Genetic Polymorphism and Speciation - An Adaptive Dynamics Perspective - Eva Kisdi & Stefan Geritz Dept. of Mathematics, University of Turku

Evolutionary branching

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

Continuum of Alleles, Small Mutations phenotype (x) f 1 (x) f 2 (x) d  fitness within habitat f 1 (x)f 2 (x) c1c1 c2c2 offspring adults (1)Clonal (haploid) inheritance (2)Diploid, 1 locus with additive allelic effects on the phenotype (3)Diploid with assortative mating

d/  =3, c 1 = x1x1 x2x2 d/  Clonal model Evolutionary branching of phenotypes

d/  c1c1 Clonal model: evolutionary branching of phenotypes Diploid 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/c 1 c 2

Fixed alleles: Hoekstra et al 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 disadvantage of similar alleles fine-tuning done by directional evolution if the singularity is an ESS, then the polymorphism is transient on the long-term evolutionary timescale not every polymorphism is evolutionarily permanent Genetic Polymorphism

d/  c1c1 evolutionarily stable polymorphism (no branching) evolutionary branching Evolutionary branching is not necessary (neither sufficient) for evolutionarily stable polymorphism Both clonal and diploid:

d/  =3, c 1 = x1x1 x2x2 d/  Clonal model After branching, two specialist phenotypes evolve

d/  =2.25, c 1 =0.5 x1x1 x2x2 x1x1 x1x1 d/  =3, c 1 =0.5d/  =5, c 1 =0.5 Diploid model Will assortative mating restore the simplicity of the clonal model?

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: in the dominant (BB+Bb) mating group in the recessive (bb) mating group Zygote frequencies: overall u = freq( x 1 ) = 0.5 v = freq(b) Population Genetics of Assortative Mating except

Zygote frequencies: Selection by the ecological locus: relative fitnesses Gamete frequencies by the standard Mendelian rules within each mating group recombination rate r 6 variables – 1 (sum of the Q 's is 1) – 1 (symmetry, u =0.5) Population Genetics of Assortative Mating except

Bistability of the gamete frequency dynamics: v =freq(b) D = q ib - uv LE is stable LE is unstable p = 0.75 r = 0.5 s = (max s with d/  =3, c 1 =0.5) v crit Population Genetics of Assortative Mating

p = 0.85, r = 0.5 (Δx given for d/  = 3, c 1 =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) v crit frequency of allele b linkage disequilibrium, D = q ib - uv Population Genetics of Assortative Mating

recombination (r) penetrance (p) LD evolves LD evolves if v is high enough LD does not evolve 1 s = (maximum for d/  =3, c 1 =0.5) Population Genetics of Assortative Mating

p=0.9, r=0.5, d/  =3, c 1 =0.5 x1x1 x2x2 Assortative mating during branching LE only LD + LE LD only Switch from LE to LD somewhere in the orange band depending on the frequency of b

Adaptive dynamics of alleles at LD p=0.9, r=0.5, d/  =3, c 1 =0.5 x1x1 x2x2 d/  heterozygote deficiency before / after selection F

p=0.9, r=0.5, d/  =3, c 1 =0.5 x1x1 x2x2 Assortative mating during branching LE only LD + LE LD only Switch from LE to LD somewhere in the orange band depending 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, c 1 =0.5 x1x1 x2x2 p=0.85, r=0.5, d/  =3, c 1 =0.5 x1x1 x2x2

Prospects for speciation recombination (r) penetrance (p) Levene model with d/  = 3, c 1 = 0.5 Left to the red line: AD saddle LD does not evolve LD may evolve but will be lost Right 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 sufficient for an evolutionarily stable polymorphism to exist... on speciation evolution can lead to strong disruptive selection but 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!