Variance Is Measure of Variation in Natural Populations

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 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


 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


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


 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: example

 Trillium that produce fruit have smaller storage organs, lower survival


 Daphnia selection experiment lead to faster growth, earlier reproduction, larger size: “Über-fleas”

 Where’s the trade-off?


 Über-fleas do well only when resources unlimited. Otherwise, “Ünter-fleas” have higher fitness.

 Differ in acquisition, not allocation