Tuesday, June 30, 2009

Mathematics and evolution

I've been doing some research on mathematics related to the effects of natural selection. I found one interesting web page at http://machineslikeus.com/Evolution-13%3A+Differential+rates+of+survival

"The way that even a very small natural selection advantage can result in that variety dominating a species can be appreciated using the more familiar example of compound interest. Suppose a parent gives each of two children $1,000 at the same time. One of the children invests in a bank that offers an interest rate of 5.0% while the other, being slightly more thrifty, shops around and invests in a different bank at 5.1%. Although they start out with the total money being split 50-50, in 7,000 years the second child (or rather that child's descendents) will have 99.9% of the total money, thanks to that very small advantage in the annual rate of return.

"It is exactly this kind of differential survival rate that plays such an important role in natural selection. Even minute differences in fitness can result, over the long term, in the runaway domination of a preferred variety. To see how fast this can happen, population geneticists have carried out calculations...

"The selection advantage is a measure of how much more likely it is that that particular variety will propagate itself in future generations when compared with the standard type. So if, on average, the new mutated variety produces 101 fertile adult descendents while the same number of the standard organism produces 100, then s=0.01.

"When this selection advantage is included in the calculation, the number of generations T it will take for a mutation to increase its frequency in the population from an initial value of f to a final value of F is given by the formula T=(1/s)ln[F(1-f)/f(1-F)], where 'ln' stands for the natural logarithm. (Molecular Evolution, Wen-Hsiung Li, 1997, p. 39)

"So if we start with a trait that is present in just 0.1% of the population (i.e., f=0.001), and if this has a small selection advantage of size s=0.01, this variety will grow to 99.9% (F=0.999) of the population in just under 1,400 generations, which is a very short time on the geological scale."


Obviously the math is fairly complicated. But this article does demonstrate how specific, SCIENTIFIC and even MATHEMATICAL evolutionary predictions can be.

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