There are many reasons that we'd like to know more about the lives and habits of elephants; even leaving pure curiosity aside, on a practical level it might help us to find ways to manage elephant populations so that they can peacefully co-exist with our expanding agricultural and residential footprint.
But there is a problem to really getting to grips with elephant "societies" and how they function. That's because, in addition to being large, elephants are also remarkably long-lived. If you go out into the wild and study a herd of elephants for five years, you will get a lot of information, but it's really just a snapshot of what's going on in the course of their lives. Elephants can live for at least seventy years, and a generation lasts for about 25 years, so getting a really good picture of an elephant's life would take... well, a human lifetime.
Scientific studies don't come free of charge, and the funding cycle is rarely longer than three years or so (the length of time it takes to do a PhD), which means that even, say, ten-year studies face more obstacles than mere commitment on the part of the researchers. Nonetheless, a number of genuinely long-term studies have been conducted on elephants, sufficient to give us some insights into how their societies work on scales of a decade or more.
There are three recognised species of elephant alive today: the bush or savannah elephant (Loxodonta africana), the forest elephant (L. cyclotis), and the Indian or Asian elephant (Elephas maximus). It's probably fair to say that the first of those three is the most studied species, and the second, which was only confirmed as a separate species in 2010, is the least. Even so, we can make some generalisations about elephants as a whole, and it's perhaps worth noting that, since they descend from the same common ancestor (rather than being an evolutionary side-branch), anything that's true of all three living species has a good chance of being true for mammoths as well. Not that we're likely to ever know that for sure...
At any rate, one of the most distinctive features of elephant herds is the importance of matriarchs. These are dominant, older females, often no longer reproducing themselves, who are able to use their extensive knowledge to aid the rest of the herd. It has been shown, for instance, that herds led by older, more experienced, matriarchs are more successful at rearing infants. This is partly due to their knowledge about the world around them; where to find water holes during the dry season, for instance, or which predators it's most important to watch out for.
But they also retain considerable social knowledge. For example, bush elephant matriarchs have been shown to be able to recognise and identify an average of 14 other herds by the precise sounds that they make, and respond accordingly. As a result of this social networking, dominance hierarchies even exist between herds, as well as between individuals within a herd, with higher ranking herds being able to access better resources, thus maintaining their status. Elsewhere among mammals, this sort of complex, multi-level social structure is only common among primates, although it has also been observed in whales and horses, among others.
While this arrangement seems to be best developed in bush elephants, it is found to a lesser extent in the other species, too. At times, it can allow different herds to merge together, whether for protection, wider mating opportunities, or seemingly just for the social benefits. This happens primarily where food resources are plentiful, so that there is little competition or disadvantage to having a single large herd, and is more common between elephants related on their mother's side than we'd expect from purely random mixing.
It has been calculated that, under perfect conditions, elephant populations would grow by about 7% per year. Obviously, such conditions rarely occur, being limited by such things as the number of available water holes as well as the local abundance of food. For example, elephants are more likely to become pregnant in years with high rainfall, probably because their pregnancy lasts so long that it can take them literally years to fully recover from the loss of a calf during an extended drought.
What about the males? Much of their life is centred around the need to compete for dominance, and hence, females. Nonetheless, males of a similar age bond with one another, hanging out together, perhaps to provide themselves with evenly matched sparring partners to practice fighting with. At higher social levels, older males dominate, influencing the formation and maintenance of the smaller all-male groups. The regular dominance hierarchies established in this way tend to break down in wet years when food is plentiful, and can be disrupted on a temporary basis when males enter musth - a period of high aggression and sexual activity similar to the rut seen in other animals, except that males can and do mate and sire young even when they aren't in musth.
It is because elephants are so intelligent that such complex social structures can develop, and the elephants can respond to the changing world around then, modifying their behaviour as required. On the other hand, the development of these social lives will be a part of the reason that they have developed this intelligence in the first place - the two likely go hand-in-hand in a cycle of cause of effect. For instance, elephants can not only identify one another as individuals by their sound, smell and (presumably) appearance, but they seem to understand what this means, being able to keep track of where they - or should be - even when they can't see them.
At least fourteen different call types have been identified among elephants, even though it's currently far from clear what they all "mean". Even so, it seems likely they have a lot to do with maintaining the structure of elephant societies, and helping to pass at least some information between individuals
Ivory hunting is an obvious problem, not just because it kills elephants, but because it focuses on the larger, and hence older and more experienced, individuals. But even if we could do away with that, human activity will almost inevitably disturb the complex interrelationships between elephants, and there would still be the issue that elephants genuinely do cause enough crop damage for farmers to want to retaliate against them. They can also either damage or enhance the natural ecology of the world around them by their mere presence.
All of this should give us good reason to want to understand their lives and behaviour more thoroughly.
[Photo by Jayanand Govindaraj, from Wikimedia Commons.]