What are the Chances? Probability Solves an Evolutionary Puzzle

Jan 30, 2009

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

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

Natural selection may provide some answers, but simple probability yields a surprisingly elegant solution. Pinelis explains: Say you have a carp and a perch swimming in a pond and its equally likely that one of them will evolve a third species. Say the goldfish evolves from the common carp. 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 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."

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

One of these is 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.

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.

Michigan Technological University is a leading public research university, conducting research, developing new technologies and preparing students to create the future for a prosperous and sustainable world. Michigan Tech offers more than 120 undergraduate and graduate degree programs in engineering, forestry and environmental sciences, computing, technology, business and economics, natural and physical sciences, arts, humanities and social sciences.

Reference: Pinelis, et al. Evolutionary models of phylogenetic trees. Proceedings of the Royal Society B, Vol. 270, 1425-1431.

Provided by Michigan Technological University

Explore further: When vaccines are imperfect: What math can tell us about their effects on disease propagation

add to favorites email to friend print save as pdf

Related Stories

Genetic evidence clears Ben Franklin (w/ Video)

Jul 29, 2011

The DNA evidence is in, and Ben Franklin didn't do it. Genetic tests on more than 1,000 Chinese tallow trees from the United States and China show the famed U.S. statesman did not import the tallow trees ...

Size of lunch dictates force of crunch (w/ Video)

Feb 12, 2013

Many animals prefer food—snails, nuts, etc.—that must be cracked and crushed. Scientists have measured the maximum force of their impressive bites before, but a new study introduces a significant subtlety: bite force ...

Smallest eel-loach fish discovered

Feb 08, 2010

(PhysOrg.com) -- The world's smallest species of eel-loach fish has been discovered by a Natural History Museum scientist and his colleague this month and is featured on the Museum's Species of the day today.

Dracula minnow has teeth, almost

Mar 11, 2009

A new species of tiny fish with jaw structures that look like huge teeth has been identified, Natural History Museum scientists report in the Proceedings of the Royal Society journal today.

Recommended for you

Tracking Chinese aid to Africa

2 hours ago

Is a fancy new school in an African government official's hometown a coincidence, or evidence of systematic favouritism in the distribution of aid?

User comments : 7

Adjust slider to filter visible comments by rank

Display comments: newest first

not rated yet Jan 30, 2009
Add the higher probability of fertile crossbreeding in the two related carp species then you have an even higher rate of species creation on the carp branch.
1 / 5 (5) Jan 31, 2009
Two problems:
1) Have evolutionary trees been found in nature or are they artificial constructions?
2) Has anyone ever observed the origination of a new species in nature?
3) What is the use of this mathematical theory in the context of the evolution theory?
not rated yet Jan 31, 2009
1. yes, evolutionary trees can be easily seen in nature all around us, or go back 40,000 years and meet our cousin species the neanderthal....or go see the frog species in south america that is the same species, yet some can glide, others can climb, etc....
2. see answer 1..we do it all the time...hell look at viruses as teh best example there...
3. i tend to agree, an algorithm based off of probability always has the probability it too will be wrong.
5 / 5 (1) Jan 31, 2009
This analysis seems flawed. If there are two species A and B then A evolves a third species C there are several outcomes. At the time evolution occurs there will be 50% A and B with a small population of C. The species C competes with A and B. It can be better, equal or worse. If the rate of mutation is lower than the time it takes for population to reach equilibrium then we will see:

1) A large population of C and equal but smaller populations of A and B

2) Equal populations of A, B and C.

3) A small population of C and equal populations of A and B.

In all three cases there are more relatives of A than there are of B. This is the conclusion that the authors seem to draw.

However, all bets are off if the mutation rate is equal or higher than the time it takes population to reach equilibrium. In this case a species D, evolved from B, evolves before the population reaches equilibrium. There is then a chance that D is better than A and B or even better than A, B or C. Population C then dominates an there are more relatives of B than A even though A evolved first. Mix in the fact that A may or may not interbreed with C and B may or may not interbreed with D. The situation becomes very complex rapidly.

So, I think this analysis is oversimplified and therefore flawed
not rated yet Jan 31, 2009
Agree with daqman.

The article seems to present evolution in terms similar to those I learned in grammar school. Something seems wrong with (this account of) the research, e.g., I don't see that coelacanth is explained at all. How could an animal remain the same over millions of years, with "everything" else changing around it? Sounds more like a broken mechanism...hmmm...now there's a interesting theory.
not rated yet Feb 01, 2009
I can't find fault with the researcher's argument, providing you accept his unrealistic assumption that each species has an equal chance of developing a new species.
However, it's not only the coleanth which defies this assumption. I bet that all species will, providing the environment is conducive enough. Think of Darwin's finches and Lake Victoria's cichlids as exceptions which will increase the 'rich get richer' effect that the article outlines.
It's the changing environment which adds to this effect, on top of the statistical probabilities. How much radiation of species there will be will depend to a large extent on how much the environment allows. In the relative stability of the deep oceans the coleanth doesn't evolve new species. In the case of fast varying environments like new islands it'll be those mobile species like birds that will radiate.
There also possibly seems to be a newly discovered snowballing effect, as hinted at in
Here an increase in speciation seems to cause an increase in the rate of gene variation, which one would expect to up the rate speciation by another gear.
not rated yet Mar 31, 2009
I agree with the comments that this analysis seems oversimplified and that environmental factors must be considered in evolution. For a counterargument I offer another sea-dwelling creature, the shark. While having a larger family tree than the coelacanth these organisms have remained largely unchanged for 100 million years. The reason why can be understood from a look at some of their physiological traits. They can smell trace amounts of blood from miles away. They have a sensory organ (ampullae of lorenzini) which can detect the electric impulse of a heartbeat. Their immune systems are virtually impervious to disease and can fight off malignant cancer. In effect sharks are such successful predators that they have reached a an evolutionary local minima. Their success makes them very insensitive to small changes in their environment. The type of systemic and potentially catastrophic environmental factors that are required to knock them out of their local minima are statistically very rare so their evolution slows down, even though before their current state they might have been (and probably were) highly adaptive organisms.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.