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random dispersal to two habitats within-habitat selection: within-habitat competition: fixed number of adults emerge random mating in the entire population f1if1i f2if2i c1c1 c2c2 offspring adults Levene's Soft Selection Model
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Genetic Polymorphism and Speciation- An Adaptive Dynamics Perspective -
Eva Kisdi & Stefan GeritzDept. of Mathematics, University of Turku
Evolutionary branching
Resource competition * Christiansen & Loeschcke 1980 * Abrams et al. 1993 * Doebeli 1996 * Metz et al. 1996 * Meszéna & Metz 1996 * Dieckmann & Doebeli 1999 * Day 2000 * Drossel & McKane 2000 * Day 2001 * Claessen & Dieckmann 2002 * Schreiber & Tobiason 2003 * Vukics et al. 2003
Asymmetric competition * Abrams et al. 1993 * Geritz et al. 1999 * Kisdi 1999 * Jansen & Mulder 1999 * Kisdi & Geritz 2001
Predation * Abrams et al. 1993 * Van der Laan & Hogeweg 1995 * Doebeli & Dieckmann 2000 * Day et al. 2002 * Bowers et al. 2003 * Dercole et al. 2003
Host-parasite systems * Boots & Haraguci 1999 * Koella & Doebeli 1999 * Regoes et al. 2000
Cannibalism * Dercole & Rinaldi 2002 * Dercole 2003 * Nishimura & Isoda 2004
Mutualism * Doebeli & Dieckmann 2000 * Law et al. 2001 * Ferdy et al. 2002 * Ferriere et al. 2002
Spatial heterogeneity * Brown & Pavlovic 1992 * Meszéna et al. 1997 * Geritz et al. 1998 * Kisdi & Geritz 1999 * Geritz & Kisdi 2000 * Kisdi 2001 * Mathias & Kisdi 2002 * Doebeli & Dieckmann 2003 * Mizera & Meszéna 2003 * Egas et al. 2004
Temporal fluctuations * Kisdi in prep.
Metapopulations * Cohen & Levin 1991 * Doebeli & Ruxton 1997 * Parvinen 1999 * Mathias et al. 2001 * Kisdi 2002 * Parvinen 2002
Mating systems * Hoekstra 1980 * Metz et al. 1992 * Cheptou & Mathias 2001 * De Jong & Geritz 2001 * Maire et al. 2001 * Van Dooren & Leimar 2003
Sexual selection * Van Doorn & Weissing 2001 * Van Doorn et al. 2001
Microbial metabolism * Doebeli 2002 * Friesen et al. 2004
Prebiotic replicators * Meszéna & Szathmáry 2001
Resource competition * Christiansen & Loeschcke 1980 * Abrams et al. 1993 * Doebeli 1996 * Metz et al. 1996 * Meszéna & Metz 1996 * Dieckmann & Doebeli 1999 * Day 2000 * Drossel & McKane 2000 * Day 2001 * Claessen & Dieckmann 2002 * Schreiber & Tobiason 2003 * Vukics et al. 2003
Asymmetric competition * Abrams et al. 1993 * Geritz et al. 1999 * Kisdi 1999 * Jansen & Mulder 1999 * Kisdi & Geritz 2001
Predation * Abrams et al. 1993 * Van der Laan & Hogeweg 1995 * Doebeli & Dieckmann 2000 * Day et al. 2002 * Bowers et al. 2003 * Dercole et al. 2003
Host-parasite systems * Boots & Haraguci 1999 * Koella & Doebeli 1999 * Regoes et al. 2000
Cannibalism * Dercole & Rinaldi 2002 * Dercole 2003 * Nishimura & Isoda 2004
Mutualism * Doebeli & Dieckmann 2000 * Law et al. 2001 * Ferdy et al. 2002 * Ferriere et al. 2002
Spatial heterogeneity * Brown & Pavlovic 1992 * Meszéna et al. 1997 * Geritz et al. 1998 * Kisdi & Geritz 1999 * Geritz & Kisdi 2000 * Kisdi 2001 * Mathias & Kisdi 2002 * Doebeli & Dieckmann 2003 * Mizera & Meszéna 2003 * Egas et al. 2004
Temporal fluctuations * Kisdi in prep.
