Multidimensional convergence stability

Evolutionary Ecology Research

Volumn 11, Issue 2, 2009, Pages 191-208

  Leimar, Olof ^a  

^a STOCKHOLM UNIVERSITY   (Sweden)

Author keywords

Adaptive dynamics; Canonical equation; Evolutionary stability; Genetic correlations

Indexed keywords

EID: 67650707048     PISSN: 15220613     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. Abrams, P.A., Matsuda, H. and Harada, Y. 1993. Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol., 7: 465-487. (Pubitemid 24414429)
2. Brown, J.S., Cohen, Y. and Vincent, T.L. 2007. Adaptive dynamics with vector-valued strategies. Evol. Ecol. Res., 9: 719-756. (Pubitemid 47122675)
3. Charnov, E.L. 1982. The Theory of Sex Allocation. Princeton, NJ: Princeton University Press
4. Christiansen, F.B. 1991. On conditions for evolutionary stability for a continuously varying character. Am. Nat., 138: 37-50.
5. Cressman, R. and Hines, W.G.S. 1984. Correction to the appendix of 'three characterizations of population strategy stability'. J. Appl. Prob., 21: 213-214.
6. Cressman, R., Hofbauer, J. and Riedel, F. 2006. Stability of the replicator equation for a single species with a multi-dimensional continuous trait space. J. Theor. Biol., 239: 273-288. (Pubitemid 43319566)
7. Dercole, F. and Rinaldi, S. 2008. Analysis of Evolutionary Processes: The Adaptive Dynamics Approach and its Applications. Princeton, NJ: Princeton University Press.
8. Dieckmann, U. and Law, R. 1996. The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol., 34: 579-612. (Pubitemid 126768843)
9. Dieckmann, U., Heino, M. and Parvinen, K. 2006. The adaptive dynamics of function-valued traits. J. Theor. Biol., 241: 370-389. (Pubitemid 43993967)
10. Durinx, M., Metz, J.A.J. and Meszéna, G. 2008. Adaptive dynamics for physiologically structured population models. J. Math. Biol., 56: 673-742. (Pubitemid 351177980)
11. Eshel, I. 1983. Evolutionary and continuous stability. J. Theor. Biol., 103: 99-111
12. Eshel, I. and Motro, U. 1981. Kin selection and strong evolutionary stability of mutual help. Theor. Pop. Biol., 19: 420-433.
13. Eshel, I., Motro, U. and Sansone, E. 1997. Continuous stability and evolutionary convergence. J. Theor. Biol., 185: 333-343. (Pubitemid 27192503)
14. Ferriere, R. and Gatto, M. 1995. Lyapunov exponents and the mathematics of invasions in oscillatory or chaotic populations. Theor. Pop. Biol., 48: 126-171. (Pubitemid 26454082)
15. Geritz, S.A.H. 2005. Resident-invader dynamics and the coexistence of similar strategies. J. Math. Biol., 50: 67-82. (Pubitemid 40240754)
16. Geritz, S.A.H., Kisdi, É., Meszéna, G. and Metz, J.A.J. 1998. Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol., 12: 35-57. (Pubitemid 28139607)
17. Geritz, S.A.H., Gyllenberg, M., Jacobs, F.J.A. and Parvinen, K. 2002. Invasion dynamics and attractor inheritance. J. Math. Biol., 44: 548-560. (Pubitemid 44200118)
18. Hammerstein, P. 1996. Darwinian adaptation, population genetics and the streetcar theory of evolution. J. Math. Biol., 34: 511-532. (Pubitemid 126768840)
19. Hammerstein, P. and Selten, R. 1994. Game theory and evolutionary biology. In Handbook of Game Theory, Vol.2 (R.J. Aumann and S. Hart, eds.), pp. 929-993. Amsterdam: Elsevier Science.
20. Hines, W.G.S. 1980. Three characterizations of population strategy stability. J. Appl. Prob., 17: 333-340.
21. Iwasa, Y., Pomiankowski, A. and Nee, S. 1991. The evolution of costly mate preferences II: The handicap principle. Evolution, 45: 1431-1442.
22. Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to the brain: body size allometry. Evolution, 33: 402-416.
23. Lande, R. 1981. Models of speciation by selection on polygenic traits. Proc. Natl. Acad. Sci. USA, 78: 3721-3725. (Pubitemid 11060449)
24. Leimar, O. 2001. Evolutionary change and Darwinian demons. Selection, 2: 65-72
25. Leimar, O. 2005. The evolution of phenotypic polymorphism: randomized strategies versus evolutionary branching. Am. Nat., 165: 669-681. (Pubitemid 40748344)
26. Leimar, O., Van Dooren, T.J.M. and Hammerstein, P. 2004. Adaptation and constraint in the evolution of environmental sex determination. J. Theor. Biol., 227: 561-570. (Pubitemid 38376172)
27. Lessard, S. 1990. Evolutionary stability: one concept, several meanings. Theor. Pop. Biol., 37: 159-170.
28. Marrow, P., Dieckmann, U. and Law, R. 1996a. Evolutionary dynamics of predator-prey systems: an ecological perspective. J. Math. Biol., 34: 556-578.
29. Marrow, P., Johnstone, R.A. and Hurst, L.D. 1996b. Riding the evolutionary streetcar: where population genetics and game theory meet. Trends Ecol. Evol., 11: 445-446.
30. Matessi, C. and Di Pasquale, C. 1996. Long-term evolution of multilocus traits. J. Math. Biol., 34: 613-653. (Pubitemid 126768844)
31. Meszéna, G., Kisdi, É., Dieckmann, U., Geritz, S.A.H. and Metz, J.A.J. 2001. Evolutionary optimisation models and matrix games in the unified perspective of adaptive dynamics. Selection, 2: 193-210.
32. Metz, J.A.J., Nisbet, R.M. and Geritz, S.A.H. 1992. How should we define 'fitness' for general ecological scenarios? Trends Ecol. Evol., 7: 198-202. (Pubitemid 23397213)
33. Metz, J.A.J., Geritz, S.A.H., Meszéna, G., Jacobs, F.J.A. and van Heerwaarden, J.S. 1996. Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In Stochastic and Spatial Structures of Dynamical Systems (S.J. van Strien and S.M. Verduyn Lunel, eds.), pp. 183-231. Amsterdam: North-Holland.
34. Metz, J.A.J., Mylius, S.D. and Diekmann, O. 2008. When does evolution optimize? Evol. Ecol. Res., 10: 629-654.
35. Motro, U. 1994. Evolutionary and continuous stability in asymmetric games with continuous strategy sets: the parental investment game as an example. Am. Nat., 144: 229-241. (Pubitemid 2130636)
36. Pomiankowski, A., Iwasa, Y. and Nee, S. 1991. The evolution of costly mate preferences I: Fisher and biased mutations. Evolution, 45: 1422-1430.
37. Taylor, P.D. 1989. Evolutionary stability in one-parameter models under weak selection. Theor. Pop. Biol., 36: 125-143.
38. Van Dooren, T.J.M. and Leimar, O. 2003. The evolution of environmental and genetic sex determination in fluctuating environments. Evolution, 57: 2667-2677. (Pubitemid 38078350)
39. Weissing, F.J. 1996. Genetic versus phenotypic models of selection: can genetics be neglected in a long-term perspective? J. Math. Biol., 34: 533-555. (Pubitemid 126768841)