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If you think too much about the interplay between mathematics and behavior, you start to feel like Neo from The Matrix.* Reality as you know it begins to dissolve and, slowly, something else comes into focus:

Equations. Code. The Matrix. A complex web of ledgers and calculations that influences nearly everything we do.

Some calculations are built into an animal’s DNA and are carried out without conscious awareness. Take kin selection, for example, which explains why we and other animals might act against our own self-interest to help our relatives. We take this drive for granted—of course you help your family!—but at first blush it seems to run counter to the cold, unforgiving calculus of natural selection, in which our own genes have evolved to “selfishly” replicate themselves. That is, until you remember that there’s more than one way for our genes to survive and reproduce. After all, we share roughly half of our DNA with our siblings, a quarter with our nieces and nephews, an eighth with our cousins, and so on. When animals help relatives at cost to themselves, they may still be promoting their own genes’ reproductive success—provided they help the right relatives in the right proportion. Biologist J.B.S. Haldane had his tongue firmly planted in his cheek when he said, “I’d lay down my life for two brothers or eight cousins,” but this same idea, formulated as a biological rule, can be used to predict behavior as disparate as which orphans will be adopted by which red squirrels and how humans will behave in economic games. It’s behavior, explained—in part—by math.

Not all heritable predispositions can be reduced to equations so neatly, but if you squint you can still see the tally marks on the ledger. As I mentioned in a previous post, chimps tend to exhibit different rates of lethal violence depending on whether the victims are members of their community or strangers from a neighboring community. The benefits to killing a neighbor are clear: less competition equals more food and mating opportunities. And the costs are limited to the potential injuries a chimp might sustain during the attack. But what about aggression within the community? If dominance is beneficial, why not kill your way to the top? Well, for one thing, you’d be awfully lonely when you got there. Chimps live in communities because they benefit from group living. Community members help find food and raise offspring, they signal when predators are near, and they assist in territorial defense. To reference another movie: APES TOGETHER, STRONG.** The costs and benefits of aggression relative to the benefits of cooperation in these different circumstances have been calculated over millions of years of evolution and have resulted in feelings, emotions, and tendencies that favor ingroups while treating outgroup members as things to be kidnapped or eliminated.

In these cases chimps are acting largely unconsciously on the math of natural selection, but there are times when they are most definitely doing the calculating themselves. Territorial patrols are a good example of this. As Craig Stanford writes in The New Chimpanzee:

A patrol begins when a group of males breaks off from some other activity and makes a beeline toward parts unknown. The males travel with increasing caution as they approach the territorial border…The males appear to be on edge, freezing at distant sounds to listen intently before continuing. They begin to show intense interest in objects that might be evidence of the enemy, stopping to examine and sniff stick tools, leaf wadges, nests, and feces. But the patrol may penetrate further, making a deep incursion in to enemy territory. The tension is palpable as the males continue for hundreds of meters before turning back. On most of the patrols I accompanied at Gombe in the 1990s, such a deep incursion ended with the males freezing when they heard distant calls from the enemy community, then wheeling around and racing back into the home range, whereupon they hooted and displayed as though venting the emotional tension of their mission.

He writes:

Chimpanzee intercommunity conflicts are really raids. A party from one community attacks one or a few individuals from an adjacent community, usually in the overlap zone of their territorial boundaries. Such attacks may be carried out strategically when the attackers detect an imbalance of power. Ten chimpanzees rarely engage in a battle with ten or more enemies…So male chimpanzees monitor their territorial boundaries, picking and choosing their battles based on their perception of when a critical mass in their ranks can successfully challenge neighbors. [emphasis mine]

Like humans, chimpanzees may be endowed with behavioral predispositions but they don’t act on instinct alone. They are always crunching the numbers—and in the case of patrols, performing calculations based off of evidence, like detectives investigating a crime scene. Nine fresh nests and a chorus of pant-hoots in the distance—we’d better turn back. They may want to attack, but will not do so unless they’ve determined that the odds are in their favor.

