Modeling population dynamics and species interactions in a changing climate
Rinnan, Darwin Scott
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Many species are expected to undergo significant distributional shifts in response to changes in climate. This adaptive response can impact population dynamics in many ways, including decreasing reproductive fitness, limiting dispersal, shrinking habitat, and exposing organisms to new competition from invasive species. What determines the successful persistence of a population exposed to climate change? In this dissertation I address different aspects of this fundamental question in three chapters. In the first chapter, I focus on the challenges of modeling asymmetric dispersal. I use a spatially explicit integro-difference equation (IDE) to model a population whose habitat is shifting due to climate change, and demonstrate its equivalence to a stationary IDE model with asymmetric dispersal behavior. The cumulative effects of population dispersal in space and time have been described with some success by Van Kirk and Lewis's average dispersal success approximation (Van Kirk and Lewis, 1997), but this approximation has been demonstrated to perform poorly when applied to asymmetric dispersal. I provide a comparison of different characterizations of dispersal success and demonstrate how to accurately approximate the effects of asymmetric dispersal with a method known as geometric symmetrization. I apply these different methods to a variety of IDE population models with asymmetric dispersal, and I examine the methods' effectiveness in approximating key ecological traits of the models, such as the critical patch size and the critical speed of climate change for population persistence. I show that the method using geometric symmetrization performs considerably better than other approximations for a variety of models and across a wide range of parameter values. In the second chapter, I examine a coupled system of IDEs that models two species competing for the same resources in a shifting habitat. I determine under what conditions the two populations can coexist and the criteria for persistence in a changing climate. I demonstrate how the speed of climate change can shift the stable-state solution of the population model from mutual coexistence to a single species outcompeting the other and how these effects can be mitigated by niche differentiation, with the potential for habitat considered inhospitable to one species to provide refuge for the other. I illustrate this model with a simulated population of native bull trout (<i>Salvelinus confluentus</i>) experiencing competition from invasive brook trout (<i>S. fontinalis</i>) as their river habitat warms due to climate change. Based on current climate projections, this simulation suggests that bull trout are likely to disappear from the study area by 2080, with brook trout expanding their range in the absence of competition. In the third chapter, I describe a new type of model that combines climate-envelope modeling with IDEs to utilize the strengths of both correlative and process-based modeling. I apply this framework to a case study of the American pika (<i>Ochotona princeps</i>), a small montane mammal that is widely recognized as threatened by climate change, and compare this with both a traditional climate-envelope model and an IDE. The results suggest that climate-envelope models alone can substantially underestimate the impacts of climate change, but the predictions of integro-difference models can be considerably improved by incorporating the modeled climate envelope.