The concept of adaptive phenotypic polymorphism in evolutionary theory

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1 The concept of adaptive phenotypic polymorphism in evolutionary theory Olof Leimar, Stockholm University Polymorphic outcomes in evolutionary games A. Conditional strategy - genetic monomorphism B. Mixed or randomized strategy - can be limit of A (Harsanyi) C. Genetic polymorphism - a version of B? (exemplified by the Hawk-Dove game) Is there a unifying perspective? Push the concept of a conditional strategy as far as it can go Study evolutionary games in structured populations

2 Two traditions in evolutionary theory The phenotypic gambit Adaptationism Evolutionary game theory Life history theory Population genetics Explicit evolutionary dynamics Single- or multi-locus models Quantitative genetics The phenotypic gambit emphasizes evolutionary equilibria Population genetics emphasizes genetic variation The traditions differ in their view on genetic polymorphism Phenotypic gambit: genetic polymorphism is an example of imperfect adaptation (for instance because of constraints) Population genetics: genetic polymorphism is an important issue in itself Can the traditions be united under a single umbrella?

Some forgotten ideas about polymorphism The Dobzhansky - Cain & Sheppard - Fisher debate Dobzhansky (1951) Genetics and the origin of species Polymorphism as such is frequently adaptive; polymorphism

but it is not clear what is meant by one population being more highly adapted than another to a particular environment Fisher (1958) Polymorphism and natural selection "I would not have alluded to

3 Some forgotten ideas about polymorphism The Dobzhansky - Cain & Sheppard - Fisher debate Dobzhansky (1951) Genetics and the origin of species Polymorphism as such is frequently adaptive; polymorphism enables a species to exploit the environment more efficiently (referring to genetic polymorphism) Cain & Sheppard (1954) The theory of adaptive polymorphism This interesting theory may be correct, but it is not clear what is meant by one population being more highly adapted than another to a particular environment Fisher (1958) Polymorphism and natural selection "I would not have alluded to this storm in a tea-cup, but for the circumstance that I mean to put forward some ideas on this problem of the possible adaptive value of polymorphisms" Dobzhansky is essentially right, but the idea traces back to "a little-known book of nearly a hundred years ago, called The Origin of Species" "I propose to suggest that one way of making this intricate system intelligible to the human mind is by the analogy of games of skill, or to speak somewhat more pretentiously, of the Theory of Games" (referring to species interactions, like those between predator and prey) Balanced polymorphism can be viewed as a randomized strategy in a game Genetic polymorphism regarded as a randomized strategy?

4 Dobzhansky (1951) on adaptive polymorphism "... polymorphism within a species, or any other kind of diversity of sympatric forms, increases the efficiency of the exploitation of the resources of the environment by the living matter. A single genotype, no matter how versatile, could hardly function with maximal efficiency in all environments. Hence, natural selection has preserved a variety of genotypes, more or less specialized to render the organism efficient in a certain range of the existing environments."

5 Evolutionary ecology perspective Alternative phenotypes Phenotypic polymorphism Members of a population fall into two or more fairly distinct categories (morphs) with respect to some of their traits Three systems of phenotype determination genetic environmental random (combinations possible) Look for general evolutionary theory of phenotype determination Important idea: genetic variation can act as an adaptive cue for phenotype determination

Phenotypic polymorphism Basic idea: advantage from specialization

advantage can arise in different ways varied environments (in space or

Good to match phenotype to conditions this is the basic idea for both

6 Phenotypic polymorphism Basic idea: advantage from specialization compared to generalist phenotype Levins, 1968, Changing Environments An advantage can arise in different ways varied environments (in space or time), local frequency dependence, competitive character displacement Good to match phenotype to conditions this is the basic idea for both adaptive phenotypic plasticity and local genetic adaptation Hoplothrips Ambystoma

environmental cue morph 2 Developmental switching

7 Sketch of phenotype determination recent selection genotype genetic cue morph 1 switching device environment environmental cue morph 2 Developmental switching genotypic environmental random (combinations) Switching can be adaptive

8 Sketch of phenotype determination recent selection genotype genetic cue morph 1 switching device environment environmental cue morph 2 Genetic variation can act as adaptive cue for switching predictor of the coming selective conditions Environmental variation can act as adaptive cue in the same manner Random variation produced by switching device component of genetic or environmental variation can regulate morph frequencies

