Simulation

Rate of environmental change

Good Harsh
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)
Good Harsh
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
Good Harsh
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


Observations

  • AA vs. Sexual: coexist
  • Aa vs. Sexual: sex lose
  • GM fail to predict outcome:
Good Harsh AM GM
AA 800 100 450 282.84
Aa 400 400 400 400
aa 100 800 450 282.84
Sexual 212.5 212.5 212.5 212.5