Power Law Distribution in Wildebeest (Connochaetes taurinus) Herds in the Serengeti National Park, Tanzania

Abstract

The aim of our study was to investigate whether social interactions between individual wildebeest can generate the empirical power law distributions of wildebeest aggregations. Animals are often found in groups such as fish schools, bird flocks, insect swarms, and ungulate herds. Being in a group helps members to engage in different behavioral activities such as in foraging, predator avoidance, and resistance to toxic environmental conditions, reproduction or socialization. In this study, we present the power law, truncated power law and the exponential distribution. We also quantified the distribution of real herds by analyzing the frequency distribution of wildebeest counts in aerial survey images collected in 2015. We then used a Lagrangian model of animal interactions to simulate individual movement and herd aggregation patterns. The simulations of our agent-based model exhibited characteristic aggregation patterns that were most similar to the empirical data. We observed a close match between parameters from the empirical data and agent based model. These parameters include the scaling parameter from the power law (\(\alpha\)) and the standard deviation \(\sigma\). With parameter values that matched empirical distributions, we fitted the model. Our analysis of the empirical data shows that the aggregation patterns of wildebeest herds are governed by a truncated power law. We contend that social interactions between individual wildebeest can explain this behaviour.