Rock, paper, and

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Real ESS games in the wild!
Rock, paper, and scissors
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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

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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.
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Three player RPS game in theSide-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.

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The phenotype of lizards reflects the genes --
real handy
bb
oo
bo
yo
by
yy
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Observed cycles -- 5 yr RPS, 2yr r-K Can we model
them?
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Females payoffs with neighbors (data)
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Modeling the female game (Sinervo et al. Nature
2000)
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The female game (Sinervo et al. 2000)
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Model female game with one locus except b-allele
is neutral in females
bb
oo
bo
yo
by
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Modeling the male game Sinervo Lively Nature
1996
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Observed male payoffs -- both are RPS
Number of females Sinervo Lively (1996)
DNA paternity Zamudio Sinervo (2000)
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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).
Sinervo Lively payoffs
DNA paternity payoffs
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1-locus 2-allele male game - no cycles
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Dominance in a 1-locus 3-allele game
Home range overlap
DNA paternity
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One-locus Male game oscillates slowly
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Modeling Epistasis -- gene interactions
Blue locus with b and null alleles interacts with
an o-y locus (or any form of epistasis!)
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Two-locus male game oscillates slowly
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The female game (one locus, 2 alleles)
When coupled to a male RPS game
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One-locus 3-allele Male RPS coupled to female
game drives fast cycles
But the amplitude is still too small
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2-locus models are worse -- they do not
generate regular 2yr female cycles or any form Of
RPS male cycles
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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.
bb
oo
bo
yo
by
yy
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Transformation of by males appears to be
triggered by testosterone (T)
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After transforming by males settle on smaller
home range like a bb male
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Male game (1-locus 3-allele) with plastic
by-genotype -- fast and high amplitude RPS cycles
-- Eureka!
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Theory matches observed oscillations!
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Theory