This is a question that needs to be approached mathematically or not at all.
Given a phenotypical property P (supposed binary), currently present in a proportion X of the population, and having heritability H and selective disadvantage D, how will X vary over time, measured in units of a generation?
Solving this mathematical problem requires a mathematical definition of H and D, which I don’t have, but this must be standard population genetics. Is there a population geneticist in the house?
One can also add various complications to the model, such as heterozygous advantage, spontaneous mutations that reintroduce P, etc.
The goal is to find a model whose parameters are as accurate as we can estimate them, which is consistent with whatever is known about the prevalence of P now and in the past.
Here, He could stand for homozygote fitness or homosexual fitness, and He is hetro fitness:
(hetrozygotes only have one gene to pass on, so this term is divided by two)
Sanity check: He=Ho=1 ⇒ x=x i.e. neutrality implies stability at all levels of prevalence (exc. stochasisity)
He=(1-x * Ho)/(1-x)
So, if 5% of people are gay (supported by e.g. number of people signed up to ok cupid) x=0.22, and Ho=0 (oversimplfication) then He=1/0.78=1.28
If only 20% of gayness (to use the scientific term) is explained by genetics, then x=0.1 and He=1.01.
I don’t know enough to even guess whether He=1.28 is plausible, but He=1.01 certainly is a modest fitness increase.
As far as being supported by random mutations, well, the mutation rate is around 10^-8 (I think there are more sublties to this, but its accurate to a first approximation), and since homozygotes have prevalence of x^2, this is enough to support a prevalence [EDIT: a prevalence of hetrozygote carriers] of 10^-4.
the mutation rate is around 10^-8 [...] and since homozygotes have prevalence of x^2, this is enough to support a prevalence of 10^-4.
Surely that can’t be right. If an allele is present with probability 10^-8, the probability of its being present in one of two places is 1-(1-10^-8)^2, which is not anything like 10^-4; it’s almost exactly 2.10^-8.
(This doesn’t change the point I think you’re making, namely that there is no possible way that every instance of non-heterosexuality is the result of an independent mutation at the same site.)
What I meant to say was that if 10^-4 of the population are hetrozygote carriers, then 10^-8 will be homozygotes and their genes will be lost to the next generation (assuming zero fitness), so if new mutations are created at 10^-8, then a prevalence of 10^-4 of the population being hetrozygote carriers is the steady state. In this case, the proportion of homosexuals (or heamophiliacs or whatever) would be 10^-8 times the number of nucleotides that will cause the condition if they mutate.
If the gene in question is dominant, then it’s still 10^-8. But yes, homosexuality cannot be primary caused by random mutations.
Oh, I’m very sorry: I completely misunderstood what you were doing, and failed to read your last paragraph as an application of the calculation you’d just done.
Just to say it again in a different way for the benefit of anyone else who misunderstood in the same way as I did, the point is this:
In equilibrium, the rate at which a mutation enters the population has to equal the rate at which it leaves. If it’s rare and recessive, the main way it leaves will be by homozygotes being less fit. So, taking the simplest possible approximations everywhere: if the mutation rate is m and the prevalence of this thing in (the genes of) the population is f, then every new generation will gain a fraction m and lose a fraction f^2 from dead/infertile homozygotes, so we should have m=f^2. So, e.g., if m=10^-8 then we will eventually get f=10^-4.
All of this needs adjusting if having the thing heterozygously makes a difference to fitness, or if having it homozygously doesn’t reduce your fitness to zero, and that adjustment is what the more complicated formula in skeptical_lurker’s earlier comment is for.
Given a phenotypical property P (supposed binary), currently present in a proportion X of the population, and having heritability H and selective disadvantage D, how will X vary over time, measured in units of a generation?
Not sure this model is adequate: if there is no advantage whatsoever, the proportion X can only go down—there is nothing which can increase it. That begs the question of how did the original mutation spread to X percentage of the population. And if X is only going down, you’re probably looking at some variety of exponential decay...
