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Approaching Size and Age in Matrix Population Models

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Size-Structured Populations

Abstract

Matrix projection models are a simple and powerful way to analyze the life cycles of organisms whose demography is determined by size or developmental stage, rather than age. Here I address three problems: (1) choosing between age and size as state variables, (2) using size-classified models as approximations when both age and size are important, and (3) recovering age-specific information from sizeclassified models.

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References

  • Alm G (1959) Connection between maturity, size, and age in fishes. Rep Drottningholm Inst Freshwater Res 40:5–145.

    Google Scholar 

  • Anderson RJ, Landis JR (1980) CATANOVA for multidimensional contingency tables: nominal-scale response. Commun Stat Theor Meth A9:1191–1206.

    Google Scholar 

  • Bishop YMM, Fienberg SE, Holland PW (1975) Discrete multivariate analysis: theory and practice. MIT, Cambridge, Mass.

    Google Scholar 

  • Blythe SP, Nisbet RM, Gurney WSC (1984) The dynamics of population models with distributed maturation periods. Theor Popul Biol 25:289–311.

    Article  PubMed  CAS  Google Scholar 

  • Burns BR, Ogden J (1985) The demography of the temperate mangrove [Avicennia marina (Forsk.) Vierh.] at its southern limit in Zew Zealand. Aust J Ecol 10:125–133.

    Article  Google Scholar 

  • Caswell H (1978) A general formula for the sensitivity of population growth rate to changes in life history parameters. Theor Popul Biol 14:215–2320.

    Article  PubMed  CAS  Google Scholar 

  • Caswell H (1982) Stable population structure and reproductive value for populations with complex life cycles. Ecology 63:1223–1231.

    Article  Google Scholar 

  • Caswell H (1983) Phenotypic plasticity in life history traits: demographic effects and evolutionary consequences. Am Zoologist 23:35–46.

    Google Scholar 

  • Caswell H (1984) Optimal life histories and the costs of reproduction: two extensions. J Theor Biol 107:169–172.

    Article  PubMed  CAS  Google Scholar 

  • Caswell H (1985) The evolutionary demography of clonal reproduction. In: Jackson JBC, Buss LW, Cook, RE (eds) Population biology and evolution of clonal organisms. Yale Univ Press.

    Google Scholar 

  • Caswell H (1986) Life cycle models for plants. Lect Math Life Sci 18:171–233.

    Google Scholar 

  • Caswell H (1988) Matrix population models: construction, analysis and interpretation. (in preparation).

    Google Scholar 

  • Caswell H, Koenig H, Resh J, Ross Q (1972) An introduction to systems analysis for ecologists. In: Patten BC (ed) Systems analysis and simulation in ecology, vol 2. Academic Press, New York London.

    Google Scholar 

  • Caswell H, Naiman RJ, Morin R (1984) Evaluating the consequences of reproduction in complex salmonid life cycles. Aquaculture 43:123–134.

    Article  Google Scholar 

  • Coale AJ (1972) The growth and structure of human populations: a mathematical approach. Univ Press, Princeton.

    Google Scholar 

  • Cook RE (1983) Clonal plant populations. Am Sci 71:244–253.

    Google Scholar 

  • Crouse DT, Crowder LB, Caswell H (1987) A stage-based population model for loggerhead sea turtles and implications for conservation. Ecology 68:1412–1423.

    Article  Google Scholar 

  • Fienberg SE (1977) The analysis of cross-classified categorical data. MIT, Cambridge, Mass.

    Google Scholar 

  • Fingleton B (1984) Models of category counts. Univ Press, Cambridge.

    Book  Google Scholar 

  • Goodman LA, Kruskal WH (1954) Measures of association for cross classifications. J Am Stat Assoc 49:732–764.

    Article  Google Scholar 

  • Gray LN, Williams JS (1975) Goodman and Kruskal’s tau b: multiple and partial analogs. Proc Soc Stat Sect Am Stat Assoc 444–448.

    Google Scholar 

  • Gross KL (1981) Predictions of fate from rosette size in four “biennial” plant species: Verbascum thapsus, Oenothera biennis, Daucus carota, and Tragopogon dubius. Oecologia (Berlin) 48:209–213.

