Abstract
Our understanding of zooplankton dynamics is constrained by the difficulty of estimating stage-specific vital rates from field data. In this paper, we approach demographic estimation as an inverse problem, using stage-classified matrix projection models. We allow the vital rates to vary between stages and over time, and do not assume stable age distributions or that discrete cohorts can be identified. We obtain least-squares estimates of survival and growth probabilities, which can be obtained from as few as three consecutive censuses. However, the estimates are ill-conditioned in the presence of sampling noise. Two regularization methods, truncated singular value decomposition and Tikhonov regularization (ridge regression) are examined as possible solutions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aksnes, D. L. 1986. Resource allocation in the study of copepod population dynamics. Ph.D. Thesis, University of Bergen, Bergen, Norway.
Aksnes, D. L. & T. J. Hoisaeter. 1987. Obtaining life table data from stage—frequency distributional statistics. Limnol Oceanogr. 32: 514–517.
Albert, A. 1972. Regression and the Moore—Penrose pseudoinverse. Academic Press, New York.
Bertero, M. 1986. Regularization methods for linear inverse problems, pp. 52–112 in G. Talenti [ed.] Inverse Problems. Springer—Verlag, New York.
Caswell, H. 1972. On instantaneous and finite birth rates. Limnol Oceanogr. 17: 787–791.
Caswell, H. 1978. A general formula for the sensitivity of population growth rate to changes in life history parameters. Theor. Pop. Biol14: 215–230.
Caswell, H. 1982. Stable population structure and reproductive value for populations with complex life cycles. Ecology63: 1223–1231.
Caswell, H. 1983. Phenotypic plasticity in life-history traits: demographic effects and evolutionary consequences. Amer. Zool23: 35–46.
Caswell, H. 1985. The evolutionary demography of clonal organisms. In L. Buss, J. B. C. Jackson and R. Cook [eds.]. The Population Biology of Clonal Organisms. Yale Univ. Press, New Haven.
Caswell, H. 1986. Life cycle models for plants. Led. Math. Life Sci.18: 171–223.
Caswell, H. 1986. Life cycle models for plants. Led. Math. Life Sci.18: 171–223.
Edmondson, W. T. 1960. Reproductive rates of rotifers in natural populations. Mem. 1st. Ital Idrobiol12: 21–77.
Gabriel, W., B. E. Taylor & S. Kirsch-Prokosch. 1987. Cladoceran birth and death rates estimates: experimental comparisons of egg-ratio methods. Freshwat. Biol18: 361–372.
Gehrs, C. W. & A. Robertson. 1975. Use of life tables in analyzing the dynamics of copepod populations. Ecology56: 665–672.
Golub, G. H., M. Heath, & G. Wahba. 1979. Generalized cross—validation as a method for choosing a good ridge parameter. Technometrics21: 215–223.
Hairston, N. G., Jr. & S. Twombly. 1985. Obtaining life table data from cohort analyses: a critique of current methods. Limnol Oceanogr. 30: 886–893.
Hairston, N. G., Jr., M. Braner & S. Twombly. 1987. Perspective on prospective methods for obtaining life table data. Limnol Oceanogr. 32: 517–520.
Hoerl, A. E. & R. W. Kennard. 1970a. Ridge regression: biased estimation for nonorthogonal problems. Technometrics12: 55–67.
Hoerl, A. E. k R. W. Kennard. 1970b. Ridge regression: applications to nonorthogonal problems. Technometrics12: 69–82.
Keller, J. B. 1976. Inverse problems. Amer. Math. Monthly83: 107–118.
Lande, R. 1982. A quantitative genetic theory of life history evolution. Ecol. 63: 607–615.
Law, R. 1983. A model for the dynamics of plant populations containing individuals classified by age and size. Ecology64: 224–230.
Lefkovitch, L. P. 1964. Estimating the Malthusian parameter from census data. Nature204: 810.
Lefkovitch, L. P. 1965. The study of population growth in organisms grouped by stages. Biometrics21: 1–18.
Paloheimo, J. E. 1974. Calculation of instantaneous birth rate. Limnol Oceanogr. 19: 692–694.
Rigler, F. H. & J. M. Cooley. 1974. The use of field data to derive population statistics of multivoltine copepods. Limnol. Oceanogr.19: 636–655.
Sharpe, P. J. H., G. L. Curry, D. W. DeMichele & C. L. Cole. 1977. Distribution model of organism development times. J. Theor. Biol.66: 21–38.
Taylor, B. E. & M. Slatkin. 1981. Estimating birth and death rates of zooplankton. Limnol Oceanogr. 26: 143–158.
Threlkeld, S. T. 1979a. Estimating cladoceran birth rates: the importance of egg mortality and the egg age distribution. Limnol. Oceanogr.24: 601–612.
Tikhonov, A. N. 1965. Ill—posed problems of linear algebra and a stable method of solving them. Doklady Akad. Nauk USSR 163: 6.
Tikhonov, A. N. & V. Y. Arsenin. 1977. Solutions of ill—posed problems. V. H. Winston and Sons, Washington, D.C.
Wahba, G. 1977. The approximate solution of linear operator equations when the data are noisy. SIAM J. Num. Anal.14: 651–667.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Caswell, H., Twombly, S. (1989). Estimation of Stage—Specific Demographic Parameters for Zooplankton Populations: Methods Based on Stage—Classified Matrix Projection Models. In: McDonald, L.L., Manly, B.F.J., Lockwood, J.A., Logan, J.A. (eds) Estimation and Analysis of Insect Populations. Lecture Notes in Statistics, vol 55. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3664-1_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3664-1_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96998-5
Online ISBN: 978-1-4612-3664-1
eBook Packages: Springer Book Archive