Simulating trait evolution for cross-cultural comparison

Abstract

Cross-cultural anthropologists have increasingly used phylogenetic methods to study cultural variation. Because cultural behaviours can be transmitted horizontally among socially defined groups, however, it is important to assess whether phylogeny-based methods--which were developed to study vertically transmitted traits among biological taxa--are appropriate for studying group-level cultural variation. Here, we describe a spatially explicit simulation model that can be used to generate data with known degrees of horizontal donation. We review previous results from this model showing that horizontal transmission increases the type I error rate of phylogenetically independent contrasts in studies of correlated evolution. These conclusions apply to cases in which two traits are transmitted as a pair, but horizontal transmission may be less problematic when traits are unlinked. We also use the simulation model to investigate whether measures of homology (the consistency index and the retention index) can detect horizontal transmission of cultural traits. Higher rates of evolutionary change have a stronger depressive impact on measures of homology than higher rates of horizontal transmission; thus, low consistency or retention indices are not necessarily indicative of 'ethnogenesis'. Collectively, these studies demonstrate the importance of using simulations to assess the validity of methods in cross-cultural research.

Figure 1.

Simulation procedure. A simplified version of the simulation procedure using a 3-row by 4-column spatial matrix partway through a simulation run. The following stochastic processes occur in sequence for each generation in the simulation: (a) step 1: extinction of filled cells; (b) step 2: colonization of empty cells; (c) step 3: horizontal transmission among neighbouring societies; and (d) step 4: trait evolution. Empty cells indicate unfilled niches in the spatial model.

Figure 2.

Horizontal transmission and independent contrasts. Horizontal dotted line indicates expected type I error rate (α = 0.05). Plots show how the probability of trait donation (p_donation) affects type I error rates for independent contrasts (black circles) and in non-phylogenetic analyses (circles) for p_extinction = 0.02 (top) and 0.08 (bottom row). There was no correlation between trait changes in these simulations of continuously varying characters (r = 0). Different plots reflect different combinations of spatial configuration (i.e. matrix dimensions) and probability of extinction (p_extinction), and values plotted reflect the proportion of results in a given simulation run (n = 1000) in which a significant association was found between traits X and Y. Simulations were run with colonization probability (p_colonize) of 0.96 and a trait change variance of 0.02.

Figure 3.

Causes of higher type I error rates. Distribution of correlation coefficients statistics for (a) paired and (b) unpaired transmission of continuously varying traits across 5000 simulations. Paired transmission of traits during horizontal transmission events does not result in biased parameter estimates (mean value for paired transmission = 0.0064, versus −0.002 for unpaired transmission). Instead, the elevated type I error rates for paired compared with unpaired trait transmission result from a wider expected distribution of statistics (s.d. of 0.2996 and 0.1724 for paired and unpaired transmission, respectively). Results are from a 6 × 6 matrix with probability of extinction of 0.08, horizontal donation of 0.01, no correlation among the traits, variance of trait change of 0.02 and 60 generations.

Figure 4.

Regression tree analyses. Regression trees for the (a) CI and (b) RI using phylogenies from the parsimony analyses of the simulated cultural trait data; (c) RI using phylogenies from the ‘true tree’ saved in the simulation program; and (d) the difference in the RI between the parsimony and ‘true’ trees.

Figure 5.

The RI on the true tree. The RI declines with increasing rate of evolution (a), whereas the RI shows only a weak relationship with the probability of horizontal donation (b). Based on 5000 simulations.

Figure 6.

The RI on the parsimony tree and true tree. The RI is higher on the parsimony tree, as compared with the true tree. The dashed line indicates equal values and thus goes through the origin. Based on 5000 simulations.