| Alleles | Female fitnesses | Male fitnesses | ||
|---|---|---|---|---|
| with trait | without trait | with trait | without trait | |
| A1B1 | wf111 = 1 + b - 2κ | wf110 = 1 | wm111 = 1 + b | wm110 = 1 |
| A1B2 | wf121 = 1 + b - κ | wf120 = 1 | wm121 = 1 + b | wm120 = 1 |
| A2B1 | wf211 = 1 + b - κ | wf210 = 1 | wm211 = 1 + b | wm210 = 1 |
| A2B2 | wf221 = 1 + b | wf220 = 1 | wm221 = 1 + b | wm220 = 1 |
Table C.2: Expected fitnesses for encultured and unencultured individuals of each allele and sex. $w_{sjk1}$ is the expected fitness for an encultured individual of sex s and allele $A_j B_k$. $w_{sjk0}$ is the expected fitness for an unencultured individual. b is the benefit of the cultural trait and $\kappa$ is the cost of teaching offspring of one sex.
a mother's future reproductive potential after her first offspring. In the model, females who teach offspring of one sex pay a reproductive cost of $\kappa$ and females who teach offspring of both sexes pay a reproductive cost of $2\kappa$. Individual of both sexes who learn the trait gain a reproductive benefit of $b$. Table C.2 gives the expected fitnesses for individuals where $w_{sjk1}$ is the fitness for an individual of sex s and allele $A_j B_k$ that has learned cultural trait and $w_{sk0}$ is the fitness of an individual who has not learned the cultural trait.
As in the main text, reproductive competition occurs in both males and females with each individual's contribution to the next generation determined by its relative fitness with its sex, as described in Equation C.1. The frequency of individuals of type $A_j B_k$ in sex s is $x_{sjkc}$, where $c=1$ if the individual knows the cultural trait and $c=0$ if the individual does not. $x'{sjkc}$ is the type frequency after genetic selection and $x''{sjkc}$ as the frequency after cultural transmission and innovation.
An individual only acquires a cultural trait through teaching if its mother has both an allele for teaching offspring of the individual's sex and the cultural trait. This is reflected in Equation C.2, which gives the frequency of individuals of sex s who have allele $A_j B_k$ and the cultural trait after cultural transmission.