The feedback loops that direct the growing ant empire also decide how those same ants will get a meal. Outside our ant nest, a delicious juicy orange has just dropped from the branches of a tree. Within days, under the warmth of the sun, it begins to rot, oozing its sugary interior onto its surroundings. An ant, scouting around outside the nest, its antennae feverishly flicking, picks up the scent of the moribund fruit. It stumbles across this treasure trove and swings into action. Scurrying around the orange, it bumps into one of its fellow workers and, in a brief meeting of heads, instructs the other to return to the nest and recruit more workers. Soon, a trail is established to the nest, ants darting back and forth along the trail, great globs of sugary fluid in their mandibles. As each ant in the trail recruits others nearby, the numbers multiply rapidly and soon we have a miniature road crammed with them dashing back and forth.
As the ants smother the orange, no amount of extra workforce will be much use. Now there are too many cooks in the kitchen. Soon the orange, dismembered in the feasting mandibles of the colony, runs dry and thus the numbers of ants recruited to the orange declines. Other ants, ensuring that the nest does not rely on only one orange, react to “keep-away” messages. These black sheep of the colony, if you will, deliberately head off in new directions to find new food sources. Eventually, the orange is depleted and the trail dies away. In the appearance and disappearance of ant trails, we have no queen ant sitting in her chamber with a map, planning new excursions to find food, drawing lines on a grid, and instructing her minions to systematically scour each square for food. Instead, plain rules, beginning with a lone scout ant trekking across the home turf, lead to mathematical processes that end in food.
Like other aspects of the ant world, we can even write this entire scenario in an equation:
p1 = (x1 + k)β / [(x1 + k)β + (x2 + k)β]
where p1 is the probability that an ant will choose a particular trail to run down. The probability is predicted using x1, which is the amount of attracting pheromone on that trail, which may just equate to the number of ants already on the trail. The variable x2 is the amount of pheromone on an unmarked trail, which an ant might follow instead. The variable k is the attraction level of a pheromone on the unmarked trail, and β is a factor that takes into account the nonlinear behavior of ants, in essence some of their social complexities and behavior that vary from species to species. The higher the value of β, the greater the probability that an ant will go down a trail even if the trail has only slightly more pheromone.
This is the equation of feeding ants. Here, in essence, we have an equation that predicts where ants like to go for food.
A human analogy to this whole episode is the arrival of a new artisan cheesecake shop in Edinburgh. Delicious new cheesecake, handmade at that, is a delight for city dwellers to offer at their summer luncheons. Delia accidently stumbles across the shop and buys some for her next gathering. Her guests are delighted, so she tells her friend Sophia. Now Delia and Sophia are both telling their friends, and soon, everyone is calling everyone else. There is a run on the cheesecake shop. It’s the place to go. A cheesecake feeding frenzy engulfs Edinburgh. Soon, however, there is no one left in Edinburgh to call. Everyone knows about the cheesecake shop. The number of people dropping in at Bruntsfield Cheesecakes, begins to plateau. But there is worse. Now cheesecake is no longer chic. Soufflé is the order of the day, and a new shop opened up on George Street that does some pretty nice stuff. Those in the know now call their friends to get ahead of the game. Avoiding the cheesecake shop in favor of the new trend, the shop’s clientele declines. As the shop cuts back on making cheesecake, this sets in motion an even smaller demand and the cheesecake shop is all but abandoned.
Delia and her cheesecake or soufflé preferences look like a complex social arrangement, but they follow simple rules. She and her friends have received no instructions from Edinburgh Council (or the queen herself) on whether to buy cheesecake or soufflé. In the ant world, without the real complication of the somewhat intricate social mores of humans, these simple feedback processes also drive the ants to switch from one food source to another.
The world is never as straightforward as a single orange. Perhaps several oranges have fallen from that tree. Faced with a tantalizing choice, even the smallest fluctuations in the number of ants running around could lead to one orange or another being chosen first. So predictability comes from the equations—we can define the rules that decide in principle which trail an ant will go down, but there is unpredictability in how the equation is manifested and the exact trail it will work its effects on. In the complex variations of the natural world, these small fluctuations play an immensely important role in shaping behavior, and no doubt they contribute to our sense that living things are inherently unpredictable, different from inanimate objects.
Other occasions cause the rules to be less easily discerned. A particularly large ant colony may have so many individuals that they simultaneously swarm many oranges, tearing them apart in a feeding frenzy. Under these conditions, our delicate feedback effects are all but gone to the wall. And, of course, the environment itself will mess up those nice, elegant equations. Put one of these oranges in a crack in the ground or under some particularly cumbersome vegetation, and the trails and feedback processes suddenly become motley and tortuous. Nevertheless, beneath these quirks, the equations of ants work their way.
The feedback systems operating in the nest might even help explain another enchanting and mysterious feature of animals: synchronicity. This quality appears not merely in ants, but also in termites, birds, and other animals. If ants are just communicating one to one with no overarching supervision, then why do we see mass organization, sudden bursts of nest building or food foraging interspersed with quiet times, synchronous behavior between many individuals?
