Density distribution and size sorting in fish schools: an individual-based model

In fish schools the density varies per location and often individuals are sorted according to familiarity and/or body size. High density is considered advantageous for protection against predators and this sorting is believed to be advantageous not only to avoid predators but also for finding food. In this paper, we list a number of mechanisms and we study, with the help of an individual-based model of schooling agents, which spatial patterns may result from them. In our model, schooling is regulated by the following rules: avoiding those that are close by, aligning to those at intermediate distances, and moving towards others further off. Regarding kinship/familiarity, we study patterns that come about when agents actively choose to be close to related agents (i.e., ‘active sorting’). Regarding body size, we study what happens when agents merely differ in size but behave according to the usual schooling rules (‘size difference model’), when agents choose to be close to those of similar size, and when small agents avoid larger ones (‘risk avoidance’). Several spatial configurations result: during ‘active sorting’ familiar agents group together anywhere in the shoal, but agents of different size group concentrically, whereby the small agents occupy the center and the large ones the periphery (‘size difference model’ and ‘active sorting’). If small agents avoid the risk of being close to large ones, however, small agents end up at the periphery and large ones occupy the center (‘risk avoidance’). Spatial configurations are also influenced by the composition of the group, namely the percentage of agents of each type. Furthermore, schools are usually oblong and their density is always greatest near the front. We explain the way in which these patterns emerge and indicate how results of our model may guide the study of spatial patterns in real animals.