Comments on: Sexual dimorphism with no costs takes some time

By: David B

David B — Sun, 01 Jul 2007 05:23:27 +0000

I must look up Haldane's article some time.

I can see now why there can be a stable polymorphism for genes on the X.

Suppose for example the order of fitnesses is:

AA > a (in males) > Aa > A (in males) > aa.

When the allele 'a' is rare in the population, the homozygote aa will be very rare (assuming random mating), so the low fitness of aa will make little difference to the fortunes of the 'a' allele. If in males 'a' has sufficient advantage over A, as compared with the advantage of AA over Aa in females, the overall frequency of the allele 'a' in the population will increase. But as it does so, the homozygote aa will become more common, and its low fitness will act as a brake on the rise of 'a', and (with the appropriate fitness values) will eventually bring it to a halt at an equilibrium frequency.

The underlying principle is the same as with heterozygote advantage: the overall relative fitness of the alleles varies with the rarity of the disadvantageous homozygote.

By: David B

David B — Sat, 30 Jun 2007 05:15:11 +0000

I think I misread Cannings’s fitness formulae. Apologies.

By: Looc

Looc — Fri, 29 Jun 2007 20:31:30 +0000

If you want a large macho son, marry a large macho woman.

EEEEEEeeeeeee

So obvious it would probably work. If it doesn't work you really screwed yourself.

By: Alan

Alan — Fri, 29 Jun 2007 10:37:33 +0000

Dunno if this is an example of ‘sexual antagonism’ but among animal breeders there are definitely ‘paternal’ and ‘maternal’ breeds which are used in livestock crossbreeding programs to produce commercial offspring destined for the dinner table.

I have a sheep farm and breed one of the quintessential British “maternal” sheep breeds – the Clun Forest Sheep. Farmers have selected for certain ‘maternal’ traits over the past several centuries in this breed. Maternal is in quotes because I’m not necessarily sure that some of these traits are necessarily more feminine than masculine, but the emphasis has been on maternal instincts, wider pelvic carriages, milk production (more milk and higher butterfat), and multiple births. Other breeds were selected for more ‘masculine’ traits such as size, muscling, and body frame. Again, the determination of what is a ‘masculine’ or ‘feminine’ trait was somewhat subjective on the part of the farmer, but however unscientific, there was a tendency to assign different phenotypes to each sex.

Ewes from my breed of sheep were always crossed with rams of two other breeds of sheep – the Scottish Black-faced or the Border Leicester. Never the other way around.

Maybe because I have an animal breeding background, but I’ve often looked a humans this way too (though I’d never admit it to anyone), but I can generally look at a dainty, small-framed very feminine woman and know that her dad was certainly not a big hulking macho guy. Same goes in reverse, I’ve seen some fairly tough looking dames, where it’s quite clear daddy must have been a bruiser. It’d be pretty easy to breed humans for hyper masculine or hyper feminine phenotypes. You would definitely run into some fecundity issues (women with narrower pelvises, etc), but I know plenty of families (or even ethnic groups) where some, both male and female have more gracile features, and some, both male and female, have coarser features.

Just some very, very unscientific observations.

- Alan

By: p-ter

p-ter — Fri, 29 Jun 2007 09:03:42 +0000

hm, good point. scanning the literature, I see haldane (1962) shows the conditions for the maintenance of variation at autosomal locus by sexual antogonism (at least for a recessive locus). don’t know why I assumed it would only work on the X.

http://scholar.google.com/scholar?q=conditions+for+stable+polymorphism+at+an+autosomal+locus&hl=en&lr=&btnG=Search

By: David Boxenhorn

David Boxenhorn — Fri, 29 Jun 2007 08:37:32 +0000

fitness in males:
A:1-x
a:1+x

females:
AA:1+x
Aa: 1
aa:1-x

Are you saying that that will work but not this:

fitness in males:
AA:1-x
Aa: 1
aa:1+x

females:
AA:1+x
Aa: 1
aa:1-x

?

By: p-ter

p-ter — Fri, 29 Jun 2007 08:03:50 +0000

Equilibrium seems to depend on heterozygote fitness advantage?

not necessarily. I'm trying to find the paper that derived all the conditions (in genetics in like 1980 or something), but I can't find it. One set of fitness models that leads to a stable equilibrium is:

fitness in males:
A:1-x
a:1+x

females:
AA:1+x
Aa: 1
aa:1-x

with x between 0 and 1.

By: David B

David B — Fri, 29 Jun 2007 07:56:49 +0000

…(there can also be a (non-trivial) equilibrium if both homozygote forms are fitter than the heterozygote, but in this case the equilibrium is unstable and one of the homozygotes will soon go to fixation).