What appears to look like good evidence for social organization at a high level may yet again reduce to some plain rules. Some of the synchronicity is thought to be caused by those feedback loops we saw in operation as the ants built their nest. A trigger from a few ants ripples through the colony as they communicate with one another. Add in some programmed tendencies, like a natural period of quiescence after a sudden bout of activity, a sort of rest period not uncommon in many animals, and distinctive patterns of behavior can quickly appear to engulf the whole population. These phenomena require no superintendent to coordinate and watch over them, but rather they emerge from the self-organizing behavior of populations in communication at the individual level.
In seeing our capacity to describe ant behavior using equations, we are tempted to think that this is the whole story. Of course, ants are not mere atoms of a gas. An ant is made up of a quarter of a million neurons, the cells that transmit electrical information in our brains and in the nervous systems of other animals, including the tiniest insects. Like a miniature computer, an ant is not a mere passive observer of the world around it, like a small atom of gas bouncing and colliding with other atoms. It has oddities of behavior, perhaps molded by the ant that fell on it early in the day or the number of ants it was with earlier. And alongside that behavior, new calculations are constantly being made. The number of ants it bumps into in a given time allows it to estimate the sum of other ants nearby and so modify its conduct. Even the concentration of carbon dioxide, the gas exhaled by other ants, provides a measure of the density of ants in any part of the nest, feeding into that mini calculating machine to make it redirect its action. Proactively, ants can respond to many cues being sent their way and can initiate new behaviors that propagate through the swarm. The behaviors amplify those infinitesimal feedback loops and changes in the environment that a passive particle would ignore.
In some ways, this capacity of a living thing to respond to what is going on around it rather than merely acquiescing to perturbations in its world is a categorical difference between a living and nonliving entity. However, those reactions are still within the fold of the overarching physical principles a
t work. The reactions complicate the matter, but they do not put living things outside the realms of rules and principles within which they can operate—principles that we can, with enough experimental and theoretical effort, fathom.
This union between physics and biology operates beyond the imperium of insects. Far above the troglodyte lair of the ants, physicists have been attempting to unravel the mysteries of birds.
Since the ancients, humans have gazed with joy at the sight of geese gracefully winding their way across the sky in echelon or V formations, apparently coordinated and organized. Equally impressive and grander in scale are the murmurations of starlings. Sometimes thousands of birds, huddled together in a giant pulsating wave, sweep and dive in an evening sky. The self-organization of these masses attracted the attention of physicists in the 1990s; perhaps with some trepidation, the scientists launched into attempts to understand these phenomena, apparently some of the most complex in the natural world.
Hampering efforts to explain how birds organize themselves in such splendid displays was a lack of computer power to run simulations and the difficulty of getting real data. Tracking several thousand birds jostling and changing direction in three dimensions is no minor technical task. Yet advances in computer processing power, better cameras, and image-recognition software allowed people to collect some real information about bird flocking. Perhaps most surprisingly, computer gamers and filmmakers threw their efforts into the fray. Sometimes, help comes from unexpected places. Need a flock of birds in your film? You had better make them look realistic. As computer-generated sequences in blockbusters became more prevalent, so too arose the need to accurately portray birds, fish, migrating wildebeests, and a whole variety of Disney superstars. Hollywood met science.
At the core of these new attempts to simulate how birds flock are some basic assumptions about their behavior. We must establish some basal rules on how they operate. It is safe to assume that birds want to avoid collision as one condition of their behavior. Otherwise, flocking would be a bruising and messy business. They want to align their headings and stay grouped together. If they do not do that, the group will disperse, and we would quickly have individual birds heading off in random directions. We can get more complicated if we want to. We could assume that birds will try to match the speed of nearby birds, part of the strategy for staying grouped together.
Take these properties, and put them into a computer, and you can produce strikingly lifelike simulations of clusters of birds and other flying animals. So much so that the bat swarms in the film Batman Returns were generated using these simple algorithms.
The complexity and the subtlety of these models have been magnified in recent years with arguments and discussions over the details. Should the important rule be keeping a certain radius around each bird, or is it the number of individuals nearby that matters? How do you estimate and account for attraction and repulsion between birds, considering that they do not merely behave like particles that either collide or stay apart, but that they will avoid neighbors or try to get closer? Deciding on these sorts of intricate elements is no easy task, and the whole enterprise is made more difficult because we do not actually know what is going on in a bird’s head. What calculations are really being made? A model may reproduce something realistic, but it is not based on how birds are thinking in the natural world. A scientist without a birdbrain is limited.
Like our ants, birds too are subjected to evolutionary pressures. They might want to minimize the energy they use, to conserve it for breeding. They might be in an area with a high density of predators intensifying the birds’ tendency to swoop and veer to avoid being eaten. As darkness falls and their visual acuity drops, their behavior might change. And so on. Myriad environmental cues and selection pressures influence flocking. But similar to the situation with our ants, these influences seem to be just a veneer of complexity on the underlying rules that guide their patterns of behavior.
