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Darwin's log: a toy model of speciation and extinction

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

David Aldous
David Aldous*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of Statistics, University of California, Berkeley, CA 94720, USA.
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Abstract

Stochastic models for the origin and extinction of species have been rather neglected in applied probability. As an alternative to modelling speciation and extinction as intrinsically random, I shall describe and show simulations of a rulebased model. This involves mathematical representations of notions such as genetic type of species, environmental niche, fitness of a species in a niche, and adaptation. There are underlying random mechanisms for changes of niche sizes and for disconnection and reconnection of geographical regions, and these ultimately drive the evolution of species.

Other approaches to mathematical modelling of evolution are briefly mentioned.

Keywords

EVOLUTIONSTOCHASTIC MODELFITNESS

MSC classification

Primary: 60K99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 279 - 295
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported by N.S.F. Grant DMS92-24857 and by the Miller Institute for Basic Research in Science.

Presented as the second Applied Probability Lecture in Sheffield, July 1993.

References

[1] Aldous, D. J. (1993) Probability distributions on cladograms. Unpublished.Google Scholar
[2] Cohen, J. E., Briand, F. and Newman, C. M. (1990) Community Food Webs. Biomathematics 20, Springer-Verlag, Berlin.Google Scholar
[3] Eldredge, N. and Cracraft, J. (1980) Phylogenic Patterns and the Evolutionary Process. Columbia University Press, New York.Google Scholar
[4] Gould, S. J. (1977) Ever Since Darwin: Reflections in Natural History. W. W. Norton, New York.Google Scholar
[5] Gould, S. J. (1989) Wonderful Life: The Burgess Shale and the Nature of History. W. W. Norton, New York.Google Scholar
[6] Gould, S. J., Raup, D. M., Sepkoski, J. J., Schopf, T. J. M. and Simberloff, D. S. (1977) The shape of evolution: a comparison of real and random clades. Paleobiology 3, 23–40.Google Scholar
[7] Guyer, C. and Slowinski, J. B. (1993) Adaptive radiation and the topology of large phylogenies. Evolution 47, 253–263.Google Scholar
[8] Heyde, C. C. (1985) On macroscopic stochastic modelling of systems subject to criticality. Math. Scientist 10, 3–8.Google Scholar
[9] Kauffman, S. A. (1993) The Origins of Order: Self Organization and Selection in Evolution. Oxford University Press, New York.Google Scholar
[10] Kingman, J. F. C. (1988) Typical polymorphisms maintained by selection at a single locus. In A Celebration of Applied Probability, ed. Gani, J., J. Appl. Prob. 25A, 113–125.Google Scholar
[11] Maddison, W. P. and Slatkin, M. (1991) Null models for the number of evolutionary steps in a character on a phylogenic tree. Evolution 45, 1184–1197.Google Scholar
[12] Plotnick, R. E. and Mckinney, M. L. (1993) Ecosystem organization and extinction dynamics. PALAIOS 8, 202–212.Google Scholar
[13] Raup, D. M. (1985) Mathematical models of cladogenesis. Paleobiology 11, 42–52.Google Scholar
[14] Raup, D. M. (1991) Extinction: Bad Genes or Bad Luck. W. W. Norton, New York.Google Scholar
[15] Raup, D. M., Gould, S. J., Schopf, T. J. M. and Simberloff, D. S. (1973) Stochastic models of phylogeny and the evolution of diversity. J. Geology 81, 525–542.Google Scholar
[16] Ray, T. S. (1994) Evolution, complexity, entropy, and artificial reality. Physica D 75, 239–263.Google Scholar
[17] Ray, T. S. (1994) An evolutionary approach to synthetic biology, Zen and the art of creating life. Artificial Life 1.Google Scholar