Petteri, I think I can explain. First throw away the lemma that says one death can’t remove more than one gene. That’s a red herring.
Imagine a population of asexual bacterial. Imagine that they have a collection of sites that will kill them immediately if any one of those sites mutates. If a cell averages 1 such mutation per generation, it will on average produce one live and one dead daughter cell per generation. It will not survive. This is an absolute limit for the mutation rate, for that kind of mutation.
Now suppose that it has a lot of sites that result in loss of function when mutated, but that don’t simply kill the cell. Imagine that it averages 1 such mutation per generation. So assuming a poisson distribution, after the first generation all but about 40% will have lost a capability. More than 20% will have lost two or more capabilities. The population as a whole will degrade and no amount of selection can prevent it. Of course each mutation can be reversed about as easily as it happened. If the mutations are all independent then at equilibrium about half of the nonessential functions would work even without selection. But they aren’t independent. On average there are usually around a hundred different ways to make an enzyme stop working with one mutation, and in each case only one way to reverse it. So without selection each function would be destroyed 50 times over. And again the mutations are happening faster than they could be selected against. If the population is size N and you get less than N/2 perfect individuals in the next generation you can’t keep up.
Mutations with very small effect are insignificant. Things that are selected at 0.01% have never been made common due to that selection and it doesn’t matter that they won’t be maintained by selection. Mutations with small disadvantage are not so important and unless there are a whole lot of them they can be mostly ignored in a population that’s still evolving. Most of them will disappear pretty fast, like gamblers who have a very low reserve in a casino where the odds are a little bit against them. The majority of them disappear the first generation, many of the rest disappear the second generation, the ones that hang on awhile are the ones that accidentally got a fair number of instances early, by random chance. Like flipping 20 heads in a row with a coin that’s slightly biased toward tails. It happens, but rarely. And those will usually be wiped out when a favorable mutation gets established. About the time there are hundreds of mutations that provide a 1% disadvantage but haven’t been removed, a single mutation with a 1% advantage shows up and pushes them all out over the next thousand generations or so. Mutations that persist with a 1% disadvantage are rare; mutations that persist against a 2% relative advantage are rarer. The presence of advantageous mutations can overcome large numbers of disadvantageous mutations provided the disadvantageous ones don’t come fast enough to seriously slow their spread.
When a favorable mutation spreads, it reduces the variation in fitness in the population. It spreads mostly by replacing the ones with lower fitness. About the time it approaches fixation, most of the others are gone. If there are ten different favorable mutations spreading at the same time probably no one of them will be fixed; the others will get their share. That doesn’t increase the speed of evolution much at all. The big thing is that selection has decreased the variability and so decreased the speed for further selection. The descendants of the mutant continue to mutate and build up variability to replace what was lost, but that’s a slow process.
SEXUALITY CHANGES THIS ALL AROUND.
Given sexuality and chromosome assortment but no recombination, a species with 100 chromosomes can evolve much faster than an asexual bacterial population! Each individual chromosome can be selected, mostly independently of the others. MacKay basicly says this should go by the square root of the number of linkage groups. Here’s my explanation—if the different mutations present affect fitness in orthogonal ways, then their total effect on fitness is likely to be something like sqrt(a^2 + b^2 + c^2 etc). It comes from them being orthogonal.
Recombination breaks up the linkages within chromosomes and lets things go even faster.
So ignoring other effects, the smaller the chromosomes and the smaller the linkage groups, the higher the limit on evolution speed. But the limits on lethal (or crippling) mutations are still there. If you have too high a chance to get a dominant lethal mutation, it doesn’t matter how many chromosomes you’ve split the genome over, it’s still lethal.
So ideally it might be proper to be extra careful not to mutate DNA sequences that have been maintained unchanged for a long time, and less so with things that are less important. I don’t know how much that happens.
Petteri, I think I can explain. First throw away the lemma that says one death can’t remove more than one gene. That’s a red herring.
Imagine a population of asexual bacterial. Imagine that they have a collection of sites that will kill them immediately if any one of those sites mutates. If a cell averages 1 such mutation per generation, it will on average produce one live and one dead daughter cell per generation. It will not survive. This is an absolute limit for the mutation rate, for that kind of mutation.
Now suppose that it has a lot of sites that result in loss of function when mutated, but that don’t simply kill the cell. Imagine that it averages 1 such mutation per generation. So assuming a poisson distribution, after the first generation all but about 40% will have lost a capability. More than 20% will have lost two or more capabilities. The population as a whole will degrade and no amount of selection can prevent it. Of course each mutation can be reversed about as easily as it happened. If the mutations are all independent then at equilibrium about half of the nonessential functions would work even without selection. But they aren’t independent. On average there are usually around a hundred different ways to make an enzyme stop working with one mutation, and in each case only one way to reverse it. So without selection each function would be destroyed 50 times over. And again the mutations are happening faster than they could be selected against. If the population is size N and you get less than N/2 perfect individuals in the next generation you can’t keep up.
Mutations with very small effect are insignificant. Things that are selected at 0.01% have never been made common due to that selection and it doesn’t matter that they won’t be maintained by selection. Mutations with small disadvantage are not so important and unless there are a whole lot of them they can be mostly ignored in a population that’s still evolving. Most of them will disappear pretty fast, like gamblers who have a very low reserve in a casino where the odds are a little bit against them. The majority of them disappear the first generation, many of the rest disappear the second generation, the ones that hang on awhile are the ones that accidentally got a fair number of instances early, by random chance. Like flipping 20 heads in a row with a coin that’s slightly biased toward tails. It happens, but rarely. And those will usually be wiped out when a favorable mutation gets established. About the time there are hundreds of mutations that provide a 1% disadvantage but haven’t been removed, a single mutation with a 1% advantage shows up and pushes them all out over the next thousand generations or so. Mutations that persist with a 1% disadvantage are rare; mutations that persist against a 2% relative advantage are rarer. The presence of advantageous mutations can overcome large numbers of disadvantageous mutations provided the disadvantageous ones don’t come fast enough to seriously slow their spread.
When a favorable mutation spreads, it reduces the variation in fitness in the population. It spreads mostly by replacing the ones with lower fitness. About the time it approaches fixation, most of the others are gone. If there are ten different favorable mutations spreading at the same time probably no one of them will be fixed; the others will get their share. That doesn’t increase the speed of evolution much at all. The big thing is that selection has decreased the variability and so decreased the speed for further selection. The descendants of the mutant continue to mutate and build up variability to replace what was lost, but that’s a slow process.
SEXUALITY CHANGES THIS ALL AROUND.
Given sexuality and chromosome assortment but no recombination, a species with 100 chromosomes can evolve much faster than an asexual bacterial population! Each individual chromosome can be selected, mostly independently of the others. MacKay basicly says this should go by the square root of the number of linkage groups. Here’s my explanation—if the different mutations present affect fitness in orthogonal ways, then their total effect on fitness is likely to be something like sqrt(a^2 + b^2 + c^2 etc). It comes from them being orthogonal.
Recombination breaks up the linkages within chromosomes and lets things go even faster.
So ignoring other effects, the smaller the chromosomes and the smaller the linkage groups, the higher the limit on evolution speed. But the limits on lethal (or crippling) mutations are still there. If you have too high a chance to get a dominant lethal mutation, it doesn’t matter how many chromosomes you’ve split the genome over, it’s still lethal.
So ideally it might be proper to be extra careful not to mutate DNA sequences that have been maintained unchanged for a long time, and less so with things that are less important. I don’t know how much that happens.