The argument runs like this. Let's say that a particular species produces more females than males. Then males will have more mating opportunities than females, and will, on average, have more offspring. If a mutation then arises in a given individual that makes her more likely to give birth to sons, she will tend to have more grandchildren, many of whom will carry that mutation. Since they will also have an advantage, the mutation will spread through the population... until males are more common, at which point it's preferable to have more female offspring, and so on.
Thus, any bias in one direction should be swiftly cancelled out by a swing in the opposite one.
This is a general principle that should hold for any creature that reproduces in roughly the way that we do. In the case of mammals specifically, it's helped in large part by the way that sex is determined. Although there are a few odd exceptions, the general rule is that sex in mammals is determined by the sex chromosomes: males are XY and females are XX. Each ovum carries an X chromosome, and each sperm has either an X or a Y; these latter are produced by an even split in the genetic material of the XY progenitor cells so that X-sperm and Y-sperm should be produced in exactly equal quantities, and be just as likely to fertilise any given egg. (And, yes, this is a specifically mammalian thing, reptiles, birds, and so on have different systems).
Except well, small problem here: it's not actually true. Well, not for every species, anyway: sometimes one sex really is more likely to be born than the other. It's not common and, at least in mammals, it's never a huge bias, but it does happen. So... how and why?
To answer the second question first, Fisher's Principle relies on the assumption that it's equally easy to raise either sex to maturity. (In fairness to Fisher, he realised this, and made it explicit in his argument). If, say, females are more likely to die before breeding, you'll want to give birth to more of them so that it evens out when they reach adulthood. Or, since most male mammals leave home to find partners elsewhere, if resources are limited locally females, forced to stay where food is in short supply, will have a harder time of it than males, so it makes sense to produce more male offspring so that they can go somewhere that's hopefully better.
For that matter, if it's just plain harder to raise offspring of one sex then, especially if you're not in peak condition (say, because you're getting older), you ought to produce more of the "easy" one - at least they'll survive. Then there's the "sexy son" hypothesis, which states that if a female's partner is particularly attractive, her sons are likely to be sexy too, so she should have more of them if she wants to maximise her number of grandchildren.
In reality, there are several reasons why a sex bias could be advantageous, and they are not all mutually exclusive.
Well, all right... but how? The obvious assumption is that, since X and Y sperm should be produced in equal quantities, the mother is doing something during the very early stages of pregnancy that means one sex or the other is more likely to reach term. The only other choice she has would be to somehow determine which sperm were X or Y and ensure she is more likely to be fertilised by one than the other. Which may sound unlikely but, surprisingly, does appear to be possible in at least some species.
Given that he's not the one with the womb, you'd think that the father gets less choice in the matter. But that's not necessarily true, either.
There are, in fact, a number of ways that a male could potentially produce unequal amounts of X and Y sperm. There's no firm evidence that the initial creation of the two types can be biased, since, after all, you have to cut the initial XY set in half and messing that up would lead to other problems. But, after their formation, sperm cells have to go through several stages before they leave the male's body. If these can be affected, more sperm of one sex or the other might survive until required, as is seen, for example, in pygmy hippos.
There is some evidence that, if the male has fertility problems, those can affect his Y-sperm more often than those carrying the X chromosome, so if he does have children at all, they are more likely to be girls. This has been shown in both humans and red deer, but, since it's the result of something going wrong, it's not really a means of "controlling" things. (Plus, it's not entirely clear why this should be so).
It has been suggested that a male's frequency of mating may also have an effect on the sex ratio of his offspring. Abstinence doesn't seem to make much difference, but the opposite might: one experiment on male rats showed that if they mated more often than they normally would, they eventually had more daughters than sons... although, again, we don't really know why.
In humans, there is some evidence to suggest that Y-sperm survive for longer in the female reproductive tract than X-sperm. If that's true for other animals, a male could increase his chance of fathering sons by mating with his partner a few days before she ovulated... or she could adjust the odds by only letting him mate at the relevant time. Just after conception, higher levels of glucose in the reproductive tract of mice favour the early survival of male embryos... something that the mother could theoretically control, but that the father could also influence by producing (or not) sugar-rich semen. Other components of the seminal fluid may also be relevant, since removal of the prostate in hamsters makes them more likely to sire sons, so it's presumably doing something.
Much of this, however, while supported by observation, remains mysterious at a detailed level; it's more obvious that it's happening than how it's happening. A deeper understanding of the mechanisms involved could be advantageous, not just in agricultural animals - where one sex may be more useful to we humans than the other - but in conservation.
A recent study on numbats at Perth Zoo showed that while the origin of the mother made no difference, males born in captivity tended to have more sons than those born in the wild and recently captured. That may be due to stress or being raised close to a higher number of other males than would be the case in nature, but understanding exactly why might help us devise better ways of preserving this particular endangered species.
[Photo by Luc Viator, from Wikimedia Commons.]
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