# Table of parameters for Models 1-10

Parameter | Definition | Model first introduced |
---|---|---|

\(N\) | Number of agents in the population. | 1 |

\(t_{max}\) | Maximum number of timesteps or generations. | 1 |

\(r_{max}\) | Maximum number of independent simulation runs. | 1 |

\(p\) | Frequency of trait \(A\). | 1 |

\(p_0\) | Starting value of \(p\). | 1 |

\(\mu\) | Probability of unbiased cultural mutation. Specifically, the probability of trait \(A\) mutating into trait \(B\), or trait \(B\) mutating into trait \(A\). | 2 |

\(\mu_b\) | Probability of biased cultural mutation. Specifically, the probability of trait \(B\) mutating into trait \(A\). | 2 |

\(s\) | Strength of biased transmission / cultural selection. Specifically, in Model 3 (direct bias) the probability of switching to a more favourable trait upon encountering another agent with that trait, or in Model 4 (indirect bias) the payoff advantage to trait \(A\) relative to trait \(B\). | 3 |

\(q\) | Frequency of a second trait in a two-trait model (trait \(X\) in Model 4), or the frequency of trait \(A\) in a second sub-population or group (Model 7). | 4 |

\(q_0\) | Starting value of \(q\). | 4 |

\(L\) | Probability in two-trait models that the two traits are linked. Specifically, the probability that, if trait 1 is \(A\), then trait 2 is \(X\). | 4 |

\(D\) | Strength of conformity. Specifically, the increased probability of adopting a majority trait, relative to unbiased transmission. | 5 |

\(s_v\) | Strength of biased transmission / cultural selection under vertical cultural transmission. Specifically, the increased probability of adopting a favoured trait, relative to unbiased transmission, when only one parent holds that favoured trait. | 6 |

\(s_h\) | Strength of biased transmission / cultural selection under horizontal cultural transmission. Specifically, the probability of switching to a more favourable trait upon encountering at least one of \(n\) demonstrators with that trait. | 6 |

\(a\) | Probability of assortative mating under vertical cultural transmission, such that both parents have identical cultural traits. | 6 |

\(n\) | Number of demonstrators from whom an agent learns under horizontal transmission (Model 6) or blending inheritance (Model 8). | 6 |

\(m\) | Strength of migration. Specifically, the probability that each agent migrates to a randomly chosen sub-population. | 7 |

\(e\) | Error in copying the traits of \(n\) demonstrators under blending inheritance. Specifically, the variance of the normal distribution with mean of the demonstrator trait value, from which the copied trait value is drawn. | 8 |

\(\alpha\) | Copying error in the ‘Tasmanian’ model of cultural gain/loss. Specifically, the amount by which the mode of a gumbel distribution is reduced relative to the highest skill level in the previous generation. | 9 |

\(\beta\) | Inferential guesses or experimentation in the ‘Tasmanian’ model of cultural gain/loss. Specifically, the dispersion of the gumbel distribution from which the new skill level is drawn. | 9 |

\(z_i\) | Culturally transmitted skill level of the \(i\)th agent in the ‘Tasmanian’ model of cultural gain/loss. | 9 |

\(\bar{z}\) | Mean culturally transmitted skill level across all agents of one generation in the ‘Tasmanian’ model of cultural gain/loss. | 9 |

\(g\) | The number of cultural features in Axelrod’s model of polarization, with each feature taking one of ten possible trait values. | 10 |

\(N_{side}\) | The number of agents along one side of a square grid in Axelrod’s model of polarization, giving \({N_{side}}^2\) agents in total. | 10 |