Honeybee Democracy - Thomas D. Seeley (2010)
Chapter 9. SWARM AS COGNITIVE ENTITY
I’m a systems neurobiologist who studies how the three
pounds of goo we call a human brain makes decisions.
—William Newsome, 2008.
The previous six chapters of this book describe what is known about how the three pounds of bees we call a honeybee swarm makes a decision about where it will build its new home. The starting point was the mystery of how a bunch of tiny-brained bees, hanging from a tree branch, can make a good choice for their future living quarters and can take timely action on their decision. We then reviewed the observational and experimental evidence concerning each specific mechanism of the house-hunting process—an ingenious and sophisticated tangle of behaviors, communication systems, and feedback loops. Throughout, we’ve seen that a swarm of bees is a democratic decision-making body that is remarkably accessible to analysis, since we can easily observe what the individual bees are doing while an entire swarm is conducting its decision-making process. It is an amazing bit of good fortune that all of the important individual-level actions occur in full view, either on the surface of the swarm or at the prospective home-sites, not deep inside the mass of tightly clustered bees. It has been important to first work our way through the nuts and bolts of the bees’ house-hunting process, so we really know this process, but now it is time to step back from the detailed analysis and synthesize what we know by considering the general features of a swarm as a decision-making system.
In doing so, we will find it useful to compare what is known about the mechanisms of decision making in bee swarms and primate brains. This may seem a bizarre comparison, for swarms and brains are vastly different biological systems whose subunits—bees and neurons—differ greatly. But these systems are also fundamentally similar in that both are cognitive entities that have been shaped by natural selection to be skilled at acquiring and processing information to make decisions. Furthermore, both are democratic systems of decision making, that is, ones in which there is no central decider who possesses synoptic knowledge or exceptional intelligence and directs everyone else to the best course of action. Instead, in both swarms and brains, the decision-making process is broadly diffused among an ensemble of relatively simple information-processing units, each of which possesses only a tiny fraction of the total pool of information used to make a collective judgment. We will see that natural selection has organized honeybee swarms and primate brains in intriguingly similar ways to build a first-rate decision-making group from a collection of rather poorly informed and cogni-tively limited individuals. These similarities point to general principles for building a sophisticated cognitive unit out of far simpler parts.
Conceptual Framework for Decision Making
In essence, decision making is a process in which information is acquired and processed in order to make a choice between two or more alternatives. Thus a honeybee swarm performs decision making when it obtains information about the qualities of a dozen or more potential homesites, processes this information, and selects the most desirable site for its new residence. A good example of a primate brain performing a decision-making task is when a monkey is presented with a visual display consisting of a cloud of white dots moving against a black background (fig. 9.1). Most of the dots move randomly, but a small fraction move coherently in one of two possible directions, left or right. The monkey has been trained to decide whether the motion direction of the coherently moving dots is left or right and to indicate its decision by making an eye movement to a left or right target. The percentage of the displayed dots that move coherently can be varied to make the quality of the information higher or lower, and thus the decision-making task easier or harder.
While other behavioral biologists and I have been working to understand the mechanisms of a honeybee swarm’s decision making at the level of individual bees, neuroscientists have been working to understand the mechanisms of a human brain’s decision making at the level of individual cells. The best progress in unraveling the neural basis of human decision making has been made by studying monkeys (serving as human surrogates) as they perform the decision-making task just described in which a monkey sees a “noisy” visual stimulus, makes a decision in the two-alternative (left or right) choice test, and indicates its decision with an eye movement. By recording neural activity in the various areas of the brain involved in reporting visual information, in processing this information, and in
controlling eye movements, neurophysiologists have identified the neural processes that underlie this particular decision-making task.
