Abstract: The selfish herd hypothesis provides an explanation for group aggregation via the selfish avoidance of predators. Conceptually, and as was first proposed, this movement should aim to minimise the danger domain of each individual. Whilst many reasonable proxies have been proposed, none have directly sought to reduce the danger domain. In this work we present a two dimensional stochastic model that actively optimises these domains. The individuals’ dynamics are determined by sampling the space surrounding them and moving to achieve the largest possible domain reduction. Two variants of this idea are investigated with sampling occurring either locally or globally. We simulate our models and two of the previously proposed benchmark selfish herd models: k-nearest neighbours (kNN); and local crowded horizon (LCH). The resulting positions are analysed to determine the benefit to the individual and the groups ability to form a compact group. To do this, the group level metric of packing fraction and individual level metric of domain size are observed over time for a range of noise levels. With these measures we show a clear stratification of the four models when noise is not included. kNN never resulted in centrally compacted herd, while the local active selfish model and LCH did so with varying levels of success. The most centralised groups were achieved with our global active selfish herd model. The inclusion of noise improved aggregation in all models. This was particularly so with the local active selfish model with a change to ordering of performance so that it marginally outperformed LCH in aggregation. By more closely following Hamilton’s original conception and aligning the individual’s goal of a reduced danger domain with the movement it makes increased cohesion is observed, thus confirming his hypothesis, however, these findings are dependent on noise. Moreover, many features originally conjectured by Hamilton are also observed in our simulations.

Speaker Biography: Dr Thomas Stemler studied Physics and completed his doctorate at the Technische Universität Darmstadt/ Germany. In 2007 he moved to Australia and started working as a Research Associate at the School of Mathematics and Statistics, The University of Western Australia (UWA). Today he is a Senior Lecturer and member of the Complex Data Modelling Group in the Engineering and Mathematical Science Faculty, UWA. His research interests are in dynamical systems, time series analysis and network science with applications in various fields ranking from genetics and paleo-climate to traffic modelling.

Webpage: https://research-repository.uwa.edu.au/en/persons/thomas-stemler

https://orcid.org/0000-0003-2485-6666