Continuous Structured Population Models with Application to Green Treefrogs

本计画将著重于发展与分析决定性结构化族群模式，并应用于描述都市青蛙族群的动态。 分析和计算方法的结合将被用来了解人口动态。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青蛙种群数量。 然后将这些近似群体大小与结构化群体模型的输出进行比较，通过最小二乘法提供模型参数的估计值。 此外，随机人口模型的基础上确定性的将开发和数值分析。 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无尾两栖类种群动态的理解。 通过深入研究一个相对孤立的群体，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一个栖息地岛屿在城市界面，洞察的过程中，影响无尾两栖类在拟人化的景观将获得从模型的理论和数值分析。 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案。 统计方法使用适当的概率分布的现场数据提供了一种有效的技术，微调的确定性模型，以更好地了解无尾两栖动物种群的动态。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，而且还将促进人口生态学，数学和统计学相结合的多学科研究。

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.