Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, USA.
Bull Math Biol. 2012 Mar;74(3):641-65. doi: 10.1007/s11538-011-9682-0. Epub 2011 Oct 13.
We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates are used to illustrate the long-time behavior of the population under investigation.
我们从 2006 年至 2009 年期间获得的捕获-标记-重捕野外数据中推导出绿树蛙（Hyla cinerea）城市种群的点估计和区间估计。我们提出了一种无限维最小二乘方法，该方法将数学种群模型与从野外数据中获得的统计种群估计进行比较。该模型由描述两栖动物种群动态的非线性一阶双曲方程组成，其中个体分为幼体（蝌蚪）和成体（青蛙）。为了解决最小二乘问题，我们开发了显式有限差分逼近。给出了计算参数的收敛结果。得到了幼体和成体的关键比率的参数估计，并计算了这些估计的标准偏差。给出了模型对这些参数的敏感性的数值结果。最后，使用上述参数估计来说明所研究种群的长时间行为。
