Variance Is Measure of Variation in Natural Populations
Measuring variation
A review and revision
Measure of variation
Variance is measure of variation in natural populations
Average of squared deviations from the mean of a sample
Standard deviation is the square root of the variance
If a variable has a normal distribution, 68% of the observations will be within 1 SD, 96% in 2 SD and 99.7 in 3 SD
Variation in phenotype is due to many factors
Partitioning variation by influence
Phenotypic variation (VP)
Variation associated with additive genetic variability (VA)
Variation associated with non-additive genetic variability (VNA)
VNA is composed of dominance effects (VD), and interaction between genes (VI)
Variation associated with environmental variability (VE)
Variation associated with gene-environment interactions (VGE)
For one locus,
Midpoint between two homozygotes as a point of reference
Mean phenotype of A1A1 individuals is A+a, and mean phenotype of A2A2 individuals is A–a.
a is the additive effect of an allele
If the inheritance of the phenotype is completely additive, then the heterozygote is exactly in between that of the two homozygotes
Phenotypic variance within populations is the environmental variance, VE
Additive genetic variance
Component of genetic variance denoted VA
VA depends on magnitude of a and genotype frequencies
Variance is lower if one genotype is most common
At one locus, VA = 2pqa2
At several loci,
Average phenotype of any particular genotype is the sum of the phenotypic values of each loci
VA is the sum of the additive genetic variance contributed by each of the loci
Additive genetic variance
The additive effects of alleles are responsible for the degree of similarity between parents and offspring
Therefore, are the basis for response to selection within populations
Expected average phenotype of a brood of offspring equals the average of their parents’ phenotypes
Additive genetic inheritance allows a response to selection
Broad-sense heritability
The fraction of phenotypic variability attributable to non-environmental effects
More-or-less genetic vs. environmental effects
Broad sense heritability = H = VG/VP = VG/(VG + VE)
Variation due to dominance and interactions not truly heritable
H is seldom used, ‘heritability’ is usually heritability in the narrow sense (h2)
Narrow-Sense Heritability
h2 = VA/VP = VA/(VA + VD + VE)
Heritability in the narrow sense
Explicitly specifies additive, genetic influences
Heritability is determined by the additive genetic variance (depends on allele frequencies) and environmental variance (depends on environment)
hN2 = VA/VP = VA /(VG + VE) = VA/(VA + VNA + VE)
hN2
hN2 is the slope of the regression of offspring phenotypes on the average of the parents of each brood of offspring
How can one separate VA and VE?
Problem: offspring can resemble parents through sharing environments
Transplant experiments are the classic approach to sorting out different influences
Regression analysis approach
Controlling for environmental influences
Evolution of quantitative characters
Can we quantify the response of QT to selection?
Selection differential: the difference in average phenotype between the general population and the surviving subset
Selection gradient: the shift in relative fitness for the starting population and surviving subset
election experiments
Only particular individuals allowed to breed
Difference between mean phenotype of population and mean of selected group = selection differential, S
Selection experiments
The change in offspring phenotype between selected group and unselected population is the response to selection, R
Selection differential vs response: high hN2
Selection differential vs response: low hN2
Selection differential vs. response:
high hN2 and high S
Response to Selection
The response to selection will depend on:
The selection differential (S)
The heritability of the trait (h2)
R = hN2S
Directional selection
Mean of a polygenic character shifts beyond the original range of variation
Due to favorable gene combinations that effectively did not exist
Bristle number original mean was 9
Natural selection in natural populations
Intensity of selection
i = za – zb
sqrt(VP)
Selection gradient – slope of the relationship between phenotype values and fitness of these values
Directional selection: Darwin’s finches
Grant’s study
Disruptive selection
Curvilinear fitness function, lowest in center, highest at extremes
Broadens distribution, does not change mean
Example: African finches
Disruptive selection
Stabilizing selection
Curvilinear fitness function, highest in center, lowest at extremes
Narrows distribution, does not change mean
Stabilizing selection
Gallflies
How is variability maintained in populations, given that selection “removes” genotypes?
Frequency-dependent selection
Varying selection
Gene flow
New mutations
Linkage disequilibrium
Correlated characters
Correlated selection
Genetic correlation
Correlation between two characters
Phenotypic correlation – body size and fecundity
Genetic correlation
Linkage disequilibrium
Pleiotropy
Example: genetic correlations
Sizes of different flower parts are correlated in radish
Very strong selection required to ‘break’ correlations and change shape of flowers
Evolution and genetic correlation
Can selection act on characters that respond to different environments?
Sundew: green & red morphs
What are the questions?
Can flexibility be an adaptation?
What is phenotypic plasticity?
How does phenotypic plasticity contrast with canalization?
What aspects of phenotypic plasticity are heritable?
How can we test the hypothesis of adaptive plasticity?
Phenotypic plasticity
The capacity of an organism to develop any of several phenotypic states, dependent on environment
Antonym: canalization
A developmental process that produces the same phenotype in spite of environmental variability (= homeostasis)
Reduces the effect of environmental “noise”
Variability in a trait in a population represents a balance between plasticity and canalization
Phenotypic plasticity example
Behavioral change due to changed stimuli in Daphnia
Morphological difference between clones grown in different environments
Phenotypic plasticity
Morphological variation within an organism with continuous development
Phenotypic plasticity
A graphical representation of plasticity
Measuring phenotypic plasticity
Norm of Reaction
Different phenotypes produced by the same genotype in different environments
“X- axis” represents range of environmental conditions
“Y-axis” represents the resulting phenotype
Norms of Reaction
Is plasticity adaptive?
Light availability and elongation in Impatiens
Polyphenism in tadpoles – adaptive?
Relyea, R. A. 2005. The heritability of inducible defenses in tadpoles. J. Evol. Biol. 18: 856-866.
Morphological measurements
Tadpole norms of reaction
Heritability of plasticity
Trade-offs
With limited resources, no organism can be best at all things
Common trade-offs: size vs. number; early reproduction vs. growth or survival
Trade-offs
Trade-offs: example
Trillium that produce fruit have smaller storage organs, lower survival
Superfleas
Daphnia selection experiment lead to faster growth, earlier reproduction, larger size: “Über-fleas”
Where’s the trade-off?
Superfleas
Über-fleas do well only when resources unlimited. Otherwise, “Ünter-fleas” have higher fitness.
Differ in acquisition, not allocation
Trade-offs
Trade-offs