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ABMmodels_parameters.Rmd
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ABMmodels_parameters.Rmd
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---
title: "Simulation Models of Cultural Evolution in R"
author: "Alex Mesoudi"
output: pdf_document
---
# 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 | 2 |
| | | |
| | probability of trait $A$ mutating into trait $B$, or trait $B$ | |
| | | |
| | mutating into trait $A$. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $\mu_b$ | Probability of biased cultural mutation. Specifically, the | 2 |
| | | |
| | probability of trait $B$ mutating into trait $A$. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $s$ | Strength of biased transmission / cultural selection. | 3 |
| | | |
| | 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 $B$. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $q$ | Frequency of a second trait in a two-trait model (trait $X$ | 4 |
| | | |
| | in Model 4), or the frequency of trait $A$ in a second | |
| | | |
| | sub-population or group (Model 7). | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $q_0$ | Starting value of $q$. | 4 |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $L$ | Probability in two-trait models that the two traits are linked. | 4 |
| | | |
| | Specifically, the probability that, if trait 1 is $A$, then trait 2 is $X$. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $D$ | Strength of conformity. Specifically, the increased probability | 5 |
| | | |
| | of adopting a majority trait, relative to unbiased transmission. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $s_v$ | Strength of biased transmission / cultural selection under | 6 |
| | | |
| | vertical cultural transmission. Specifically, the increased probability | |
| | | |
| | of adopting a favoured trait, relative to unbiased transmission, | |
| | | |
| | when only one parent holds that favoured trait. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $s_h$ | Strength of biased transmission / cultural selection under | 6 |
| | | |
| | horizontal cultural transmission. Specifically, the probability of | |
| | | |
| | switching to a more favourable trait upon encountering at least | |
| | | |
| | one of $n$ demonstrators with that trait. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $a$ | Probability of assortative mating under vertical cultural | 6 |
| | | |
| | transmission, such that both parents have identical | |
| | | |
| | cultural traits. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $n$ | Number of demonstrators from whom an agent learns under | 6 |
| | | |
| | horizontal transmission (Model 6) or blending inheritance | |
| | | |
| | (Model 8). | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $m$ | Strength of migration. Specifically, the probability that each | 7 |
| | | |
| | agent migrates to a randomly chosen sub-population. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $e$ | Error in copying the traits of $n$ demonstrators under blending | 8 |
| | | |
| | inheritance. Specifically, the variance of the normal distribution | |
| | | |
| | with mean of the demonstrator trait value, from which the | |
| | | |
| | copied trait value is drawn. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $\alpha$ | Copying error in the 'Tasmanian' model of cultural gain/loss. | 9 |
| | | |
| | Specifically, the amount by which the mode of a gumbel | |
| | | |
| | distribution is reduced relative to the highest skill level in | |
| | | |
| | the previous generation. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $\beta$ | Inferential guesses or experimentation in the 'Tasmanian' | 9 |
| | | |
| | model of cultural gain/loss. Specifically, the dispersion of | |
| | | |
| | the gumbel distribution from which the new skill level is drawn. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $z_i$ | Culturally transmitted skill level of the $i$th agent in the 'Tasmanian' | 9 |
| | | |
| | model of cultural gain/loss. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $\bar{z}$ | Mean culturally transmitted skill level across all agents of one | 9 |
| | | |
| | generation in the 'Tasmanian' model of cultural gain/loss. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $g$ | The number of cultural features in Axelrod's model of polarization, | 10 |
| | | |
| | with each feature taking one of ten possible trait values. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+
| $N_{side}$ | The number of agents along one side of a square grid in Axelrod's | 10 |
| | | |
| | model of polarization, giving ${N_{side}}^2$ agents in total. | |
+------------+-----------------------------------------------------------------------------+------------------------+
| | | |
+------------+-----------------------------------------------------------------------------+------------------------+