Random copying in space

Details Random copying in space Random copying in space

2011-04-04

arxiv.org/abs/1104.0529v1

Physics

Physics and Society

26 pages, 11 figures. Based on invited talk at AHRC CECD Conference on "Cultural Evolution in Spatially Structured Populations

Scientific paper

Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We focus in particular on how a measure of the diversity in the population changes over time. We show that even when the vast majority of a population's history may be well-described by a spatially-unstructured model, spatial structure may nevertheless affect the expected level of diversity seen at a local scale. We demonstrate this phenomenon explicitly by examining the random copying process on small-world networks, and use our results to comment on the use of simple random-copying models in an empirical context.

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