Community context and dispersal stochasticity drive variation in spatial spread

Density-dependent within-patch movement behavior of two competing species

Movement behavior is central to understanding species distributions, population dynamics and coexistence with other species. Although the relationship between conspecific density and emigration has been well studied, little attention has been paid to how interspecific competitor density affects another species' movement behavior. We conducted releases of two species of competing Tribolium flour beetles at different densities, alone and together in homogeneous microcosms, and tested whether their recaptures-with-distance were well described by a random-diffusion model. We also determined whether mean displacement distances varied with the release density of conspecific and heterospecific beetles. A diffusion model provided a good fit to the redistribution of T. castaneum and T. confusum at all release densities, explaining an average of >60% of the variation in recaptures. For both species, mean displacement (directly proportional to the diffusion rate) exhibited a humped-shaped relationship with conspecific density. Finally, we found that both species of beetle impacted the within-patch movement rates of the other species, but the effect depended on density. For T. castaneum in the highest density treatment, the addition of equal numbers of T. castaneum or T. confusum had the same effect, with mean displacements reduced by approximately one half. The same result occurred for T. confusum released at an intermediate density. In both cases, it was total beetle abundance, not species identity that mattered to mean displacement. We suggest that displacement or diffusion rates that exhibit a nonlinear relationship with density or depend on the presence or abundance of interacting species should be considered when attempting to predict the spatial spread of populations or scaling up to heterogeneous landscapes.

The Ricker Competition Model of Two Species: Dynamic Modes and Phase Multistability

The model of two species competing for a resource proposed by R. May and A.P. Shapiro has not yet been fully explored. We study its dynamic modes. The model reveals complex dynamics: multistable in-phase and out-of-phase cycles, and their bifurcations occur. The multistable out-of-phase dynamic modes can bifurcate via the Neimark–Sacker scenario. A value variation of interspecific competition coefficients changes the number of in-phase and out-of-phase modes. We have suggested an approach to identify the bifurcation (period-doubling, pitchfork, or saddle-node bifurcations) due to which in-phase and out-of-phase periodic points appear. With strong interspecific competition, the population’s survival depends on its growth rate. However, with a specific initial condition, a species with a lower birth rate can displace its competitor with a higher one. With weak interspecific competition and sufficiently high population growth rates, the species coexist. At the same time, the observed dynamic mode or the oscillation phase can change due to altering of the initial condition values. The influence of external factors can be considered as an initial condition modification, leading to dynamics shift due to the coexistence of several stable attractors.

Initial abundance and stochasticity influence competitive outcome in communities

Predicting competitive outcomes in communities frequently involves inferences based on deterministic population models since these provide clear criteria for exclusion (e.g. R* rule) or long-term coexistence (e.g. mutual invasibility). However, incorporating stochasticity into population- or community-level processes into models is necessary if the goal is to explain variation in natural systems, which are inherently stochastic. Similarly, in systems with demographic or environmental stochasticity, weaker competitors have the potential to exclude superior competitors, contributing to what is known as 'competitive indeterminacy'. The importance of such effects for natural communities is unknown, in part because it is difficult to demonstrate that multiple forms of stochasticity are present in these communities. Moreover, the effects of multiple forms of stochasticity on competitive outcomes are largely untested, even in theory. Here, we address these issues by examining the role of stochasticity in replicated communities of flour beetles (Tribolium sp.). To do so, we developed a set of two-species stochastic Ricker models incorporating four distinct forms of stochasticity: environmental stochasticity, demographic stochasticity, demographic heterogeneity and stochastic sex determination. By fitting models to experimental data, and simulating fit models to examine long- term behaviour, we found that both the duration of transient coexistence and the degree of competitive indeterminacy were sensitive to the forms of stochasticity included in our models. These findings suggest the current estimates of extinction risk, coexistence and time until competitive exclusion in communities may not be accurate when based on models that exclude relevant forms of stochasticity.