This is a simple simulation to predict sex roles in parental care that we would expect to evolve under assumptions specified below. The model follows game-2 of Maynard Smith (1977), but makes the game self-consistent and incorporates the following assumptions about male rematings and partial paternity.
The game assumes an equal number of males and females in the population who pair up with each other to lay their first clutches of the season-- the number of eggs laid by the female is Wc (which is also the total number of eggs she lays if she cares for the young). The female can lay a second clutch (of size Wd-Wc) if she deserts, and we assume that deserting females always get to remate. There is no third clutch. The first clutch matings are synchronous, as are the second clutch matings.
The offspring's survival depends on the number of parents caring: V0 with 0 parents caring, V1 with 1 parent (either father or mother) caring and V2 with both parents caring. We require that 0 ≤ V0 ≤ V1 ≤ V2 ≤ 1.
Females can mate multiply, and hence males to have only partial paternity of their clutches. The paternity of a caring male is p and that of a deserting male is r. Due to mechanisms such as mate guarding, we require 0 ≤ r ≤ p ≤ 1.
Either caring or deserting males can have an advantage with respect to matings for the second clutch-- the direction and extent of this advantage is specified by the parameter α. It denotes the fraction of the deserting males' second clutch matings that caring males obtain. Hence when α=0, deserting males completely dominate these matings. When α = 1, caring and deserting males are equally likely to mate in the second round. When α < 1, deserting males have an advantage in the second round of matings and when α > 1, caring males have an advantage in the second round of matings.
Similar to α, the direction and extent of the advantage with respect to extra-pair matings is specified by β. When β=1, caring and deserting males are equally likely to father the extra-pair young in the population. When β=0, deserting males completely exclude caring males from extra-pair matings. When β < 1, deserting males have an advantage in these matings, and when β > 1, caring males have an advantage.
Please specify the parameter values you would like to run this simulation for:
1. How many eggs does a female lay if she provides parental care (Wc) and if she does not provide parental care(Wd)?
2. What is the survival probability of eggs with zero(V0), one(V1) or both(V2) parent caring?
3. What is the paternity of a caring male in his first clutch (p) and what is the paternity of a deserting male in his first clutch? (r)
4. Please specify parameter for direction and extent of advantage with respect to second round of matings: (α)
(α has to be non-negative)
5. Please specify parameter for direction and extent of advantage with respect to extra-pair matings: (β)
(β has to be non-negative)
Results of the simulation:
We would predict for the parameter values you have input that:
Males should desert with probability (value of md)
Females should desert with probability (value of fd)