Niwa HS
National Research Institute of Fisheries Engineering, Hasaki, Ibaraki, 314-0421, Japan.
J Theor Biol. 1998 Dec 7;195(3):351-61. doi: 10.1006/jtbi.1998.0801.
A system of a fixed population size is considered in which fish schools break up and unite with other schools. The size distribution of schools is investigated on the basis of a balance equation, which corresponds to the mean-field theory of Smoluchowski-equation model of the coagulation-fragmentation process. The rates of fission and fusion are determined from a simple dynamic viewpoint of schooling. The size distribution, in effect, follows a power law up to a cutoff size, which can be fitted to data. The power index and the cutoff size depend on the population size. It is also elucidated how statistical properties of the system are regulated by the total population size. As the population size increases the number of schools increases, and asymptotically approaches a fixed value. If the population size is large, the mean school size depends linearly upon the population size. The standard deviation of the school-size distribution is proportional to the mean school size which is checked with data. Copyright 1998 Academic Press
考虑一个固定种群规模的系统，其中鱼群会分裂并与其他鱼群合并。基于一个平衡方程对鱼群的大小分布进行研究，该平衡方程对应于凝聚 - 分裂过程的斯莫卢霍夫斯基方程模型的平均场理论。裂变和融合速率是从鱼群聚集的简单动力学观点确定的。实际上，大小分布在达到一个截止大小之前遵循幂律，该截止大小可以拟合数据。幂指数和截止大小取决于种群规模。还阐明了系统的统计特性是如何由总种群规模调节的。随着种群规模增加，鱼群数量增加，并渐近地趋近于一个固定值。如果种群规模很大，平均鱼群大小与种群规模呈线性关系。鱼群大小分布的标准差与平均鱼群大小成比例，这一点通过数据得到了验证。版权所有1998年学术出版社
