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.

Niche theory for positive plant-soil feedbacks.

Interactions between plants and the soil are an important ecological process in terrestrial ecosystems as they affect plant community structure: when and where we find different plant species. Those interactions are typically thought of as one-directional: local soil conditions filter through dispersing species to produce a community of locally adapted plants. However, plants can modify local physicochemical soil conditions via their roots and associations with soil microbes. These may in turn affect the local fitness of other plants, making plant-soil interactions bidirectional. In order to understand how they differ from other ecological processes that structure plant communities, we need a theory connecting these individual-level plant-soil feedbacks to community-level patterns. Here, we build this theory with a mathematical model of plant community dynamics in which soil conditioning is explicitly modeled over time and depends on the density of the plants. We analyze this model to describe the long-term composition and spatial distribution of the plant community. Our main result is that positive plant-soil feedbacks will create clustering of species with similar soil preferences. The composition of these clusters is further influenced by niche width and conditioning strength. In contrast with competitive dynamics driven by niche overlap, only species belonging to the same cluster can maintain high relative abundance in the community. Spatial heterogeneity in the form of an environmental gradient generates patches, each representing a single cluster. However, such patchiness is disfavored when species differ in dispersal ability. We show that stronger dispersers cannot take over the habitat as long as an exogenous driver favors soil conditions that benefit the other species. If exogenous drivers supersede soil conditioning by plants, we retrieve classic habitat filtering, where species are selected based on their suitability to the local environment. Overall, we provide a novel mathematical model for positive plant-soil feedback that we use to describe the spatial patterns of plant abundance and traits related to soil preference and conditioning ability.

An Empiricist's Guide to Using Ecological Theory.

AbstractA 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.

The dynamics of cooperation, power, and inequality in a group-structured society.

Most human societies are characterized by the presence of different identity groups which cooperate but also compete for resources and power. To deepen our understanding of the underlying social dynamics, we model a society subdivided into groups with constant sizes and dynamically changing powers. Both individuals within groups and groups themselves participate in collective actions. The groups are also engaged in political contests over power which determines how jointly produced resources are divided. Using analytical approximations and agent-based simulations, we show that the model exhibits rich behavior characterized by multiple stable equilibria and, under some conditions, non-equilibrium dynamics. We demonstrate that societies in which individuals act independently are more stable than those in which actions of individuals are completely synchronized. We show that mechanisms preventing politically powerful groups from bending the rules of competition in their favor play a key role in promoting between-group cooperation and reducing inequality between groups. We also show that small groups can be more successful in competition than large groups if the jointly-produced goods are rivalrous and the potential benefit of cooperation is relatively small. Otherwise large groups dominate. Overall our model contributes towards a better understanding of the causes of variation between societies in terms of the economic and political inequality within them.

Ecological Consequences of Intraspecific Variation in Coevolutionary Systems.

AbstractThe patterns and outcomes of coevolution are expected to depend on intraspecific trait variation. Various evolutionary factors can change this variation in time. As a result, modeling coevolutionary processes solely in terms of mean trait values may not be sufficient; one may need to study the dynamics of the whole trait distribution. Here, we develop a theoretical framework for studying the effects of evolving intraspecific variation in two-species coevolutionary systems. In particular, we build and study mathematical models of competition, exploiter-victim interactions, and mutualism in which the strength of within- and between-species interactions depends on the difference in continuously varying traits between individuals reproducing asexually. We use analytical approximations based on the invasion analysis and supplement them with numerical results. We find that intraspecific variation can be maintained if stabilizing selection is weak in at least one species. When intraspecific variation is maintained under competition or mutualism, coexistence in a stable equilibrium is promoted when between-species interactions mostly happen between individuals similar in trait values. In contrast, in exploiter-victim systems coexistence typically requires strong interactions between dissimilar exploiters and victims. We show that trait distributions can become multimodal. Our approach and results contribute to the understanding of the ecological consequences of intraspecific variation in coevolutionary systems by exploring its effects on population densities and trait distributions.

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 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.