Simulation
Rate of environmental change
Good |
\(1-p_{gh}\) |
\(p_{gh}\) |
Harsh |
\(p_{hg}\) |
\(1-p_{hg}\) |
Payoff Matrix
- \(K\) as fitness
- Fitness \(=\) \(\displaystyle 100\times\)(original payoff matrix)
- Assume sex ratio \(=0.5\)
- Assume HWE in sexual population
- constant proportion of AA, Aa, aa
- constant payoff (237.5)
- Simulate for \(10^4\) generations (orginal: \(10^6\) generations)
AA |
800 |
200 |
Aa |
450 |
450 |
aa |
200 |
800 |
Sex |
237.5 |
237.5 |
1-1 Sex Invade AA, \(p_{gh}=p_{hg}=0.2\)
Pars_g <- c(r1=0.1,r2=0.1, a12=0.6,a21=0.6, K1=237.5,K2=800)
Pars_h <- c(r1=0.1,r2=0.1, a12=0.6,a21=0.6, K1=237.5,K2=200)
Good year state: sex lose
equi.point(sex, asex): -378.91, 1027.34
Harsh year state: Stable Equilibrium
equi.point(sex, asex): 183.59, 89.84
A.mean(N) (sex, asex): 67.19, 282.13
G.mean(N) (sex, asex): 64.82, 281.13
SD(N) (sex, asex): 11.47, 23.92
1-2 Sex Invade AA, \(p_{gh}=p_{hg}=0.5\)
Good year state: sex lose
equi.point(sex, asex): -378.91, 1027.34
Harsh year state: Stable Equilibrium
equi.point(sex, asex): 183.59, 89.84
A.mean(N) (sex, asex): 66.06, 284.07
G.mean(N) (sex, asex): 62.73, 280.8
SD(N) (sex, asex): 16.32, 43.61
1-3 Sex Invade AA, \(p_{gh}=p_{hg}=0.8\)
## Good year state: sex lose
## equi.point(sex, asex): -378.91, 1027.34
##
## Harsh year state: Stable Equilibrium
## equi.point(sex, asex): 183.59, 89.84
## A.mean(N) (sex, asex): 37.01, 333.02
##
## G.mean(N) (sex, asex): 23.64, 317.02
##
## SD(N) (sex, asex): 29.96, 109.53
2-1 AA Invade Sex, \(p_{gh}=p_{hg}=0.2\)
Good year state: sex lose
equi.point(sex, asex): -378.91, 1027.34
Harsh year state: Stable Equilibrium
equi.point(sex, asex): 183.59, 89.84
A.mean(N) (sex, asex): 73.76, 273.52
G.mean(N) (sex, asex): 72.39, 266.15
SD(N) (sex, asex): 18.74, 35.62
2-2 AA Invade Sex, \(p_{gh}=p_{hg}=0.5\)
Good year state: sex lose
equi.point(sex, asex): -378.91, 1027.34
Harsh year state: Stable Equilibrium
equi.point(sex, asex): 183.59, 89.84
A.mean(N) (sex, asex): 68.37, 282.6
G.mean(N) (sex, asex): 65.37, 272.79
SD(N) (sex, asex): 23.12, 52.85
2-3 AA Invade Sex, \(p_{gh}=p_{hg}=0.8\)
Good year state: sex lose
equi.point(sex, asex): -378.91, 1027.34
Harsh year state: Stable Equilibrium
equi.point(sex, asex): 183.59, 89.84
A.mean(N) (sex, asex): 47.28, 317.61
G.mean(N) (sex, asex): 35.54, 297.8
SD(N) (sex, asex): 32.86, 103.89
3-1 Sex Invade Aa, \(p_{gh}=p_{hg}=0.5\)
Good year state: sex lose
equi.point(sex, asex): -50.78, 480.47
Harsh year state: sex lose
equi.point(sex, asex): -50.78, 480.47
A.mean(N) (sex, asex): 0.02, 449.57
G.mean(N) (sex, asex): 0, 449.47
SD(N) (sex, asex): 0.13, 7.82
3-2 Aa Invade Sex, \(p_{gh}=p_{hg}=0.5\)
Good year state: sex lose
equi.point(sex, asex): -50.78, 480.47
Harsh year state: sex lose
equi.point(sex, asex): -50.78, 480.47
A.mean(N) (sex, asex): 2.93, 445.17
G.mean(N) (sex, asex): 0, 435
SD(N) (sex, asex): 22.59, 41.19
Sex better than AA?
Change payoff matrix
AA |
800 |
100 |
Aa |
400 |
400 |
aa |
100 |
800 |
Sex |
212.5 |
212.5 |
Sex Invade AA, \(p_{gh}=p_{hg}=0.5\)
Good year state: sex lose
equi.point(sex, asex): -417.97, 1050.78
Harsh year state: asex lose
equi.point(sex, asex): 238.28, -42.97
A.mean(N) (sex, asex): 163.21, 80.22
G.mean(N) (sex, asex): 159.18, 75.74
SD(N) (sex, asex): 20.95, 28.16