What? When something becomes less deadly, its frequency increases
Not necessarily. If an allele has no selection pressure on it then we should expect the frequency to be as likely to go up as it will be to go down. The situation is more complicated when one has multiple alleles interacting, but as a rough approximation in non-pathological contexts this should still be true. Since schizophrenia is largely genetic, we should expect the frequency to stay about the same.
There are some exceptional cases to this sort of logic. If for example one has a trait that is often inflicted by the environment (say deafness or blindness) then one should expect as it becomes less deadly that more people will survive with the trait and so the percentage with it will go up. But schizophrenia doesn’t seem to act that way.
So, without a very detailed analysis, if the deleterious effects of schizophrenia have been reduced we should expect the percentage of the population that has it to stay roughly constant. However, if there are alleles which have positive selection effects by themselves but which have deleterious effects when found together (a likely scenario for a complicated mental trait like schizophrenia), then it may be that reduced negative selection pressure on schizophrenia makes those alleles have an equilibrium ratio in the population that has moved up. In that context, one would expect to see more schizophrenics.
The upshot is that without a lot more data about the underlying genetics, predicting an increase seems unjustified.
ETA: Curious about cause for downvote. Everything above is essentially what one will get in an intro genetics course. Nothing above should be controversial. Is this being downvoted as too trivial?
If an allele has no selection pressure on it then we should expect the frequency to be as likely to go up as it will be to go down.
If an allele exists currently at frequency X, and the selection pressure on it changes upwards, what should we expect? The frequency to increase. Of course it is possible for the frequency to decrease, and I made no comments on the variance of that expectation.
if the deleterious effects of schizophrenia have been reduced we should expect the percentage of the population that has it to stay roughly constant.
Why is this the case? The deleterious effects of schizophrenia are that schizophrenics and those suspected of sharing their genes have less grandchildren. If those effects are reduced, that means that there are more grandchildren.
Curious about cause for downvote. Everything above is essentially what one will get in an intro genetics course. Nothing above should be controversial. Is this being downvoted as too trivial?
I didn’t downvote the comment, but I suspect someone saw it as trivially wrong.
If an allele exists currently at frequency X, and the selection pressure on it changes upwards, what should we expect? The frequency to increase.
Barring cases the rare cases where new copies of the allele are being generated from individuals who do not have copies of that allele (such as the example JoshuaZ gave), then if the selection pressure for an allele is negative, we should expect its frequency to go down, although for rare recessive alleles this rate will tend to be extremely slow. If the selection pressure goes up, but continues to be negative, then we should expect the frequency to continue to decrease, but more slowly than before. The rate at which the frequency goes down will depend on the strength of the negative selection pressure, not the relative negative selection pressure to whatever it used to be.
Having thought about this for a week, I think I’ve realized what the disagreement was about, and where I went wrong in expressing what I was thinking. I didn’t distinguish between long-term averages and short-term averages, which was a mistake. My statements were wrong if we only knew short-run frequency but I believe were correct if we knew long-run frequency.
Consider the prevalence of a gene in a finite population in each generation as a Markov chain. If you start off in state i, that is i individuals having the gene, the sum of the transition probabilities to lower numbers represents the chance that there are less individuals with that gene in the next generation, the sum of the transition probabilities to higher numbers represents the chance that there are more individuals in that gene in the next generation, and the remainder (the transition probability back to i) is the chance that nothing changes.
Selection pressure is related to the chance that the gene becomes less frequent compared to the chance that it becomes more frequent, and depends on the frequency. One can easily imagine situations in which a gene is pushed towards a frequency that isn’t 0 or 1, but instead, say, .3, and so has positive selection pressure below that and negative selection pressure above it. (Frequency = Prevalence / Population Size)
For a deleterious gene, it can easily be the case that for all positive states the chance of transitioning downwards is greater than the chance of transitioning upwards. Even in that case, the stationary distribution of states on that chain will have a positive mean (because there are no negative states). Consider a two-state system, with p(1|0)=.1 and p(0|1)=1. The stationary distribution is (10/11, 1⁄11), with mean 1⁄11.
As the the gene become less deleterious- the selection pressure becomes less negative- the stationary distribution will spread upwards. We expect the long-term mean will increase, and are less surprised to find the system in a state where a larger population is carrying that gene than we were before. In the same example, if we change p(0|1) to .9 then the stationary distribution is now (.9,.1), with mean .1.
Under such a view, it’s obvious that when you decrease the selection pressure on a rare, deleterious condition, the long-term average of individuals with such a condition will increase, but will not grow to dominate the population.
