Population dynamics in migratory networks

Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights.

Background Migratory animals comprise a significant portion of biodiversity worldwide with annual investment for their conservation exceeding several billion dollars. Designing effective conservation plans presents enormous challenges. Migratory species are influenced by multiple events across land and sea–regions that are often separated by thousands of kilometres and span international borders. To date, conservation strategies for migratory species fail to take into account how migratory animals are spatially connected between different periods of the annual cycle (i.e. migratory connectivity) bringing into question the utility and efficiency of current conservation efforts. Methodology/Principal Findings Here, we report the first framework for determining an optimal conservation strategy for a migratory species. Employing a decision theoretic approach using dynamic optimization, we address the problem of how to allocate resources for habitat conservation for a Neotropical-Nearctic migratory bird, the American redstart Setophaga ruticilla, whose winter habitat is under threat. Our first conservation strategy used the acquisition of winter habitat based on land cost, relative bird density, and the rate of habitat loss to maximize the abundance of birds on the wintering grounds. Our second strategy maximized bird abundance across the entire range of the species by adding the constraint of maintaining a minimum percentage of birds within each breeding region in North America using information on migratory connectivity as estimated from stable-hydrogen isotopes in feathers. We show that failure to take into account migratory connectivity may doom some regional populations to extinction, whereas including information on migratory connectivity results in the protection of the species across its entire range. Conclusions/Significance We demonstrate that conservation strategies for migratory animals depend critically upon two factors: knowledge of migratory connectivity and the correct statement of the conservation problem. Our framework can be used to identify efficient conservation strategies for migratory taxa worldwide, including insects, birds, mammals, and marine organisms.