Mathematicians Offer Elegant Solution to Evolutionary Conundrum
|Building on classical competition models for single traits, Michael Doebeli has designed a mathematical theory to gauge the evolutionary impact of multiple traits in concert.
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 the University of British Columbia (UBC) 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.”
So Doebeli and research associate Iaroslav Ispolatov applied a new model to the riddle, which they outline in Science. Building on classical competition models for single traits, they designed their mathematical theory to gauge the evolutionary impact of multiple traits in concert, and found that adding this layer of complexity significantly lowered the threshold for the maintenance of diversity and the evolution of new species.
“When you model one trait at a time — in isolation — you often find that ecological interactions aren’t strong enough to drive divergence. But, with many traits acting in concert, even very weak interactions can generate diversity. Our approach mirrors the complexity of reality more closely — if you think about it, all living organisms have at least dozens, if not hundreds, of ecologically relevant traits,” says Doebeli.
Mathematically, the biological phenomenon is reflected in fundamental properties of eigenvalues of quadratic forms. The theory would help explain the extraordinary amount of diversity found in many ecosystems, for example, in the microbial world of oceans. In fact, the initial proving ground for the model might well be microbial populations.
“It would be interesting to test whether, at the genetic level, pathways controlling different traits are regulated in concert to enable the inheritability of diversifying traits along multiple phenotypic axes,” Doebeli says.