TY - JOUR
T1 - The dynamics of group formation
AU - Gueron, Shay
AU - Levin, Simon Asher
N1 - 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.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1995
Y1 - 1995
N2 - 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.
AB - 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.
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U2 - 10.1016/0025-5564(94)00074-A
DO - 10.1016/0025-5564(94)00074-A
M3 - Article
C2 - 7606136
AN - SCOPUS:0028989481
VL - 128
SP - 243
EP - 264
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 1-2
ER -