[This is a reply to a message on this topic that Fred accidentally posted in the Fred Williams' Mutation Rate Article Obsolete thread at Message 27.]
Hi Fred,
When I didn't see a reply from Rei yesterday I started composing my own, but went to bed before I finished. This morning I see Rei has posted a reply, and it says pretty much what I would have said only better, so I'll just post this as it is. This *does* have some very useful additional information, probably worth reading, but that's my opinion. Enjoy!
--Percy
Hi Fred,
First, nice job noticing that bug where the percentages don't add up. That I didn't notice that bug myself really puzzled me, so I went back to the code and saw that I never bothered to check this because Rei had included a check right in the code:
if (fabs(MUT_PERCENT_MINUS_90 + MUT_PERCENT_MINUS_50 + MUT_PERCENT_MINUS_20 +
MUT_PERCENT_MINUS_10 + MUT_PERCENT_MINUS_5 + MUT_PERCENT_MINUS_1 +
MUT_PERCENT_NOCHANGE + MUT_PERCENT_PLUS_1 + MUT_PERCENT_PLUS_2 +
MUT_PERCENT_PLUS_5 + MUT_PERCENT_PLUS_10 - 100.0) < 0.0001)
{
printf("Error: Mutation rates aren't sufficiently close to 100%.\n");
return 1;
}
So I figured she had it covered and never bothered to check. So why isn't this code detecting the problem? Especially since this checking code itself has a bug because
MUT_PERCENT_MINUS_2 isn't included, so instead of being just 4% short of 100% it's 10% short?
The answer is that the direction of comparison is wrong - she should be using ">" instead of "<". Correcting these problems and running again the program produces the same results but with overall fitness increasing at a slower rate.
So now that we've got that little bug out of the way, let's move on to address your specific criticisms.
So let’s consider your example (aka fantasyland), that produces an increasing fitness average across the population. Well, for starters you selected a beneficial mutation rate of 1 out of every 12 (8%)!!! A whopping 1 out of 25 have a 10% advantage! No wonder your program succeeded!
How you could find that bug while ignoring the significance of Rei's way high deleterious rates, all the way up to 90% while the favorable rate is 10% max, is beyond me. Perhaps you're using a biased selection mechanism, Fred? Beyond that, the program's harmful mutation rate is a whopping 42%. The likelihood of a harmful mutation is 10.5 times more likely than a beneficial mutation. But let's try an even lower beneficial mutation rate and see what happens. Setting it to 1% (I set the beneficial rates to .4, .3, .2 and .1, and I added the remainder to the neutral mutation rate) so that the harmful mutation rate is 42 times greater we find...THE SAME THING. Fitness increases, but of course more gradually.
Certainly as we increase the ratio of harmful mutations to beneficial mutations there will come a point where fitness no longer increases. Where is that point? Let's try setting the beneficial mutation rate to .1%, making the harmful mutation rate a whopping 420 times greater. This one was a struggle in the early generations with fitness gradually decreasing during the first 10's of generations, but by generation 60 enough good genes are becoming fixated that fitness has once again begun increasing, and steadily thereafter.
We set the beneficial mutation rate even lower, making harmful mutations 4200 times more likely. Trying this we find that as before fitness decreases in the early generations, but by generation 90 fitness begins increasing again, and steadily thereafter once more, though at the slowest rate yet, as expected.
At some point harmful mutations will outnumber beneficial mutations to such an extent that the small number of beneficial genes that become fixated cannot overcome it and fitness won't increase, and in fact will likely decrease steadily and cause eventual extinction. But let's examine how well these experiments with mutation rates support your assertions. You said the following:
You can make many things happen when you tinker with the mutation ratio and selection. In your example you tinker mightily with the mutation ratio to create your fantasyland.
It doesn't appear that Rei had to do much tinkering. Whether the harmful mutation rate was 42 times greater, 420 times greater, 4200 times greater, fitness still increased, so your assertion is false.
You *do* raise a pertinent question:
What primarily matters is the ratio of beneficial mutations to deleterious mutations, and that realistic selection is occurring.
The program was to illustrate the principle that random chance can produce improved fitness. Even if this is not your current position, in the past you have denied that this is possible even in principle. The program demonstrates that this claim is false. You go on to make related comments:
No one believes the frequency of beneficial mutations is 1 in 1000, let alone your fantasyland 1 in 12! Is 1 in a million possible? Unlikely. It certainly isn’t supported by the years of research on bacteria and drosophila where we can only find a handful of questionable examples.
The evidence of beneficial mutations in bacteria is unequivocal, and
Drosophila experiments are useful more for understanding heredity, not beneficial/harmful mutation ratios. I'm guessing we don't have a good idea of what the beneficial/harmful ratio is outside the bacterial realm, but in that realm beneficial mutations are so likely that they happen over and over and over again. Is it one in a thousand? A million? A billion? I don't know, Fred, (please realize that doesn't mean no one knows - I'm not a biologist) but whatever the ratio the results of bacterial experiments on this are very clear that beneficial mutations are sufficiently common that they can be depended upon to turn up in experiment after experiment after experiment.
A standard experiment in university biology programs has the experimenter begin with a single bacterium which reproduces in a controlled environment so that he can know when adaptational mutations emerge. There are biology departments at so many universities that experiments along these lines must get performed for educational purposes alone at least a hundred times a year.
--Percy
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