The starting point is the middle temporal (MT) area of the brain, which processes sensory information about the motions that the monkey sees (fig. 9.2a, b). Each neuron in the MT area has a receptive field that corresponds to a particular portion of a monkey’s entire visual field. Also, each MT neuron is motion sensitive for a particular direction of movement, that is, it is activated to fire when a stimulus moves across its receptive field in the preferred direction, and it is inhibited from firing when the moving stimulus travels in the opposite direction. Thus the population of neurons in the MT area is a set of direction-tuned motion detectors that report, in their firing rates, information about the strength of visual movement in their preferred directions within their particular portions of the monkey’s visual field. Collectively, they provide the monkey’s brain with information regarding the strength of rightward motion and leftward motion over the monkey’s whole visual field, hence over the full display of moving dots. At any given instant, however, this information is somewhat ambiguous because of randomness in the moving dot display and because of noise (random fluctuations) in the representation of the information by the MT neurons.
The next step in the monkey’s decision-making process occurs in the lateral intraparietal (LIP) area of the brain. The neurons in this area receive inputs from the MT area, and they are organized into direction-specific integrators that sum over time the noisy information being provided by the corresponding MT neurons (fig. 9.2a, b). Thus, as time progresses in the decision-making task, evidence about what the monkey is seeing accumulates in the LIP neurons. For example, if a monkey is watching a visual display containing rightward-moving dots, then LIP neurons that function as rightward-motion integrators will increase gradually their firing rates. The rate at which their firing rates increase depends on the stimulus strength, that is, the number of the dots moving to the right. Also, the various integrators corresponding to different motion directions are mutually inhibitory. One effect of this mutual inhibition is that even if the firing rates of the LIP neurons associated with rightward and leftward motion increase at approximately the same rate at first, later only those neurons associated with the stronger stimulus (rightward motion) will continue to increase their firing rate; those associated with the weaker stimulus (leftward motion) will start to decrease their firing rate (fig. 9.2c). Each population of LIP neurons inhibits the others to a degree proportional to its level of activity, so eventually only the neurons in one LIP population will have high firing rates. This mutual inhibition improves the monkey’s discrimination by enhancing the perceived difference in strength between rightward and leftward stimuli, and so helps the monkey avoid attempting to make rightward and leftward eye movements simultaneously.
When the activity of one integrator exceeds a threshold, the decision is made and an eye movement in the appropriate direction is initiated. The eye movement is driven by the output (motor) neurons in the final stage in the monkey’s decision circuit. These are neurons in the frontal eye field (FEF) and superior colliculus (SC) regions of the brain, and they receive inputs from the LIP area. Here again, the FEF and SC neurons are direction-specific; each neuron will drive an eye movement in just one direction.
Leo Sugrue, Greg Corrado, and William Newsome, neuroscientists at Stanford University, have devised a helpful conceptual framework for thinking about the multiple stages of information processing that underlie making a simple perceptual decision, like what we’ve been considering (fig. 9.3). Their framework contains three stages or transformations. First, a sensory transformation converts the information about the external world that has been registered by the animal’s sensory organs into a “sensory representation,” which makes the information available for further processing within the animal’s brain. This is what the MT neurons do in the monkey’s motion-detection task. Second, a decision transformation converts the sensory representation into a set of probabilities for adopting the alternative courses of action. In the monkey’s brain, this transformation is implemented by the LIP neurons, as they convert the sensory representation of visual motion into a set of “evidence accumulations,” specifically the set of firing rates of the integrators representing different motion directions. The level of firing in a particular integrator population determines the animal’s relative probability of choosing the alternative represented by this population. Third, an “action transformation” converts this set of probabilities into a specific behavioral act. This final process of action implementation is performed in the monkey’s brain by motor output neurons in the FEF and SC regions when they are activated by the population of LIP neurons whose firing rates have reached a threshold level.
Remarkably, even though this conceptual framework was devised for helping us understand decision making in primate (including human) brains, it can also help us conceptualize the decision-making process in honeybee swarms. In both types of decision-making systems, sensory units create a representation of the outside world inside the system. Also, in both types of systems the processing of the information in the sensory representation consists of a competition between mutually inhibitory integrators of the information (evidence) flowing into the system. And finally, in both brains and swarms, the decision is made when the accumulation of evidence in one integrator reaches a sufficiently high (threshold) level.
