What Are The Chances? Mathematician Solves Evolutionary Mystery

NewsWise ^ | 26 September 2003 | Staff

[PatrickHenry]

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"* [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.

"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.

[PatrickHenry]

* Footnote in original article. Bold font added by me.

Everybody be nice.

[PatrickHenry]

PING. [This ping list is for the evolution side of evolution threads, and sometimes for other science topics. FReepmail me to be added or dropped.]

[woofer]

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

Like, say, some family trees in Arkansas that resemble telephone poles?

[Egon]

"The rich get richer; money goes to money."

So, artificial wealth re-distribution would be...unnatural?

[woofer]

So, artificial wealth re-distribution would be...unnatural?

At least, according to the article, it would be against a couple of laws.

Specifically:
The Laws of Nature
The Law of Evolutionary Speciation.

[WhiteGuy]

So...................

The answer was 42?


Seriously, who pays these people?

[Ichneumon]

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.

A common misperception, but still wrong. The coelacanth has *not* survived "unchanged". Modern coelacanths are significantly changed from the 340-million-year-old ancestral version, to the point where they are assigned not only to different species, but even to a different genus altogether.

They're still recognizably in the same family, though, which is considerably less evolutionary change than, say, a modern pelican compared to its ancestral therapsid dinosaur over the same timespan, but the point remains that the coelacanth is not actually "unchanged", and its evolution did not somehow "stop" during the last 300+ million years.

And varying amounts of evolutionary change in different lineages is no challenge to "darwinism", as some like to claim, since Darwin himself predicted this effect in his "Origin of Species" book back in 1859.

[Taliesan]

Seriously, who pays these people?

You do.

[Stultis]

had survived unchanged

That always bother me too. Thanks for clarifying. Also it should be noted (I *think* I'm correct here) that our fossil lobe-fins are all shallow water species, whereas the living coelacanth is a deep water fish.

[WhiteGuy]

Seriously, who pays these people?

You do.


I HATE THAT ANSWER!!!!!!!!!

Could I be excused from paying for a while please????

(The answer WAS 42 right?)

[Sabertooth]

"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.

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

[Sabertooth]

That always bother me too. Thanks for clarifying. Also it should be noted (I *think* I'm correct here) that our fossil lobe-fins are all shallow water species, whereas the living coelacanth is a deep water fish.

Lungfish are shallow-water, lobe-finned fish.

Bichirs are another shallow-water fish, though their disposition as lobe-finned or ray-finned has been up in the air.

The following article utilizes mitochondrial sequencing to propose the latter...

Second, our markers demonstrate that the extant tetrapods are monophyletic and lungfishes are the closest living relatives of tetrapods as proposed in phylogenetic model 1a (Fig. 1). The extant tetrapods can be divided into two groups: amphibians and amniotes, with amphibians represented by three living orders, Anura (frogs), Caudata (salamanders), and Gymnophiona (caecilians), and the amniotes, including reptiles, birds, and mammals. Although a large number of morphological characters supports a monophyletic status of these tetrapods (1, 2), some systematists have argued a diphyletic origin of tetrapods, suggesting that salamanders and newts arose from a lobe-finned fish lineage different from that which led to frogs and other tetrapods (17, 18). Furthermore, it has not been possible so far to resolve the phylogenetic position of tetrapods in relation to the extant lobe-finned fishes, the lungfish and the coelacanth (3-6). Our synapomorphies confirm the monophyletic status of the living tetrapods and provide evidence for a sister-group relationship between the living lungfishes and tetrapods.

Third, the markers cloned by us resolve the phylogenetic position of bichirs, a group of freshwater fishes endemic to Africa. The classification of bichirs has been problematic, as they display a mixture of ancestral and derived characters and share many characters with both lobe-finned fishes and ray-finned fishes (2). For example, they possess paired fins with fleshy bases and lungs that arise from the ventral side of the digestive tract, similar to the anatomy of lobe-finned fishes, but ganoid rhombic scales and a single elongated dorsal fin that is directly inserted into the body, as in ray-finned fishes (2). Phylogenetic analysis of the complete mitochondrial sequence of bichirs was also unable to determine whether they are ray-finned fishes or lobe-finned fishes (19). Based on the phylogenetic distribution of some nuclear introns, we had shown that bichirs lie outside the clade comprising (sturgeon + gar + bowfin + Teleostei) but did not resolve whether bichirs are within the ray-finned fish lineage or lobe-finned fish lineage (13). The additional data presented here clearly demonstrate that bichirs are in the ray-finned fish lineage basal to all other living ray-finned fishes. Thus bichirs occupy an important position in the ray-finned fish lineage and are a useful model for understanding the evolution, development, and physiology of the diverse ray-finned fishes.
Molecular synapomorphies resolve evolutionary relationships of extant jawed vertebrates
Byrappa Venkatesh, Mark V. Erdmann, and Sydney Brenner
Proceedings of the National Acadamy of Sciences - September 25th, 2001

[Doctor Stochastic]

I read the Statistical Science article several years ago. I'll try to find the Proceedings of the Royal Society this week. (There is more than one Royal Society.)

[Taliesan]

It's not the math and science my tax dollars support, by and large, that bothers me. It's the liberal arts. As I sit here, the government is paying lots of people to think about things like gender symbols in 12th century tapestries.

Don't get me wrong; I read about this sort of thing myself. Because I love it. I don't think you ought to pay me to do it.

[Doctor Stochastic]

I guess not. I only have access to those issues 5 or more years old.

[PatrickHenry]

I did a Google search on the author's name, found a wee bit, but not the article.

[Doctor Stochastic]

PubMed does have an abstract:
The most widely used evolutionary model for phylogenetic trees is the equal-rates Markov (ERM) model. A problem is that the ERM model predicts less imbalance than observed for trees inferred from real data; in fact, the observed imbalance tends to fall between the values predicted by the ERM model and those predicted by the proportional-to-distinguishable-arrangements (PDA) model. Here, a continuous multi-rate (MR) family of evolutionary models is presented which contains entire subfamilies corresponding to both the PDA and ERM models. Furthermore, this MR family covers an entire range from 'completely balanced' to 'completely unbalanced' models. In particular, the MR family contains other known evolutionary models. The MR family is very versatile and virtually free of assumptions on the character of evolution; yet it is highly susceptible to rigorous analyses. In particular, such analyses help to uncover adaptability, quasi-stabilization and prolonged stasis as major possible causes of the imbalance. However, the MR model is functionally simple and requires only three parameters to reproduce the observed imbalance.

Asymmetry in the branches shouldn't be too unexpected. In a simple random walk in 1-d (moving left or right with equal probability), it's highly likely that any individual walk with be biased in one direction or the other. The totalitiy of walks is symmetric, however. The same thing should happen with trees.

[Dementon]

The answer WAS 42 right?

It always is...

[longshadow]

IF I understand this article correctly, it sounds like it could be summarized as saying: "the species that branches first, branches more often."

Or, it is as if with every speciation event, the branches each receive a lottery ticket; the more branches, the more lottery tickets in your family. The more tickets, the greater the odds that your family will frequently win the lottery.

Or, to but it another way, the more branches a given parent species has, the higher the probability that that some of it's branches will have favorable mutations, whereas the parent species that doesn't branch as much will have fewer chances of producing favorable mutations.

This reminds me of the phenomona of self-exciting systems. It's a form of positive feedback that reinforces the initial process (speciation).

[js1138]

Evolutionary clocks, like many phenomena, are useful only over a limited range of conditions. 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.