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

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 behaviour, 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 analyse 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.Comment: 19 pages, 8 figure

An Empiricist’s Guide to Using Ecological Theory

A scientific understanding of the biological world arises when ideas about how nature works are formalized, tested, refined, and then tested again. Although the benefits of feedback between theoretical and empirical research are widely acknowledged by ecologists, this link is still not as strong as it could be in ecological research. This is in part because theory, particularly when expressed mathematically, can feel inaccessible to empiricists who may have little formal training in advanced math. To address this persistent barrier, we provide a general and accessible guide that covers the basic, step-by-step process of how to approach, understand, and use ecological theory in empirical work. We first give an overview of how and why mathematical theory is created, then outline four specific ways to use both mathematical and verbal theory to motivate empirical work, and finally present a practical tool kit for reading and understanding the mathematical aspects of ecological theory.We hope that empowering empiricists to embrace theory in their work will help move the field closer to a full integration of theoretical and empirical research

Ecological consequences of heritable intraspecific variation

Trait variation among individuals of a population is now considered to be an important part of biodiversity. Many empirical studies have quantified this variation and showed that it can change over time. These studies have also made it clear that intraspecific variation is important in determining a population\u27s response to disturbances. Heritable changes in traits that determine how species interact with its biotic and abiotic environment lead to eco-evolutionary feedbacks. Mathematical models that integrate some aspects of evolutionary models with those of ecological models are required to study these feedbacks. In this dissertation, I build and extend a series of population dynamics models focusing on heritable intraspecific variation in continuously varying traits. My models capture trait-based ecological interactions as well as stabilizing natural selection. With this mathematical approach I study (i) two-species competition, exploiter-victim interaction and mutualism, and (ii) biotic-abiotic interactions with a conditionable or a consumable abiotic factor. I show that (i) weak stabilizing selection promotes stable coexistence in two-species interactions and (ii) population dynamics and trait evolution are significantly different when a species interacts with a conditionable abiotic factor and a consumable abiotic factor. In a special case of the biotic-abiotic interaction, I show that smaller body size is intrinsically beneficial in a competition for space. Overall, my results point that heritable intraspecific variation has important ecological consequences and could significantly change our expectations relative to those based on purely ecological models

athma25/psf_comp_SI: Tested codes for EL

Codes ready for Ecology Letters submissio

A1 Appendix from Smaller is better in competition for space

Body size is a prominent morphological trait which affects many aspects of an organism’s life. Although large body size is generally considered to be advantageous, ecologists have wondered about the benefits of being small. Many studies of body size depend on the metabolic theory of ecology since body size is an irremovable part of an organism’s energy budget. Body size is also a spatial quantity and therefore is linked to spatial processes. Here, I show that competition for space leads to a benefit of being small and hence selects for increasingly smaller body size. I build a deterministic population dynamics model and a stochastic model of birth, death and dispersal in a population of individuals with two different body sizes and show that only the smaller individuals survive. I also extend the population dynamics model to continuously varying body sizes and include a stabilizing natural selection for an intermediate body size. I find that the intrinsic advantage of smaller body size in competition for space can only be overcome when natural selection for a large body size is sufficiently strong. Overall, my results point to a novel benefit of being small