ScienceDaily (Apr. 25, 2010) — UBC researchers have proffered a new mathematical model that seeks to unravel a key evolutionary riddle--namely what factors underlie the generation of biological diversity both within and between species.
Evolutionary biologists have long recognized that the emergence of rare traits within a population can spur diversity. For example, being one of a few under-sized predators in a population dominated by larger-sized predators can offer advantages--access to an abundance of small prey--and increase the likelihood of that trait prospering in the population.
"But existing mathematical models that incorporate these 'rare type' advantages tend to have some serious shortcomings," says Michael Doebeli, a researcher at UBC's Biodiversity Research Centre and professor with the departments of Mathematics and Zoology. "They rely on single traits--like body size--and predict that the advantage offered by that trait has to be very significant in order to maintain large amounts of diversity."
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Science 23 April 2010:
Vol. 328. no. 5977, pp. 494 - 497
Complexity and DiversityMichael Doebeli* and Iaroslav Ispolatov*
The mechanisms for the origin and maintenance of biological diversity are not fully understood. It is known that frequency-dependent selection, generating advantages for rare types, can maintain genetic variation and lead to speciation, but in models with simple phenotypes (that is, low-dimensional phenotype spaces), frequency dependence needs to be strong to generate diversity. However, we show that if the ecological properties of an organism are determined by multiple traits with complex interactions, the conditions needed for frequency-dependent selection to generate diversity are relaxed to the point where they are easily satisfied in high-dimensional phenotype spaces. Mathematically, this phenomenon is reflected in properties of eigenvalues of quadratic forms. Because all living organisms have at least hundreds of phenotypes, this casts the potential importance of frequency dependence for the origin and maintenance of diversity in a new light.
Department of Zoology and Department of Mathematics, University of British Columbia, 6270 University Boulevard, Vancouver, BC V6T 1Z4, Canada.
* To whom correspondence should be addressed. E-mail: firstname.lastname@example.org (M.D.); email@example.com (I.I.)
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