Symmetry breaking and coarsening in spatially distributed evolutionary processes including sexual reproduction and disruptive selection

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 5, 2000, Pages 7065-7069

  Sayama, Hiroki ^a   Kaufman, Les ^a,b   Bar Yam, Yaneer ^a  

^a NEW ENGLAND COMPLEX SYSTEMS INSTITUTE   (United States)

^b Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; STATISTICAL METHODS;

EVOLUTIONARY PROCESSES; SEXUAL REPRODUCTION;

LARGE SCALE SYSTEMS;

ALLELE; BIOLOGICAL MODEL; ECOLOGY; EVOLUTION; FOURIER ANALYSIS; GENETIC SELECTION; GENETIC VARIABILITY; GENETICS; GENOME; REPRODUCTION;

ALLELES; BIOLOGICAL EVOLUTION; ECOLOGY; FOURIER ANALYSIS; GENETIC VARIATION; GENOME; MODELS, BIOLOGICAL; REPRODUCTION; SELECTION, GENETIC;

EID: 0034310662     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.7065     Document Type: Article

References (18)

1. Y. Bar-Yam, Dynamics of Complex Systems (Perseus Books, Reading, MA, 1997).
2. P. Higgs and B. Derrida, J. Phys. A 24, L985 (1991).
3. F. Bagnoli and M. Bezzi, Phys. Rev. Lett. 79, 3302 (1997). While the authors state that they are studying speciation, they are actually treating trait divergence of asexually reproducing organisms, rather than speciation, since they do not include sexual reproduction in their model.
4. B. Drossel and A. McKane, J. Theor. Biol. 204, 467 (2000).
5. A. S. Kondrashov, and F. A. Kondrashov, Nature (London) 400, 351 (1999).
6. U. Dieckmann and M. Doebeli, Nature (London) 400, 354 (1999).
7. M. Higashi, G. Takimoto, and N. Yamamura, Nature (London) 402, 523 (1999).
8. M. Eigen, J. McCaskill, and P. Schuster, Adv. Chem. Phys. 75, 149 (1989).
9. The evolutionary indivisibility of genes is also not necessarily well justified.
10. Y. Bar-Yam, Adv. Complex Syst. 2, 277 (1999).
11. R. Dawkins, The Selfish Gene, 2nd ed. (Oxford University Press, New York, 1989), p. 86.
12. For a collection of articles discussing the “levels of selection controversy” see Genes, Organisms, Populations: Controversies Over the Units of Selection, edited by R. N. Brandon and R. M. Burian (MIT Press, Cambridge, MA, 1984).
13. The general relationship between the mean-field approximation and the gene-centered view can be shown by considering a two-step process of reproduction and selection: (Formula presented) (Formula presented)where s is a particular genome and (Formula presented) are numbers of reproduced, selected organisms, respectively. Using a mean-field approximation for offspring, the probability of a particular genome s is the product of probabilities of the alleles (Formula presented) (Formula presented) This enables the two-step update equations to be written as a one-step update equation for each allele: (Formula presented)where (Formula presented) is the number of allele (Formula presented) For details see 10.
14. E. Sober and R. C. Lewontin, Philos. Sci. 49, 157 (1982).
15. Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions, edited by D. Tilman and P. Kariena (Princeton University Press, Princeton, NJ, 1997).
16. R. Durett and S. A. Levin, Philos. Trans. R. Soc. London, Ser. B 343, 329 (1994).
17. A. J. Bray, Adv. Phys. 43, 357 (1994).
18. G. B. Ermentrout and L. Edelstein-Keshet, J. Theor. Biol. 160, 97 (1993).