The Sensory Transformation in a Swarm
In refecting on the structural parallels between swarms and brains, I like to think of a swarm as a kind of exposed brain that hangs quietly from a tree branch but is able to “see” many potential nest sites spread over a vast expanse of the surrounding countryside. As we have seen, what gives a swarm such an immense “visual feld” is its squadron of several hundred scout bees who fly out for several kilometers in all directions and scour the environment for prospective dwelling places. We now know that when a scout bee finds a site sufficiently desirable to be worthy of attention by others, she flies back to the swarm and reports her find on the swarm’s surface by performing a waggle dance. We also now know that the strength of her dance—the number of dance circuits performed—is proportional to the quality of the site. Thus a scout bee functions as a sensory unit of the swarm, one that transduces the quality of a nest site into the strength of a dance signal. It should be noted too that each scout is a site-specific sensory unit, for each bee reports on just one nest site in the surrounding area, much like each MT neuron reports on just one small portion of the visual field. Over time, as dozens of scout bees return to the swarm and perform dances, they gradually deliver a body of sensory information about the locations and qualities of the potential nest sites that they have found (fig. 9.4). This display of bee dances can be thought of as the swarm’s sensory representation of the landscape of possible nest sites. It is analogous to the pattern of MT neuron firings that forms a monkey’s sensory representation of the stimuli moving across its visual field.
Several features of the way that the scout bees build their swarm’s sensory representation are worth noting, for each makes an important contribution to the success of a swarm as a decision-making system.
1. The sensory apparatus of a swarm is a sizable population of scout bees. By field-ing several hundred scout bees, a swarm is able to gather a wealth of information about potential nest sites, usually within just a few hours. We have seen, for example in figure 4.7, how a swarm’s scouts can locate, inspect, and report on nearly a dozen possible home sites in an afternoon. Also, by distributing the information-collection process among numerous bees, a swarm averages out the bee-to-bee variations in strength of dancing for the sites and thereby increases the accuracy of its information acquisition.
2. Scouts collect sensory information for several hours or several days. It is important that swarms base their decisions on an extended sequence of samplings of sensory information because this information is acquired sporadically, especially at first. We have seen that even with several hundred scouts exploring simultaneously, several hours may pass before one of them returns with news of an outstanding find. And even after news has been received about all the alternatives, the further reporting on them tends to be episodic, as is shown in figure 6.5. A lengthy period of information gathering enables a swarm to assemble a sizable, and thus reliable, body of sensory information on each site.
3. Each scout makes an independent evaluation of a site. Even though most of the scouts reporting on a site are recruited to it, the recruitment process only brings a scout to a site. It does not compel her to report favorably on the site. Instead, each scout makes an independent evaluation and decides for herself how strongly to announce the site when she returns to the swarm and performs a dance. This independence of the scouts means that an evaluation error made by one bee won’t be propagated or amplified by blind imitation, and this helps ensure that the total amount of dancing for a site in a swarm’s sensory representation is an accurate indication of the quality of the site.
4. Scouts reporting on a site recruit additional scouts to the site. Recruitment by scouts creates positive feedback in the number of scouts reporting on a site as recruited bees become recruiters. This means that the sensory information representing a particular site can amplify itself. Because the strength of each scout’s dance depends on her site’s quality, the positive feedback (amplification) is stronger for higher-quality sites, and eventually the better sites will tend to monopolize the display of dances on a swarm. Thus over time, a swarm’s sensory input, or attention, will become focused on superior sites (see figs. 4.2, 4.3, 4.6, and 4.7).
5. Scouts reduce their dance responses over time. Even though the quality of a nest site generally does not change, the dances produced by each scout reporting on it gradually weaken over time (see figs. 6.9, 6.10, and 6.11). This decay in the dance response gradually purges a swarm’s sensory representation of information about inferior sites. The purging occurs because scouts that report on poor sites with weak dances tend not to attract replacements, so the feeble reporting of these poor sites withers away. Thus the decay in the dance response also contributes to the way that a swarm, over time, increasingly focuses its attention on better sites.
