Model Definitions and Equations

• Patch Productivity: K

• Altruists: A’s

• Nonaltruists: N’s

• Frequency of A’s: P

• Average Payoff: W

Initial Patch Productivity: Kzero = 100

Direct Dependence of W on K: B=1

Exploitation factor of an N: X=0.05

Growth increment of patches: k=0.3

Number of patches/groups: m=10

Individuals per group: n=10

Global updating percentage: g=0.8

Idiosyncratic updating rate: mut=0.5

Number of time steps: time=200

• Payoff of an N on patch j:

WNj = B _ Kj _ (1 + X)

• Payoff of an A on patch j:

WAj = B _ Kj _ (1 + 0)

• Productivity of Patch j at time t:

Kj(t) = Kj(t-1) _[1– (Nj(t-1) _ X)]_(1+k)

Note: Nj(t-1) is the number of N’s in j at t-1

• Replicator Dynamic for t _ t+1:

_Pj = Pj _ (1-Pj) _ (WAj – WNj) / Wj

Notice: since X > 0, _Pj < 0 for all j

How will the A’s ever survive?!

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