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Plasticity and GEin Evolutionary Genetics
Gerdien de JongUtrecht University
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Overview talk• phenotypic plasticity
• selection gradient
• predictable selection
• unpredictable selection
• life history complications– density– zygote migration
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Phenotypic Plasticity
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27.5C
17.5C
a systematic change in morphology of an organism due to a developmental response to environmental conditions
phenotypic plasticity
Drosophila melanogaster
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temperature
Drosophila wing lengthreaction norm: genotype represents
a function:
genotypic value isfunction value ingiven environment
function value:character state
phenotypic plasticity
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temperature
Drosophila wing lengthGenotype-by-Environment Interaction
GE
reaction norms different slope or shape
phenotypic plasticity
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phenotypic plasticity
Genotype-by-Environment Interaction
GEgenetically largelow temperaturegenetically smallhigh temperature
47°N17.5°C
9°N27.5°C
Drosophila melanogaster
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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
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Selection Gradient
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multivariate selection
• phenotypic trait i
zi = gi + ei
• vector of changes in phenotypic means
z
• phenotypic variance covariance matrix
P
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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)
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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
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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
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multivariate selection
• genotypic value trait i
gi
• vector of changes in genotypic means
g
• genotypic variance covariance matrix
G
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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
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Evolutionary Biology:z= g
g = G z
phenotypic plasticity:multivariate traitscharacter states
reaction norm coefficients
multivariate selection
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Predictable Selection
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life
history
zygote pool z1
mating pool
selection in x
zygote pool z0
predictable selection
z1
z0
m
x=0 x=1
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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)
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character state
in environment x:all selection gradients
2fx s(x-gx)=0
selection finds optimum character state in each x
gx= x
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Unpredictable Selection
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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
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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
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selection gradient for phenotypethat should develop in environment x: weighted average!
(weak selection)
unpredictable selection
y f(y|x) wx,y/gx
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evolved phenotypic mean:character state
(weak selection)
unpredictable selection
evolved mean phenotype g0=0.3
gx= y f(y|x) y
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evolved phenotypic mean:character state
(weak selection)
unpredictable selection
compromise phenotype evolves
gx= y f(y|x) y
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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
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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
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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
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Life History Complications
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Life History Complications density dependence
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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
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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
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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
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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
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Life History Complications zygote migration
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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
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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
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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
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Selection on phenotypic plasticityis efficient if:
selection predictableno adult migration
and therefore no life history complication
conclusions
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