6. Scouts may adaptively choose between exploring versus exploiting. It remains to be shown, but it may be that scouts choose between exploring for unknown (and potentially better) sites versus exploiting already known sites, and that they do so by sensing the abundance of dances on the swarm. If so, then this would endow a swarm with a means of regulating its intake of sensory information, increasing it when the swarm’s sensory representation is still poorly formed, and limiting it when the swarm is well supplied with sensory information.
Besides these six features of scout bees as sensory units that foster successful swarm decision making, there are two features that almost certainly hamper successful decision making. The first is that scouts often make their reports asynchronously, which means that at any given moment their dances will tend to provide a poor indication of the true qualities of the alternative sites. For example, in figure 6.5, we can see that from 10:00 to 10:15 all of the dancing on this swarm represented the 15-liter, medium-quality nest box, as if this were the only—and thus the best—option available. The second shortcoming of the scout bees’ reporting system is that each scout provides noisy information regarding site quality. Figure 6.6 shows how, for any given site, different scout bees produce markedly different numbers of dance circuits. To cope with this time-based and individual-based variation in the reporting system, a swarm integrates its sensory information over several hours and across hundreds of bees. This critically important integration of the sensory information occurs during the next stage of a swarm’s decision-making process.
The Decision Transformation in a Swarm
The second stage of decision making in a monkey brain or a bee swarm is a decision transformation. This is where the sensory representation is converted into a set of probabilities for adopting the alternative outcomes. The main function of this second transformation is to integrate noisy sensory information so that the decision-making system (brain or swarm) knows how much evidence overall it has received in support of each of its alternatives. These evidence totals determine the relative probabilities of choosing the different courses of action.
In a monkey’s brain, the sensory information provided by neurons in the MT area is integrated by neurons in the LIP area. As explained above, different populations of LIP neurons representing different motion directions are stimulated by their corresponding MT neurons, and each population of LIP neurons sums over time the input (stimulation) that it receives and adjusts its output (firing rate) according to the total input received. In effect, each population of LIP neurons functions as an integrator, accumulating evidence in support of one possible direction of eye movement and providing a readout of how much evidence it has tallied. Thus, the greater the visual motion in a certain direction, the stronger the reports by the corresponding MT neurons, and the faster the evidence accumulation in the associated LIP neurons, the more likely the monkey is to move its eyes in this direction.
The decision transformation process in a honeybee swarm works in basically the same way as in a monkey brain. Just as a monkey brain has an integrator of sensory information for each eye-movement direction, a honeybee swarm has an integrator of sensory information for each nest-site option. The integrator for each potential homesite is the number of bees visiting that site (fig. 9.4). As we have seen in chapter 6, uncommitted scouts are stimulated by the dances they encounter on the swarm’s surface to visit the sites represented by these dances. The dances for any given site start and stop as the scouts committed to each site come and go from the swarm, and different scouts from the same site produce dances that differ in strength, so there is much minute-to-minute variation in the strength of the signals activating additional scouts to visit any given site. But the number of bees visiting a site refects the total number of dance circuits that were produced to advertise this particular site over the previous several hours, so the number of bees at a site integrates the noisy sensory/dance information about the site. And the better the site, the greater the pool of dances advertising it, and the stronger the stream of newcomers to it. Hence the evidence in support of a particular site—the number of bees visiting it—accumulates most rapidly at the best site. In this way, the best site acquires the highest probability of becoming the chosen site.
An important design feature of the integrators in monkey brains is that they are mutually inhibitory. That is, as evidence builds up in one integrator, it inhibits the accumulation of evidence in all the others. We see this same design feature in honeybee swarms. In figure 5.7, for example, we see that in each instance of swarm decision making the steep rise in the number of bees at the chosen site was accompanied by conspicuous declines in the number of bees at all the rejected sites, similar to the pattern of rising or falling firing rates for different LIP neurons shown in figure 9.2c. The mutual inhibition among the populations of bees at the different candidate sites results from competition for a finite pool of uncommitted scout bees. As more uncommitted scouts are recruited to one site, fewer are available for recruitment to other sites. Hence, when the total strength of dancing for a superior site and then the number of bees visiting this site goes up, there is inhibition of recruitment to the inferior sites. Eventually, the number of bees visiting the poorer sites will decrease because when the bees from these sites retire and reenter the process as uncommitted scouts (as discussed in chapter 6), they are likely to be recruited to a better site whose pool of dances has grown faster and become a larger fraction of the dances on the swarm (see fig. 6.7). One can think of the mutual inhibition among integrators as a means of preventing the emptier ones from refilling after leaking.
