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On the mechanistic derivation of various discrete-time population models. (English) Zbl 1133.92355
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)
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[1] Beverton, R.J.H., Holt, S.J., 1957. On the dynamics of exploited fish populations. Fisheries Investigations, Series 2, vol. 19. H. M. Stationery Office, London.
[2] Brännström, Å., Sumpter, D.J.T., 2005. The role of competition and clustering in population dynamics. Proc. R. Soc. Lond. Ser. B 272, 2065–2072. · doi:10.1098/rspb.2005.3185
[3] Geritz, S.A.H., Kisdi, É., 2004. On the mechanistic underpinning of discrete-time population models with complex dynamics. J. Theor. Biol. 228, 261–269. · doi:10.1016/j.jtbi.2004.01.003
[4] Hassell, M.P., 1975. Density-dependence in single-species populations. J. Anim. Ecol. 44, 283–295. · doi:10.2307/3863
[5] Johansson, A., Sumpter, D.J.T., 2003. From local interactions to population dynamics in site-based models of ecology. Theor. Popul. Biol. 64, 497–517. · Zbl 1109.92052 · doi:10.1016/S0040-5809(03)00076-5
[6] Ricker, W.E., 1954. Stock and recruitment. J. Fish. Res. Bd. Can. 11, 559–623.
[7] Skellam, J.G., 1951. Random dispersal in theoretical populations. Biometrika 38, 196–218. · Zbl 0043.14401
[8] Sumpter, D.J.T., Broomhead, D.S., 2001. Relating individual behaviour to population dynamics. Proc. R. Soc. Lond. Ser. B 268, 925–932. · doi:10.1098/rspb.2001.1604
[9] Thieme, H.R.T., 2003. Mathematics in Population Biology. Princeton University Press, Princeton, NJ. · Zbl 1054.92042
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