Continuous Structured Population Models with Application to Green Treefrogs

连续结构化种群模型在绿色树蛙中的应用

• 批准号: 0718465
• 负责人: Azmy Ackleh
• 金额: $ 25万
• 依托单位: University of Louisiana at Lafayette
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0718465&HistoricalAwards=false
• 关键词: Continuous; Structured; Population; Models; Application

This project will focus on the development and analysis of deterministic structured population models, which will be applied to describe the dynamics of a frog population in an urban area. A combination of analytical and computational methods will be used to understand the population dynamics. New theories on well-posedness, long-time behavior, numerical methods, and parameter estimation techniques will be established. Based on capture-mark-recapture field data, statistical techniques will be employed to approximate weekly frog population sizes. These approximate population sizes will then be compared with the output of the structured population models via the least-squares approach to provide estimates for the model parameters. Furthermore, stochastic population models based on the deterministic ones will be developed and numerically analyzed. These models will be useful for obtaining information about the expected time to population extinction.This research will advance the understanding of the dynamics of anuran populations in urban systems. By intensively studying a relatively isolated population, information on survivorship and life history patterns will be produced. Because the field study site is a habitat island in an urban interface, an insight into the processes that affect anurans in an anthropomorphic landscape will be gained from the models' theoretical and numerical analyses. The analytical and computational methods developed will provide alternatives to the existing methods that are used to study structured population models. The statistical methods using appropriate probability distributions on the field data provide an effective technique to fine tune the deterministic models for an improved understanding of the dynamics of the anuran population. These mathematical and statistical approaches not only can be used as instructional tools in biomathematics graduate studies, but also will enhance the multidisciplinary research combining population ecology, mathematics, and statistics.

该项目将侧重于开发和分析确定性结构种群模型，该模型将用于描述城市地区青蛙种群的动态。将使用分析和计算方法相结合的方法来了解种群动态。将建立关于适定性、长时间行为、数值方法和参数估计技术的新理论。根据捕获-标记-再捕获现场数据，将采用统计技术来估计每周的青蛙种群规模。然后通过最小二乘方法将这些近似的种群大小与结构化种群模型的输出进行比较，以提供模型参数的估计。此外，将在确定性人口模型的基础上建立随机人口模型并进行数值分析。这些模型将有助于获得有关种群灭绝的预期时间的信息。这项研究将促进对城市系统中anuran人口动态的理解。通过对相对孤立的种群进行深入研究，将产生关于生存和生活史模式的信息。由于实地研究地点是城市界面中的栖息地岛屿，因此将从模型的理论和数值分析中获得对拟人化景观中影响无头动物的过程的见解。所开发的分析和计算方法将为用于研究结构化人口模型的现有方法提供替代方法。在野外数据上使用适当概率分布的统计方法提供了一种有效的技术来微调确定性模型，以便更好地了解anuran种群的动态。这些数学和统计方法不仅可以作为生物数学研究生学习的教学工具，而且可以促进人口生态学、数学和统计的多学科研究。