K. Salau

Landscape connectivity and predator-prey population dynamics

Landscapes are increasingly fragmented, and conservation programs have started to look at network approaches for maintaining populations at a larger scale. We present an agent-based model of predator–prey dynamics where the agents (i.e. the individuals of either the predator or prey population) are able to move between different patches in a landscaped network. We then analyze population level and coexistence probability given node-centrality measures that characterize specific patches. We show that both predator and prey species benefit from living in globally well-connected patches (i.e. with high closeness centrality). However, the maximum number of prey species is reached, on average, at lower closeness centrality levels than for predator species. Hence, prey species benefit from constraints imposed on species movement in fragmented landscapes since they can reproduce with a lesser risk of predation, and their need for using anti-predatory strategies decreases.

Insights for managers from modeling species interactions across multiple scales in an idealized landscape

In recent years there has been a shift in biodiversity efforts from protected areas to one of interlinked habitat patches across multiple land tenure types. Much work remains on how managers can intervene in such systems to achieve basic goals. We use an agent-based model of a metapopulation with predator-prey dynamics and density-dependent migration to examine theoretically the capacity of a manager to modify the ecosystem to achieve conservation goals. We explore management strategies aimed at maintaining one of two goals - local or global coexistence of species. To achieve their goal, the manager varies the connectivity between patches based on one of three strategies - the monitoring of predator, prey, or the vegetation carrying capacity of the patches. We find that strategies that lead to highest coexistence monitor mid-tier populations globally. Our goal is to use our model results to advance decision-making in conservation beyond protected areas, typical in todays conservation.

Bioeconomic analysis supports the endangered species act

The United States Endangered Species Act (ESA) was enacted to protect and restore declining fish, wildlife, and plant populations. The ESA mandates endangered species protection irrespective of costs. This translates to the restriction of activities that harm endangered populations. We discuss criticisms of the ESA in the context of public land management and examine under what circumstance banning non-conservation activity on multiple use federal lands can be socially optimal. We develop a bioeconomic model to frame the species management problem under the ESA and identify scenarios where ESA-imposed regulations emerge as optimal strategies. Results suggest that banning harmful activities is a preferred strategy when valued endangered species are in decline or exposed to poor habitat quality. However, it is not optimal to sustain such a strategy in perpetuity. An optimal plan involves a switch to land-use practices characteristic of habitat conservation plans.

A global bifurcation theorem for Darwinian matrix models

Motivated by models from evolutionary population dynamics, we study a general class of nonlinear difference equations called matrix models. Under the assumption that the projection matrix is non-negative and irreducible, we prove a theorem that establishes the global existence of a continuum with positive equilibria that bifurcates from an extinction equilibrium at a value of a model parameter at which the extinction equilibrium destabilizes. We give criteria for the global shape of the continuum, including local direction of bifurcation and its relationship to the local stability of the bifurcating positive equilibria. We discuss a relationship between backward bifurcations and Allee effects. Illustrative examples are given.