Abstract
Recently, Eskola and Geritz (Bull. Math. Biol. 69:329–346, 2007) showed that several discrete-time population models can be derived mechanistically within a single ecological framework by varying the within-season patterns of reproduction and inter-individual aggression. However, these models do not have the Allee effect. In this paper, we modify the original modelling framework by adding different mate finding processes, and thus derive mechanistically several population models with the Allee effect.
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Allee, W.C., 1931. Animal Aggregations, a Study in General Sociology. University of Chicago Press, Chicago.
Allee, W.C., 1938. The Social Life of Animals. Heineman, London.
Allee, W.C., Emerson, A., Park, T., Schmidt, K., 1949. Principles of Animal Ecology. Saunders, Philadelphia.
Anazawa, M., 2009. Bottom-up derivation of discrete-time population models with the Allee effect. Theor. Popul. Biol. 75, 56–67.
Berec, L., Angulo, E., Courchamp, F., 2007. Multiple Allee effects and population management. Trends Ecol. Evol. 22, 185–191.
Beverton, R.J.H., Holt, S.J., 1957. On the dynamics of exploited fish populations. Fisheries Investigations, Series 2, vol. 19.
Boukal, D.S., Berec, L., 2002. Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters. J. Theor. Biol. 218, 375–394.
Brännström, A., Sumpter, D.J.T., 2005. The role of competition and clustering in population dynamics. Proc. R. Soc. B 272, 2065–2072.
Courchamp, F., Berec, L., Gascoigne, J., 2008. Allee Effects in Ecology and Conservation. Oxford University Press, London.
Courchamp, F., Clutton-Brock, T., Grenfell, B., 1999. Inverse density dependence and the Allee effect. Trends Ecol. Evol. 14, 405–410.
Eskola, H.T.M., 2009. On the evolution of the timing of reproduction. Theor. Popul. Biol. 75, 98–108.
Eskola, H.T.M., Geritz, S.A.H., 2007. On the mechanistic derivation of various discrete-time population models. Bull. Math. Biol. 69, 329–346.
Eskola, H.T.M., Parvinen, K., 2007. On the mechanistic underpinning of discrete-time population models with Allee effect. Theor. Popul. Biol. 72, 41–51.
Gascoigne, J.C., Lipcius, R.N., 2004. Allee effects driven by predation. J. Appl. Ecol. 41, 801–810.
Geritz, S.A.H., Kisdi, E., 2004. On the mechanistic underpinning of discrete-time population models with complex dynamics. J. Theor. Biol. 228, 261–269.
Hassell, M.P., 1975. Density-dependence in single-species populations. J. Anim. Ecol. 44, 283–295.
Holling, C.S., 1959. Some characteristics of simple types of predation and parasitism. Can. Entomol. 91, 385–398.
Molnár, P.K., Derocher, A.E., Lewis, M.A., Taylor, M.K., 2008. Modelling the mating system of polar bears: a mechanistic approach to the Allee effect. Proc. R. Soc. B 275, 217–226.
Pachepsky, E., Nisbet, R.M., Murdoch, W.W., 2008. Between discrete and continuous: Consumer-resource dynamics with synchronized reproduction. Ecology 89, 280–288.
Parvinen, K., 2005. Evolutionary suicide. Acta Biotheor. 53, 241–264.
Singh, A., Nisbet, R.M., 2007. Semi-discrete host-parasitoid models. J. Theor. Biol. 247, 733–742.
Skellam, J.G., 1951. Random dispersal in theoretical populations. Biometrika 38, 196–218.
Stephens, P.A., Sutherland, W.J., 1999. Concequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol. Evol. 14, 401–405.
Stephens, P.A., Sutherland, W.J., Freckleton, R.P., 1999. What is the Allee effect? Oikos 87, 185–190.
Thieme, H.R.T., 2003. Mathematics in Population Biology. Princeton University Press, Princeton.
Wells, H., Wells, P.H., Cook, P., 1990. The importance of overwinter aggregation for reproductive success of monarch butterflies (Danaus plexippus L.). J. Theor. Biol. 147, 115–131.
Wells, H., Strauss, E.G., Rutter, M.A., Wells, P.H., 1998. Mate location, population growth and species extinction. Biol. Conserv. 86, 317–324.
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Eskola, H.T.M., Parvinen, K. The Allee Effect in Mechanistic Models Based on Inter-individual Interaction Processes. Bull. Math. Biol. 72, 184–207 (2010). https://doi.org/10.1007/s11538-009-9443-5
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DOI: https://doi.org/10.1007/s11538-009-9443-5