By: David B

David B — Fri, 29 Jun 2007 04:34:30 +0000

…I took a quick look at the paper by Cannings. Equilibrium seems to depend on heterozygote fitness advantage?

By: David B

David B — Fri, 29 Jun 2007 04:22:02 +0000

I’m not clear why it makes a difference (to the point at issue, i.e. whether the outcome is a stable polymorphism) if the gene concerned is on an X chromosome. OK, this means it would on average spend twice as long in female bodies as in male bodies, but that can be factored into the average fitness effect. Am I missing something?

By: David Boxenhorn

David Boxenhorn — Fri, 29 Jun 2007 00:47:07 +0000

It occurs to me that what I am talking about is ordinary frequency-dependent selection, just with an interesting way of figuring out the average fitness effect.

By: David Boxenhorn

David Boxenhorn — Thu, 28 Jun 2007 21:23:06 +0000

yes, i know story telling is easy assuming frequency dependence, but datz wut i got.

I agree with this "story" - it will be true as long as the initial average effect of the allele is positive, and increasing frequency of the allele makes the effect increasingly negative.

By: Steve Sailer

Steve Sailer — Thu, 28 Jun 2007 19:21:30 +0000

You would think there would be some folk wisdom on the subject if it was true among humans (e.g., manly dads have horsefaced daughters, or whatever), but I’m not aware of any.

By: p-ter

p-ter — Thu, 28 Jun 2007 11:43:14 +0000

Just think about a gene that is wildly advantageous in males- it can be pretty bad for females, but there is still a NET increase in reproductive success-i.e. the high quality male makes up for the low quality female..

yes, but that won't lead to a stable polymorphism unless the locus is on the X.

By: Matt

Matt — Thu, 28 Jun 2007 11:23:13 +0000

There is a whole literature about sexual antagonism, and the idea that the “average effect” has been discussed, but is generally thought to not be the case- at least in most situations.. Obviously, most of these sexually antagonistic phenotypes are coded my X chromosome genes (as p-ter points out), but that is not always the case..

Just think about a gene that is wildly advantageous in males- it can be pretty bad for females, but there is still a NET increase in reproductive success-i.e. the high quality male makes up for the low quality female..

By: razib

razib — Thu, 28 Jun 2007 10:50:51 +0000

I haven't thought this through, but my kneejerk reaction is that if a gene has different fitness effects on males and females, the genes will be selected for its average effect

this makes sense, but what about

1) initially allele gives huge benefits to males, smaller decrements to females (assuming this is a polygynous species and reproductive skew results in bigger benefit to alphas in males)

2) frequency increases of alpha males but sub-par females

3) at a certain point the benefit to males has decreased on a relative level because more "alphas" are out, but the frequency of hyper-masculinized females means that the fitness of non-hyper-masculinized females has increased. at a particular equilibrium point the allele is maintained in the population a particular frequency. you go down in frequency and it is selected for, up it is selected against.

yes, i know story telling is easy assuming frequency dependence, but datz wut i got.

By: bbartlog

bbartlog — Thu, 28 Jun 2007 09:04:04 +0000

Left-handedness has a genetic component and seems to be advantageous in men and deleterious in women, at least when viewed in terms of number of grandchildren produced. It also seems to be expressed differentially (fewer left-handed women than left-handed men) but dimorphism is obviously not complete…

By: p-ter

p-ter — Thu, 28 Jun 2007 09:00:46 +0000

I haven't thought this through, but my kneejerk reaction is that if a gene has different fitness effects on males and females, the genes will be selected for its average effect, and I don't see in principle why the sex difference in fitness effects would preserve genetic variation.

true. unless the locus is on the X [pdf]. which seems to be the case for many sexually antagonistic loci.

By: Looc

Looc — Thu, 28 Jun 2007 08:13:35 +0000

Large men and small, petite women tend to be the top feeders in the human species. This has an averaging effect and I've seen it first hand.

My grandfather from Austria was an enormous, hyper-masculinized man. Even though he was born around 1900 he was still over 6 feet tall and had a massive frame. Being an alpha male he married a petite, very attractive American woman.

Along came my dad. He was 5'10" but was still a massively built guy. Being a top feeder he also married a small, very attractive woman.

Along came me. I'm just 5'8" and have a somewhat stocky frame. I married a woman who is only 5'5". I have 2 sons of average size. DOH! All the genes for physical size were finally wiped out.

If the story was about larger daughters, it might have averaged the other direction and come up with the same answer.

By: Matt

Matt — Thu, 28 Jun 2007 06:29:08 +0000

I also blogged about this, although I had not see the press coverage yet...Britany Spears Dad Must be Butt-Ugly