exceptions (especially among bats), it's usually the male that's the larger and more physically imposing sex.
I discussed this a few months ago, in the context of seals, where this size difference is especially noticeable. But it's true in other mammal groups, too, including the primates. In general, the reasons for this are much the same among primates as they are among other mammals; males compete with one another for access to mates, and the most successful ones have more mating opportunities, and hence more children, as a result. Genetic inheritance then carries the trait of "large males" down to future generations, amplifying it until other constraints get in the way.
This isn't to say that no other factors play a role, because they may well do, but evidence suggests that it's the overwhelming reason in primates, as it is in many other mammals. But clearly there must be some complexity to it, or it would be equally true of all primate species - and it isn't. For example, bamboo lemurs (also called "gentle lemurs", which may give a clue as to their levels of aggression) don't seem to have any sexual dimorphism, with males and females averaging out at the same size. And this despite the fact that they aren't especially monogamous - something that tends to reduce dimorphism since, if you're only ever going to mate with one partner, there's no need to fight.
At the opposite extreme, the average male orangutan weighs about twice as much as a typical female of the same species. Most other species are somewhere in between, with humans (at least in the United States, which may not be typical of, say, Somalia) scoring a little under a 20% weight difference.
This would imply that the degree of sexual competition varies between primate species, and not always for obvious reasons. Trying to measure this is complicated by the fact that there are a number of different ways we can measure the potential benefits of increased size to a male, compared with a female. The most obvious, as mentioned above, is the degree of polygyny in the species: how many females does the dominant male typically mate with?
At least two other factors are also likely to be significant when it comes to evolving larger males. Firstly, there's the matter of how often the dominant male has to fight off his rivals, or, more generally, how aggressive they are. The males of sexually dimorphic primate species, for instance, tend to also have larger canine teeth than females, even after taking account of their greater size overall. (Of course, they might also be using those teeth to show their prowess by fighting off predators, something that seems to be particularly true of baboons, which don't have the benefit of hiding in trees).
The remaining factor is just how successful all of this is. It's all very well being the dominant male, having multiple sexual partners and fighting off your biggest rivals... but if some weedy subordinate sneaks in for a quick one when you aren't looking, that's not a lot of help in the evolutionary stakes. By definition, this is hard for scientists out in the field to spot, but we can get around that by doing paternity tests on individual animals and seeing just how many really are the child of the dominant male.
To put it another way: you really do need to consider the effects of female choice when it comes to mating. It's not just all about the males.
A recent review confirmed much of this, examining the degree of sexual dimorphism and the associated factors in 50 different species of primate. These included lemurs, multiple different kinds of monkey, various apes and, yes, humans. But, if you take all of the above factors into account, they seem to plot well with the degree of dimorphism in the relevant species, as we'd expect, and as a number of previous, more individual, studies have also shown.
A number of other trends also become visible, some of them also previously predicted by earlier work. For instance, dimorphism is stronger in apes and monkeys than it is in lemur-like animals. Possibly related to this, primates also seem to broadly follow Rensch's rule, which states that, for any given species, the larger the average size of the animal, the greater the degree of sexual dimorphism it will exhibit, if it shows any at all. Thus, bamboo lemurs, which are small, have males and females of about the same size, while the greatest proportional size differences are seen in the primates that are the largest in the first place - baboons, orangutans, and gorillas.
The size of the groups the animals live in typically also plays a part, especially in polygynous species where the group consists of a single male and a number of females. You might expect that this would lead to greater dimorphism, where the male needs to be larger to control, and defend, a larger group of females. But, although the correlation isn't especially strong, it seems to be the opposite. This may well be that third factor I mentioned above coming into play - if the male has to defend a particularly large number of females from rivals, that becomes increasingly difficult. As a result, a higher proportion of young belong to smaller males that he couldn't catch, and the selection pressures to be large fall away somewhat.
(As an aside, we don't see this in birds, pretty much the only other animal group where males tend to be larger. Even if neither partner is as faithful as we'd expect, it's still in the male's interest to have as many offspring as possible by his actual partner, possibly because those are the ones he's compelled to help care for. Since polygynous male mammals don't look after their young, this isn't an issue for them).
What this last finding, in particular, seems to suggest is that the size difference may have evolved before the inter-male competition became strong, and what we see in living species is the result of that in initial signal being amplified once it began to come into play. This has been proposed for other mammal species, and there are a number of reasons why at least a small difference in size might arise through non-sexual selection.
For instance, it has been shown that in mammals in general, being large can be a disadvantage for females. Primates are no exception to this, and it seems to down to the fact that smaller females can have more offspring over the course of their lifespan than larger ones - perhaps because, since they don't have to spend quite so long growing to full size, they can start breeding earlier.
That frees up males to be larger, whether for the obvious reason of competition for mates, or perhaps because it's handy to have someone large enough to fight off the predators. There may also be some ecological advantages to having the sexes be of different sizes, in that they won't compete so directly for resources, although that alone wouldn't favour one sex in particular.
That's been proposed for humans, too, with women in cultures where they perform a greater share of manual labour being genetically taller than those elsewhere. As for reproduction, we're not notably a polygynous species, despite a few cultural exceptions here and there, but neither do we live in isolated family units where different mated pairs rarely interact with one another. Due to some of our anatomical oddities, however, the situation for us may be the opposite way around to that in other primate species.
This is because shorter women are at greater risk of having problems in childbirth than taller ones. That may not be an issue in the West, where obstetric care is good and the number of children isn't very high to start with, but in poorer societies where the opposite is true... even allowing for the relevant levels of nutrition, they're also not quite as short relative to the men as they are in other cultures.
[Photo by "DetroitZoo" from Wikimedia Commons.]