Fission-fusion dynamics and group-size-dependent composition in heterogeneous populations

Nair, GG and Senthilnathan, A and Iyer, SK and Guttal, V (2019) Fission-fusion dynamics and group-size-dependent composition in heterogeneous populations. In: Physical Review E, 99 (3).

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Abstract

Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behavior, however, typically assume that groups and populations consist of identical individuals. In this paper, using the mathematical framework of the coagulation-fragmentation process, we develop and analyze a model of merge and split group dynamics, also called fission-fusion dynamics, for heterogeneous populations that contain two types (or species) of individuals. We assume that more heterogeneous groups experience higher split rates than homogeneous groups, forming two daughter groups whose compositions are drawn uniformly from all possible partitions. We analytically derive a master equation for group size and compositions and find mean-field steady-state solutions. We predict that there is a critical group size below which groups are more likely to be homogeneous and contain the abundant type or species. Despite the propensity of heterogeneous groups to split at higher rates, we find that groups are more likely to be heterogeneous but only above the critical group size. Monte Carlo simulation of the model show excellent agreement with these analytical model results. Thus, our model makes a testable prediction that composition of flocks are group-size-dependent and do not merely reflect the population level heterogeneity. We discuss the implications of our results to empirical studies on flocking systems. © 2019 American Physical Society.

Item Type:	Journal Article
Publication:	Physical Review E
Publisher:	American Physical Society
Additional Information:	The copyright for this article belongs to the Authors.
Keywords:	Animals; Intelligent systems; Monte Carlo methods, Computational model; Empirical studies; Fragmentation process; Heterogeneous populations; Homogeneous group; Mathematical frameworks; Population levels; Steady state solution, Dynamics
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	11 Apr 2019 11:16
Last Modified:	25 Aug 2022 08:18
URI:	https://eprints.iisc.ac.in/id/eprint/62068

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