The popularity spectrum applied to a cross-cultural question

Spatial evolution of human cultures inferred through Bayesian phylogenetic analysis

Spatial distribution of human culture reflects both descent from the common ancestor and horizontal transmission among neighbouring populations. To analyse empirically documented geographical variations in cultural repertoire, we will describe a framework for Bayesian statistics in a spatially explicit model. To consider both horizontal transmission and mutation of the cultural trait in question, our method employs a network model in which populations are represented by nodes. Using algorithms borrowed from Bayesian phylogenetic analysis, we will perform a Markov chain Monte Carlo (MCMC) method to compute the posterior distributions of parameters, such as the rate of horizontal transmission and the mutation rates among trait variants, as well as the identity of trait variants in unobserved populations. Besides the inference of model parameters, our method enables the reconstruction of the genealogical tree of the focal trait, provided that the mutation rate is sufficiently small. We will also describe a heuristic algorithm to reduce the dimension of the parameter space explored in the MCMC method, where we simulate the coalescent process in the network of populations. Numerical examples show that our algorithms compute the posterior distribution of model parameters within a practical computation time, although the posterior distribution tends to be broad if we use uninformative priors.

Application of a Markovian ancestral model to the temporal and spatial dynamics of cultural evolution on a population network

Cultural macroevolution concerns a long-term evolutionary process involving transmission of non-genetic or cultural traits between populations as well as birth and death of populations. To understand the spatial dynamics of cultural macroevolution, we present a one-locus model of cultural diffusion in which a cultural trait is transmitted on a network of populations. Borrowing the method of ancestral backward process from population genetics, our model explores the lineage of a trait variant sampled in the present generation to quantify when and where the variant was invented. Mathematical analysis of the model enables us to predict the distribution of cultural age in each population of the network, estimate the frequencies of trait variants originating from given populations, and discuss the time it takes for a trait variant to diffuse between a given pair of populations. We also perform numerical analysis on random scale-free network of populations to investigate the effect of network topology and innovation rate on the age and origin of variants in each population. The result suggests that trait variants are more likely to derive from a population with higher innovation rate. Our numerical analysis also shows that trait variants invented in populations with higher network-centrality values are likely to be maintained at a higher frequency and transmitted to other populations in a shorter time period.

The potential to infer the historical pattern of cultural macroevolution

Phylogenetic analyses increasingly take centre-stage in our understanding of the processes shaping patterns of cultural diversity and cultural evolution over time. Just as biologists explain the origins and maintenance of trait differences among organisms using phylogenetic methods, so anthropologists studying cultural macroevolutionary processes use phylogenetic methods to uncover the history of human populations and the dynamics of culturally transmitted traits. In this paper, we revisit concerns with the validity of these methods. Specifically, we use simulations to reveal how properties of the sample (size, missing data), properties of the tree (shape) and properties of the traits (rate of change, number of variants, transmission mode) might influence the inferences that can be drawn about trait distributions across a given phylogeny and the power to discern alternative histories. Our approach shows that in two example datasets specific combinations of properties of the sample, of the tree and of the trait can lead to potentially high rates of Type I and Type II errors. We offer this simulation tool to help assess the potential impact of this list of persistent perils in future cultural macroevolutionary work. This article is part of the theme issue 'Foundations of cultural evolution'.

The uses and abuses of tree thinking in cultural evolution

Modern phylogenetic methods are increasingly being used to address questions about macro-level patterns in cultural evolution. These methods can illuminate the unobservable histories of cultural traits and identify the evolutionary drivers of trait change over time, but their application is not without pitfalls. Here, we outline the current scope of research in cultural tree thinking, highlighting a toolkit of best practices to navigate and avoid the pitfalls and 'abuses' associated with their application. We emphasize two principles that support the appropriate application of phylogenetic methodologies in cross-cultural research: researchers should (1) draw on multiple lines of evidence when deciding if and which types of phylogenetic methods and models are suitable for their cross-cultural data, and (2) carefully consider how different cultural traits might have different evolutionary histories across space and time. When used appropriately phylogenetic methods can provide powerful insights into the processes of evolutionary change that have shaped the broad patterns of human history. This article is part of the theme issue 'Foundations of cultural evolution'.

Time to extinction of a cultural trait in an overlapping generation model

How long a newly emerging trait will stay in a population is a fundamental but rarely asked question in cultural evolution. To tackle this question, the distribution and mean of the time to extinction of a discrete cultural trait are derived for models with overlapping generations, in which trait transmission occurs from multiple role models to a single newborn and may fail with a certain probability. We explore two models. The first is a Moran-type model, which allows us to derive the exact analytical formula for the mean time to extinction of a trait in a finite population. The second is a branching process, which assumes an infinitely large population and allows us to derive approximate analytical formulae for the distribution and mean of the time to extinction in the first model under a large population size. We show that in the first model, the mean time to extinction apparently diverges (becomes so large that even numerical computation is impractical) under a certain parameter condition as the population size tends to infinity. Using the second model, we explain the underlying mechanism of the apparent divergence found in the first model and derive the mathematical condition for this divergence in terms of transmission efficiency and the number of role models per newborn. When this mathematical condition is satisfied in the second model, the probability of extinction is less than 1, and the mean extinction time does not exist. In addition, we find that in both models, the time to extinction of the trait becomes longer as the number of role models per individual increases and as cultural transmission becomes more efficient.

Fifty years of Theoretical Population Biology

The year 2020 marks the 50th anniversary of Theoretical Population Biology. This special issue examines the past and continuing contributions of the journal. We identify some of the most important developments that have taken place in the pages of TPB, connecting them to current research and to the numerous forms of significance achieved by theory in population biology.