“If the male is successful in forming a friendship with a female, that gives him an opening with her relatives and allows him to work his way into the whole female network,” said Barbara Smuts, a biologist at the University of Michigan. “In olive baboons, friendships with females can be much more important than political alliances with other males.”

Because males are often the so-called dispersing sex, while females stay behind in the support network of their female kin, females form the political backbone among many social mammals; the longer-lived the species, the denser and more richly articulated that backbone is likely to be.

With life spans rivaling ours, elephants are proving to possess some of the most elaborate social networks yet observed, and their memories for far-flung friends and relations are well in line with the species’ reputation. Elephant society is organized as a matriarchy, said George Wittemyer, an elephant expert at the University of California, Berkeley, with a given core group of maybe 10 elephants led by the eldest resident female. That core group is together virtually all the time, traveling over considerable distances, stopping to dig water holes, looking for fresh foliage to uproot and devour.

“They’re constantly making decisions, debating among themselves, over food, water and security,” Dr. Wittemyer said. “You can see it in the field. You can hear them vocally disagree.” Typically, the matriarch has the final say, and the others abide by her decision. If a faction disagrees strongly enough and wants to try a different approach, “the group will split up and meet back again later,” said Dr. Wittemyer.

Age has its privileges, he said, and the older females, even if they are not the biggest, will often get the best spots to sleep and the best food to eat. But it also has its responsibilities, and a matriarch is often the one to lead the charge in the face of conflicts with other elephants or predatory threats, sometimes to lethal effect.

Hal Whitehead of Dalhousie University and his colleagues have found surprising parallels between the elephant and another mammoth mammal, the sperm whale, possessor of the largest brain, in absolute terms, that the world has ever known. As with elephants, sperm whale society is sexually segregated, the females clustering in oceanic neighborhoods 40 degrees north or south of the Equator, and the males preferring waters around the poles.

As with elephants, the core social unit is a clan of some 10 or 12 females and their offspring. Sperm whales also are highly vocal. They communicate with one another using a Morse code-like pattern of clicks. Each clan, Dr. Whitehead said, has a distinctive click dialect that the members use to identify one another and that adults pass to the young. In other words, he said, “It looks like they have a form of culture.”

Nobody knows what the whales may have to click and clack about, but it could be a form of voting  time to stop here and synchronously dive down in search of deep water squid, now time to resurface, move on, dive again. Clans also seem to caucus on which males they like and will mate with more or less as a group and which ones they will collectively spurn. By all appearances, female sperm whales are terrible size queens. Over the generations, they have consistently voted in favor of enhanced male mass. Their dream candidate nowadays is some fellow named Moby, and he’s three times their size.