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ChristianKl comments on When does heritable low fitness need to be explained? - All
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Comments (146)
Then where does the heritability come from?
You're right, this is a problem.
If something is heritable but also uncommon, it should be possible for selection pressure to act on it. So why doesn't it? That clarifies the issue for me. What I wrote before (in this comment thread) now seems mistaken. Thank you for helping me to understand better.
It seems my original question was partly due to a misunderstanding. The crucial fact about homosexuality isn't just the lowered fitness or relatively high incidence, but the (partial) heritability. Then the only relevant remaining question is: can we quantitatively estimate the reduced fitness due to homosexuality and so calculate the unlikelihood of its 3% rate being due to chance, drift, etc?
Your original post does not talk about heritability. So my answer was: heritability. But then I noticed that it was in the post title and I was confused and did not change my answer.
I posted a calculation on SSC. Let’s say that there is a mutation that is spontaneously created in 1 in 10,000, that it has a 10% chance of producing a homosexual phenotype and that the phenotype has 0.9 fitness, that is, yields an average of 1.8 children. Then the fitness of the gene in 0.99. So in equilibrium, the gene only reproduces itself 99%, so the remaining 1% must be made up by the spontaneous mutation. That is, the prevalence is 100x the spontaneous mutation rate. The prevalence is 1% of the population, of which 0.99% inherit the gene and 0.01% spontaneously acquire it. That’s a genotypic prevalence of 1%. The phenotypic prevalence is 0.1%.
I think 1 in 10,000 is the standard rule of thumb mutation rate. For example, achondroplasia (dwarfism) has a spontaneous mutation rate of 3 in 100,000 and an inherited rate of 1 in 100,000. Apparently dwarfs have about 1/4 of replacement fertility. (The fatality of homozygous achondroplasia complicates the situation. The gene definitely has a fitness of 1/4, but if dwarfs only marry dwarfs, the fitness of the people would be 3/8, I think.)
Also, the approach to equilibrium is exponential with base the fitness.
Its more like 10^-8.
http://www.sciencemag.org/content/328/5978/636.abstract
Nope, that's the wrong rate.
I gave you a worked example, with real empirical data: achondroplasia has a spontaneous rate of 3/100,000. Try to understand the example rather than pulling facts out of your head with no understanding.
That seems needlessly inflammatory.
The rate of spontaneous mutation in humans is on the order of 10^-8 per haploid base-pair per generation. A few references: one (a blog post summarizing multiple academic papers), two (I think this is one of the papers cited by the foregoing), three (older; rate is ~2x higher), four (intermediate in age and also in estimated rate).
A given gene is many base-pairs long. Accordingly, the "per locus" mutation rate -- which you can think of as how often a particular gene goes wrong, treating all its failure modes as equivalent -- is on the order of 1000x higher. (This, I take it, is where the ~3x10^-5 spontaneous rate for achondroplasia comes from.) The usual cited per-locus rates are, accordingly, on the order of 10^-5, typically a bit lower; see e.g. one (a textbook, which specifically mentions achondroplasia and gives some reasons not to take its rate of spontaneous occurrence too literally as a per-locus mutation rate), two (old paper by J B S Haldane, mostly of historical interest now), three (journal article).
Which figure is more relevant in a given case depends on whether it's one where messing up a single protein, no matter how, causes the effect you're interested in (which seems to be the case for achondroplasia) or one where a very specific change is needed. Which is more likely for homosexuality? I've no idea; more likely than either, I'd have thought, is that sexuality is complicated, that there are lots of genetic changes that can affect someone's propensity for same-sex attraction, and that treating homosexuality as the result of a single genetic change is just wrong.
Anyway, to summarize: no one, so far as I can tell, says that 10^-4 is "the standard rule-of-thumb mutation rate", either per locus or per nucleotide; 10^-8 is roughly the right figure per nucleotide; the right figure per locus is more like 10^-5; which of these figures, if either, is most relevant when considering homosexuality is unclear but for any remotely credible figure it's clear that most homosexuality is not the result of spontaneous mutations.
[EDITED to fix a typo.]
punnet square: Aa x Aa
..................A...........a
. A...........AA.........Aa
. a............Aa..........aa
AA = death or infertile
Aa = like the parents
aa = normal
looks like 3/4 to me. not sure where you got 3/8. (also where two dwarves can have a normal child).
If you selectively look at the living (of which there are 3 options - Aa, Aa or aa) the gene has a 2/3 chance of being passed on. Assuming no other pressures apply.
First of all, you should distinguish between the fitness of the gene and the fitness of the people. Second, I am using as input the empirical observation that the fitness of the achondroplasia gene is 1/4. Third, and tangentially, you should distinguish between the fitness of the children and parents.
(1 gene vs parents) Let us consider the 3 surviving children. Out of the 6 copies of the gene, 4 are wild type and 2 are achondroplasia. But in the parents, half of the genes are achondroplasia. Thus, regardless of how many children the parents have, the fitness of the gene is 2/3 the fitness of the parents.
(2) Empirically, 1/4 of achondroplasia births are inherited and 3/4 are de novo. Assuming equilibrium, the gene is producing 1/4 of replacement fertility, so it has a fitness of 1/4. If dwarfs only reproduce with non-dwarfs, they, too, have a fitness of 1/4. But if they only reproduce with dwarfs, they have a fitness 3/2 of the gene, thus 3/8.
(3 parents vs children) The 3/4 you compute is the reduction in the proportion of pregnancies yield children. This is a kind of infertility, though more emotionally difficult. It is only relevant if the parents are trying to reproduce as fast as possible. In the modern world, parents usually target a small fixed number of children and infertility has little effect. In both farmer and forager societies, children were probably modulated to available food supply. Such a wasted pregnancy does not reduce the number of children by 1, but probably delays future children by a year. If the usual interval is 4, this might reduce fitness by 1/4. But the effect is probably significantly smaller. If people are reproducing at the optimal speed, taking into account risk of famine, a small perturbation probably has little effect.
sorry; point 2 again, (Aa x aa should product a 1/2 not a 1/4)
acondroplasia X normal
............A.............a
...a.......Aa..........aa
...a......Aa...........aa
50%Aa acondroplasia
50%aa normal
or am I confused somewhere? Is that not the punnet square?
Sure, that's the punnet square. You should stop drawing punnet squares and ask yourself why you are drawing them and ask what role they play.
The number 1/4 is the empirical fitness. It is mainly about how many children dwarfs have. You cannot guess that number by looking at punnet squares.
Thanks for the calculation! I'll probably revise the post tonight when I have some leisure time to integrate all the new info.
Congratulation for good updating.