Stochastic Metapopulation Models Applied to Amphibians on the Southern High Plains

南部高平原(SHP)上的25,000个Playa湿地是动植物多样性混合的栖息地。Playa是浅水的补给湿地，每个单独的Playa都存在于自己的分水岭内。SHP上的两栖动物依靠Playas繁殖。Playas必须在繁殖期含有水，才能使卵和幼虫成熟。两栖动物生存的关键参数是Playa水期的时间和长度(Playa水期)。Playa湿地在小水电和整个大平原上的零星出现表明，湿地居民生活在多个局部种群中，由集合种群之间偶尔的相互作用维持。这些湿地马赛克如何维持其集合种群的机制还知之甚少。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的减少，并增加了湿地之间的隔离。事实上，普拉亚湿地的沉积缩短了水文周期，增加了水分流失的速度，最终填满了普拉亚，以至于它成为没有湿地功能的地方。从长远来看，人口和环境的多变性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。目前的集合种群理论主要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)收集游戏区两栖动物群落组成的数据，以及(4)基于本项目收集的数据将这些新的随机集合种群模型应用于小水电两栖动物种群。生态学中的随机微分方程建模是一个相对较新的领域，但也是数学和生物科学中一个重要且迅速发展的领域。对于南高平原(SHP)的物种动态，还没有全面的数学模型。这个项目除了推进随机微分方程的理论和应用之外，还将提供对两栖动物种群和小水电生态的更多了解。德克萨斯理工大学和俄克拉荷马州立大学将对研究生进行生物建模、随机数学、野生动物管理和生态学方面的培训，并加强项目。此外，该项目的结果还将为保护两栖动物种群和保持Playa完整性提出建议，这些建议将对今后对小水电、整个大平原以及其他类似的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.