Stochastic Metapopulation Models Applied to Amphibians on the Southern High Plains

Texas Tech University, Lubbock TX

Investigators

Abstract

The 25,000 playa wetlands on the Southern High Plains (SHP) serve as habitat for a diverse mixture of flora and fauna. Playas are shallow recharge wetlands with each individual playa existing within its own watershed. Amphibians on the SHP depend on the playas for breeding. Playas must contain water during the breeding period in order for eggs and larvae to mature. The timing and length of the playa hydroperiod (the period of time during which the playa contains water) are critical parameters in amphibian survival. The patchy occurrence of playa wetlands on the SHP, and on the Great Plains as a whole, suggest that wetland inhabitants live in multiple local populations sustained by occasional interaction among metapopulations. The mechanisms of how these wetland mosaics maintain their metapopulations are poorly understood. Yet clearly, mounting destruction (through sedimentation and chemical runoff) results in reduced wetland hydroperiod and wetland density, and increased isolation among wetlands. Indeed, sedimentation in playa wetlands decreases hydroperiod, increases the rate of water loss, and eventually fills the playa to such an extent that it is rendered non-functional as a wetland. Demographic and environmental variability, as well as global climate change, will have a significant impact on the reproduction and survival of amphibian populations over the long term. Current metapopulation theory is primarily based on deterministic mathematical models, i.e, systems of ordinary differential equations. The objectives of this project are (1) to extend standard deterministic metapopulation models to new stochastic differential equation models, (2) to develop new stochastic metapopulation models for populations that depend on a dynamic landscape, (3) to collect data on amphibian community composition in the playas, and (4) to apply these new stochastic metapopulation models to amphibian populations on the SHP based on the data collected in this project. Stochastic differential equation modeling in ecology is a relatively new area but is an important and rapidly expanding area of interest in the mathematical and biological sciences. There have been no comprehensive mathematical models for the dynamics of species inhabiting the Southern High Plains (SHP). This project, in addition to advancing the theory and application of stochastic differential equations, will provide a greater understanding of amphibian populations and the ecology of the SHP. Graduate students will be trained and programs strengthened at Texas Tech University and Oklahoma State University in biological modeling, stochastic mathematics, wildlife management, and ecology. In addition, the results of this project will lead to recommendations for conservation of amphibian populations and for maintenance of playa integrity that will have a broad impact on future research on the SHP, the Great Plains as a whole, and on other similar semiarid environments.