Math in the News
Mathematicians Offer Solution to Evolution Mystery
April 23, 2010
Determining what factors underlie biological diversity within and among species is one of the biggest riddles of evolution. Mathematicians at the University of British Columbia (UBC) offer a mathematical model to unravel the mystery.
Building on classical competition models dealing with single traits, UBC mathematicians Michael Doebeli and Iaroslav Ispolatov designed an approach to gauge the evolutionary impact of multiple traits. The theory would help explain the extraordinary amount of diversity found in many ecosystems.
Mathematically, the biological phenomenon is reflected in fundamental properties of eigenvalues of quadratic forms.
“When you model one trait at a time—in isolation—you often find that ecological interactions aren’t strong enough to drive divergence," Doebeli said. "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.”
Adding a layer of complexity lowered the threshold for the maintenance of diversity and the evolution of new species. The initial proving ground for the model could be the arena of 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 said.
Their findings are outlined in Science (April 23, 2010).