Estimation of growth rate distributions in size structured population models
Authors:
H. T. Banks and B. G. Fitzpatrick
Journal:
Quart. Appl. Math. 49 (1991), 215-235
MSC:
Primary 92D25; Secondary 62G05, 62P10
DOI:
https://doi.org/10.1090/qam/1106389
MathSciNet review:
MR1106389
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Abstract: We propose models for size-structured populations which allow growth rates to vary with individuals (growth rate distribution across all possible individual growth rates). A theoretical framework for the estimation of the growth rate distribution from data of sized population densities is developed. Numerical examples are presented to demonstrate feasibility of the ideas.
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- H. T. Banks, Computational techniques for inverse problems in size structured stochastic population models, Control of partial differential equations (Santiago de Compostela, 1987) Lect. Notes Control Inf. Sci., vol. 114, Springer, Berlin, 1989, pp. 3–10. MR 987961
- H. T. Banks, L. W. Botsford, F. Kappel, and C. Wang, Modeling and estimation in size structured population models, Mathematical ecology (Trieste, 1986) World Sci. Publ., Teaneck, NJ, 1988, pp. 521–541. MR 1040350
- H. T. Banks and B. G. Fitzpatrick, Statistical methods for model comparison in parameter estimation problems for distributed systems, J. Math. Biol. 28 (1990), no. 5, 501–527. MR 1069009, DOI https://doi.org/10.1007/BF00164161
- H. T. Banks and K. Kunisch, Estimation techniques for distributed parameter systems, Systems & Control: Foundations & Applications, vol. 1, Birkhäuser Boston, Inc., Boston, MA, 1989. MR 1045629
- H. T. Banks and K. A. Murphy, Quantitative modeling of growth and dispersal in population models, Mathematical topics in population biology, morphogenesis and neurosciences (Kyoto, 1985) Lecture Notes in Biomath., vol. 71, Springer, Berlin, 1987, pp. 98–109. MR 913328, DOI https://doi.org/10.1007/978-3-642-93360-8_10
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L. W. Botsford, Effect of individual growth rates on expected behavior of the northern California Dungeness crab (Cancer magister) fishery, Can. J. Fish. Aquat. Sci. 41, 99–107 (1984)
L. W. Botsford, B. Vandracek, T. Wainwright, A. Linden, R. Kope, D. Reed, and J. J. Cech, Population development of the mosquitofish, Gambusia Affinis, in rice fields, Envir. Biol, of Fishes 20, 143–154 (1987)
- Stewart N. Ethier and Thomas G. Kurtz, Markov processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. Characterization and convergence. MR 838085
- J. A. J. Metz and O. Diekmann (eds.), The dynamics of physiologically structured populations, Lecture Notes in Biomathematics, vol. 68, Springer-Verlag, Berlin, 1986. Papers from the colloquium held in Amsterdam, 1983. MR 860959
- Akira Okubo, Diffusion and ecological problems: mathematical models, Biomathematics, vol. 10, Springer-Verlag, Berlin-New York, 1980. An extended version of the Japanese edition, Ecology and diffusion; Translated by G. N. Parker. MR 572962
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
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H. T. Banks, On a variational approach to some parameter estimation problems, Distributed Parameter Systems, Springer Lecture Notes in Control and Information Sciences, Vol. 75, 1985, pp. 1–23
H. T. Banks, Computational techniques for inverse problems in size structured stochastic population models, LCDS-CCS Report 87-41, Brown University; Proceedings IFIP Conference on Optimal Control of Systems Governed by Partial Differential Equations, Santiago de Compostela, Spain (July 6–9, 1987), Springer Lecture Notes in Control and Information Sciences, Vol. 114, 1988, pp. 3–10
H. T. Banks, L. W. Botsford, F. Kappel, and C. Wang, Modeling and estimation in size structured population models, LCDS-CCS Report 87-13, Brown University; Proceedings 2nd Course on Mathematical Ecology, (Trieste, December 8–12, 1986) World Press, Singapore, 1988, pp. 521–541
H. T. Banks and B. G. Fitzpatrick, Statistical methods for model comparison in parameter estimation problems for distributed systems, CAMS Rep. 89–4, September 1989, University of Southern California; J. Math. Biol. 28, 501–527 (1990)
H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhaüser, Boston, 1989
H. T. Banks and K. A. Murphy, Quantitative modeling of growth and dispersal in population models, LCDS Report 86–4, Brown University, Proc. Symp. on Math. Biology, Springer Lecture Notes in Biomath, Vol. 71, 1987, pp. 98–109
P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968
L. W. Botsford, Effect of individual growth rates on expected behavior of the northern California Dungeness crab (Cancer magister) fishery, Can. J. Fish. Aquat. Sci. 41, 99–107 (1984)
L. W. Botsford, B. Vandracek, T. Wainwright, A. Linden, R. Kope, D. Reed, and J. J. Cech, Population development of the mosquitofish, Gambusia Affinis, in rice fields, Envir. Biol, of Fishes 20, 143–154 (1987)
S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986
J. A. J. Metz and O. Diekmann, The Dynamics of Physiologically Structured Populations, Springer Lecture Notes in Biomathematics, Vol. 68, 1986
A. Okubo, Diffusion and Ecological Problems: Mathematical Models, Springer-Verlag, New York, 1980
W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966
M. H. Schultz, Spline Analysis, Prentice Hall, Englewood Cliffs, 1973
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Article copyright:
© Copyright 1991
American Mathematical Society
