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WingLoss2003 - letters to nature being more tractable by...

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being more tractable by deterministically describing the dynamics of a population density n ( x , u ), these approximations are problematical. First, such continuum approximations are based on the limit of infinite local population sizes (local both in x and u ), which is even more difficult to justify biologically than the limit of infinite global population size, widely used in population ecology. Second, a conveniently simple reaction-diffusion approximation of this system, derived for small j m and j s , is dynamically unstable. Third, these approximations ignore the implications of reproductive (and other) pair correlations and local density fluctuations, both of which have been shown to critically affect ecological and evolutionary dynamics 30 . Fourth, the deterministic approximation blurs the sharp bifurcation boundary in Fig. 3a and is also inaccurate in predicting the boundary’s location. Fifth, extending the deterministic approximation to multilocus genetics is not feasible without incurring further unjustified assumptions. Received 12 July; accepted 18 October 2002; doi:10.1038/nature01274. 1. Mayr, E. Animal Species and Evolution (Harvard Univ. Press, Cambridge, Massachusetts, 1963). 2. Endler, J. A. Geographic Variation, Speciation, and Clines (Princeton Univ. Press, Princeton, New Jersey, 1977). 3. Coyne, J. A. Genetics and speciation. Nature 355, 511–515 (1992). 4. Felsenstein, J. Scepticism towards Santa Rosalia, or why are there so few kinds of animals. Evolution 35, 124–138 (1981). 5. Schliewen, U. K., Tautz, D. & Pa ¨a ¨bo, S. Sympatric speciation suggested by monophyly of crater lake cichlids. Nature 368, 629–632 (1994). 6. Schluter, D. Experimental evidence that competition promotes divergence in adaptive radiation. Science 266, 798–801 (1994). 7. Johannesson, K., Rola ´n-Alvarez, E. & Ekendahl, A. Incipient reproductive isolation between two sympatric morphs of the intertidal snail Littorina saxatilis . Evolution 49, 1180–1190 (1995). 8. Knox, E. B. & Palmer, J. D. Chloroplast DNA variation and the recent radiation of giant senecios (Asteraceae) on the tall mountains of Eastern Africa. Proc. Natl Acad. Sci. USA 92, 10349–10353 (1995). 9. Feder, J. L. Endless Forms (eds Howard, D. J. & Berlocher, S. H.) 130–144 (Oxford Univ. Press, Oxford, UK, 1998). 10. Rainey, P. B. & Travisano, M. Adaptive radiation in a heterogeneous environment. Nature 394, 69–72 (1998). 11. Gislason, D., Ferguson, M., Skulason, S. & Snorrason, S. S. Rapid and coupled phenotypic and genetic divergence in Icelandic Arctic char ( Salvelinus alpinus ). Can. J. Fish. Aquat. Sci. 56, 2229–2234 (1999). 12. Schliewen, U. K., Rassmann, K., Markmann, M., Markert, J. & Tautz, D. Genetic and ecological divergence of a monophyletic cichlid species pair under fully sympatric conditions in Lake Ejagham, Cameroon. Mol. Ecol. 10, 1471–1488 (2001). 13. Wilding, C. S., Butlin, R. K. & Grahame, J. Differential gene exchange between parapatric morphs of Littorina saxatilis detected using AFLP markers. J. Evol. Biol. 14, 611–618 (2001).
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