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Evolving social influence in large populations

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Abstract

Darwinian studies of collective human behaviour, which deal fluently with change and are grounded in the details of social influence among individuals, have much to offer “social” models from the physical sciences which have elegant statistical regularities. Although Darwinian evolution is often associated with selection and adaptation, “neutral” models of drift are equally relevant. Building on established neutral models, we present a general, yet highly parsimonious, stochastic model, which generates an entire family of real-world, right-skew socio-economic distributions, including exponential, winner-take-all, power law tails of varying exponents, and power laws across the whole data. The widely used Barabási and Albert (1999) Science 286: 509-512 “B-A” model of preferential attachment is a special case of this general model. In addition, the model produces the continuous turnover observed empirically within these distributions. Previous preferential attachment models have generated specific distributions with turnover using arbitrary add-on rules, but turnover is an inherent feature of our model. The model also replicates an intriguing new relationship, observed across a range of empirical studies, between the power law exponent and the proportion of data represented in the distribution.

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Acknowledgments

We thank the Leverhulme Trust for the “Tipping points” programmatic bid. Batty was partially supported by the EPSRC Spatially Embedded Complex Systems Engineering Consortium (EP/C513703/1). Amy Heineike, formerly of Volterra and now at George Mason University, provided programming support.

Conflict of Interests

The authors of this manuscript declare no conflict of interests

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Authors and Affiliations

  1. Department of Anthropology, Durham University, Dawson Building, South Road Durham, Durham, DH1 3LE, UK

    R. Alexander Bentley & Paul Ormerod

  2. Volterra Consulting, 135c Sheen Lane, London, SW14 8AE, UK

    Paul Ormerod

  3. Centre for Advanced Spatial Analysis, University College London, 1–19 Torrington Place, London, WC1E 6BT, UK

    Michael Batty

Authors
  1. R. Alexander Bentley
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  2. Paul Ormerod
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Corresponding author

Correspondence to R. Alexander Bentley.

Additional information

Communicated by Guest Editor A. Houston

This contribution is part of the Special Issue “Mathematical Models in Ecology and Evolution: Darwin 200” (see Marshall et al. 2010).

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Bentley, R.A., Ormerod, P. & Batty, M. Evolving social influence in large populations. Behav Ecol Sociobiol 65, 537–546 (2011). https://doi.org/10.1007/s00265-010-1102-1

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