There's been a bit of talk about "Evolutionary Speed Limits" over at the Intelligent Design weblog Uncommon Descent. Most of the discussion involves "Haldane's Dilemma." This concept is rooted in an article written by the noted evolutionary geneticist J. B. S Haldane in 1957. There's a lot of math involved, and you can see it over at the Wikipedia page I linked above. The bottom line, for those not interested in the math, is this: according to Haldane's calculations, a species cannot reasonably fix beneficial mutations (a particular mutation becomes "fixed" when it is present in all of the population) at a rate any faster than 1 mutation per 300 generations.
A number of anti-evolutionists have taken this as evidence against evolution. If, they argue, genetic changes can only be fixed at a rate of 1 per 300 generations, how can evolution possibly explain the differences between species like humans and chimps, where not nearly enough generations have passed to account for the number of differences that we observe. There are a number of problems with using Haldane's calculations in this way, and in this post I'm going to look at one of those - the one that I think is the most important. For clarity, I should probably make sure that I am very explicit about what, exactly, the problem is before I start, so here it is:
Using Haldane's 1 substitution per 300 generations as a speed limit for all evolution is wrong because Haldane's calculations and concerns only apply under certain very specific circumstances.
Having just said that, I will now proceed to totally ignore Haldane, his dilemma, and his mathematics for most of the rest of the post. Instead of trying to look at equations, abstract concepts, and other confusing things, I'm going to use a set of very simple examples to show how a new mutation can spread through a population until it reaches a point when all other versions of that gene are gone.
These examples are necessarily going to be very much simplified. The population sizes will be very small and the effects of the mutations will be very large because I want the changes to be obvious very quickly. This is not because I want to trick you into thinking that evolution really moves really, really fast, or make things seem easier than they really are. The simplification has one purpose and one purpose only: it makes the math easy and the results clear.
Let's start with the basic scenario that is going to be used in these examples, and look at the hypothetical population as it exists before any mutant forms arise. The starting population will consist of ten individuals, each of whom is about to have ten children. The whole starting population will die right after reproducing (this is called "discrete generations," and it makes the math easier). The children will be mature in two years - if they live that long. Most won't. Only 20% will make it until the end of the first year, and only 50% of those who do will make it through the second.
Here's how this population changes from generation to generation:
|# of offspring||100||100||100||100||100|
|# at age 1||20||20||20||20||20|
|# at age 2||10||10||10||10||10|
It's easy to see in this example that the population size is absolutely constant from generation to generation. Now, let's look at what happens if we add a favorable mutation that works early on in the life history of this population. This mutation will arise in one individual in the new starting population, and will result in offspring having twice as much of a chance to make it through that first year - 40% will survive instead of 20%.
|# of offspring||standard||90||90||90||90||90|
|# at age 1||standard||18||18||18||18||18|
|# at age 2||standard||9||9||9||9||9|
In this example, the population as a whole is growing - at the start, there were 10 individuals (9 "normals" and 1 mutant), and at the end there were 41 (32 "mutants" and 9 "normals"). This means that the frequency of the mutant gene was becoming more common over time. At the start of the scenario, 10% of the population were mutants, and after 5 generations that number had climbed to 78%. At the same time, though, the numbers of "normal" individuals weren't changing much - there were still nine every generation. As long as no mechanism is in place to eliminate them from the population, the mutant gene will never become fully "fixed." The "normal" form will become very, very rare, but it will still be there. (By my calculations, after about 15 generations, less than 0.02% of the population will have the old "normal" form.)
So how do mutants become fixed, then? There are quite a few different ways, all of which work, but I'm just going to look at one of the possibilities. In that last scenario, the population was growing. We know that doesn't normally happen - most populations are relatively stable. So let's add one more assumption: no matter how many individuals make it to reproductive age, only 10 will reproduce, and those 10 will be randomly selected from those who get that far.
|# of offspring||standard||90||80||70||50||30|
|# at age 1||standard||18||16||14||10||6|
|# at age 2||standard||9||8||7||5||3|
I could continue to carry that out, but I think that's enough to show the trend. In this case, the population size stays the same. The gene frequencies change more slowly than they did in the last example, with the unlimited growth, but the trend is the same - the mutant increases in frequency while the standard form decreases. Here, unlike in the previous example, the numbers of "standard" individuals in the population also drop, and the "mutant" will become fixed fairly quickly.
Moving back to Haldane (finally), here are the important things that this example demonstrates:
- The change in gene frequencies changes (in both versions of the example) without any decrease in the overall population size.
- The changes in numbers of individuals for each of the two "versions" occur without any increase in the number of births per parent.
The first of those two points is important because Haldane was looking at the maximum practical rate of evolution in cases where the environment had changed, and only the "mutants" were able to survive (and/or reproduce) at the old rate. His 1 substitution per 300 generations was the maximum rate at which the substitution could proceed, under those circumstances, without the population size dropping so far that extinction would become very likely. This very specific situation is sometimes referred to as "hard selection." The situation I outlined does not take place in a changed environment, and does not result in any changes in population size. This is sometimes referred to as "soft selection," and in situations like this the rate of change can be much faster because there is no need to worry about the effects of a shrinking population.
The second point is important because some have claimed that reproduction places speed limits on evolution, and that any substitution requires more reproduction if it is to spread. As the scenario I outlined shows, substitutions can occur without the need for more births, as long as the selection is opertating in a way that makes survival to reproduction more likely.
A second, separate point that has been raised involves the question of how many mutations can be in the process of becoming fixed in a single population. The anti-evolution objections to the speed of evolution assume that only one mutation can be moving toward fixation at a time. This is incorrect, but this post has already run long enough, so I'll save that point for another post in a couple of days.