Animal Behavior Statistics Assignments (Four very short)

Assignment 8 Name Parental Care Pn =Probability of egg survival if cared by n parents P0 < P1 < P2 p= probability of male mating again if he deserts after mating E= number eggs produced by female if she deserts. e = number of eggs produced by female if she stays. Matrix Female Guard Desert

Guard eP2 P2

EP1 P1

Desert eP1 P1(1+p)

EP0 P0(1+p)

Rules ESS1 If EP0 > eP1 and P0(1+p) > P1 Then male and female will desert ESS2 If EP1 > eP2 and P1>P0(1+p) Then male guards and female deserts (Stickleback) ESS3 If eP1> EP0 and P1(1+p) > P2 Then male deserts and female guards (Duck) ESS4 If eP2 > EP1 and P2 > P1(1+p) Then male and female guard 1) Suppose in the pink spotted crab

1) Females can lay 22 eggs if they care for the young but 55 if they leave. 2) The sex ratio is male biased such that the probability of finding a second female is 0.35 3) The probabilities of the eggs surviving are the following: 0 parents = 0.60 1 parent =0.70 2 parents =0.85 What will the male and female do under these circumstances?

Male

2) Suppose in the Phelayo Fish

1) Females can lay 34 eggs if they care for the young but 48 if they leave. 2) The probability of a male finding a second female is 0.25 3) The probabilities of the eggs surviving are the following: 0 parents = 0.20 1 parent = 0.50 2 parents =0.65 What will the male and female do under these circumstances? 3 Suppose in the Veggy Fly

1) Females can lay 36 eggs if the care and 40 if they stay. 2) The probabilities of the eggs surviving are the following: 0 parents = 0.13 1 parent = 0.42 2 parents =0.57

What probability of finding a mate would be the cutoff for the male to help or not?

4) Suppose in the Silver Trout

1) The male has a .10 probability of finding another mate 2) The probabilities of the eggs surviving are the following:

0 parents =0 .12 1 parent = 0.56 2 parents =0.71 3) If the female lays 43 eggs when caring for the young, how many eggs would she need to lay if she deserted to make it a viable ESS? Note: Model from Maynard Smith, J. 1977. Parental investment: a prospective analysis. Animal Behavior 25:1-9.