Apaloo, Joseph Revisiting strategic models of evolution: The concept of neighborhood invader strategies. (English) Zbl 0889.92019 Theor. Popul. Biol. 52, No. 1, 71-77 (1997). Summary: In game-theoretic or strategic models of species evolution, the phenotypes of individual organisms in a population are regarded as alternate strategies for playing a competitive game. The evolutionary outcome is predicted to conform to the “solution” of that game. The most usual solution concept adopted for the evolutionary game is that of J. Maynard Smith [Evolution and the theory of games. (1982); see also Proc. R. Soc. Lond., Ser. B 219, 315-325 (1983; Zbl 0531.92015)], the so-called “evolutionary stable strategies” (ESS). We explore an alternative solution concept. We call it neighborhood invader strategy (NIS). A NIS is a phenotype which is capable of invading all established populations of its neighbors. This phenotype need not be, at the same time, an ESS; and the reverse is true as well. We shall analyze this concept for a single species whose evolutionary-possibility set is a one-dimensional continuum. Cited in 33 Documents MSC: 92D15 Problems related to evolution 91A40 Other game-theoretic models Keywords:evolutionary stable strategies; neighborhood invader strategy Citations:Zbl 0531.92015 PDFBibTeX XMLCite \textit{J. Apaloo}, Theor. Popul. Biol. 52, No. 1, 71--77 (1997; Zbl 0889.92019) Full Text: DOI References: [2] Brown, J. S.; Vincent, T. L., Coevolution as an evolutionary game, Evolution, 41, 66-79 (1987) [3] Christiansen, F. B., On conditions for evolutionary stability for continuously varying character, Amer. Natur., 138, 37-50 (1991) [4] Eshel, I.; Motro, U., Kin selection and strong evolutionary stability of mutual help, Theor. Popul. Biol., 19, 420-433 (1981) · Zbl 0473.92014 [5] Eshel, I., Evolutionary and continuous stability, J. Theor. Biol., 103, 99-111 (1983) [6] Hastings, A., An evolutionary optimization principle, J. Theor. Biol., 75, 519-525 (1978) [7] Kisdi, E.; Meszéna, G., Density dependent life history evolution in fluctuating environments, Adaptation in a Stochastic Environment. Adaptation in a Stochastic Environment, Lecture Notes in Biomathematics, 99 (1993), Springer-Verlag: Springer-Verlag Berlin, p. 26-62 · Zbl 0803.92020 [8] Kisdi, E.; Meszéna, G., Life histories with lottery competition in a stochastic environment: ESSs which do not prevail, Theor. Popul. Biol., 47, 191-211 (1995) · Zbl 0823.92016 [9] Lawler, L. R.; Smith, J. M., The coevolution and stability of competing species, Amer. Natur., 110, 79-99 (1976) [10] Lessard, S., Evolutionary stability: One concept, several meanings, Theor. Popul. Biol., 37, 159-170 (1990) · Zbl 0692.92016 [11] Ludwig, D.; Levin, S. A., Evolutionary stability of plant communities and the maintenance of multiple dispersal types, Theor. Popul. Biol., 40, 285-307 (1991) · Zbl 0737.92022 [12] Maynard Smith, J., Evolution and the Theory of Games (1982), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0526.90102 [13] Maynard Smith, J.; Price, G. R., The logic of animal conflict, Nature, 246, 15-18 (1973) · Zbl 1369.92134 [14] Maynard Smith, J.; Slatkin, M., The stability of predator-prey systems, Ecology, 54, 384-391 (1973) [15] McKelvey, R.; Apaloo, J., The structure and evolution of competition-organized ecological communities, Rocky Mountain J. Math., 25, 417-436 (1995) · Zbl 0857.92016 [16] Nowak, M., An evolutionary stable strategy may be inaccessible, J. Theor. Biol., 142, 237-241 (1990) [17] Reed, J.; Stenseth, N. C., On evolutionary stable strategies, J. Theor. Biol., 108, 491-508 (1984) [18] Roughgarden, J., Theory of Population Genetics and Evolutionary Ecology (1979), MacMillan: MacMillan New York [19] Roughgarden, J., The theory of coevolution, (Futuyma, D. J.; Slatkin, M., Coevolution (1983), Sinauer: Sinauer Sunderland), 33-64 [20] Roughgarden, J., Community coevolution: A comment, Evolution, 41, 1130-1134 (1987) [21] Rummel, J. D.; Roughgarden, J., A theory of faunal buildup for competition communities, Evolution, 39, 1009-1033 (1985) [22] Strobeck, C., \(N\), Ecology, 54, 650-654 (1973) [23] Taylor, P. D., Evolutionary stability in one-parameter models under weak selection, Theor. Popul. Biol., 36, 125-143 (1989) · Zbl 0684.92014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.