Download The female game

Real ESS games in the wild!
Rock, paper, and
scissors
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
oo
bo
yo
bb
by
yy
Observed cycles -- 5 yr RPS, 2yr r-K
Can we model them?
Females payoffs with neighbors (data)
Wi (t)  Wi , solitary  GijNij(t)
j
Modeling the female game
(Sinervo et al. Nature 2000)
Wi (t)  Wi , solitary  GijNij(t)
j
dNi (t)
wi (t) (Ki  Ni (t))
 Ni (t)  Fi 

dt
w
Ki
The female game (Sinervo et al. 2000)
Model female game with one locus
except b-allele is neutral in females
oo
bo
yo
bb
by
yy
Modeling the male game
Sinervo & Lively Nature 1996
Wi (t)  Wi , solitary  GijNij(t)
j
 p (t)w
j
M i (t) =
j
w
i, j
Observed male payoffs -- both are RPS
Number of females
Sinervo & Lively (1996)
5.0
Relative
A
W=
4.0
Fitness
DNA paternity
Zamudio & Sinervo (2000)
2.5
2.0
3.0
1.5
2.0
1.0
1.0
0.5
0
0
WO,OWB,OWY,O WO,BWB,BWY,B WO,YWB,YWY,Y
O
B
Y
B
WO,OWB,OWY,O WO,BWB,BWY,B WO,YWB,YWY,Y
O
B
Common behavioral phenotype
Y
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
1-locus 2-allele male game - no cycles
Dominance in a 1-locus 3-allele game
Home range overlap
5.0
Relative
A
W=
Fitness 4.0
DNA paternity
2.5
2.0
3.0
1.5
2.0
1.0
1.0
0.5
0
WO,OWB,OWY,O WO,BWB,BWY,B WO,YWB,YWY,Y
O
B
0
B
WO,OWB,OWY,O WO,BWB,BWY,B WO,YWB,YWY,Y
Y
O
B
Common behavioral phenotype
Wab= hab WAA +(1-hab) WAB
Y
One-locus Male game oscillates slowly
Phenotype
frequency
1
hby=0.5
hob=0.5
hyo=0.5
hby=0
hob=0.5
hyo=0.5
hby=1
hob=1
hyo=1
hby=1
hob=0.5
hyo=0.5
hby=0.5
hob=0
hyo=0.5
hby=0
hob=1
hyo=1
hby=0.5
hob=1
hyo=0.5
hby=0.5
hob=0.5
hyo=0
hby=1
hob=0
hyo=1
hby=0.5
hob=0.5
hyo=1
hby=0
hob=0
hyo=0
hby=1
hob=1
hyo=0
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
0
50
100
150
200 0
50
100
150
Generation
200 0
50
100
150
200
Modeling Epistasis -- gene interactions
Wab = ab WAA+ (1-ab) WAB
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.
oo
bo
yo
bb
by
yy
Transformation of by males appears
to be triggered by testosterone (T)
Early
Season
Plasma T
(ng/ml)
175
175
150
150
125
125
100
**
n.s.
100
75
75
50
50
Yellow Blue
bb
by
Late
Season
Now B Blue
by
bb
After transforming by males settle on
smaller home range like a bb male
Home Range
Area (m 2)
120
1993
†
*
1994
120
80
80
40
40
0
0
8
17 12
30
Yellow Blue Orange
†
*
8 32 19
41
Yellow Blue Orange
Male game (1-locus 3-allele) with plastic bygenotype -- fast and high amplitude RPS cycles -Eureka!
Theory matches observed oscillations!
Double click on Dr. Lizardo for tips
on Game Theory…
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