The Evolutionary Games We Play

1. The Evolutionary Games We Play Psychology 3107

2. Introduction • Animals tend to behave in ways that maximize their inclusive fitness • Usually pretty straightforward • But, sometimes we must know what others are doing before we adopt a strategy • What if your mating call is drowned out by others’ calls, what to do, ahh what to do…

3. Fitness and Strategies • In certain cases payoffs, and hence fitness maximization, depend on what other populations are doing • When the payoff to one individual depends on the behaviour of others we cannot use the principle of fitness maximization until we know: • What the alternatives are • P(encountering alternatives) • Consequences of encounter

4. Game Theory • Think of it like a game • Each individual’s behaviour is its strategy, payoffs are in units of fitness • Players produce more players (offspring) • Changes in fitness are directly proportional to payoffs • An evolutionary Stable Strategy is one that, when adopted by enough individuals, maximizes payoff

5. Pure Strategy • One that cannot be replaced • Food storing • Recover your own seeds (Anderssen and Krebs, 1978) • If they recovered communally, a selfish hoarder would replace the communals damned quckly

6. Mixed Strategies • Hawks and Doves • Not real hawks or doves, strategies • Always fight, or always give up • Look at the payoffs • Look at the costs • Determine what proportion should be hawks and should be doves

7. Hawks and Doves • Say its all Doves • Hawk shows up, wins resource • Spreads genes • Now more hawks • Oh oh, now you are fighting, P(injury) = .5 • Now being a dove pays • Either strategy good when rare, bad when common

8. Doves and Hawks • V =V alue of resource for winner • W = cost of a wound • T = cost of display (no fighting) • (John Maynard Smith, 1978)

9. Whoa, I know Kung Fu • Set up a payoff Matrix Opponent in the contest Hawk Dove Payoff Hawk ½(V-W) V Received By Dove 0 ½V-T

10. ESS as easy as 123 • If W > V then there can be no pure ESS • In a population of hawks, a small number of doves do better than hawks • E(dove,hawk) > E(hawk, hawk) • E(dove, hawk) = 0 • E(hawk, hawk) = ½(V-W) • W > V, therefore ½(V-W) < 0

11. Pure Doves don’t do it either • Payoff to Hawk is V • Payoff to doves is less than that • (½W – T) • Hmmm • So, what proportion of hawks and doves balances it out?

12. What is theoretical population biologist to do? • Find the proportion (p) of hawks of hawks such that the following equation balances: • p ½(V-W) = (1-p) V = p (0) + (1-p) (½V– T) • Simply (?) solve for p • p = (V+2T) / (W+ 2T)

13. Apply it, sort of • Say V = 10 • W = 20 • T = 3 Opponent in the contest Hawk Dove Payoff Hawk -5 10 Received By Dove 0 2

14. Now, sub that back into the formula • P = 16/26 or 8/13 • 8/13ths of the population, with these payoff values, must be hawks • The values are not that important really, the point is that you can determine the point at which a strategy can coexist with another strategy as an ESS • Could be percentage of population, or percentage of time each animal adopts a given strategy

15. So? • It is actually applicable that’s so • Toads looking for breeding grounds (Davies and Hallaway, 1979) • Payoffs determined

16. Another so • Dungflies • Should a male hang around poo as it gets older?

17. Conclusions • This is a very brief intro to game theory • This stuff is way powerful • You have to sit and think some about the payoffs and costs • Dynamic programming models are becoming more popular