I don’t think the second case can fit homosexuality. If homosexuality-promoting alleles are losing ground to mutations that do better, why haven’t they completely vanished yet? It’s unlikely that going back, homosexuality rates were far higher; that would make prehistorical men very unusual among other mammals.
That begs the question of how did the original mutation spread to X percentage of the population.
Spontaneous mutations and random genetic drift. (There’s also the case where X is the original variant and has been decaying for a long time, but that’s not relevant to homosexuality.)
A spontaneous mutation produces 1 (one) individual and pure genetic drift is unlikely to get to noticeable percentages of the population (with some exceptions, of course).
pure genetic drift is unlikely to get to noticeable percentages of the population
The random walk will either lead to fixation or extinguishing the spontaneous mutation, and the probability of fixation for a neutral mutation is meaningful: “the rate of fixation for a mutation not subject to selection is simply the rate of introduction of such mutations.” Hence, genetic drift is powerful enough that it can separate isolated populations.
Well, the rate of fixation of any neutral mutation is the rate of neutral mutations in general and so is meaningful. The chances of fixation of a particular neutral mutation are the chances of this particular mutation happening and so are very very small.
So if you look at a newborn baby and go “Hmm, this baby has a novel mutation X, it looks to be neutral, what are the chances that this specific mutation X will fix itself in the population?”, the chances are very low.
On the other hand, if you aggregate all novel mutations of all babies born, say, during this year, then the chances that one (and we don’t know which one) of these mutations will survive and get fixed are more meaningful.
So if you look at a newborn baby and go “Hmm, this baby has a novel mutation X, it looks to be neutral, what are the chances that this specific mutation X will fix itself in the population?”, the chances are very low.
if there is no advantage whatsoever, the proportion X can only go down—there is nothing which can increase it
This is totally wrong. It can easily increase: genetic drift/random walk. Not only is it possible, all sorts of neutral mutations reach fixation all the time. It’s true any particular instance of any mutation may not win the lottery, but it’s quite different to argue that there is no such thing as a lottery and no one has ever won a lottery!
That begs the question of how did the original mutation spread to X percentage of the population
There is no question to beg; the gene in question may simply be yet another lottery winner like what regularly happens. At any time, there are countless variants which are slowly working their way up to fixation or down to extinction.
It is entirely meaningful to ask about the probability they will make it to either endpoint and how fast, and if you are looking at an existing variant with a particular prevalence, weird to object to it on the basis that each time the novel mutation appeared (and it could have appeared many times before succeeding in spreading as much as it did) it had little chance of spreading; perhaps, yet, it did.
Read the comment you linked more carefully. I’m not talking about reality—I’m talking about the model which RichardKennaway proposed. Specifically, I find this model too simple because it has a single force acting on the spread of a gene—the “selective disadvantage D”. Note, by the way, that it’s not about neutral mutations at all, presumably D is not zero and we are talking about mutations which are actually selected against.
Given that, the expected value of X (I’ll grant you that I should have been more clear that I’m talking about the expected value and not about what one instantiation of a random process could possibly be) must decrease.
Yes, exactly this: I would like very much to know if a quantitative model predicts homosexuality should not persist at current rates without positive selection.
Alternatively it could mean something in the environment has recently changed that causes some genotypes that wouldn’t previously manifest phenotype P to do so.
A virus which we would not have been exposed to in our evolutionary environment? If this hypothetical virus was confined to a specific geographical location before being transmitted during the age of sail, then there could be a population with ancestory from that location who would have evolved natural immunity. Do you know of any such population? If so, it could be a way to prove the theory.
That’s would certainly prove the theory, as well as helping pinpoint the virus. But many viruses appeared in historical times, either making the jump from other species or evolving. The rate at which new viruses evolve is greater than before due to the very large and connected human populations they evolve in.
This is a question that needs to be approached mathematically or not at all.
