On the mechanistic derivation of various discrete-time population models. (English) Zbl 1133.92355

Eskola, Hanna T. M.; Geritz, Stefan A. H.

Bull. Math. Biol. 69, No. 1, 329-346 (2007).

Summary: We present a derivation of various discrete-time population models within a single unifying mechanistic context. By systematically varying the within-year patterns of reproduction and aggression between individuals we can derive various discrete-time population models. These models include classical examples such as the W. E. Ricker model [J. Fish. Res. Bd. Can. 11, 559–623 (1954)], the R. J. H. Beverton and S. J. Holt model [Fish. Investig., Ser. 2, Vol. 19 (1957)], the J. G. Skellam model [Biometrika 38, 196–218 (1951; Zbl 0043.14401)], the M. P. Hassell model [J. Anim. Ecol. 44, 283–295 (1975)], and others. Some of these models until now lacked a good mechanistic interpretation or have been derived in a different context. By using this mechanistic approach, the model parameters can be interpreted in terms of individual behavior.

MSC:

92D40	Ecology
37N25	Dynamical systems in biology
92D25	Population dynamics (general)

Keywords:

Beverton-Holt model; Hassell model; Ricker model; Skellam model

References:

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