Stochastic Metapopulation Models Applied to Amphibians on the Southern High Plains

南部高平原（SHP）上的25000片playa湿地是各种动植物的栖息地。盐湖是浅层补给湿地，每个盐湖都存在于自己的流域内。SHP上的两栖动物依靠playas繁殖。在繁殖期间，Playas必须含有水分，以便卵和幼虫成熟。盐湖水期的时间和长度（盐湖含水的时间）是两栖动物生存的关键参数。在SHP和整个大平原上，洼地湿地的斑块状分布表明，湿地居民生活在多个地方种群中，这些种群通过偶尔的相互作用维持生存。这些湿地群落维持其元种群的机制尚不清楚。然而，显然，不断增加的破坏（通过沉积和化学径流）导致湿地水期和湿地密度减少，并增加了湿地之间的隔离。实际上，盐湖湿地的沉积减少了水期，增加了失水速率，最终填满了盐湖，使其丧失了湿地的功能。人口和环境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长期的重大影响。当前的元人口理论主要基于确定性数学模型，即常微分方程系统。本项目的目标是：(1)将标准的确定性元种群模型扩展到新的随机微分方程模型；(2)为依赖动态景观的种群建立新的随机元种群模型；(3)收集湿地两栖动物群落组成的数据；(4)基于本项目收集的数据将这些新的随机元种群模型应用于SHP上的两栖动物种群。生态学中的随机微分方程建模是一个相对较新的领域，但在数学和生物科学中是一个重要且迅速发展的领域。目前还没有一个综合的数学模型来描述栖息在南方高平原（SHP）的物种动态。除了推进随机微分方程的理论和应用外，该项目还将使人们对两栖动物种群和SHP生态有更深入的了解。研究生将在德克萨斯理工大学和俄克拉荷马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保护两栖动物种群和维护playa完整性的建议，这将对未来对SHP，整个大平原和其他类似半干旱环境的研究产生广泛影响。

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.