Given a phenotypical property P (supposed binary), currently present in a proportion X of the population, and having heritability H and selective disadvantage D, how will X vary over time, measured in units of a generation?
Solving this mathematical problem requires a mathematical definition of H and D, which I don’t have, but this must be standard population genetics. Is there a population geneticist in the house?
One can also add various complications to the model, such as heterozygous advantage, spontaneous mutations that reintroduce P, etc.
The goal is to find a model whose parameters are as accurate as we can estimate them, which is consistent with whatever is known about the prevalence of P now and in the past.
I’ve studied population genetics.
Let x be the prevalence of the genes.
N hetrozygotes=2x(1-x)
N homozygotes=x^2
For stability:
x(1-x) He+Ho x^2=x
Here, He could stand for homozygote fitness or homosexual fitness, and He is hetro fitness:
(hetrozygotes only have one gene to pass on, so this term is divided by two)
Sanity check: He=Ho=1 ⇒ x=x i.e. neutrality implies stability at all levels of prevalence (exc. stochasisity)
He=(1-x * Ho)/(1-x)
So, if 5% of people are gay (supported by e.g. number of people signed up to ok cupid) x=0.22, and Ho=0 (oversimplfication) then He=1/0.78=1.28
If only 20% of gayness (to use the scientific term) is explained by genetics, then x=0.1 and He=1.01.
I don’t know enough to even guess whether He=1.28 is plausible, but He=1.01 certainly is a modest fitness increase.
As far as being supported by random mutations, well, the mutation rate is around 10^-8 (I think there are more sublties to this, but its accurate to a first approximation), and since homozygotes have prevalence of x^2, this is enough to support a prevalence [EDIT: a prevalence of hetrozygote carriers] of 10^-4.
Surely that can’t be right. If an allele is present with probability 10^-8, the probability of its being present in one of two places is 1-(1-10^-8)^2, which is not anything like 10^-4; it’s almost exactly 2.10^-8.
(This doesn’t change the point I think you’re making, namely that there is no possible way that every instance of non-heterosexuality is the result of an independent mutation at the same site.)
What I meant to say was that if 10^-4 of the population are hetrozygote carriers, then 10^-8 will be homozygotes and their genes will be lost to the next generation (assuming zero fitness), so if new mutations are created at 10^-8, then a prevalence of 10^-4 of the population being hetrozygote carriers is the steady state. In this case, the proportion of homosexuals (or heamophiliacs or whatever) would be 10^-8 times the number of nucleotides that will cause the condition if they mutate.
If the gene in question is dominant, then it’s still 10^-8. But yes, homosexuality cannot be primary caused by random mutations.
Oh, I’m very sorry: I completely misunderstood what you were doing, and failed to read your last paragraph as an application of the calculation you’d just done.
Just to say it again in a different way for the benefit of anyone else who misunderstood in the same way as I did, the point is this:
In equilibrium, the rate at which a mutation enters the population has to equal the rate at which it leaves. If it’s rare and recessive, the main way it leaves will be by homozygotes being less fit. So, taking the simplest possible approximations everywhere: if the mutation rate is m and the prevalence of this thing in (the genes of) the population is f, then every new generation will gain a fraction m and lose a fraction f^2 from dead/infertile homozygotes, so we should have m=f^2. So, e.g., if m=10^-8 then we will eventually get f=10^-4.
All of this needs adjusting if having the thing heterozygously makes a difference to fitness, or if having it homozygously doesn’t reduce your fitness to zero, and that adjustment is what the more complicated formula in skeptical_lurker’s earlier comment is for.
Not sure this model is adequate: if there is no advantage whatsoever, the proportion X can only go down—there is nothing which can increase it. That begs the question of how did the original mutation spread to X percentage of the population. And if X is only going down, you’re probably looking at some variety of exponential decay...
One possibility is spontaneous mutation. Again you would have to plug in a rate for that and see what the mathematics says.