    Article  Google Scholar 

  • Hartshorn GS (1975) A matrix model of tree population dynamics. In: Golley FB, Medina E (eds) Tropical ecological systems. Springer, Berlin Heidelberg New York, pp 41–51.

    Google Scholar 

  • Hubbell SP, Werner PA (1979) On measuring the intrinsic rate of increase of populations with heterogeneous life histories. Am Nat 113:277–293.

    Article  Google Scholar 

  • Hughes TP, Connell JH (1987) Population dynamics based on size or age? A reef-coral analysis. Am Nat 129:818–829.

    Article  Google Scholar 

  • Kendall MG, Stuart A (1958) The advanced theory of statistics, vol 1. Hafner, New York.

    Google Scholar 

  • Keyfitz N (1977) Applied mathematical demography. John Wiley & Sons, New York.

    Google Scholar 

  • Lande R (1982a) A quantitative genetic theory of life history evolution. Ecology 63:607–615.

    Article  Google Scholar 

  • Lande R (1982b) Elements of a quantitative genetic model of life history evolution. In: Dingle H, Hegmann JP (eds) Evolution and genetics of life histories. Springer, Berlin Heidelberg New York.

    Google Scholar 

  • Law R (1983) A model for the dynamics of a plant population containing individuals classified by age and size. Ecology 64:224–230.

    Article  Google Scholar 

  • Liebetrau AM (1983) Measures of association. Quantitative applications in the social sciences 32. Sage, Beverly Hills.

    Google Scholar 

  • Light RJ, Margolin BH (1971) An analysis of variance for categorical data. J Am Stat Assoc 66:534–544.

    Article  Google Scholar 

  • McGraw JB (1987) Age-and size-specific shoot life histories and shoot population growth in Rhododendron maximum (submitted).

    Google Scholar 

  • Metz JAJ, Diekmann O (1986) The dynamics of physiologically structured populations. Springer, Berlin Heidelberg New York.

    Google Scholar 

  • Pinero D, Martinez-Ramos M, Sarukhan J (1984) A population model of Astrocaryum mexicanum and a sensitivity analysis of its finite rate of increase. J Ecol 72:977–991.

    Article  Google Scholar 

  • Potts DC (1983) Evolutionary disequilibrium among indo-pacific corals. Bull Mar Sci 33:619–632.

    Google Scholar 

  • Potts DC (1984) Generation times and the Quaternary evolution of reef-building corals. Paleobiology 10:48–58.

    Google Scholar 

  • Robertson A (1968) The spectrum of genetic variation. In: Lewontin RC (ed) Population biology and evolution. Univ Press, Syracuse.

    Google Scholar 

  • Saether BE, Haagenrud H (1983) Life history of the moose (Alces alces): fecundity rates in relation to age and carcass weight. J Mammal 64:226–232.

    Article  Google Scholar 

  • Werner PA (1975) Prediction of fate from rosette size in teasel (Dipsacus fullonum L.). Oecologia (Berlin) 20:197–201.

    Article  Google Scholar 

  • Zadeh LA (1969) The concepts of system, aggregate, and state in system theory. In: Zadeh LA, Polak E (eds) System theory. McGraw-Hill, New York, pp 3–42.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Biology Department, Woods Hole Oceanographic Institution, Woods Hole, MA, 02543, USA

    H. Caswell

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  1. H. Caswell
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Editor information

Editors and Affiliations

  1. Department of Biology, University of Linköping, S-581 83, Linköping, Sweden

    Bo Ebenman

  2. Department of Ecology, Limnology, P.O. Box 65, S-22100, Lund, Sweden

    Lennart Persson

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© 1988 Springer-Verlag Berlin Heidelberg

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Caswell, H. (1988). Approaching Size and Age in Matrix Population Models. In: Ebenman, B., Persson, L. (eds) Size-Structured Populations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74001-5_7

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  • DOI: https://doi.org/10.1007/978-3-642-74001-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-74003-9

  • Online ISBN: 978-3-642-74001-5

  • eBook Packages: Springer Book Archive

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