Indeed, another shared design feature of the integrators in monkey brains and honeybee swarms is that they are leaky. In other words, in both systems, the accumulation of evidence in any given integrator declines unless additional evidence flows into it. In chapter 6, we saw how each scout bee’s commitment to advertising and visiting “her” site steadily declines over repeated visits to the site (figs. 6.5 and 6.9), hence each scout eventually leaks from the accumulated evidence supporting the choice of her site. Leakage in the accumulation of evidence is a key feature of several models developed by mathematical psychologists to model the information processing that underlies decision making in primate brains (e.g., the “leaky, competing accumulator model” developed by Marius Usher of the University of London and James McClelland of Stanford University). In these models, leakage evidently improves decision making by increasing the time over which the noisy evidence accumulates until sufficient information for a decision is gained. Leakage also enables a decision-making system to update itself if the situation changes, as when a superior alternative is discovered. In other words, leaky integrators help a system avoid producing fast mistakes.
This explanation for the function of leakage evidently applies also to honeybee swarms. I make this claim based on what Kevin Passino and I learned when we explored the design of a swarm as a decision-making system by building a mathematical model of the nest-site selection process. Our model simulated the activities of 100 scout bees presented with a landscape containing six nest sites that differed in quality. Each scout bee was endowed with all of the known behavioral rules of these bees: uncommitted scouts search for new sites or follow dances to be recruited to known sites, committed scouts evaluate their sites and advertise them with dances whose strengths depend on site quality, and so forth. We first checked the validity of our model by testing whether it would replicate real-world examples of nest-site selection, like those represented in figure 5.7. In fact, it does so beautifully. Then we used our model to create “pseudomutant” swarms—ones whose scout bees behave a bit differently from what we see in nature—that would show us how small changes in the behavioral rules of the scouts affect a swarm’s decision-making performance. For example, we varied the dance decay rate of scout bees to see how this affects the speed and accuracy of decision making by swarms. In nature, the average scout bee reduces the strength of her dancing by 15 dance circuits per trip back to the swarm (see figs. 6.10 and 6.11), so we looked at what would happen if this dance decay rate were raised (up to 35 dance circuits per trip) or lowered (down to five dance circuits per trip). Changing the dance decay rate also changes the integrator leakage rate, since a scout bee stops visiting a site—hence leaks from the integrator—shortly after she stops dancing for the site.
We found that when we lowered the dance decay rate, so that bees continued dancing longer and “leaked” from the nest site more slowly, our model swarms made more rapid but less accurate decisions. Their decision making deteriorated because slowing the leakage accelerated the evidence accumulation at all the sites, so if the best site happened to get discovered late, one of the inferior sites could accumulate the threshold level of evidence first and win the competition among the sites. Conversely, when we raised the leakage rate, our model swarms made less rapid but more accurate decisions. They were sluggish decision makers because the scouts quit visiting their sites so quickly that even the best site’s integrator had difficulty accumulating the threshold level of evidence. It was extremely pleasing to discover that the dance decay/scout leakage rate that we measured in natural swarms is such that these swarms operate with a good balance between speed and accuracy in choosing their homes.
