Rock, paper, and scissors Real ESS games in the wild! and the r- and K strategists

Darwin (the Origin) It may metaphorically be said that natural selection is daily and hourly scrutinizing, throughout the world, the slightest variations; rejecting those that are bad, preserving and adding up all that are good; silently and insensibly working, whenever and wherever opportunity offers, at the improvement of each organic being in relation to its organic and inorganic conditions of life. We see nothing of these slow changes in progress, until the hand of time has marked the lapse of ages... Well, natural selection and evolution is really fast in lizards…

A brief history of cyclical games Maynard Smith (1982) considered the rock-paper-scissors game using game theory and showed that 3 strategies can cycle. He could not think of a natural analogue for the game (Wright also considered the RPS game, but earlier in 1968). Chitty (1958) suggested that natural selection could produce genetic female morphs which drive stable population cycles. Despite a lifetime of field studies he did not find definitive evidence for morphs in mammals. The female strategies are: 1) high quality (low quantity) wins at high density, and 2) high quantity (poor quality) wins at low density.

Three player RPS game in the Side-blotched lizards Three basic throat color types are associated with three RPS alternative behaviors: Orange (Rock) -- Ultradominant, large, high testosterone, aggressive, polygynous, and muscular Yellow (Paper) -- Not aggressive, female mimic, no territory, “floats” between dominant male territories Blue (Scissors) -- Dominant, mate-guarder Orange (Rock) is beaten by Yellow (Paper) is beaten by Blue (Scissors) which is beaten by Orange (Rock) ad infinitum….

The phenotype of lizards reflects the genes -- real handy bbooboyobyyy

Observed cycles -- 5 yr RPS, 2yr r-K Can we model them?

Females payoffs with neighbors (data)

Modeling the female game (Sinervo et al. Nature 2000)

The female game (Sinervo et al. 2000)

Model female game with one locus except b-allele is neutral in females bbooboyobyyy

Modeling the male game Sinervo & Lively Nature 1996

Observed male payoffs -- both are RPS Number of females Sinervo & Lively (1996) DNA paternity Zamudio & Sinervo (2000)

Replicator game (Y-chromosome) Basic problem with replicator game: Cycles are too slow. Can we get cycles as fast as 4-6 years seen in nature? What follows are models of the RPS and r-K strategy games from a Genetic paper (in press). DNA paternity payoffs Sinervo & Lively payoffs

1-locus 2-allele male game - no cycles

Dominance in a 1-locus 3-allele game Home range overlapDNA paternity

One-locus Male game oscillates slowly

Modeling Epistasis -- gene interactions Blue locus with b and null alleles interacts with an o-y locus (or any form of epistasis!)

Two-locus male game oscillates slowly

The female game (one locus, 2 alleles) When coupled to a male RPS game…

One-locus 3-allele Male RPS coupled to female game drives fast cycles But the amplitude is still too small…

2-locus models are worse -- they do not generate regular 2yr female cycles or any form Of RPS male cycles…

Solution to increase amplitude limited (adaptive) morph plasticity: genotype by can be Y when surrounded by O or B when surrounded by B See Sinervo et al 2000b Horm. Behav. bbooboyobyyy

Early Season Late Season * n.s. Now B by Blue bb Plasma T (ng/ml) * Yellow by Blue bb Transformation of by males appears to be triggered by testosterone (T)

After transforming by males settle on smaller home range like a bb male

Male game (1-locus 3-allele) with plastic by- genotype -- fast and high amplitude RPS cycles -- Eureka!

Theory matches observed oscillations!

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