Plasticity and G  E in Evolutionary Genetics Gerdien de Jong Utrecht University

Overview talk phenotypic plasticity selection gradient predictable selection unpredictable selection life history complications – density – zygote migration

Phenotypic Plasticity

27.5  C 17.5  C a systematic change in morphology of an organism due to a developmental response to environmental conditions phenotypic plasticity Drosophila melanogaster

temperature Drosophila wing length reaction norm: genotype represents a function: genotypic value is function value in given environment function value: character state phenotypic plasticity

temperature Drosophila wing length Genotype-by- Environment Interaction G  E reaction norms different slope or shape phenotypic plasticity

Genotype-by- Environment Interaction G  E genetically large low temperature genetically small high temperature 47°N 17.5°C 9°N 27.5°C Drosophila melanogaster

phenotypic plasticity Genotype-by- Environment Interaction Drosophila melanogaster two populations: tropical temperate two temperatures 17.5°C 27.5°C IN: body size adults gene expression pupation probability larval glycogen level development time larval competitive ability female fecundity

Selection Gradient

multivariate selection phenotypic trait i z i =g i + e i vector of changes in phenotypic means  z phenotypic variance covariance matrix P

One trait Selection differential equals the covariance between phenotype z i and fitness w : Selection gradient equals the slope of fitness on phenotype selection gradient w S i = cov(z i,w)  z,i = cov(z i,w)/var(z i )

One trait Selection gradient equals the slope of fitness on phenotype Selection gradient equals the derivative of fitness towards phenotype selection gradient  z,i = cov(z i,w)/var(z i )  w/  z i =  z,i

slope  z,i multivariate selection phenotypic selection gradient each trait multivariate phenotypic selection  w/  z i =  z,i  z = P  z  w/  z i =  z,i

multivariate selection genotypic value trait i g i vector of changes in genotypic means  g genotypic variance covariance matrix G

slope  g,i multivariate selection genotypic selection gradient each trait multivariate genotypic selection  w/  g i =  g,i  g = G  g  w/  g i =  g,i

Evolutionary Biology:  z =  g  g=G  z phenotypic plasticity: multivariate traits character states reaction norm coefficients multivariate selection

Predictable Selection

life history zygote pool z 1 mating pool selection in x zygote pool z 0 predictable selection z1z1 z0z0 m x=0x=1

character state in environment x : character state g x selection gradient f x  w x /  g x fitnessoptimising 1- s(  x -g x ) 2 optimum in x  x selection gradient 2f x s(  x -g x )

character state in environment x : all selection gradients 2f x s(  x -g x )=0 selection finds optimum character state in each x g x =  x

Unpredictable Selection

life history zygote pool z 1 mating pool selection in: y adult migration development: x zygote pool z 0 unpredictable selection z1z1 z0z0 m x=0x=1 y=0y=1

migration frequency from x to y: f(y|x) unpredictable selection z1z1 z0z0 m x=0 y=0 y=1  y =0  y =

selection gradient for phenotype that should develop in environment x : weighted average! (weak selection) unpredictable selection  y f( y | x )  w x,y /  g x

evolved phenotypic mean: character state (weak selection) unpredictable selection evolved mean phenotype g 0 =0.3 g x =  y f( y | x )  y

evolved phenotypic mean: character state (weak selection) unpredictable selection compromise phenotype evolves g x =  y f( y | x )  y

evolved phenotypic mean: reaction normcoefficients heightat x=0 slope (weak selection) unpredictable selection g 0 =  0 g 1 =  1 cov(x,y)/var(x) compromise phenotype evolves

evolved reaction norm slope shallower than optimal slope if reacton norm linear andfew environments orasymmetrical migration unpredictable selection g 1 =  1 cov(x,y)/var(x) compromise phenotype evolves

environment value optimum reaction norm slope:  1 evolved reaction norm: slope:  1 cov(x,y)/var(x) unpredictable selection

Life History Complications

Life History Complications density dependence

zygote pool z 1 mating pool density dependence c selection in: y density dependence b adult migration density dependence a development: x zygote pool z 0 density dependent numbers z1z1 z0z0 m x=0x=1 y=0y=1

frequency environments now includes density dependent viability v y in environments y f’ x,y = f x,y v y Effective frequency of selection environments can become complicated density dependent numbers

equal density depence leads to evolved mean genotypic values reflecting the frequencies of the environment, y 0 =0.3 and y 1 =0.7 density dependent numbers

density dependence in y 1 gets so high that nobody survives in environment y 1 ; effectively only environment y 0 exists

Life History Complications zygote migration

zygote migration mating pool density dependence c selection in: y density dependence b adult migration density dependence a development: x zygote migration no zygote pool x=0x=1 y=0y=1 x=0x=1

if both zygotes and adults migrate, selection equations only approximate requires matrix methods introduces “reproductive value” in evolved genotypic value no zygote pool x=0x=1 y=0y=1 x=0x=1

if zygotes migrate but adults not, and selection is predictable zygote migration gives no problem no zygote pool x=0x=1 y=0y=1 x=0x=1

Selection on phenotypic plasticity is efficient if: selection predictable no adult migration and therefore no life history complication conclusions