An obvious example are alarm calls, in which one member of a herd or other group will alert its fellows of a predator or other threat. Another are the distressed 'separation calls' that young mammals use when they can' find their mother. And then, of course, there are mating calls, or aggressive roars and the like intended to intimidate a rival.
But there are also peaceful, non-sexual, contact calls whose primary intent appears to be simply maintaining the cohesion of the group. For example, meerkats regularly use calls to decide when to move on to new foraging grounds, keeping the group together using the principle that if three or more members 'vote' to move by making the appropriate call, then everybody moves at once. African elephants can even use long-distance communication to maintain social bonds with individuals that may be literally miles away.
For the most part, we study these kinds of things using playbacks: we make a recording of the sound we're interested in, play it back at the animals from a hidden speaker, and see what they do. The alternative, of course, is simply watching them behave normally, recording everything that they do. Which takes a lot longer, but provides a more complete picture of what's going on.
There's also the issue (as always) of the sheer number of mammal species we might wish to study, even if we stick, in this case, to the relatively large and sociable ones. Fortunately, there's a general rule of thumb that, if the animals are closely related, and have a fairly similar lifestyle, the odds are that their communication signals aren't that different, either. The problem, of course, is that's not necessarily true in all cases.
The largest primates, after the apes, are the baboons. There are, as currently recognised, eight species of baboon, although molecular studies have shown that they aren't all each other's closest relatives, and thus that the word 'baboon' as used in English doesn't represent a real evolutionary group. Having said which, if we trim away the gelada baboons and the two kinds of 'drill' baboon, the remaining five species are indeed closely related, having their last common ancestor some time around the early Ice Ages - not really long at all, as such things go.
Among these 'true' baboons, the one that has been studied most thoroughly is probably the chacma baboon (Papio ursinus). That's likely because it's the one that lives in South Africa (among other places), one of the more prosperous African nations. From studies on vocalisations of these baboons, we know that they can identify familiar individuals by the sounds of their voices, that they can tell when another baboon is specifically trying to 'talk' to them, and that the various sounds are used for a variety of purposes, including coordinating group movements and 'making up' after a dispute.
How far can this sort of understanding be extended to the other baboon species? That may depend on subtle differences in their social structures - they are, after all, different species, and something separated them and stopped them interbreeding. For instance, while male chacma baboons loudly scream at one another to try and demonstrate their physical fitness and (implicitly) fighting ability, male Guinea baboons from western Africa, do not, apparently because their mating system involves less violence to start with.
|Baboons and their relatives|
Chacma baboons are probably not the closest living relatives of the olive sort (that's probably the yellow baboon, which lives in the region between the other two species). But they do live in much the same manner, at least when it comes to their social arrangements, and the structure of their troops.
In this light, it's notable that it has recently been confirmed that female olive baboons signal friendship in almost exactly the same way as the previously studied chacma species do. This is marked by a "grunt" that is, acoustically, similar to a human making a vowel sound. Observations of olive baboon troops in Kenya show that when a female makes this sound as she approaches another female, she is more likely to be greeted positively, often being allowed to handle the other female's baby. If she makes the sound after approaching, this has a calming effect, reducing the risk of violence.
We can tell something about the concerns of life as a female baboon by noting when females choose to use this sound. It doesn't seem to be employed every time they approach another of their kind - that would presumably happen rather a lot - but only when the baboon being approached might otherwise have something to fear. So, they are more likely to use it on mothers with young children, who might be understandably nervous about the consequences of any potential violence.
Similarly, junior, submissive, females don't bother to use it when approaching stronger and more dominant ones, presumably because the latter already know that they have nothing much to fear. In the opposite situation, however, dominant females do use these placating grunts, perhaps as a signal that, while violence is always an option, in this case, they come in peace. Mothers and daughters also don't typically grunt to one another, likely sufficiently comfortable in one another's company that friendliness goes without saying.
All of this suggests a fairly sophisticated communication system, in which baboons are able to make inferences about one another's motives based on context as well as direct verbal cues. The fine details may vary between species, depending on the exact social structure of the troops, which are known to be unusually nuanced in baboons, compared with other monkey species. But there's clearly an underlying core here, laying the foundations for the sort of peaceful cooperation that we often also see in apes.
[Photo by Charles J. Sharp, from Wikimedia Commons. Cladogram adapted from Springer et al. 2012].