Plasticity and GEin Evolutionary Genetics

Gerdien de JongUtrecht University

Overview talk• phenotypic plasticity

• selection gradient

• predictable selection

• unpredictable selection

• life history complications– density– zygote migration

Phenotypic Plasticity

27.5C

17.5C

a systematic change in morphology of an organism due to a developmental response to environmental conditions

phenotypic plasticity

Drosophila melanogaster

temperature

Drosophila wing lengthreaction norm: genotype represents

a function:

genotypic value isfunction value ingiven environment

function value:character state

phenotypic plasticity

temperature

Drosophila wing lengthGenotype-by-Environment Interaction

GE

reaction norms different slope or shape

phenotypic plasticity

phenotypic plasticity

Genotype-by-Environment Interaction

GEgenetically largelow temperaturegenetically smallhigh temperature

47°N17.5°C

9°N27.5°C

Drosophila melanogaster

phenotypic plasticity

Genotype-by-Environment InteractionDrosophila melanogastertwo populations:

tropical temperate

two temperatures17.5°C27.5°C

IN:

body size adultsgene expression

pupation probabilitylarval glycogen level

development timelarval competitive ability

female fecundity

Selection Gradient

multivariate selection

• phenotypic trait i

zi = gi + ei

• vector of changes in phenotypic means

z

• phenotypic variance covariance matrix

P

One traitSelection differential equals the covariance

between phenotype zi and fitness w:

Selection gradient equals the slope of fitness on phenotype

selection gradient

w Si = cov(zi,w)

z,i = cov(zi,w)/var(zi)

One traitSelection gradient equals the slope of

fitness on phenotype

Selection gradient equals the derivative of fitness towards phenotype

selection gradient

z,i = cov(zi,w)/var(zi)

w/zi = z,i

selection gradient

0

5

10

0 5

phenotype zfi

tnes

s w

slope z,i

multivariate selection

• phenotypic selection gradient each trai t

• multivariate phenotypic selection

w/zi = z,i

z = P z

w/zi = z,i

multivariate selection

• genotypic value trait i

gi

• vector of changes in genotypic means

g

• genotypic variance covariance matrix

G

selection gradient

0

5

10

0 5

genotype gfi

tnes

s w

slope g,i

multivariate selection

• genotypic selection gradient each trait

• multivariate genotypic selection

w/gi = g,i

g = G g

w/gi = g,i

Evolutionary Biology:z= g

g = G z

phenotypic plasticity:multivariate traitscharacter states

reaction norm coefficients

multivariate selection

Predictable Selection

life

history

zygote pool z1

mating pool

selection in x

zygote pool z0

predictable selection

z1

z0

m

x=0 x=1

character state

in environment x:

character state gx

selection gradient fx wx/gx

fitness optimising 1- s(x-gx)2

optimum in x x

selection gradient 2fx s(x-gx)

character state

in environment x:all selection gradients

2fx s(x-gx)=0

selection finds optimum character state in each x

gx= x

Unpredictable Selection

life

history

zygote pool z1

mating pool

selection in: y

adult migration

development: x

zygote pool z0

unpredictable selection

z1

z0

m

x=0 x=1

y=0 y=1

migration

frequency

from x to y:

f(y|x)

unpredictable selection

z1

z0

m

x=0

y=0 y=1

y=0 y=1

0.7 0.3

selection gradient for phenotypethat should develop in environment x: weighted average!

(weak selection)

unpredictable selection

y f(y|x) wx,y/gx

evolved phenotypic mean:character state

(weak selection)

unpredictable selection

evolved mean phenotype g0=0.3

gx= y f(y|x) y

evolved phenotypic mean:character state

(weak selection)

unpredictable selection

compromise phenotype evolves

gx= y f(y|x) y

evolved phenotypic mean:reaction normcoefficientsheight at x=0 slope

(weak selection)

unpredictable selection

g0 = 0

g1 = 1 cov(x,y)/var(x)

compromise phenotype evolves

evolved reaction norm slope shallower than optimal slope

if reacton norm linear and few environmentsor asymmetrical migration

unpredictable selection

g1 = 1 cov(x,y)/var(x)

compromise phenotype evolves

5

10

15

-10 -5 0 5 10

environment value

optimum reaction normslope:

1

evolved reaction norm:slope:

1 cov(x,y)/var(x)

unpredictable selection

Life History Complications

Life History Complications density dependence

zygote pool z1

mating pooldensity dependence c

selection in: ydensity dependence b

adult migrationdensity dependence a

development: xzygote pool z0

density dependent numbers

z1

z0

m

x=0 x=1

y=0 y=1

frequency environments now includes density dependent viability vy

in environments y

f’x,y = fx,y vy

Effective frequency of selection environments

can become complicated

density dependent numbers

optima in y 0: 0 and in y 1: 1evolved mean genotypic value:

0

0.2

0.4

0.6

0.8

1

0 0.003 0.006 0.009 0.012

density dependence in y 1

in x0

in x1

equal density depence leads to

evolved mean genotypic values

reflecting the frequencies of the

environment, y0=0.3 and y1=0.7

density dependent numbers

optima in y 0: 0 and in y 1: 1evolved mean genotypic value:

0

0.2

0.4

0.6

0.8

1

0 0.003 0.006 0.009 0.012

density dependence in y 1

in x0

in x1

density dependent numbers

density dependence in y1 gets so high

that nobody survives in

environment y1;effectively only environment y0

exists

Life History Complications zygote migration

zygote migrationmating pool

density dependence cselection in: y

density dependence badult migration

density dependence adevelopment: xzygote migration

no zygote pool

x=0 x=1

y=0 y=1

x=0 x=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=0 x=1

y=0 y=1

x=0 x=1

if zygotes migrate

but adults not,

and selection is predictable

zygote migration

gives

no problem

no zygote pool

x=0 x=1

y=0 y=1

x=0 x=1

Selection on phenotypic plasticityis efficient if:

selection predictableno adult migration

and therefore no life history complication

conclusions