If an allele exists currently at frequency X, and the selection pressure on it changes upwards, what should we expect? The frequency to increase. Of course it is possible for the frequency to decrease, and I made no comments on the variance of that expectation.
No. This doesn’t follow. Consider for example an allele that is normally recessive and in the homozygous case is nearly lethal. Such an allele will generally be pushed to a very low frequency. The only way that such an allele stays at a substantial fraction of the population is if it is has a constant influx of new copies (For example Huntington’s disease is sort of this way. The allele is dominant and extremely negative in that form, and is homozygous lethal, but Huntingon precursor alleles are constantly mutating into new cases of Huntington’s and the specific biochem of the allele in question makes this much more likely). Now, if an allele has no impact in the heterozygous case. As the allele becomes extremely rare, the selection pressure will drop more and more to the point where it becomes negligible. Now, consider what happens if we discover a cure for this very rare disease that occurs in the homozygous case, or that we make it much easier to survive. What should we expect to happen to the frequency in the population? We should expect it to stay roughly constant, because there’s no positive selection pressure.
In general, decreasing negative selection effects does not increase the frequency of an allele.
I suspect I’m being unclear. I’m not discussing a state where we have good knowledge of the underlying mechanics, but one where we have some original frequency of a heritable condition, and then we make people with that condition / their relatives more likely to procreate than they were before. The equilibrium has shifted, and it has shifted upwards. We don’t need to know the strength of the selection pressures (positive and negative) or their mechanisms to make that prediction; we just know that the scales were probably balanced before, and we pulled some weight off of one side. The scales should tip away from the side we pulled weight off of.
Yes, you are being clear, and this doesn’t follow. It might help to reread my example. If we reduce a negative selection pressure it doesn’t mean that things will shift. In the example I gave there’s no real equilibrium, the allele just gets to stay under the radar of evolution because it is so rare evolution doesn’t get a chance to act on it. (This is by the way a well-known ev-bio issue, that bad recessive alleles can easily stay at low levels in a population.) Making the allele have a less negative selection pressure won’t necessarily change that state. If the pressure is moved to close to zero then one then expects neutral drift to occur as usual which can move things up or down, and if the pressure is still negative then it should stay about where it is unless neutral drift moves it a bit downwards.
What should we expect to happen to the frequency in the population? We should expect it to stay roughly constant, because there’s no positive selection pressure.
If there is still an influx of new copies due to mutation, then the frequency will increase because there’s now less selection pressure driving the mutations out.
Influx of new copies for most alleles is generally negligible for any specific allele. Examples like Huntington’s are extremely rare. The probability that any mutation will arise more than once in the population is generally extremely small. Standard genetic models often don’t even bother taking into account the chance that a mutation will be matched because the chance is so small.
Not necessarily. If an allele has no selection pressure on it then we should expect the frequency to be as likely to go up as it will be to go down. The situation is more complicated when one has multiple alleles interacting, but as a rough approximation in non-pathological contexts this should still be true. Since schizophrenia is largely genetic, we should expect the frequency to stay about the same.
There are some exceptional cases to this sort of logic. If for example one has a trait that is often inflicted by the environment (say deafness or blindness) then one should expect as it becomes less deadly that more people will survive with the trait and so the percentage with it will go up. But schizophrenia doesn’t seem to act that way.
So, without a very detailed analysis, if the deleterious effects of schizophrenia have been reduced we should expect the percentage of the population that has it to stay roughly constant. However, if there are alleles which have positive selection effects by themselves but which have deleterious effects when found together (a likely scenario for a complicated mental trait like schizophrenia), then it may be that reduced negative selection pressure on schizophrenia makes those alleles have an equilibrium ratio in the population that has moved up. In that context, one would expect to see more schizophrenics.
The upshot is that without a lot more data about the underlying genetics, predicting an increase seems unjustified.
ETA: Curious about cause for downvote. Everything above is essentially what one will get in an intro genetics course. Nothing above should be controversial. Is this being downvoted as too trivial?
If an allele exists currently at frequency X, and the selection pressure on it changes upwards, what should we expect? The frequency to increase. Of course it is possible for the frequency to decrease, and I made no comments on the variance of that expectation.
Why is this the case? The deleterious effects of schizophrenia are that schizophrenics and those suspected of sharing their genes have less grandchildren. If those effects are reduced, that means that there are more grandchildren.
I didn’t downvote the comment, but I suspect someone saw it as trivially wrong.