Metapopulations * Cohen & Levin 1991 * Doebeli & Ruxton 1997 * Parvinen 1999 * Mathias et al. 2001 * Kisdi 2002 * Parvinen 2002
Mating systems * Hoekstra 1980 * Metz et al. 1992 * Cheptou & Mathias 2001 * De Jong & Geritz 2001 * Maire et al. 2001 * Van Dooren & Leimar 2003
Sexual selection * Van Doorn & Weissing 2001 * Van Doorn et al. 2001
Microbial metabolism * Doebeli 2002 * Friesen et al. 2004
Prebiotic replicators * Meszéna & Szathmáry 2001
http://users.utu.fi/evakis/addyn.htm
• random dispersal to two habitats
• within-habitat selection:
• within-habitat competition: fixed number of adults emerge
• random mating in the entire population
A1A1 A1A2 A2A2
Habitat 1 f11 f12 f13 Habitat 2 f21 f22 f23
f1i f2i
c1 c2
offspring
adults
Levene's Soft Selection Model
Continuum of Alleles, Small Mutations
phenotype (x)
f1(x) f2(x)d
fitne
ss
with
in h
abita
t
f1(x) f2(x)
c1 c2
offspring
adults
(1) Clonal (haploid) inheritance(2) Diploid, 1 locus with additive allelic effects on the phenotype(3) Diploid with assortative mating
d/=3, c1=0.5
+
+
-
-
x1
x2
d/
Clonal model
Evolutionary branching of phenotypes
0
0.5
1
1 2 3 4d/
c1
Clonal model: evolutionary branching of phenotypesDiploid 1-locus model: evolutionary branching of alleles
Clonal & diploid models
Infinite loci, +/- alleles: Genetic polymorphism in each locus(Spichtig & Kawecki, in press)
Two loci, continuum of alleles: Initially both loci undergo branching, but only one remains polymorphic (Kisdi & Geritz 1999)
(d/)2 > 1/c1c2
A1A1 A1A2 A2A2
Habitat 1 1 1 - s/2 1 - s Habitat 2 1 - s 1 - s/2 1
Fixed alleles:
Hoekstra et al. 1985
Genetic Polymorphism
Protected polymorphism of similar alleles – under weak selection - ?!
+
+-
-
Evolving alleles:
Generic models of a wide class, both clonal and diploid:
no polymorphism of similar alleles away from singularities invasion implies fixation
near a singularity, protected polymorphism or rare disadvantageof similar alleles
fine-tuning done by directional evolution
if the singularity is an ESS, then the polymorphism is transienton the long-term evolutionary timescale
not every polymorphism is evolutionarily permanent
Genetic Polymorphism
Genetic Polymorphism
0
0.5
1
1 2 3 4d/
c1
evolutionarily stablepolymorphism (no branching)
evolutionary branching
Evolutionary branching is not necessary (neither sufficient) for evolutionarily stable polymorphism
Both clonal and diploid:
d/=3, c1=0.5
+
+
-
-
x1
x2
d/
Clonal model
After branching, two specialist phenotypes evolve
d/=2.25, c1=0.5
x1
x2
x1 x1
d/=3, c1=0.5 d/=5, c1=0.5
Diploid model
Will assortative mating restore the simplicity of the clonal model?
x1
x2
x1
x2
x1
x2
x1
x2
heterozygote inferiorityheterozygote inferiority
Evolution to strongest heterozygote inferiority
Time window for speciation
Assortative mating
"Two-allele mechanisms": (Felsenstein, 1981)strong selection is necessary to counterbalance recombination
Population Genetics of Assortative mating
Udovic (1980) model:
mating locus with two alleles (B, b)mating groups: BB+Bb and bb
p = penetrance: mating within group with prob. p,otherwise random mating
r = recombination between the ecological and the mating locus
In linkage equilibrium, alleles B and b are neutral
Ecological locus (no mutation):Mating locus: B, b
Gamete frequencies:)(
2)(
1)(
2)(
1 ,,, dB
dB
db
db QQQQ in the dominant (BB+Bb) mating group
)(2
)(1 , b
bbb QQ in the recessive (bb) mating group
Zygote frequencies:
jlikdd
jld
ikijkl qqpQQQpP )1(/ )()()(
)()()( , diBiB
dib
bibib QqQQq overall
jbibdd
jbd
ibbb
jbb
ibijbb qqpQQQQQQpP )1(// )()()()()()(
21 xx u = freq(x1) = 0.5v = freq(b)
Population Genetics of Assortative Mating
except
Zygote frequencies:
jlikdd
jld
ikijkl qqpQQQpP )1(/ )()()(
