Persistence and Spreading Speeds in Multi-Species Models with A Shifting Habitat Edge

University Of Louisville Research Foundation Inc, Louisville KY

Investigators

Abstract

Whether or not a species can persist and spread in an environment is a fundamental and long-standing question in ecology. Recently, this question has been brought to the forefront by climate change and landscape conversion. Due to the processes of climate change, habitat regions suitable for population growth of many species have been shifting geographically. Climatically induced shifts may interface with population demographic processes in complex ways, setting the stage for impacts on species population growth and spread, long-term dynamics and interactions between species. This project aims to produce new frameworks for the analysis of persistence and spreading speeds of species in a shifting habitat. It addresses the question of how ecosystems are being affected by climate change and how ecosystems might respond in the future. It contributes to the growing body of information identifying species at a high risk for extinction and predicting the spread of invasive species under ongoing climate change. The outcomes of the project help improve strategies for coping with challenges of natural resource management. This project further stimulates interdisciplinary collaboration between mathematicians and biologists to address issues beyond the reach of single disciplines. In addition, it contributes to human resources development, focusing on training and skill development of graduate students, and providing them with experience in interdisciplinary interaction and exploration. In this project, the investigator formulates and analyzes spatial population models that describe species growth, interactions, and dispersal in shifting habitats. The goal is to understand and accurately describe how climate change affects biological invasion processes. Multi-species reaction-diffusion competition models and predator-prey models, as well as semi-discrete stage-structured spatial models with a shifting habitat edge, are studied to emphasize the role of changing habitat suitability in persistence and spread of an invasive species interacting with an existing species. In these models, shifts in habitat ranges are incorporated in species growth functions that propagate as traveling waves. Species spatial dynamics are investigated for the following cases: (i) one species spreads into a shifting habitat preoccupied by a resident species; and (ii) two species consecutively invade an open shifting habitat and the earlier species is still in the process of expanding its spatial range. New techniques are developed to determine the behaviors of solutions of the models on appropriate bounded and unbounded spatial intervals that expand and shift in time. Methods from differential equations, integral equations, and dynamical systems are employed to detect conditions under which species go extinct and to determine spreading speeds of persisting species in space. The results of this research also have impacts in other disciplines where wave propagation is studied.