One of the most common problems that laypeople have with evolution is that there doesn’t seem to have been enough time for it. Given the idea that evolution is relatively slow, and yet there’s been an enormous amount of change since the first species a few billion years ago, how could natural selection (and other processes like genetic drift) have built all these exquisite, functioning organisms?

Part of the answer, of course, is that people fail to appreciate “deep time,” since we’re evolved to regard life over years and decades, not millions and billions of years. Evolutionists often demonstrate this by compressing all of evolution into a calendar year, showing how much evolution has occurred in a short segment of that time. Using this analogy in WEIT, for example, I show that the divergence between the ancestors of humans and chimps would have occurred only at 6 a.m. on December 31.

Another difficulty is that people assume that if one species evolves into another by changing many traits, it seems highly unlikely that they can all change at the same time by simultaneous fixation of adaptive mutations. If evolutionary change of a species involves gene substitution at L genes (with L being a number), and the proportion of all genes in each generation that are more favored than the “primitive” type is 1/K (this number is low because most mutations are deleterious), then the number of “trials” it takes to get adaptive mutations at all the genes is on the order of KL . In other words, each generation new mutations arise, and if adaptive ones aren’t there for every gene required to make a descendant from an ancestor, then that whole trial is discarded and the process starts the next generation. Finally, after about KL generations have passed, you’ll get the right type.

But that can take a huge amount of time. If you want to change 20,000 genes, for example, with only 1/40 of all segregating mutational variants being advantageous, then it would take 1034,040 “trials” (roughly the time it takes for a new adaptive mutation to become fixed) to effect this change. This could never occur, since even with an organism having 100 generations per year and with a “trial” equivalent to one generation, this would take a number of years equal to 10 followed by 34,038 zeroes. (Since life began there’s only been about 3 followed by nine zeroes years.) That’s not long enough!

As you’ve probably already guessed, evolution doesn’t work this way. As evolutionary change is occurring at one gene, it’s simultaneously occurring at other genes, affecting other traits, if there are adaptive mutations in the populations for those traits too. A “trial” doesn’t involve producing variants at every gene, with evolution occurring only if all of the genes have adaptive variants. Rather, in each trial the new adaptive mutations arise and begin their march toward fixation in some genes, leaving the rest to change during subsequent trials. In other words, evolution occurs in parallel rather than in series.

How does that change the speed of evolution? This is the topic of a new paper in PNAS by Herbert Wilf and Warren Ewens, a paper with the endearing title given above, “There’s plenty of time for evolution.” (I don’t know of another scientific paper whose title contains a contraction.) The point of Wilf and Ewens’s paper is to show mathematically that simultaneous substitution is much much faster than “serial” substitution, so that substantial evolutionary change can take place relatively quickly. This isn’t a new point, but the equations are new, and they show, as the title says, that there has been plenty of time for lots of evolution to have taken place.

Wilf and Ewens simply invoke the fact that at each gene, the substitution process takes place independently, with new adaptive mutations retained at each. If letters represent adaption mutations at each position in a word, with a “word” representing the number of genes differentiating an descendant from its ancestor, they propose the correct model:

But a more appropriate model is the following: After guessing each of the letters, we are told which (if any) of the guessed letters are correct, and then those letters are retained. [JAC: you don’t start the process over each generation, since if the right adaptive mutation is around for some genes, you needn’t consider those genes any longer.] The second round of guessing is applied only for the incorrect letters that remain after this first round, and so forth. This procedure mimics the “in parallel” evolutionary process. The question concerns the statistics of the number of rounds needed to guess all of the letters of the word successfully.

Here’s their complicated equation for the number of rounds of “guessing”, that is the number of rounds it takes to achieve adaptive evolution at every one of L genes:

The mean number of rounds that are necessary to guess all of the letters of an L letter word, the letters coming from an alphabet of K letters, is [1] with β(L) being the periodic function of log L that is given by Eq. 7 below. The function β(L) oscillates within a range which for K≥2, is never larger than .000002 about the first two terms on the right-hand side of Eq. 7.

Let’s put some biological numbers to this. Let’s assume that we have to change 20,000 genes to get from an ancestor to a descendant. (That’s a LOT of genes, since the whole human genome is only a tad bigger than this.) And let’s assume that at each gene only 1/40 of all gene variants are adaptive. (We’re assuming that if the population has as few as one “adaptive” variant, that one will sweep through the population. That’s not strictly correct since some of these will get lost by genetic drift and never contribute to evolution.) The 1/40 figure comes from assuming a population has a million births each generation, that there are 20,000 genes, that each generation of new births carries about 5 million new mutations in the genome—about 250 per gene—and that only one new mutation in 10,000 will be favored over the “resident gene type” (The mutation data are taken from humans, and assume that only a small percentage of new mutations arise in regions of the genome that actually do something.)

Using the formula, Wilf and Ewens calculate that complete gene substitution at all 20,000 genes would take about 390 “rounds” of guessing.

That compares to 1034,040 rounds of guessing if you ask for all the genes to change in a single “round”.

The difference occurs because under parallel evolution the number of trials (or mutational rounds that must occur to cause evolution) enters as K(log L) rather than KL. The first number is much smaller when L is large.

Of course we already knew that evolution works in parallel, but what impresses me is the huge shortening of time that occurs under realistic assumptions. This is one step towards dispelling the idea that Darwinian evolution works too slowly to account for the diversity of life on Earth today, even given the 3.5-billion-year history of life.

We need more models like this, for the idea that things are too complex to have evolved during Earth’s history is surprisingly common. For another useful example, see the model by Nilsson and Pelger (1994) on how rapidly a complex eye can evolve from a primitive eyespot, given reasonable assumptions about mutation rate and adaptiveness. (Dawkins also has a piece in the 1994 Nature highlighting this result.)

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Wilf, H. S., and W. J. Ewens. 2010. There’s plenty of time for evolution. Proc Natl Acad Sci USA 107:22454-22456.

Nilsson, D.-E., and S. Pelger. 1994. A pessimistic estimate of the time required for an eye to evolve. Proc. Roy. Soc. Lond. B 256:53-58.

Dawkins, R. 1994. The eye in a twinkling. Nature 368:690-691.