Modeling the genealogy of a cultural trait

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.

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.

Indigenous African Leadership: Key differences from Anglo-centric thinking and writings

This article draws on historical explorers’ accounts, ethnography and organisational approaches to examine practices, discourses and perceptions of leadership in 12 prototypical indigenous communities in West and Central Africa. By so doing, it highlights how leadership meanings from this context differ from Anglo-centric thinking and writings. Key to this contribution is an unravelling of ways in which historical cultural hegemonies impose particular discursive formations, constructed practices and mind-programming in a non-Anglo-Saxon socio-cultural context. Dramaturgical power arrangement, lucid role substitution and the notion of leadership as non-human emerge as dominant themes in the analysis. Also, featuring significantly are representations of leadership in symbols, mythology and as transcendental and metaphysical. These conceptualisations are different from predominant Anglo-Saxon writings that frequently present leadership as linear hierarchies, dyadic (leader-follower) relationship, acts and behaviours of heroic figures and as an essentially human action. An Afro-centric indigenous concept of leadership reflecting the context is proposed which challenges heroism, linearity, individualism and objectivism.

Paradox of enrichment and system order reduction: bacteriophages dynamics as case study

The paradox of enrichment in a 3D model for bacteriophage dynamics, with a free infection stage of the phage and a bilinear incident rate, is considered. An application of the technique of singular perturbation theory allows us to demonstrate why the paradox arises in this 3D model despite the fact that it has a bilinear incident rate (while in 2D predator-prey models it is usually associated with the concavity of the attack rate). Our analysis demonstrates that the commonly applied approach of the model order reduction using the so-called quasi-steady-state approximation can lead to a loss of important properties of an original system.