Discrete Analysis (Matrix Models)


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. ().

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 .



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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.

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.

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.

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