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

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...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2012-03, Vol.74 (3), p.641-665
Main Authors: Ackleh, Azmy S., Carter, Jacoby, Deng, Keng, Huang, Qihua, Pal, Nabendu, Yang, Xing
Format: Article
Language:English
Subjects:
Animals
Anura
Anura - growth & development
Cell Biology
Hyla cinerea
Least-Squares Analysis
Life Sciences
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Models, Biological
Original Article
Population Dynamics
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Summary: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.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-011-9682-0