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

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/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.

Four-Types of IIT-Induced Group Integrity of Plecoglossus altivelis

“…We consider that the term ‘fission—fusion’ sums up this situation well. Although the term of ‘fission-fusion’ already exists in collective behaviour, its essence is in the collective process of merge and split dynamics [ 94 , 95 , 96 , 97 ]. We consider that the dynamics we are analysing here are not very far from their interest.…”

Data-driven modeling of group formation in the fission-fusion dynamics of Bechstein’s bats

“…Comparing our model to other agent-based models of ssion-fusion dynamics discussed above, we highlight that none so far has addressed the social and temporal aspects of the ssion-fusion dynamics together. Moreover, in comparison to formally advanced, but rather abstract models (Conradt and Roper, 2000;Nair et al, 2019) or mere simulation approaches (Sueur and Maire, 2014), our model outcome can be directly compared to the respective empirical observations in Bechstein's bats. This was also achieved by the agent-based model of red-capped mangabeys with respect to travel distance patters (Dolado et al, 2017).…”

“…Also, the impact of individual compromises between nutritional needs and social interactions on the social network between individuals and a possible irreversible ssion was simulated (Sueur and Maire, 2014) with an agent-base model. These type of models also allow to test the impact of certain parameters, for example split-rates (Conradt and Roper, 2000;Nair et al, 2019), on the principal outcome of the ssion-fusion dynamics. In most cases, however, the assumed rules cannot be directly matched to available observations.…”

Friendship across species borders: factors that facilitate and constrain heterospecific sociality

“…Joining mobile animal groups can offer benefits that are absent at an individual level ( [31,32]; see electronic supplementary material, Appendix S1 for more details). Furthermore, dynamics of merge and split among groups can result in nontrivial variations in group composition [33]. Such emergent properties of groups could be an additional factor in influencing the relative likelihood of heterospecific and conspecific partner choice.…”