If you watch a flock of birds the way people observed ants, you can become easily convinced that one bird must be leading them. If that sort of group was a bunch of human hikers out on a ramble with no leader, chaos and misdirection would soon ensue. Just as we do for insect communities, we project the structure of our own societies onto birds and assume that the apparently organized behavior of a mass of them must require an avian superintendent to guide the flock. It feels counterintuitive to think that such organization could happen without an organizer, that disintegration of the regularity of the flock must surely occur if there is no oversight. Yet rules applied to particles in a computer show that self-organization can emerge to produce the phenomenal complexity of flocking behaviors with no head bird.
The gulf between biological behaviors and our ability to present them in physical principles, in equations, is narrowing. The infant state of our true knowledge of self-organization does not lessen the quite impressive strides made in using equations to produce realistic simulations of animal flocking, bringing us to the world of computer-generated starling murmurations. As those models are refined, no doubt the accuracy will improve and the collaboration between physics and biology will deepen as their common ground is found in one of the most ambitious programs between the two fields—to predict the behavior of populations of living things.
There is one aspect of all this that we have ignored so far. It is something physics is less able to predict, but it is singularly important in understanding why those equations work. The principles that govern flocking birds do not tell us why they do it in the first place. If you watch a vast display of starling murmurations, you are immediately enticed by the question of why. An obvious idea is that they are avoiding predators, the classic notion of safety in numbers. Faced with thousands of birds, the predator, perhaps a hungry hawk, must select one, and with such large numbers, an individual’s chances of being picked off are minimal.
The problem, as keen ornithologists soon recognized, is that the birds seem to flock at the same time and place every day. Their displays often last for over thirty minutes before they settle down to roost for the night. Surely, after a few days, rather than throw off predators, this regularity would attract predators, which would quickly learn that several thousand potential meals take to the sky each evening at a particular place. Quite apart from that, the flocking behavior—every evening—seems remarkably wasteful of energy.
There is another important thing for a bird to think about other than whether it is about to be eaten. The number of birds in a flock will affect the number of available roosting sites and the available food that can go around. One advantage of taking to the air in a coordinated evening group has been suggested: individuals can assess the size of the flock and thereby make simple, instinctive calculations that might change their breeding behavior. How many chicks you want to have is sensibly organized around how much food and housing you have access to. By carrying out this regular census, the birds can modify their behavior to improve their individual chances of producing offspring, the ultimate arbiter of evolutionary success. This explanation of the evening flocking behavior may not require some spurious appeal to birds behaving for the benefit of the group or species, but could be driven by improvements in individual success. However, evidence for it is weak.
The real purpose of the murmurations remains something of a mystery and, like much in the natural world, may have no single answer. Instead, there may be multiple benefits to those magical displays. But our lack of insight into why they happen does not prevent us from making formidable progress in understanding how they occur and the universal rules that may shape them.
Turning our gaze from the starlings, we are struck by equally beautiful and alluring displays by larger birds, the echelon shapes of geese honking gently in their graceful journeys across the sky. Very different from the starlings’ murmurations, these formations too have not been lost on physicists.
Take some hypothetical computer geese, and give them some rules, similar to those that apply to the
starlings. The geese should try to stay near the closest bird and avoid collision, and they should attempt to stay where they have an unobstructed view of the way ahead. Additionally, and unlike the starlings, each individual should try to stay in the upwash of the bird ahead of it. Now this latter rule turns out to be important because one theory for why birds like geese fly in these long, strung-out formations is to save on energy. By placing yourself in the vortices of air spiraling off the wing tips of the bird in front of you, you gain the advantage of those swirling air currents curling up under your wings and giving you some lift. The notion that those fanciful formations are actually about aerodynamic efficiency in long migrations across the continents and oceans is one leading theory for why birds would do this. When you run these rules on the computer geese, they can produce extraordinarily lifelike flocks of birds that adopt all the patterns seen in the wild—echelons and V and J shapes.
But the nagging question remains: is saving energy really the reason for gander goose’s geometries? In another serendipitous link between scientists and filmmakers (the acting world seems to have an attraction to flocking birds), Henri Weimerskirch, an ecologist, stumbled across a film company training a flock of great white pelicans (Pelecanus onocrotalus) to fly alongside microlight aircraft and powerboats so the filmmakers could get stunning footage of bird formations. Weimerskirch saw an opportunity to test the aerodynamic efficiency theory. By attaching heart-rate monitors to the birds, he showed that the birds had a heart rate 11 percent or more lower than solitary birds did, supporting the idea that the upwash in flight was enough to cut down the energy demands of flying. A small margin perhaps, but over a vast migration of hundreds or thousands of miles, such savings might make all the difference.
Because pelicans are social animals, an explanation for Weimerskirch’s findings could be that the solitary birds were stressed. When the loners were deprived of their friends, perhaps their heart rates shot up, explaining why in organized groups the birds were less stressed and had lower heart rates.
The Equations of Life Page 4