Individual differences make a difference in the trajectories of simulated schools of fish

Abstract

A simulation model was designed in which each individual in a group can be programmed with a different set of movement decision rules based on: the distance of others within the group, velocity of individuals, its own previous vector (momentum), and biased (leadership) or random influences. This paper focuses on the role of variability in the group composition and its determination of group stratification and group trajectory. The ratio of one or two of these variables was varied systematically in a group of eight and the resulting group stratification and group trajectory was recorded. Individuals which were programmed with attraction/repulsion functions which led to smaller nearest neighbor distances ended up at the center of groups. The greater the number of individuals following this function in a group the higher the group turning rate and the slower the group velocity. The relationship between composition and trajectory was not linear but seemed to depend on the intermediate shape of the group which was formed. Groups composed of individuals with different velocities were cohesive, like all of the groups studied, but never acquired a forward trajectory. Random influences of individuals had a very small, but significant, influence on the trajectory of groups. In contrast, minor biased movements by one or two individuals in a group (e.g., one move in 15 by one individual in a group of eight) had a strong influence in determining the direction and speed of the group. These individuals with biased movements did not necessarily take up lead positions, but exercised their influence from within the group. For pure groups (i.e., all following the same rules) of individuals programmed to group tightly, group size had a significant effect on trajectory, with larger groups moving more slowly. However, for pure groups of individuals programmed to group more loosely, group size had less effect on trajectory. The programmed momentum of individuals had little effect on trajectory. The results of this paper provide a set of predictions of how a group would behave if individuals based their movement decisions primarily on the position of other individuals in their environment. It is the first simulation study to address the issue of how variation in group composition (i.e., individual differences) may influence group stratification and group trajectory.