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

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. Loss and fragmentation of habitats, owing to human activities, creates landscape-level spatial heterogeneity wherein patches of varying size, isolation and quality are separated by a human-modified "matrix" of varying degrees of hostility and has been a primary driver of species extinctions and declining biodiversity. How matrix hostility in combination with trait-mediated effects influence DAR, minimum patch size, and species coexistence remains an open question. In this paper, we employ a theoretical spatially explicit predator-prey population model built upon the reaction-diffusion framework to explore effects of predator-induced emigration (trait-mediated emigration) and matrix hostility on DAR, minimum patch size, and species coexistence. Our results show that when trait-mediated response strength is sufficiently strong, ranges of patch size emerge where a nonlinear hump-shaped prey DAR is predicted and other ranges where coexistence is not possible. In a conservation perspective, DAR is crucial not only in deciding whether we should have one large habitat patch or several-small (SLOSS), but for understanding the minimum patch size that can support a viable population. Our study lends more credence to the possibility that predators can alter prey DAR through predator-induced prey dispersal.

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.

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., the density-area relationship (DAR), as positive, neutral, negative or some combination of the three. However, the mechanisms responsible for these relationships remain elusive. We employ a theoretical spatially explicit population model built upon the reaction-diffusion framework with absorbing boundary conditions to model a habitat specialist dwelling in islands of habitat surrounded by a hostile matrix. We consider patches with a convex or non-convex geometry. Our results show that a single species following logistic-type population growth exhibits a strictly positive and continuous DAR. However, when multiple asymptotically stable steady states are preset in the system, a discontinuous DAR arises. In the case of two species governed by diffusive Lotka-Volterra growth and competitive interactions, we observe that overall DAR structure can be either (1) positive, (2) positive for small areas and neutral for large, or (3) hump-shaped, i.e., positive for area below a threshold and negative for area above. Patch complexity such as non-convex geometry can cause discontinuities in DAR slope for a single species and create qualitatively different patterns in a competitive system as compared to a convex patch. We also compared our theoretical results with two empirical studies (Anolis lizards on islands and crossbills and pine squirrels in forest fragments) where the pragmatic view of DAR fails to give a mechanistic understanding of what was observed. Close qualitative agreement between theoretical and observed DAR indicates that our model gives a reasonable explanation of the mechanisms underpinning DAR found in those studies. From a conservation perspective, the DAR is crucial to the identification of valuable habitat fragments that favor high abundance and the design of a reserve for a target species. When it comes to protecting a single species, these results suggest that there is unlikely to be a simple solution and that conservation decisions should always be made on a case-by-case basis.

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. However, terrestrial habitat patches are often surrounded by complex mosaics of many different land cover types, which are rarely ecologically neutral or completely inhospitable environments. We employ an extension of a reaction diffusion model to explore effects of heterogeneity in the matrix immediately surrounding a patch in a one-dimensional theoretical landscape. Exact dynamics of a population exhibiting logistic growth, an unbiased random walk in the patch and matrix, habitat preference at the patch/matrix interface, and two functionally different matrix types for the one-dimensional landscape is obtained. These results show existence of a minimum patch size (MPS), below which population persistence is not possible. This MPS can be estimated via empirically derived estimates of patch intrinsic growth rate and diffusion rate, habitat preference, and matrix death and diffusion rates. We conclude that local matrix heterogeneity can greatly change model predictions, and argue that conservation strategies should not only consider patch size, configuration, and quality, but also quality and spatial structure of the surrounding matrix.