Fitting a Structured Juvenile–Adult Model for Green Tree Frogs to Population Estimates from Capture–Mark–Recapture Field Data

Abstract

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.

A model for the interaction of frog population dynamics with Batrachochytrium dendrobatidis, Janthinobacterium lividum and temperature and its implication for chytridiomycosis management

“…We assume that tadpoles dynamics are structured by age, while frogs dynamics are structured by size (e.g., body length) and represent the density of animals in each class depending on time t due to the seasonality of such populations (cf. the frog population model in [1] without Bd, Jl, or temperature). The frog stage is modeled by the following system of hyperbolic partial differential equations.…”

“…based on a 6 year Capture-Mark-Recapture (CMR) field experiment [1]. Then the frog population at time t in each class could be calculated by integrating the densities.…”

“…We assume that a frog begins breeding once it attains a critical size (e.g., 3cm for GTF [1]) and temperature on that particular day along with the average temperature of the past three weeks is above a critical temperature.…”

A second-order characteristic line scheme for solving a juvenile–adult model of amphibians

“…However, such a requirement results in time-consuming simulations, and thus the scheme is difficult to use especially when we tried to fit model (1) to field data using a leastsquares approach which requires solving the model numerous times to achieve an optimal fit [6]. To overcome this difficulty, very recently in [3], an explicit second-order finite difference method was developed for Equation (1).…”

“…At the initial mesh points a i (0 ≤ i ≤ I) and x j (0 ≤ j ≤ L), J 0 i and A 0 j are computed by the initial data (1) 5 and (1) 6 , respectively. Then by means of the trapezoidal rule and Equation (2)…”