This type of calculating behavior is not limited to aggression. Chimpanzees are known to reconcile after conflicts with fellow community members. As we’ve already discussed, community members are valuable. But some are more valuable than others, right? Some are potential allies in an effort to move up in the hierarchy. Some may be regular hunting or grooming partners. Some may even be kin—especially in the case of males, who tend to remain in their natal communities. These relationships are, in a way, investments, in which trust has been built and years of reciprocal favors have been exchanged. These are the relationships worth saving—in primatology lingo, they are valuable relationships. And it’s the Valuable Relationship Hypothesis that is used to explain why chimps tend to reconcile more readily or more frequently with certain individuals. It can even be used to predict their likelihood of reconciliation. Just consult the ledger—how often do they groom, and in which direction is the grooming typically directed? How many times has one supported the other in a fight? How often do they mate?

OK, so to paraphrase a blog commenter from many years ago: BORING DISSERTATION, J.B. Who cares about any of this? Well, George, for one. You can bet that he has been furiously crunching numbers ever since he got here. And we’re fortunate that he seems relatively good at math. You can actually see him update his equations and alter his behavior in real time as he gains new experiences—unlike our arithmetically challenged friend, Willy B.

But we caregivers have our calculators out, too. When starting introductions, our first job is to tackle that unfortunate biological predisposition that says that strangers are enemies. We can’t change their DNA, but we can work to make strangers seem a little less strange. This is why we begin with one-on-one meetings, especially with a lone chimpanzee like George. As mentioned above, chimps are less likely to exhibit lethal violence when they lack support. Put George with a large group too soon and he may fall victim to outgroup violence. Put him with one chimp at a time and, while they may fight, they’re more likely to hold back as a matter of self-preservation. And over repeated meetings, strangers slowly become familiar—not quite members of the group, but not quite enemies, either. The calculus changes, and the behavior follows suit.

When it’s time to move beyond the one-on-one meetings and build up the group, the order—and the math—matters. Based on the outcomes of the dyadic meetings, we get a vague sense of the relationships between each dyad—which ones exhibit trust and which ones show tension, for example. As you add members to the introduction group, you might be tempted to save the tense relationships for last. That could be a mistake, because chimps will assess when they have overwhelming advantage—or critical mass, as Stanford calls it. If Terry and George have some things left to work out, let’s let them work them out with just Cy and Rayne overseeing the process, and hopefully by the time Lucky, Gordo, and Dora are added, Terry and George will have clarified their relationship. Add Terry at the end, and his threat barks could rally the rest of the group to overwhelm Cy’s defenses and gang up on George.

When conflicts do occur, and they inevitably will, it’s important to steal a glance at the chimps’ homework. How are they calculating the value of their new relationships? There’s no use reconciling with an enemy. Enemies are competition, pure and simple, and you’re better off without them. But if a relationship has value—if there’s a good chance of cooperation in the future—you’ll be quicker to repair it when it is strained. Whether chimps reconcile after a conflict, and how soon, can be an important indicator of how integrated a new chimpanzee is into a group. We’ve witnessed only a few conflicts since Terry was added to the intro group. The first was intense but somewhat limited due to a relative balance of power—while Rayne rallied to Terry’s side, Cy was able to fend them off. Terry and George largely avoided each other immediately following the incident. OK, that’s not good. But subsequent conflicts have been less intense as more interactions have been added to the positive side of the ledger, and the reconciliation has been swift, as you can see below. Does this mean that we no longer have to worry about George’s safety? Certainly not. But we can have some hope that future conflicts will more closely resemble ingroup conflicts, in which violence is typically less intense and more ritualized and the chimps actively work to repair and maintain relationships.

There’s a risk that this could all be interpreted as me stating that there is a right way to conduct introductions, or that we know more than we do about how to run them. Our efforts to integrate Willy B should dispel that notion. And even if there were a right way, the outcome is still largely out of our control, regardless of our actions. You’ll rarely feel more powerless than when you are conducting a chimpanzee intro. Nevertheless, it can still be worth occasionally peeling back the curtain and glimpsing the matrix that influences so much chimpanzee behavior.

*A movie that I don’t think I’ve ever seen in full—and yet I will overconfidently cite here as though I have because of its prevalence in American popular culture—in which a programmer named Neo is able to see the code behind a simulation that everyone had until then accepted as reality.

**I did see this one. It was about a group of apes that escaped and took over the world, and we watched it a few days before we let the chimps out into an electric fence enclosure that was the first of its kind in the U.S. and was definitely going to work on paper and hopefully in real life and I hoped that Jamie and company would allow us to live and reside in their kingdom once they took over.