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# What Are The Chances? Mathematician Solves Evolutionary Mystery

Date:
September 29, 2003
Source:
Michigan Technological University
Summary:
For the last two years, Iosif Pinelis, a professor of mathematical sciences at Michigan Technological University, has been working on a mathematical solution to a challenging biological puzzle first posed in the journal "Statistical Science"*: Why is the typical evolutionary tree so lopsided?
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The origin of species may be almost as random as a throw of the dice.

For the last two years, Iosif Pinelis, a professor of mathematical sciences at Michigan Technological University, has been working on a mathematical solution to a challenging biological puzzle first posed in the journal "Statistical Science"*: Why is the typical evolutionary tree so lopsided?

In other words, why do some descendants of a parent species evolve hundreds of different species, while others produce so few they seem to be practicing family planning?

To a certain extent, the answer lies in simple probability, says Pinelis. Say you have two species of fish swimming in a pond, the carp and the perch, and it might be equally likely that one of them will evolve a third species. Say the goldfish evolves from the common carp, and suddenly you 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 may go, until the pond is overrun with carp and their descendant species.

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

In real life, evolutionary trees are even more unbalanced than simple probability would predict. To explain this, Pinelis supposed that there must exist a significant number of species that change very slowly over time. His supposition is borne out in reality: Biologists have long puzzled over such species, which are sometimes called "living fossils."

A typical example of the living-fossil phenomenon is the coelacanth, a species of fish first identified by scientists after being caught in deep water off the coast of Africa in 1938. Scientists had believed it had gone extinct 80 million years earlier, but the discovery showed the unusual fish instead 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, branches and twigs.

"In the beginning, I just speculated that such species existed, and that they are what cause many evolutionary trees to be so unbalanced," he said. "I'd practically finished the model when I discovered about 150 papers by biologists for whom the existence of such living fossils was a given; they were only trying to explain this phenomenon.

"That was a pleasant surprise."

Pinelis had originally intended to publish his findings in a mathematics journal, but then decided to submit it to the scrutiny of specialists in another field, biology. His model is described in an article recently published in the Proceedings of the Royal Society, Series B.

So far, the reaction has been mixed. Some biologists are skeptical; others have expressed "great interest." However, Pinelis says, his model holds up under rigorous analysis and 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.

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* Aldous, David J., Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. (English. English summary) Statistical Science Vol. 16 (2001), no. 1, 23-34.

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The above post is reprinted from materials provided by Michigan Technological University. Note: Materials may be edited for content and length.