The first formal model of this concept in animal behaviour was described by Norwegian zoologist Thorleif Schjelderup-Ebbe in the 1920s. Having grown up on a farm, he had observed the behaviour of chickens, and, in his PhD dissertation in 1921, he described what is popularly known as the "pecking order". What happens is that, rather than fighting constantly, chickens establish a hierarchy where each animal knows where it stands. If two chickens face off against one another, the lower-ranking, or submissive, bird almost always backs down, allowing the higher-ranking, dominant bird to win without a proper fight.
In this way, everyone is saved the risk of potential injury and the effort of constant battle and social cohesion is maintained. This, as we might expect, doesn't just apply to chickens, and is seen in a wide range of social animals. While other, more complicated, definitions of dominance have since been adopted for particular purposes, Schjelderup-Ebbe's original description is simple enough, and widely applicable enough, that it remains among the best.
Of course, the pecking order has to be established in the first place, especially when new animals join the group (by reaching adulthood, say). The simplest method of deciding this is probably by sheer size - if the other guy is bigger than you, you're better off not pushing your luck. Innate aggressive tendencies, perhaps determined by testosterone levels, may also be a factor in allowing one animal to become dominant.
But there is also a role for actual fighting, albeit typically in some ritualised form of non-lethal combat. If when two animals face off against one another, the same individual wins more often, the other quickly becomes submissive, yielding ground rather than making any further attempts. The benefits to the dominant individual are obvious - less fighting, and more of whatever it was they were competing for. But the submissive individual gains, too, at least in the sense that it isn't regularly getting involved in fights that it will probably lose.
Here, the animal has to remember the outcomes of previous contests and back down when past experience suggests the odds are against it. At least, in some animals, this is achieved very rapidly, perhaps after only a couple of contests, and remains relatively stable until circumstances somehow change. The formation of a hierarchy in this way doesn't necessarily reduce the number of contests, since the dominant animal usually wants to constantly assert its status, but it may well prevent them from getting too bloody.
Much research on the establishment and maintenance of dominance hierarchies has been done on primates, a group with obvious relevance to ourselves. Typically, these focus on hierarchies within primates of a given sex, because these tend to be separate. Males, after all, are primarily competing with each other for mates and, while this isn't entirely untrue of females, either, they are more likely to compete for access to food with which to feed themselves or their young. The general model is that, while females are not entirely peaceful, males do a lot more fighting, and the need to be good at it helps explain why, in typical primates, the males are noticeably larger and stronger than females, and often have bigger teeth into the bargain.
But the different sexes must, to some extent, compete with each other as well. Males do still need to eat, and females do want some say over who they mate with. And here, because of the fact that male primates are usually larger than females, we'd expect to see that they would have the edge and that we'd end up with male-dominated societies.
Which... well, yeah, that has been noted.
But there are a lot of primate species, and they aren't all the same. For a start, there are some primates where males and females are about the same size, such as lemurs and marmosets. Here we find, as expected, that male dominance is largely absent. But the thing is, there are some other primate species where female emancipation seems to be a thing in the wild, but the reasons are less obvious. For instance, there seems to be no such trend (that is, having bigger males means more male dominance) in macaques, and vervet monkeys also seem to be more sexually egalitarian than we'd expect.
So what's going on in these cases?
The previously mentioned study on vervet monkeys does provide a possible explanation, which I'll get to in a minute... but it's possible that it just applies to that particular species. To see whether it's more generally applicable, we need to see if we can test the same idea against other species. Which is where capuchin monkeys come in.
Capuchins are a subfamily of monkeys consisting of a dozen or so species, whose colouration apparently reminded Portuguese explorers of the robes of Capuchin friars (which is, not coincidentally, also the colour of a cappuccino coffee). Being South American, they are only distantly related to vervets and macaques, which live in Africa and Asia, respectively.
In 2011, the group was split into two genera, with one of them (Sabajus spp.) consisting of monkeys that were noticeably larger and more muscular than those in the other. It's the former that are significant here, since females do seem to exhibit at least some degree of dominance over males, despite the fact that the latter are about two-thirds heavier.
In humans, the difference is about 17%, at least in the US. But if we had the same size discrepancy as capuchins, and the average human woman weighed around 70 kg (150 lbs), the average man would be 117 kg (250 lbs)... of muscle, not fat. So this is not insignificant.
Researchers watched capuchin monkeys belonging to three different species of Sabajus, seeing how often they fought, and who won - as measured by the loser either submitting or running away. This enabled them to determine the exact dominance hierarchy in each group, which showed that there was more gender-based variation between the groups than we might expect.
Of the fourteen groups watched in the study, two only had a single male, who was top of the hierarchy, as we'd expect. But in a further eight, while a male was the single most dominant individual, at least some males were subordinate to higher-ranking females. Three seemed more egalitarian, with co-equal males and females holding the top position (something previously thought not to happen) and individuals of both sexes at various ranks further down the pecking order. And, yes, this means that there was one group where the top monkey was female, forcing one of the males into second place.
That was specifically a group of buff-headed capuchins (Sapajus xenthosternos) but that may not be very relevant, since what the study shows is that there is considerable variation between groups, even if they belong to the same species. And even though males are typically dominant overall, they don't simply outrank all the females.
In fact, there was a pattern here; the more males there were in a group, the higher ranking the females tended to be. This was the same pattern seen in the vervets and macaques, and it seems to be related to the fact that the more males there are, the more they fought with each other. And, if they're fighting each other, some of them have to be losing. This either made the subordinate males more submissive in general, so that they would surrender even to physically weaker females, or just encouraged the females to try lording it over a male that they saw regularly getting beaten (and perhaps injured or exhausted) and it paying off often enough for that to work.
At least some species of monkey, even on different continents, are able to modify the gender bias in their pecking orders to suit local circumstances, rather than having a fixed pattern of "males over females". Females in these species do have a chance to boss about some of the males, or even become alpha monkey themselves.
And the more boys there are, the easier that becomes.
[Photo by Dario Sanches, from Wikimedia Commons.]