The origin of species may be almost as random as a throw of the dice, says Iosif Pinelis, a professor of mathematical sciences at Michigan Technological University, who claims to have worked out a mathematical solution to a biological puzzle: Why is the typical evolutionary tree so lopsided?

In other words, the reason some descendants of a parent species evolve into hundreds of different species  while others produce so few goes beyond natural selection  and into math; simple probability yields a surprisingly elegant solution, Pinelis says.

But in real life evolutionary trees are much more unbalanced than probability would predict.   Pinelis supposes that a significant number of species must change very slowly over time and says his hunch is borne out in reality: Biologists have long puzzled over species which are sometimes called "living fossils",  like the coelacanth, a species of fish first identified after being caught off the coast of Africa in 1938. Scientists believed it had gone extinct 80 million years earlier, but the discovery showed it had survived unchanged for over 340 million years.

In the fish evolutionary tree, the coelacanth branch is pretty straight. Other branches have thousands of limbs and twigs.

As an example, he lays out a scenario where you have a carp and a perch swimming in a pond and its equally likely that one of them will evolve a third species.  If a goldfish evolves from the common carp, you suddenly have three fish species in your pond.

Assume again that it is equally likely for the carp, the goldfish, and the perch to split into two distinct species. The chances that the carp branch will develop a new species are now double that of the perch branch, because the carp family now has two members.  And so it goes, until the pond is overrun with carp and their relatives.

"If one branch has more species, the chances are greater that it will speciate," Pinelis says. "The rich get richer; money goes to money."

Pinelis believes his model may have practical applications, such as better understanding and control of the evolution of various microorganisms, including viruses and bacteria, which have especially high rates of change.

Citation: Pinelis, Iosif, Evolutionary models of phylogenetic trees. Proceedings of the Royal Society, London, Ser. B, Vol. 270, 1425-1431