Barring cases the rare cases where new copies of the allele are being generated from individuals who do not have copies of that allele (such as the example JoshuaZ gave), then if the selection pressure for an allele is negative, we should expect its frequency to go down, although for rare recessive alleles this rate will tend to be extremely slow. If the selection pressure goes up, but continues to be negative, then we should expect the frequency to continue to decrease, but more slowly than before. The rate at which the frequency goes down will depend on the strength of the negative selection pressure, not the relative negative selection pressure to whatever it used to be.
Having thought about this for a week, I think I’ve realized what the disagreement was about, and where I went wrong in expressing what I was thinking. I didn’t distinguish between long-term averages and short-term averages, which was a mistake. My statements were wrong if we only knew short-run frequency but I believe were correct if we knew long-run frequency.
Consider the prevalence of a gene in a finite population in each generation as a Markov chain. If you start off in state i, that is i individuals having the gene, the sum of the transition probabilities to lower numbers represents the chance that there are less individuals with that gene in the next generation, the sum of the transition probabilities to higher numbers represents the chance that there are more individuals in that gene in the next generation, and the remainder (the transition probability back to i) is the chance that nothing changes.
Selection pressure is related to the chance that the gene becomes less frequent compared to the chance that it becomes more frequent, and depends on the frequency. One can easily imagine situations in which a gene is pushed towards a frequency that isn’t 0 or 1, but instead, say, .3, and so has positive selection pressure below that and negative selection pressure above it. (Frequency = Prevalence / Population Size)
For a deleterious gene, it can easily be the case that for all positive states the chance of transitioning downwards is greater than the chance of transitioning upwards. Even in that case, the stationary distribution of states on that chain will have a positive mean (because there are no negative states). Consider a two-state system, with p(1|0)=.1 and p(0|1)=1. The stationary distribution is (10/11, 1⁄11), with mean 1⁄11.
As the the gene become less deleterious- the selection pressure becomes less negative- the stationary distribution will spread upwards. We expect the long-term mean will increase, and are less surprised to find the system in a state where a larger population is carrying that gene than we were before. In the same example, if we change p(0|1) to .9 then the stationary distribution is now (.9,.1), with mean .1.
Under such a view, it’s obvious that when you decrease the selection pressure on a rare, deleterious condition, the long-term average of individuals with such a condition will increase, but will not grow to dominate the population.
No. This doesn’t follow. Consider for example an allele that is normally recessive and in the homozygous case is nearly lethal. Such an allele will generally be pushed to a very low frequency. The only way that such an allele stays at a substantial fraction of the population is if it is has a constant influx of new copies (For example Huntington’s disease is sort of this way. The allele is dominant and extremely negative in that form, and is homozygous lethal, but Huntingon precursor alleles are constantly mutating into new cases of Huntington’s and the specific biochem of the allele in question makes this much more likely). Now, if an allele has no impact in the heterozygous case. As the allele becomes extremely rare, the selection pressure will drop more and more to the point where it becomes negligible. Now, consider what happens if we discover a cure for this very rare disease that occurs in the homozygous case, or that we make it much easier to survive. What should we expect to happen to the frequency in the population? We should expect it to stay roughly constant, because there’s no positive selection pressure.
In general, decreasing negative selection effects does not increase the frequency of an allele.
I suspect I’m being unclear. I’m not discussing a state where we have good knowledge of the underlying mechanics, but one where we have some original frequency of a heritable condition, and then we make people with that condition / their relatives more likely to procreate than they were before. The equilibrium has shifted, and it has shifted upwards. We don’t need to know the strength of the selection pressures (positive and negative) or their mechanisms to make that prediction; we just know that the scales were probably balanced before, and we pulled some weight off of one side. The scales should tip away from the side we pulled weight off of.
Yes, you are being clear, and this doesn’t follow. It might help to reread my example. If we reduce a negative selection pressure it doesn’t mean that things will shift. In the example I gave there’s no real equilibrium, the allele just gets to stay under the radar of evolution because it is so rare evolution doesn’t get a chance to act on it. (This is by the way a well-known ev-bio issue, that bad recessive alleles can easily stay at low levels in a population.) Making the allele have a less negative selection pressure won’t necessarily change that state. If the pressure is moved to close to zero then one then expects neutral drift to occur as usual which can move things up or down, and if the pressure is still negative then it should stay about where it is unless neutral drift moves it a bit downwards.
If there is still an influx of new copies due to mutation, then the frequency will increase because there’s now less selection pressure driving the mutations out.
Influx of new copies for most alleles is generally negligible for any specific allele. Examples like Huntington’s are extremely rare. The probability that any mutation will arise more than once in the population is generally extremely small. Standard genetic models often don’t even bother taking into account the chance that a mutation will be matched because the chance is so small.