Question

Rattlesnakes (Crotalus horridus) avoid biting their opponents when fighting for a female. Instead, they slam each other to the ground. We can try to figure out how this might have evolved using a game theoretical model, with a pay-off matrix. Let’s say that if a Biter met a Slammer, it would receive 100 fitness “points” (the Value of Winning, V). But if a Biter met a Biter, then half the time it would win and receive 100 fitness points and half the time it would lose and incur -200 fitness points (the Cost of Injury, C), which would be bad (|V|-|C|/2). On the flip side, if a Slammer met a Biter, the Slammer would slither away immediately and not receive any points (0, which is not so bad). However, if a Slammer met a Slammer, then half the time it would win and receive 100 fitness points and half the time it would lose and receive 0 fitness points (V/2).

a) Using a properly labeled payoff matrix, determine whether biting or slamming is a Pure ESS for rattlesnakes. Or perhaps it is a Mixed ESS? Explain your answer using formal terminology (expected payoff / inequality statements). (10 points)

Answer 1

ESS (Evolutionary stable strategy) is adopted by population in a given environment and can't get invaded by any other strategy.

Behavioural decisions can be understood by game theory approach.

It provides a conceptual and theoretical framework.

We can understand the Mechanism by which species co-exist.

Slamming is a pure ESS for rattlesnake.

Biting is conventional and gangrenous for rattlesnake.

In slamming a rattlesnake will attain max points with no loss.