The Action Transformation in a Swarm
The final stage of the information processing that underlies decision making is the rendering of a single response from the multiple readouts of all the integrators. It is now clear that both in monkey brains making eye-movement decisions and in honeybee swarms making nest-site choices, a response is made when the evidence accumulation in one of the integrators reaches a threshold level. In both systems the mechanism for choosing a discrete response from a distribution of integrator states is simply one of letting the choice fall to whichever alternative first gains the threshold level of evidence in its integrator. This usually generates a good decision because the relative level of evidence in each alternative’s integrator normally refects the relative strength or quality of each alternative. We have seen, for example, how the better the candidate nest site, the stronger the dances produced to report it, and the swifter the buildup of scout bees at the site. Moreover, the self amplification of the sensory input for each alternative (as recruits become recruiters) and the mutual inhibition among the integrators for the alternatives (by competition for the uncommitted scouts) help ensure that the best nest site will prevail in the contest to accumulate the critical level of evidence, even if the best candidate enters the contest late, as often happens (see figs. 4.7 and 5.7).
We have seen in chapter 7 that the decision-making system of a honeybee swarm senses when one of the alternatives has amassed the threshold level of evidence by means of quorum sensing. That is, the scouts at each candidate site somehow monitor how many of them are at the site, and they note when they have assembled the threshold number (quorum) needed to take action. We have also seen that when the scouts at the chosen site have sensed a quorum they stimulate the swarm to prepare to take action by returning to the swarm and producing worker piping signals that stimulate the nonscouts to warm up their flight muscles. It seems likely that the worker piping signals also stimulate any scout still committed to a losing site to quit this site. This way, while the non-scouts in the swarm are preparing for flight, the scouts are consolidating the consensus they must build lest they give mixed guidance signals when the swarm takes flight. Eventually, once all the bees in the swarm cluster have warmed their flight muscles to a flight-ready temperature of 35+°C, the scouts who primed the swarm for flight with piping signals begin to trigger the swarm into flight with buzz-running signals (see fig. 7.13). Finally, the scouts who know the way to the chosen site steer the swarm along its chosen course of action.
A critical element in the design of this decision-making system is the quorum size, for it turns out that it strongly influences the speed and accuracy of a swarm’s choice of its new home. This fact was revealed when Kevin Passino and I turned up and down the quorum number of bees in our mathematical model of the bees’ nest-site selection process. We found that adjusting the number downward from its normal value—some 15 bees present simultaneously outside the nest site—caused swarms to make quick but error-prone decisions, while adjusting it upward gave rise to slower but only slightly more accurate decisions. It looks, therefore, like the bees normally operate with a quorum set high enough to guarantee that swarms make highly accurate decisions rather than super speedy ones. This makes sense, for a swarm has just one crack at correctly making the life-or-death choice of its dwelling place, so it should choose carefully, not rapidly. The high quorum number may also be favored by a swarm’s need to have a sizable crew of scouts who have visited the chosen site and so can guide the swarm to its new residence. There does exist the possibility that the bees will lower the quorum number in an emergency, such as when the weather turns dangerous or the swarm begins to starve. This way, a swarm that is in mortal danger may gain some shelter without further delay. Whether this possibility is an actuality remains, however, a subject for future study.
Convergence on Optimal Design?
Thirty years ago, in his book Gödel, Escher, Bach:An Eternal Golden Braid, the computer scientist Douglas Hofstadter presented the intriguing idea that “ant colonies are no different from brains in many respects.” He pointed out that in both systems a higher-level intelligence emerges from groups of “dumb” beings: groups of ants behaving and groups of neurons firing. At the time of Hofstadter’s book, the similarities between social decision-making systems and neural decisionmaking systems could be seen only hazily, for example, by noting that both kinds of systems encode information about the external world in the activity patterns of their elements. Now we know a great deal more about the decision-making mechanisms of insect societies and primate brains, and what we have learned over the past three decades provides striking support for Hofstadter’s idea that evolution has built intellectual strength in ant (or bee) colonies and in primate brains using fundamentally similar schemes of information processing.
We have recently realized that primate brains and honeybee swarms are faced with the same basic problem of choosing between alternative courses of action based on a body of noisy information that is dispersed across many component parts, none of which will ever acquire global knowledge of the alternatives. And as we have seen, the solution that both have hit upon is an information-processing system that has the design shown in figure 9.5. This design has five critical elements:
1. A population of sensory units (S1 ) that provides input about the alternatives. Each sensor reports (noisily) on just one alternative, and each sensor’s input strength is proportional to the quality of its alternative.
