What Are The Chances? Mathematician Solves Evolutionary Mystery

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"* [cite omitted]: 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.

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.

We don't trouble ourselves that H2O is liquid only over a limited range of temperatures, but some get upset over the concept that evolutionary clocks can only be used to fill in gaps where other dating methods have supplied the range.

Doesn't upset me.
However, when I see unqualified claims made on the basis of evolutionary clock computations, then I am seeing sloppy writing and/or thinking that is ostensibly for the furtherance of science, but is actually a hindrance to clear scientific thinking.
That kind of garbage needs to be rooted out.

Sounds like some common sense math. It's a double-edged sword, however, for another evolutionary notion currently in vogue, that of evolutionary clocks.
Just as we don't accrue wealth at constant rates, living fossils demonstrate that species don't accumulate mutations at constant rates, genera don't accumulate species at constant rates, etc. Evolutionary clocks are not analogous to radiometric clocks. The observed fact of relative evolutionary stasis vs. that of evolutionary dynamism calls conclusions based on evolutionary clocks into doubt

Ah, but if you had been a regular reader of, ahem, Creation/Evolution: The Eternal Debate you'duv seen the news of the new study of fast-mutating genes, where they claim that fast-mutating genes actually create more accurate deep-time molecular clock readings than slow-mutating genes:

However, Hilu and his colleagues have come up with a new approach using rapidly evolving genes to understand deep-level relationships. Those genes mutate at higher rates than the slowly evolving genes. Although evolutionary biologists previously thought rapidly evolving genes would give a misleading picture of deep evolutionary history and were useful only in more recent evolutionary events such as evolution at the species and genus levels, Hilu has demonstrated that as few as 1,200 nuclear-type bases of a rapidly evolving gene such as matK, a gene in the chloroplasty genome, will give a tree of angiosperm that is far more robust than that obtained from 13,400 bases of several slowly evolving genes combined.
With this new approach, Hilu said, scientists will be able to sample many more species, and the process will be much more economical. "This does not mean slowly evolving genes are useless," Hilu said, "but a combination of the two could give us information at different evolutionary levels."
Hilu has found that the quality of the signal is better in rapidly evolving genes due to tendencies towards neutrality and lack of as many strong functional constraints as in slowly evolving genes. He also found that rapidly evolving genes provide more characters because they keep mutating more quickly. "Between the quality and the quantity, we were able to obtain more historical signals from rapidly evolving genes," he said.

If this finding holds up, it should resurrect the notion of the molecular clock as an accurate tool for discovering phylogenetic relationships, even ones that diverged hundreds of millions of years ago or more.

it's highly likely that any individual walk with be biased in one direction or the other. The totalitiy of walks is symmetric, however.

Rosencranz and Guildenstern have evolved.

Some imbalance seems intuitively right to me, if for no other reason than that some mutations might, by their nature, expose a species to environmental factors which will lead to more mutation, or expose different populations to diverse culling mechanisms. Other mutations might lead a species to an environment where there is less exposure to mutagenic phenomena, or where most mutations will be very disadvantageous, and quickly culled.

But there are many other reasons, and a perfect balance everywhere would be the odder occurence, in a system this large. Never getting heads twice in row would be very surprising in a series of a billion coin-flips.

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