Discrete Analysis (Matrix Models)

Gordon A Fox, University of South Florida, Tampa, Florida, USA

Published online: May 2008

DOI: 10.1002/9780470015902.a0003308

Increasingly applied in conservation and invasion biology, as well as human demography, matrix models are used to estimate rates of population growth and identify demographic rates that strongly affect population growth.

Keywords: population growth; structured populations; conservation; sensitivity and elasticity; eigenvalues

Figure 1. Life-cycle graph for a hypothetical age-structured population. Individuals reach a maximum age of 3, and can reproduce at ages 2 and 3.
Figure 2. Life-cycle graph for the semelparous plant Mauna Kea silversword (Argyroxiphium sandwiciense ssp. sandwiciense). Surviving individuals may remain in the same class or progress to the next class. Most individuals die after flowering, but a few repeat flowering or regress to the adult class. Reproduced with permission from Gurevitch et al. (2002).
Figure 3. Life-cycle graph for the killer whale Orcinus orca. Surviving yearlings become juveniles. Surviving juveniles may remain juveniles or become adults. Eventually adults become postreproductive. Reproduced with permission from Brault and Caswell (1993).
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 References
    Brault S and Caswell H (1993) Pod-specific demography of killer whales (Orcinus orca). Ecology 74: 1444–1454.
    book Caswell H (2001) Matrix Population Models. Sunderland, MA: Sinauer Associates.
    Caswell H (2007) Sensitivity analysis of transient population dynamics. Ecology Letters 10: 1–15.
    Easterling MR, Ellner SP and Dixon PM (2000) Size-specific sensitivity: applying a new structured population model. Ecology 81: 694–708.
    Fox GA and Gurevitch J (2000) Population numbers count: tools for near-term demographic analysis. American Naturalist 156: 242–256.
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    Werner PA and Caswell H (1977) Population growth rates and age versus stage-distribution models for teasel (Dipsacus sylvestris Huds.). Ecology 58: 1103–1111.
 Further Reading
    Caswell H and Werner PA (1978) Transient behavior and life history analysis of teasel (Dipsacus sylvestris Huds.). Ecology 59: 53–66.
    Cochran ME and Ellner S (1992) Simple methods for calculating age-based life history parameters for stage-structured populations. Ecological Monographs 62: 345–364.
    book Ebert TA (1999) Plant and Animal Populations: Methods in Demography. San Diego: Academic Press.
    Goodman LA (1968) An elementary approach to the population projection-matrix, to the population reproductive value, and to related topics in the mathematical theory of population growth. Demography 5: 382–409.
    book Hartshorn G (1975) "A matrix model of tree population dynamics". In: Golley FB and Medina E (eds) Tropical Ecological Systems, pp 41–51. New York: Springer.
    Keyfitz N (1967) Reconciliation of population models: matrix, integral equation and partial fraction. Journal of the Royal Statistical Society 130: 61–83.
    Knight TM (2004) The effects of herbivory and pollen limitation on a declining population of Trillium grandiflorum. Ecological Applications 14: 915–928.
    Lotka AJ (1907) Relationship between birth rates and death rates. Science 26: 21–22.
    Sarukhán J and Gadgil M (1974) Studies on plant demography: Ranunculus repens L., Ranunculus bulbosus L. and R. acris L. III. A mathematical model incorportating multiple modes of reproduction. Journal of Ecology 62: 921–936.
    Wardle GM (1998) A graph theory approach to demographic loop analysis. Ecology 79: 2539–2549.

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Article Title: Discrete Analysis (Matrix Models)
 
How to Cite close
Fox, Gordon A(May 2008) Discrete Analysis (Matrix Models). In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0003308]