Quantifying the Contribution of Habitats and Pathways to a Spatially Structured Population Facing Environmental Change.

The consequences of environmental disturbance and management are difficult to quantify for spatially structured populations because changes in one location carry through to other areas as a result of species movement. We develop a metric, G, for measuring the contribution of a habitat or pathway to network-wide population growth rate in the face of environmental change. This metric is different from other contribution metrics, as it quantifies effects of modifying vital rates for habitats and pathways in perturbation experiments. Perturbation treatments may range from small degradation or enhancement to complete habitat or pathway removal. We demonstrate the metric using a simple metapopulation example and a case study of eastern monarch butterflies. For the monarch case study, the magnitude of environmental change influences the ordering of node contribution. We find that habitats within which all individuals reside during one season are the most important to short-term network growth under complete removal scenarios, whereas the central breeding region contributes most to population growth over all but the strongest disturbances. The metric G provides for more efficient management interventions that proactively mitigate impacts of expected disturbances to spatially structured populations.

Ecosystem service flows from a migratory species: Spatial subsidies of the northern pintail.

Migratory species provide important benefits to society, but their cross-border conservation poses serious challenges. By quantifying the economic value of ecosystem services (ESs) provided across a species' range and ecological data on a species' habitat dependence, we estimate spatial subsidies-how different regions support ESs provided by a species across its range. We illustrate this method for migratory northern pintail ducks in North America. Pintails support over $101 million USD annually in recreational hunting and viewing and subsistence hunting in the U.S. and Canada. Pintail breeding regions provide nearly $30 million in subsidies to wintering regions, with the "Prairie Pothole" region supplying over $24 million in annual benefits to other regions. This information can be used to inform conservation funding allocation among migratory regions and nations on which the pintail depends. We thus illustrate a transferrable method to quantify migratory species-derived ESs and provide information to aid in their transboundary conservation.

A general modeling framework for describing spatially structured population dynamics.

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network-based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life-history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network-based population is modeled with discrete time steps. Using both theoretical and real-world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network-based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles.