The dynamics of herds: From individuals to aggregations

Shay Gueron, Simon Asher Levin, Daniel Ian Rubenstein

Research output: Contribution to journalArticlepeer-review

263 Scopus citations


The dynamic behavior of small herds is investigated by means of simulations of two-dimensional discrete stochastic models. An individual-based approach is used to relate collective behavior to individual decisions. In our model, the motion of an individual in a herd is assumed to be the combined result of both density-independent and density-dependent decisions, in the latter case based on the influence of surrounding neighbors; assumed decision rules are hierarchical, balancing short-range repulsion against long-range attraction. The probability of fragmentation of the model herd depends on parameter values. We explore the variety and characteristics of spatial patterns that develop during migration, for herds that are homogeneous or heterogeneous regarding intrinsic walking speeds. Group integrity can be maintained even in mixed populations, but fragmentation results for these more easily than for a homogeneous herd. Observations of natural populations suggest that animals move away from individuals that intrude too closely into their environment, but are attracted to individuals at a distance. Between these extremes, there appears to be a neutral zone, within which other individuals engender no response. We explore the importance of this neutral zone, and offer evolutionary interpretations. In particular, the neutral zone, if not too large, permits the individual to remain in contact with the herd, while reducing the frequency with which acceleration or deceleration must be undertaken. This offers obvious energetic benefits.

Original languageEnglish (US)
Pages (from-to)85-98
Number of pages14
JournalJournal of Theoretical Biology
Issue number1
StatePublished - Sep 7 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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