Gueron S, Levin S A
Department of Mathematics, Technion-Israel Institute of Technology, Haifa.
Math Biosci. 1995 Jul-Aug;128(1-2):243-64. doi: 10.1016/0025-5564(94)00074-a.
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.
提出了一种用于动物群体大小分布的一般连续模型。注意力仅限于固定规模的种群，该种群被划分为各种动态大小的群体，但该方法很容易扩展到可变规模的种群。基本思想是将群体大小分布与两个函数，即（密度依赖的）融合率和裂变率联系起来。这些函数可以从数据中估计出来，最终可以与个体行为和群体动态联系起来。对于各种函数形式，寻求群体大小的平稳分布。在几个典型案例中，平稳分布有一个峰值，即“最常见的群体大小”，它是从动态中内生出现的。作者确定了这种峰值何时出现，并更一般地证明了平稳分布的存在性和唯一性。讨论了平稳解的稳定性。虽有进展，但一般处理仍难解决。
