The dynamics of group formation

Shay Gueron, Simon A. Levin

Research output: Contribution to journalArticlepeer-review


A general continuous model is presented for animal group size distribution. Attention is restricted to a fixed size population divided into groups of various dynamic sizes, but the approach extends easily to populations of variable size. The basic idea is to relate group size distribution to two functions, the (density-dependent) rates of fusion and fission. These functions can be estimated from data and can ultimately be related to the behavior of individuals and the dynamics of groups. For various functional forms, the stationary distributions of group sizes are sought. In several prototype cases, the stationary distribution has a peak value, the "most frequent group size," which emerges endogenously from the dynamics. The authors determine when such a peak emerges and more generally show the existence and uniqueness of the stationary distribution. Stability of stationary solutions is discussed. Progress is shown, but a general treatment remains refractory.

Original languageEnglish
Pages (from-to)243-264
Number of pages22
JournalMathematical Biosciences
Issue number1-2
StatePublished - 1995
Externally publishedYes

Bibliographical note

Funding Information:
We are pleased to acknowledge insightful discussions with Dan Cohen, Odo Diekmann, Nadav Liron, and Dan Rubenstein and the support of the Office of Naval Research through its University Research Initiative Program Award to Woods Hole Oceanographic Institute. This paper is dedicated to our late friend and colleague, Stavros Busenberg.

ASJC Scopus subject areas

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


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