Predator-induced prey dispersal can cause hump-shaped density-area relationships in prey populations.

Predation can both reduce prey abundance directly (through density-dependent effects) and indirectly through prey trait-mediated effects. Over the years, many studies have focused on describing the density-area relationship (DAR). However, the mechanisms responsible for the DAR are not well understood.

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 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.

Modeling effects of matrix heterogeneity on population persistence at the patch-level.

Habitat loss and fragmentation is the largest contributing factor to species extinction and declining biodiversity. Landscapes are becoming highly spatially heterogeneous with varying degrees of human modification. Much theoretical study of habitat fragmentation has historically focused on a simple theoretical landscape with patches of habitat surrounded by a spatially homogeneous hostile matrix.

Ecological release and patch geometry can cause nonlinear density-area relationships.

A primary driver of species extinctions and declining biodiversity is loss and fragmentation of habitats owing to human activities. Many studies spanning a wide diversity of taxa have described the relationship between population density and habitat patch area, i.e.

Modeling the effects of trait-mediated dispersal on coexistence of mutualists.

Even though mutualistic interactions are ubiquitous in nature, we are still far from making good predictions about the fate of mutualistic communities under threats such as habitat fragmentation and climate change. Fragmentation often causes declines in abundance of a species due to increased susceptibility to edge effects between remnant habitat patches and lower quality "matrix" surrounding these focal patches. It has been argued that ecological communities are replete with trait-mediated indirect effects, and that these effects may sometimes contribute more to the dynamics of a population than direct density-mediated effects, e.

Frequency of Occurrence and Population-Dynamic Consequences of Different Forms of Density-Dependent Emigration.

Emigration is a fundamental process affecting species' local, regional, and large-scale dynamics. The paradigmatic view in ecology is that emigration is density independent (DIE) or positive density dependent (+DDE). However, alternative forms are biologically plausible, including negative (-DDE), U-shaped (uDDE), and hump-shaped (hDDE) forms.

Modeling the effects of density dependent emigration, weak Allee effects, and matrix hostility on patch-level population persistence.

The relationship between conspecific density and the probability of emigrating from a patch can play an essential role in determining the population-dynamic consequences of an Allee effect. In this paper, we model a population that inside a patch is diffusing and growing according to a weak Allee effect per-capita growth rate, but the emigration probability is dependent on conspecific density. The habitat patch is one-dimensional and is surrounded by a tuneable hostile matrix.

Effects of Patch-Matrix Composition and Individual Movement Response on Population Persistence at the Patch Level.

Fragmentation creates landscape-level spatial heterogeneity which in turn influences population dynamics of the resident species. This often leads to declines in abundance of the species due to increased susceptibility to edge effects between the remnant habitat patches and the lower quality "matrix" surrounding these focal patches. In this paper, we formalize a framework to facilitate the connection between small-scale movement and patch-level predictions of persistence through a mechanistic model based on reaction-diffusion equations.

Persistence in reaction diffusion models with weak allee effect.

We study the positive steady state distributions and dynamical behavior of reaction-diffusion equation with weak allele effect type growth, in which the growth rate per capita is not monotonic as in logistic type, and the habitat is assumed to be a heterogeneous bounded region. The existence of multiple steady states is shown, and the global bifurcation diagrams are obtained. Results are applied to a reaction-diffusion model with type II functional response, and also a model with density-dependent diffusion of animal aggregation.