Stochastic Metapopulation Models Applied to Amphibians on the Southern High Plains

南部高平原（SHP）上的25，000个干盐湖湿地是多种植物群和动物群的栖息地。干盐湖是浅水补给湿地，每个干盐湖都存在于自己的流域内。小水电站的两栖动物依靠干盐湖繁殖。干盐湖在繁殖期间必须有水，以便卵和幼虫成熟。干盐湖水周期的时间和长度（干盐湖含有水的时间段）是两栖动物生存的关键参数。斑片状发生的干盐湖湿地的小水电站，并在大平原作为一个整体，表明湿地居民生活在多个当地人口之间偶尔相互作用的集合种群。这些湿地镶嵌如何维持其集合种群的机制知之甚少。 然而，很明显，越来越多的破坏（通过沉积和化学径流）导致湿地水文周期和湿地密度减少，湿地之间的隔离增加。实际上，干盐湖湿地的沉积作用降低了水文周期，增加了水分流失的速率，最终填满干盐湖，使其丧失湿地的功能。人口和环境的变化，以及全球气候变化，将对两栖动物种群的繁殖和生存产生重大影响。目前集合种群理论主要是基于确定性的数学模型，即常微分方程组。该项目的目标是（1）将标准的确定性集合种群模型扩展到新的随机微分方程模型，（2）为依赖于动态景观的种群开发新的随机集合种群模型，（3）收集有关干盐湖两栖动物群落组成的数据，以及（4）将这些新的随机集合种群模型应用于小水电站上的两栖动物种群。生态学中的随机微分方程模型是一个相对较新的领域，数学和生物科学中的一个重要且迅速扩展的领域。目前还没有针对南部高平原（SHP）物种动态的全面数学模型。本计画除了增进随机微分方程式的理论与应用外，也将提供对两栖动物族群与小水电生态的更深入了解。研究生将在德克萨斯理工大学和俄克拉荷马州州立大学接受生物建模、随机数学、野生动物管理和生态学方面的培训和项目加强。此外，该项目的结果将导致两栖动物种群的保护和维护干盐湖的完整性，将有广泛的影响，对未来的研究小水电，大平原作为一个整体，和其他类似的半干旱环境的建议。

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.