2. A population of integrator units (I ) that integrate the sensory information over time and over sensory units. Each integrator accumulates evidence in support of just one alternative.
3. Mutual inhibition among the integrators, so the growth in evidence in one suppresses with increasing strength the growth of evidence in the others.
4. Leakage of the integrators, so the growth of evidence in an integrator requires sustained input of sensory evidence supporting its alternative.
5. Threshold sensing by the integrators, such that the decision falls to the alternative whose integrator first accumulates a threshold level of evidence.
What underlies this striking convergence in the design of decision-making systems built of neurons and bees? (Also of ants; a beautiful set of studies of collective decision making during house hunting by the rock ant Temnothorax albipennis has revealed an information-processing scheme that is remarkably similar to the one described here for honeybees, though of independent evolutionary origin.) A strong possibility is that this striking similarity exists because this design is a means of implementing robust, efcient, and possibly even optimal decision making. It has been shown mathematically that the scheme shown in figure 9.5 can implement the statistically optimal strategy for choosing between two alternatives. This is the sequential probability ratio test (SPRT), which specifies when to stop integrating further evidence in order to achieve a given error rate. Among all possible tests, this one minimizes the decision time for any desired level of decision accuracy. In other words, this test achieves the optimal trade-off between decision accuracy and decision speed.
Recently, James Marshall, a computer scientist at the University of Bristol in England, and a team of colleagues, have examined theoretically how honeybee swarms might implement optimal decision making in the simple situation of a binary choice between two possible homesites. They point out that in a race between two evidence totals, the evidence for one alternative can be seen as evidence against the other, so in effect the evidence can be accumulated as a single total. This means that as time passes and the decision-making system acquires evidence for the two alternatives, at any one time only one alternative will have accumulated a nonzero level of evidence in its favor. In other words, the accumulation of evidence can be thought of as a random walk along a time line where the positive direction represents increasing evidence for one of the alternatives and the negative direction represents increasing evidence for the other alternative (fig. 9.6). The drift of the evidence line up or down denotes the tendency of the line to move toward the better alternative, and the jaggedness of the line represents the noisiness or uncertainty in the incoming evidence. It turns out that this random walk or diffusion model of decision making implements the statistically optimal SPRT.
In the case of a swarm making a choice between two possible nest sites, the existence of strong mutual inhibition between the two integrators—the two groups of scout bees visiting the sites—makes it possible that the evidence for one site will be evidence against the other. Strong mutual inhibition is likely to exist, however, only when there are few uncommitted bees in the swarm, at which time each gain of a supporter by one site will come at the cost of a supporter from the other site. This situation, or at least something close to it, is apt to arise only rather late in the decision-making process, when most of the scout bees have entered the process and have become committed to a site. This is also the time when many of the less desirable sites have been eliminated from the contest and new sites are being discovered only infrequently. Thus it seems that optimal decision making, as modeled by the SPRT, may happen only toward the end of a swarm’s decision-making process. But this is probably just when the greatest skill in decision making is needed, for toward the end only a few relatively high-quality sites are likely to remain under consideration, which makes it difficult to identify the best site. Clearly, future studies will need to examine closely whether in a binary-choice situation it is typical for all of a swarm’s scouts eventually to become committed to one site or the other, whereupon the decision making between the two sites is expected to proceed optimally.
Of course, in nature, decision makers are rarely faced with the simple binary choice situation, for which the SPRT is provably optimal. Certainly we have seen that most honeybee swarms are faced with choosing among a dozen or more possible nest sites, and that even toward the end of a swarm’s deliberations the race to gain a threshold level of evidence often involves more than two sites. Nevertheless, because the SPRT remains effective in situations with several alternatives, so long as some are markedly better than others, it is possible that primate brains and honeybee swarms have independently evolved the same basic decision-making scheme precisely because it provides a good approximation of optimal decision making. If this hunch proves correct, then we are looking at an astonishing convergence in the adaptive design of two physically distinct forms of “thinking machine”—a brain built of neurons and a swarm built of bees.