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2.2. Calculation of mating success
This protocol is extracted from research article:
More than just noise: Chance, mating success, and sexual selection
Ecol Evol, Mar 30, 2021;

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For each of the above cases (see also Table 1), mating success was calculated in two ways: (a) deterministically, such that having the preferred trait was directly proportional to mating success and mate numbers were not limited to an integer (“no chance” scenario); and (b) stochastically, such that having the preferred trait was required for mating and therefore correlated with mating success, but mate number was restricted to an integer (“chance” scenario) (Figure 1). In doing so, we explored the effect of a simple source of stochasticity—the fact that mate number must be an integer—on mating success. For each scenario in the model, only males with the preferred trait could receive one or more female mates. Female mates were equitably assigned among the males who had the preferred trait in the deterministic scenario (see also Figure 1 for an example of deterministic mate assignment). As such, mating success in the deterministic scenario was calculated as follows:

where M+ is the mating success of each trait‐bearing male in the population, N+ is the total number of trait‐bearing males in the population, F is the number of females in the population, and M is the mating success of each non‐trait‐bearing male in the population.

In the stochastic scenario, female mates were assigned as equitably as possible among males with the preferred trait while restricting mating success to an integer value (see also Figure 1 for an example of stochastic mate assignment in which mating success is restricted to integer values). As such, when the number of females was evenly divisible among the number of males with the preferred trait, mating success of trait‐bearing males was calculated following Equation 1. When the number of females was not evenly divisible among the number of males with the preferred trait, Equation 1 could not be used, as it would lead to noninteger values of mating success. Instead, mating success for trait‐bearing males was calculated such that the total mating success of all trait‐bearing males in the population summed to F. Specifically, in all cases, all males with the preferred trait had an equal likelihood of receiving one or more female mates, but mating success for each male was restricted to an integer. For example, if there were five males with the preferred trait and two female mates, two males with the preferred trait were each assigned a mating success of one and the remaining three males were assigned a mating success of zero due to the lack of additional female mates. Likewise, if there were two males with the preferred trait and five female mates, one of the males was assigned a mating success of two and the other male was assigned a mating success of three. Since all males with the preferred trait were assumed to have an equal likelihood of receiving a mate, the variation in mating success among males with the preferred trait resulted from mating success being restricted to integer values in the stochastic cases. In the stochastic scenario, the mating success of non‐trait‐bearing males was zero (Equation 2).

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