9 Genetic variation as input to a strategy? Alleles at polymorphic locus Genes coding for switching device recent selection genotype genetic cue morph 1 switching device environment environmental cue morph 2 From the point of view of adaptation of the switching device, environmental and genetic cues may play similar roles Consequences of genetic variability at certain loci can be seen as input to a developmental switch

10 Simplest possible example: two selective conditions (two habitats) and binary cues Habitats 1 and 2: Low and High predation risk P i z 1 z 2 s ik y u i m proportion of patches with habitat i alternative phenotypes survival in habitat i of z k binary environmental cue probability y = i in habitat i rate of migration Non-overlapping generations, haploid genetics Each individual observes independent copy of cue reproduction in each patch observation of cue and then development trait-based selection density regulation to carrying capacity migration through dispersal pool z 1 z 2 Assume s 11 = s 22 = 1, s 12 = s 21 = s, u 1 = u 2 = u

11 Invasion analysis Eigenvalue problem for invasion of mutant into resident population " >1 "w 1 = (1# m 1 )r 1 w 1 + m 1 r 2 w 2 "w 2 = m 2 r 1 w 1 + (1# m 2 )r 2 w 2 m 1 = mp 2, m 2 = mp 1, r i = s i s i s i = mutant survival, s i = resident survival " <1 Example resident is environmental determination mutant is z 1 (specialist on habitat 1) P 1 = P 2 = 0.5 environmental s 1 =1, s 2 = s, s 1 = s 2 = u + (1" u)s Normalization: P 1 w 1 + P 2 w 2 =1 " = r 1 P 1 w 1 + r 2 P 2 w 2 " = P 1 w 1 + P 2 w 2 s u + (1# u)s genetic Leimar, Hammerstein and Van Dooren (2006)

12 Conditional strategy interpretation An individual has a genetic cue locus, with at most two alleles, and another locus coding for a switching device Switching devices: S e pure environmental phenotype determination S g pure genetic phenotype determination S 1ge develop z 1 when allele 1 is present at cue locus, otherwise use environmental determination S 2ge develop z 2 when allele 2 is present at cue locus, otherwise use environmental determination A strategy is uninvadable if no other strategy is better at predicting coming selective conditions (habitat) General problem of a binary choice based on two binary cues E-cue G-cue S e S g S 1ge S 2ge Claim: The evolutionary outcome can be interpreted as an optimal decision rule based on environmental and genetic cues

13 Next example: alternative male mating types Habitats 1 and 2: Low and High population density P i S F f i V C x p(x,y) m proportion of patches with habitat i alternative phenotypes (Searcher, Fighter) probability of fighting interaction in habitat i value of winning injury cost of losing a fight male growth rate (potential fighting ability) probability of winning for x against y rate of migration Searcher Fighter Hoplothrips p(x,y) = 0.5 [1 + u (x - y)] x and y are iid uniform on (0,1) u is a payoff relevance parameter Strategy: become F when x > x k x k is a threshold for switching Possible outcomes: a single threshold x 0 genetic polymorphism x 1, x 2

14 Some results for the male mating type example Depending on the parameters, we can have a single evolutionarily stable threshold x 0 (pure environmental determination) a genetic polymorphism with x 1, x 2 at 0 and 1 (pure genetic determination) a genetic polymorphism with 0 < x 1, x 2 < 1 (combined environmental and genetic) Interpretation: The environmental cue x can inform a male abut how likely he is to win a fight With genetic polymorphism, a male s genotype can be though of as a habitat cue Different cues (like environmental and genetic) may predict different aspects of coming selective conditions x 0 x 2 x 1 Frequency in each habitat of x 1 Leimar, McNamara and Cuthill, in prep.

15 Summary and conclusion A developmental machinery can evolve to make efficient use of both genetic and environmental cues The availability of a genetic cue depends on the selective maintenance of polymorphism at genetic cue loci The presence of this polymorphism need not be guided by the well-being of the organism Nevertheless, both genetic and environmental phenotype determination can be viewed as conditional strategies Fully resolves the polymorphism debate from the 1950 s Genetic variation can play a part in an adaptive device for the organism Genetic polymorphism can be integrated into the phenotypic gambit

Problems for 3505 (2011)

Problems for 3505 (2011) Problems for 505 (2011) 1. In the simplex of genotype distributions x + y + z = 1, for two alleles, the Hardy- Weinberg distributions x = p 2, y = 2pq, z = q 2 (p + q = 1) are characterized by y 2 = 4xz.