
resemble parents
Figure 8.11 -Scatterplots showing offspring height as a function of parent height
The slope of these lines represents a version of heritability called
narrow-sense heritability or h2
Partitioning Genetic Effects
Additive effects (VA): effects where the contribution of
an allele to the phenotype is independent of identity of
other alleles at the same or at different loci.
Dominance (VD): non-additive interactions of alleles at
one locus
Epistasis (VI): non-additive interactions of alleles at
different loci
Maternal effects(VM): due to mother’s environment and
her ability to provision resources for offspring.
Additive Genetic Variance versus Dominance
Figure 8.13
Epistasis
The total genetic variation for a population is the sum
of these effects:
VG = VA + VD + VI + VM
• Genetic environment does not alter additive effects, so
additive effects are the basis for a response to selection
• Non-additive genetic variance is dependent on the
alleles at the same loci and alleles occurring at other loci
narrow-sense heritability = h2 = VA/VP
with VP = VA + VD + VI + VM + VE
Example 1
Fig 8.11d
Example 2: Heritability of
beak size in song sparrows
Measuring Natural Selection (differences in
survival and reproductive success)
Fig 8.15
Measuring Natural Selection cont.
Selection differential (S): the difference in mean
phenotype between the selected individuals
(survivors/breeders) and the entire population.
Selection gradient: slope of the line showing relative
fitness as a function of phenotype.
selection gradient = the selection differential/ population variance
Selection gradient:
•
Assign absolute fitnesses
•
Convert absolute fitnesses to relative fitnesses
•
Make a scatterplot of relative fitness and calculate the slope of
the line of best fit
Determining the Response to Selection
Response to selection (R): the difference between the
mean phenotype of the offspring when selection takes
place and the mean phenotype of the offspring if selection
does not take place.
Response to Selection cont.
Response to Selection cont.
h2 = the slope of the line = rise/run
= mean of selected offspring – mean of all offspring
___________________________________________
mean of selected parents – mean of all parents
h2 = R/S
Response to Selection cont.
Therefore,
R = h2 * S
In other words, the strength of the response to selection
depends upon the relative contribution of additive genetic
variance to the phenotype and the strength of natural
selection.
Revisiting Modes of Selection
Directional selection
Fitness consistently increases or decreases with the value of a trait
Changes the mean value of the trait; potentially reduces the
variance.
Stabilizing selection
Individuals with intermediate values of a trait have higher fitness
Does not change the mean; reduces the variance.
Disruptive selection
Individuals with extreme values of a trait have the higher fitness
Does not change the mean; increases the variance. Does not
necessarily cause a bimodal distribution.
Revisiting Modes of Selection cont.
Following 7 years of growth: Heritability for flower
size was between 0.2 and 1.0.
Slope = 0.13. Selection differential = gradient * variance.
0.13 * 5.66 = 0.74 mm.
0.74/14.2 = 5% change if flower size for selection differential
Response to selection was 9%
Concerns about the Environment
Heritability is dependent upon the population being examined, as
well as the environment that is being experienced.
Environment can alter both the mean of a trait, the variance, and
how heritable the trait is.
Recall: h2 = VG/(VG + VE).
So, the only way to determine the cause of differences between
populations is to rear individuals from each of the populations in
identical environments.
Clausen, Keck and Hiesey’s (1948) work with the
perennial wild flower, Achillea
High heritability within
populations tells us
nothing about the cause
of differences between
populations
What does this suggest about Human IQ and the
Book, The Bell Curve Fallacy?
(Murray and Herrstein, 1994)
Clausen, Keck and
Hiesey’s (1948)
work with the
perennial wild
flower, Achillea
THE END.
Genetic Constraints on Evolution through N. Selection:
Remember, requirements for a response to selection:
(1) Natural selection (diff. survival/reproduction)
(2) Phenotypic variation in a given trait
(3) Underlying genetic variation
Constraints:
(1) Absence of genetic variation
(2) Correlated Characters:
Pleiotropic effects: effects of single genes on multiple
traits
Linkage: the tendency for alleles at different loci to be
inherited together.
Selection will favor linkage dis-equilibrium if certain
combinations of alleles have greater fitness than other
combinations.
Example: Adaptive landscape of two traits for garter
snakes (striped versus spotted and straight-line escape
versus reversals). Striped, straight-line runners and
spotted, reversals are more fit than the other two
combinations. Recombination can constrain natural
selection in this case.