jbibdd
jbd
ibbb
jbb
ibijbb qqpQQQQQQpP )1(// )()()()()()(
Selection by the ecological locus:1 ),(1 ,1 xs relative fitnesses
Gamete frequencies by the standard Mendelian rules within each mating grouprecombination rate r
6 variables – 1 (sum of the Q's is 1) – 1 (symmetry, u=0.5)
Population Genetics of Assortative Mating
except
,,,, )(2
)(1
)(2
)(1
dB
dB
db
db QQQQ )(
2)(
1 , bb
bb QQ
Bistability of the gamete frequency dynamics:
v=freq(b)
D = qib - uv
critvv
critvv LE is stable
LE is unstable
p = 0.75r = 0.5s = 0.358(max s with d/=3, c1=0.5)
0
0.5
1
0 0.25
vcrit
Population Genetics of Assortative Mating
0
0.5
1
0 0.250
0.5
1
0 0.250
0.5
1
0 0.25
p = 0.85, r = 0.5 (Δx given for d/= 3, c1=0.5)
s=0.125 (Δx=1) s=0.194 (Δx=1.35) s=0.203 (Δx=1.4)
s=0.207 (Δx=1.42) s=0.239 (Δx=1.6) s=0.339 (Δx=2.4)
0
0.5
1
0 0.25
vcrit
vcrit0
0.5
1
0 0.250
0.5
1
0 0.25
frequ
ency
of a
llele
b
linkage disequilibrium, D = qib - uv
Population Genetics of Assortative Mating
reco
mbi
natio
n (r
)
penetrance (p)
LD evolves LD evolves if v is high enoughLD does not evolve1s = 0.358 (maximum for d/=3, c1=0.5)
Population Genetics of Assortative Mating
p=0.9, r=0.5, d/=3, c1=0.5
x1
x2
Assortative mating during branching
LE onlyLD + LELD only
Switch from LE to LDsomewhere in the orange banddepending on the frequency of b
Adaptive dynamics of alleles at LD
p=0.9, r=0.5, d/=3, c1=0.5
x1
x2
d/ -0.2 0 0.2 0.4 0.6 0.8
heterozygote deficiencybefore / after selection
F
p=0.9, r=0.5, d/=3, c1=0.5
x1
x2
Assortative mating during branching
LE onlyLD + LELD only
Switch from LE to LDsomewhere in the orange banddepending on the frequency of b
LD exists LE only
Adaptive dynamics of alleles at LD
LD permanent – incipient speciation
LD lost
p=0.73, r=0.5, d/=3, c1=0.5
x1
x2
p=0.85, r=0.5, d/=3, c1=0.5
x1
x2
Prospects for speciation
reco
mbi
natio
n (r
)
penetrance (p)
Levene model with d/= 3, c1 = 0.5
Left to the red line: AD saddle LD does not evolve LD may evolve but will be lostRight to the red line: AD attractor LD evolves LD evolves if v is high enough
1
Prospects for speciation
B and b are neutral at LE
- mutational equilibrium- drift and hitchhiking: the frequency of allele b, v, is
most often near 0 (LD in ) or near 1 (LD in and ) - sexual selection: if rare males are at a disadvantage,
B or b will be rare and selected against
Increasing penetrance
- natural selection favours increased p at LD- increasing p transforms a saddle into an attractor of AD- closes gene flow down
- role of temporary LD in increasing penetrance
(Dieckmann and Doebeli 1999)
Prospects for speciation
"Byproduct" speciation
- no LD is needed between the ecological and mating loci
- sexual selection may counterbalance disruptive natural selection (Kirkpatrick and Nuismer 2004), and causes a bistability in the evolutionary dynamics of assortment (Matessi et al. 2001, Meszéna and Christiansen in prep.)
- environmental variance in the selected trait constrains the maximum attainable level of assortment
An Adaptive Dynamics Perspective
... on polymorphism
directional evolution takes care of "fine tuning"polymorphism may be transient in evolution(evolution near an ESS, evolution to extinction)evolutionary branching is neither necessary nor sufficientfor an evolutionarily stable polymorphism to exist
... on speciation
evolution can lead to strong disruptive selectionbut can lead away from it again (time window)competing processes: evolution of dominance,sexual dimorphism, mixed strategies
An Adaptive Dynamics Perspective
... on speciation
- evolution to polymorphism under disruptive selection appears to be common
- reproductive isolation: depends on genetics
Alliance with population genetics needed!