Another is that the genes involved aren’t mutations, they’re alleles that are losing ground to mutations that do better.
Whether either of these or something else can fit the case of homosexuality I don’t know.
I don’t think the second case can fit homosexuality. If homosexuality-promoting alleles are losing ground to mutations that do better, why haven’t they completely vanished yet? It’s unlikely that going back, homosexuality rates were far higher; that would make prehistorical men very unusual among other mammals.
Spontaneous mutations and random genetic drift. (There’s also the case where X is the original variant and has been decaying for a long time, but that’s not relevant to homosexuality.)
A spontaneous mutation produces 1 (one) individual and pure genetic drift is unlikely to get to noticeable percentages of the population (with some exceptions, of course).
The random walk will either lead to fixation or extinguishing the spontaneous mutation, and the probability of fixation for a neutral mutation is meaningful: “the rate of fixation for a mutation not subject to selection is simply the rate of introduction of such mutations.” Hence, genetic drift is powerful enough that it can separate isolated populations.
Well, the rate of fixation of any neutral mutation is the rate of neutral mutations in general and so is meaningful. The chances of fixation of a particular neutral mutation are the chances of this particular mutation happening and so are very very small.
So if you look at a newborn baby and go “Hmm, this baby has a novel mutation X, it looks to be neutral, what are the chances that this specific mutation X will fix itself in the population?”, the chances are very low.
On the other hand, if you aggregate all novel mutations of all babies born, say, during this year, then the chances that one (and we don’t know which one) of these mutations will survive and get fixed are more meaningful.
This is irrelevant to the original claims you were making, which I was responding to: http://lesswrong.com/r/discussion/lw/mbl/when_does_heritable_low_fitness_need_to_be/cgrk?context=1#cgrk
You claimed:
This is totally wrong. It can easily increase: genetic drift/random walk. Not only is it possible, all sorts of neutral mutations reach fixation all the time. It’s true any particular instance of any mutation may not win the lottery, but it’s quite different to argue that there is no such thing as a lottery and no one has ever won a lottery!
There is no question to beg; the gene in question may simply be yet another lottery winner like what regularly happens. At any time, there are countless variants which are slowly working their way up to fixation or down to extinction.
It is entirely meaningful to ask about the probability they will make it to either endpoint and how fast, and if you are looking at an existing variant with a particular prevalence, weird to object to it on the basis that each time the novel mutation appeared (and it could have appeared many times before succeeding in spreading as much as it did) it had little chance of spreading; perhaps, yet, it did.
Read the comment you linked more carefully. I’m not talking about reality—I’m talking about the model which RichardKennaway proposed. Specifically, I find this model too simple because it has a single force acting on the spread of a gene—the “selective disadvantage D”. Note, by the way, that it’s not about neutral mutations at all, presumably D is not zero and we are talking about mutations which are actually selected against.
Given that, the expected value of X (I’ll grant you that I should have been more clear that I’m talking about the expected value and not about what one instantiation of a random process could possibly be) must decrease.
In the model proposed there is.
Yes, exactly this: I would like very much to know if a quantitative model predicts homosexuality should not persist at current rates without positive selection.
Alternatively it could mean something in the environment has recently changed that causes some genotypes that wouldn’t previously manifest phenotype P to do so.
For instance, the gene could cause homosexuality iff you eat soy products.
Or being exposed a some virus as westhunter hypothesizes. Or being exposed to pro-homosexual memes as the conservatives suspect.
A virus which we would not have been exposed to in our evolutionary environment? If this hypothetical virus was confined to a specific geographical location before being transmitted during the age of sail, then there could be a population with ancestory from that location who would have evolved natural immunity. Do you know of any such population? If so, it could be a way to prove the theory.
That’s would certainly prove the theory, as well as helping pinpoint the virus. But many viruses appeared in historical times, either making the jump from other species or evolving. The rate at which new viruses evolve is greater than before due to the very large and connected human populations they evolve in.