CSS, NIS and dynamic stability for two-species behavioral models with continuous trait spaces

Journal of Theoretical Biology

Volumn 262, Issue 1, 2010, Pages 80-89

  Cressman, Ross ^a  

^a WILFRID LAURIER UNIVERSITY   (Canada)

Author keywords

Adaptive dynamics; Canonical equation; Continuously stable strategy; Neighborhood invader strategy; Neighborhood superiority; Replicator equation

Indexed keywords

ADULT; ARTICLE; GAME; NEIGHBORHOOD; PSYCHOLOGICAL MODEL; ADAPTATION; ANIMAL; BEHAVIOR; COMPETITIVE BEHAVIOR; DEMOGRAPHY; ECOSYSTEM; EVOLUTION; PHYSIOLOGY; POPULATION DYNAMICS; POPULATION MIGRATION; SOCIAL DOMINANCE; SPECIES DIFFERENCE; THEORETICAL MODEL;

ADAPTATION, BIOLOGICAL; ANIMAL MIGRATION; ANIMALS; COMPETITIVE BEHAVIOR; DEMOGRAPHY; DOMINANCE-SUBORDINATION; ECOSYSTEM; EVOLUTION; GAME THEORY; MODELS, THEORETICAL; POPULATION DYNAMICS; SPATIAL BEHAVIOR; SPECIES SPECIFICITY;

MLCS; MLOWN;

EID: 76449112073     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2009.09.019     Document Type: Article

References (38)

1. Apaloo, J., Revisiting strategic models of evolution: the concept of neighborhood invader strategies. Theor. Popul. Biol. 52 (1997), 71–77.
2. Apaloo, J., Ecological species coevolution. J. Biol. Syst. 5 (1997), 17–34.
3. Apaloo, J., Muir, P.W., Hearne, J.W., Multi-species evolutionary dynamics. Evol. Ecol. 19 (2005), 55–77.
4. Bomze, I.M., Potscher, B.M., Game Theoretical Foundations of Evolutionary Stability. 1989, Springer, Berlin.
5. Brown, J.S., Vincent, T.L., Evolution of cooperation with shared costs and benefits. Proc. R. Soc. B 275 (2008), 1985–1994.
6. Christiansen, F.B., On conditions for evolutionary stability for a continuously varying character. Am. Nat. 138 (1991), 37–50.
7. Cressman, R., The Stability Concept of Evolutionary Game Theory: A Dynamic Approach. Lecture Notes in Biomathematics, 94, 1992, Springer, Berlin, 94.
8. Cressman, R., Frequency-dependent stability for two-species interactions. Theor. Popul. Biol. 49 (1996), 189–210.
9. Cressman, R., Evolutionary Dynamics and Extensive Form Games. 2003, MIT Press, Cambridge, MA.
10. Cressman, R., Stability of the replicator equation with continuous strategy space. Math. Soc. Sci. 50 (2005), 127–147.
11. Cressman, R., 2008. Learning and evolution in games: ESS. In: Durlauf, S.N., Blume, L.E., The New Palgrave Dictionary of Economics, vol. 5, second ed. Palgrave Macmillan, London, pp. 65–69.
12. Cressman, R., Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy spaces. Int. J. Game Theory 38 (2009), 221–247.
13. Cressman, R., Garay, J., Hofbauer, J., Evolutionary stability concepts for N-species frequency-dependent interactions. J. Theor. Biol. 211 (2001), 1–10.
14. Cressman, R., Hofbauer, J., Measure dynamics on a one-dimensional continuous strategy space: theoretical foundations for adaptive dynamics. Theor. Popul. Biol. 67 (2005), 47–59.
15. Cressman, R., Hofbauer, J., Riedel, F., Stability of the replicator equation for a single-species with a multi-dimensional continuous trait space. J. Theor. Biol. 239 (2006), 273–288.
16. Dieckmann, U., Law, R., The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 34 (1996), 579–612.
17. Doebeli, M., Dieckmann, U., Evolutionary branching and sympatric speciation caused by different types of ecological interactions. Am. Nat. 156 (2000), S77–S101.
18. Doebeli, M., Hauert, C., Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game. Ecol. Lett. 8 (2005), 748–766.
19. Eshel, I., Evolutionary and continuous stability. J. Theor. Biol. 103 (1983), 99–111.
20. Eshel, I., Sansone, E., Evolutionary and dynamic stability in continuous population games. J. Math. Biol. 46 (2003), 445–459.
21. Eshel, I., Motro, U., Sansone, E., Continuous stability and long-term convergence. J. Theor. Biol. 185 (1997), 333–343.
22. Garay, J., Adaptive dynamics based on ecological stability. Jorgensen, S., Quincampoix, M., Vincent, T.L., (eds.) Advances in Dynamic Game Theory, Annals of the International Society of Dynamic Games, vol. 9, 2007, Birkhäuser, Boston, MA, 271–286.
23. Heifetz, A., Shannon, C., Spiegel, Y., What to maximize if you must. J. Econ. Theory 133 (2007), 31–57.
24. Hofbauer, J., Sigmund, K., Evolutionary Games and Population Dynamics. 1998, Cambridge University Press, Cambridge.
25. Horn, R.A., Johnson, C.R., Topics in Matrix Analysis. 1991, Cambridge University Press, Cambridge.
26. Hoyle, A., Bowers, R.G., When is evolutionary branching in predator–prey systems possible with an explicit carrying capacity. Math. Biosci. 210 (2007), 1–16.
27. Impram, S.T., Johnson, R., Pavani, R., The D-stability problem for 4×4 real matrices. Arch. Math. 41 (2005), 439–450.
28. Leimar, O., The evolution of phenotypic polymorphisms: randomized strategies versus evolutionary branching. Am. Nat. 165 (2005), 669–681.
29. Leimar, O., Multidimensional convergence stability. Evol. Ecol. Res. 11 (2009), 191–208.
30. Lessard, S., Evolutionary stability: one concept, several meanings. Theor. Popul. Biol. 37 (1990), 159–170.
31. Marrow, P., Dieckmann, U., Law, R., Evolutionary dynamics of predator–prey systems: an ecological perspective. J. Math. Biol. 34 (1996), 556–578.
32. Maynard Smith, J., Evolution and the Theory of Games. 1982, Cambridge University Press, Cambridge.
33. Meszéna, G., Kisdi, É., Dieckmann, U., Geritz, S.A.H., Metz, J.A.J., Evolutionary optimisation models and matrix games in the unified perspective of adaptive dynamics. Selection 2 (2001), 193–210.
34. Oechssler, J., Riedel, F., Evolutionary dynamics on infinite strategy spaces. Econ. Theory 17 (2001), 141–162.
35. Oechssler, J., Riedel, F., On the dynamics foundation of evolutionary stability in continuous models. J. Econ. Theory 107 (2002), 223–252.
36. Weibull, J., Evolutionary Game Theory. 1995, MIT Press, Cambridge, MA.
37. Vincent, T.L., Brown, J.S., Evolutionary Game Theory, Natural Selection and Darwinian Dynamics. 2005, Cambridge University Press, Cambridge.
38. Zu, J., Wang, W., Takeuchi, Y., Zu, B., Wang, K., On evolution under symmetric and asymmetric competitions. J. Theor. Biol. 254 (2008), 239–251.