Eliezer, could you provide a link to this result? Something looks wrong about it.
Fisher’s fundamental theorem of natural selection says the rate of natural selection is directly proportional to the variance in additive fitness in the population. At first sight that looks incompatible with your result.
You mention a site with selection at 0.01%. This would take a very long time for selection to act, and it would require that there not be stronger selection on any nearby linked site. It seems implausible that this site would have been selected before, with the result that it should be a 50:50 chance whether each change is a small favorable or unfavorable one. Tiny selective effects are neutral for all practical purposes. But tiny unfavorable changes have only a tiny chance to spread in the same way that you have little chance to win big at the casino when you make a very long series of small bets with the odds a little bit against you. Tiny favorable changes have only a very small chance to spread because they’re usually lost by accident before they get a large enough stake.
Your numbers are clearly correct when all mutations are dominant lethal ones. When the mutation rate is high enough that half the offspring get a dominant lethal mutation, and there are only twice as many offspring as parents, then the population can barely survive those mutations and any higher mutation rate would drive it extinct.
I’m not sure that reasoning applies to mutations that affect relative reproduction rather than absolute, though. When a mutation lets its bearer survive better than other individuals when competing with them, but they survive just fine when it isn’t around, that could be a different story.
Clearly there are limits to the rate of natural selection. It’s proportional to the variance in fitness, so anything that limits the variation in fitness limits the rate of evolution. Mutation and recombination create variation in fitness, and there’s some limit on the mutation rate because of mutations that reduce the absolute level of functioning of the organism. But the reasoning expressed in the post doesn’t look convincing to me.
Eliezer, could you provide a link to this result? Something looks wrong about it.
Fisher’s fundamental theorem of natural selection says the rate of natural selection is directly proportional to the variance in additive fitness in the population. At first sight that looks incompatible with your result.
You mention a site with selection at 0.01%. This would take a very long time for selection to act, and it would require that there not be stronger selection on any nearby linked site. It seems implausible that this site would have been selected before, with the result that it should be a 50:50 chance whether each change is a small favorable or unfavorable one. Tiny selective effects are neutral for all practical purposes. But tiny unfavorable changes have only a tiny chance to spread in the same way that you have little chance to win big at the casino when you make a very long series of small bets with the odds a little bit against you. Tiny favorable changes have only a very small chance to spread because they’re usually lost by accident before they get a large enough stake.
Your numbers are clearly correct when all mutations are dominant lethal ones. When the mutation rate is high enough that half the offspring get a dominant lethal mutation, and there are only twice as many offspring as parents, then the population can barely survive those mutations and any higher mutation rate would drive it extinct.
I’m not sure that reasoning applies to mutations that affect relative reproduction rather than absolute, though. When a mutation lets its bearer survive better than other individuals when competing with them, but they survive just fine when it isn’t around, that could be a different story.
Clearly there are limits to the rate of natural selection. It’s proportional to the variance in fitness, so anything that limits the variation in fitness limits the rate of evolution. Mutation and recombination create variation in fitness, and there’s some limit on the mutation rate because of mutations that reduce the absolute level of functioning of the organism. But the reasoning expressed in the post doesn’t look convincing to me.