# Appendix C Model Variations

This appendix presents variations of the uniparental teaching and disparate benefits models. In the first variation, teaching rules for the uniparental teaching model are given by two loci (one for teaching sons and one for teaching daughters) each with two alleles instead of one locus with four alleles as in the main text. In the second variation of the uniparental teaching model, teaching has an error rate of 10%. Similarly, in a variation of the disparate benefits model, learning has an error rate of 10%.

## C.1 Two Locus Model

In the uniparental teaching model in the main text, individuals have one locus with four alleles. To check that my results are not dependent on the one locus assumption, here I describe an alternate model where individuals have two loci with two alleles each where one locus controls the teaching of sons and the other the teaching of daughters. Individuals are haploid with one of two sexes, male and female, and two genetic loci A and B. $A_1$ females teach daughters and $A_2$ females do not. $B_1$ females teach sons and $B_2$ females do not. Males do not teach. Cultural transmission rules for each combination of alleles are given in Table C.1.

<table><thead><tr><th>Alleles</th><th>Daughter Rule</th><th>Son Rule</th></tr></thead><tbody><tr><td>$A_1B_1$</td><td>$\tau_{f11} = 1$</td><td>$\tau_{m11} = 1$</td></tr><tr><td>$A_1B_2$</td><td>$\tau_{f12} = 1$</td><td>$\tau_{m22} = 0$</td></tr><tr><td>$A_2B_1$</td><td>$\tau_{f21} = 0$</td><td>$\tau_{m21} = 1$</td></tr><tr><td>$A_2B_2$</td><td>$\tau_{f22} = 0$</td><td>$\tau_{m22} = 0$</td></tr></tbody></table>

Table C.1: Teaching rules for each allele where $\tau_{fjk} = 1$ indicates that $A_j B_k$ mothers teach daughters and $\tau_{mjk} = 1$ indicates that mothers teach sons. When $\tau_{fjk} = 0$ or $\tau_{mjk} = 0$, mothers with allele $A_j B_k$ do not teach that sex. These rules are used in Equations C.2 and C.3

An individual's fitness depends on whether it has learned the cultural trait and whether it teaches offspring. All individuals have a baseline fitness of 1. Teaching is costly, limiting