The many facets of evolutionary dynamics

Journal of Biological Systems

Volumn 5, Issue 3, 1997, Pages 325-339

  Diekmann, Odo ^a,b,c  

^a CWI   (Netherlands)

^b LEIDEN UNIVERSITY   (Netherlands)

^c UTRECHT UNIVERSITY   (Netherlands)

Author keywords

ESS (Evolutionarily Stable Strategy); Invader; Natural selection; Resident; Trait substitution sequence

Indexed keywords

EID: 0000040595     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339097000205     Document Type: Article

References (28)

1. Christiansen F. B., On conditions for evolutionary stability for a continuously varying character, Am. Nat. 138 (1997) pp. 37-50.
2. Doedel E. and Kernevez J., AUTO: software for continuation problems in ode with applications, Technical Report, CalTech, Applied Math. (1986).
3. Van Dooren T. and Metz J. A. J., Delayed maturation in structured semelparous populations with non-equilibrium dynamics (preprint).
4. Eshel I., Evolutionary and continuous stability, J. Theor. Biol. 103 (1983) pp. 99-111.
5. Eshel I., On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution, J. Math. Biol. 34 (1996) pp. 485-510.
6. Ferrière R. and Gatto M., Chaotic population dynamics can result from natural selection, Proc. Roy. Soc. Lond. B251 (1993) pp. 33-38.
7. Ferrière R. and Gatto M., Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations, Theor. Pop. Biol. 48 (1995) pp. 126-171.
8. Gatto M., The evolutionary optimality of oscillatory and chaotic dynamics in simple population models, Theor. Pop. Biol. 43 (1993) pp. 310-336.
9. Geritz S. A. H., Kisdi E., Meszéna G. and Metz J. A. J., Evolutionary singular strategies and the adaptive growth and branching of evolutionary trees (in preparation).
10. Hansson L., Levels of density variation: the adequacy of indices and chaos, Oikos 61 (1991) pp. 285-287.
11. Hammerstein P., Darwinian adaptation, population genetics and the streetcar theory of evolution, J. Math. Biol. 34 (1996) 511-532.
12. Hofbauer J. and Sigmund K., Adaptive dynamics and evolutionary stability, Appl. Math. Lett. 3 (1990) 75-79.
13. Kaitala V. and Getz W. M., Population dynamics and harvesting of semelparous species with phenotypic and genotypic variability in reproductive age, J. Math. Biol. 33 (1995) pp. 521-556.
14. Khibnik A., Kuznetsov Y., Levitin V. and Nikolaev E., Continuation techniques and interactive software for bifurcation analysis of ode and iterated maps, Physica D62 (1993) pp. 360-371.
15. Van der Laan J. D. and Hogeweg P., Predator-prey coevolution: interactions across different time-scales (preprint), Proc. Roy. Soc. Lond. B259 (1995) pp. 35-42.
16. Marrow P., Dieckmann U. and Law R., Evolutionary dynamics of predator-prey systems: an ecological perspective, J. Math. Biol. 34 (1996) pp. 556-578.
17. Matessi C. and Di Pasquale C., Long term evolution of multilocus traits, J. Math. Biol. 34 (1996) pp. 613-653.
18. Meszena G., personal communication.
19. Metz J. A. J., personal communication.
20. Metz J. A. J., Geritz S. A. H., Meszéna G., Jacobs F. J. A. and van Heerwaarden J. S., Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In Dynamical Systems and Their Applications, ed. by van Strien S. J. and Verduyn Lunel S. M. (North Holland, Elsevier, 1996) pp. 147-194.
21. Metz J. A. J., Geritz S. A. H. and Nisbet R. M., How should we define "fitness" for general ecological scenarios? Tree 7 (1992) 198-202.
22. Metz J. A., Mylius S. D. and Diekmann O., When does evolution optimize? (preprint).
23. Mylius S. D. and Diekmann O., On evolutionary stable life histories, optimization and the need to be specific about density dependence, Oikos 74 (1995) pp. 218-224.
24. Rand D. A., Wilson H. B. and McGlade J. M., Dynamics and evolution: evolutionarily stable attractors, invasion exponents and phenotypic dynamics, Phil. Trans. Roy. Soc. Lond. B343 (1994) pp. 261-283.
25. Roff D. A., The Evolution of Life Histories: Theory and Analysis (Chapman & Hall, New York, 1992).
26. Stearns S. C., The Evolution of Life Histories (Oxford Univ. Press, 1992).
27. Taylor, P. D., Evolutionary stability in one-parameter models under weak selection, Theor. Pop. Biol. 36 (1989) pp. 125-143.
28. Weissing F., Genetic versus phenotypic models of selection: can genetics be neglected in a long term perspective? J. Math. Biol. 34 (1996) pp. 533-555.