Swarm Cognition in Honey Bees

Transcription

1 Swarm Cognition in Honey Bees Kevin M. Passino Dept. Electrical and Computer Eng. Ohio State University 215 Neil Avenue, Columbus, OH 4321, USA Thomas D. Seeley Dept. Neurobiology and Behavior Cornell University Ithaca, NY, 14853, USA P. Kirk Visscher Dept. Entomology University of California Riverside Riverside, CA 92521, USA September 27, 26 Abstract: We synthesize findings from neuroscience, psychology, and behavioral biology to show that some key features of cognition in neuron-based brains of vertebrates are also present in beebased swarms of honey bees. We present our ideas in the context of the cognitive task of nest-site selection by honey bee swarms. After reviewing the mechanisms of distributed evidence gathering and processing that are the basis of decision-making in bee swarms, we point out numerous similarities in the functional organization of vertebrate brains and honey bee swarms. These include the existence of interconnected subunits, parallel processing of information, a spatially distributed memory, layered processing of information, lateral inhibition, and mechanisms of focusing attention on critical stimuli. We also review the performance of simulated swarms in standard psychological tests of decision making: tests of discrimination ability and assessments of distractor effects. We conclude that relating swarm cognition to knowledge from cognitive neuroscience will be fruitful for broadly understanding the mechanisms of group cognition in social species. 1 Introduction The study of group decision making sometimes uses a collective intelligence or superorganism perspective where the group is viewed as a single decision-maker (Holldobler and Wilson 199; Levine et al. 1993; Franks 1989; Seeley ; Hinsz et al. 1997; Laughlin 1999; Camazine 1

2 et al. 21; Surowiecki 24; Conradt and Roper 25). Moreover, it has been recognized for some time that massively parallel inter-animal communications and actions could form a basis for complex group cognition processes that are functionally equivalent to ones in neuron-based brains (Markl 1985; Bonner 1988). The primary goal of this paper is to show explicit examples of how several of the key elements underlying cognition in neuron-based brains of vertebrates are also found in bee-based swarms of honey bees. We focus on swarm cognition in the context of the group decision-making process whereby a swarm of bees selects its new nest site. Honey bee swarms are formed in the spring through a process of colony fission wherein the mother queen and about half the workers in a colony leave their nest and form a cluster on a nearby branch (the biology of swarming is reviewed in Winston 1987). Scout bees fly from the cluster to search the countryside for potential dwelling places, usually cavities in trees. Discovered nest sites of sufficient quality are reported on the cluster via the scouts waggle dances, which recruit other bees to evaluate the sites. Higher quality sites evoke stronger dancing and hence more recruits. When, via recruitment, 1-2 bees are assembled at a candidate nest site a quorum threshold is reached which triggers choice of the site. The scouts from the chosen site return to the cluster, initiate lift off, and the swarm flies as a group to the new nest. The study here of what we call swarm cognition during this nest-site selection task uses the model in (Passino and Seeley 26) (others are in (Britton et al. 22; Myerscough 23)). This model was validated using the experiments in (Seeley and Buhrman 1999; Camazine et al. 1999; Seeley and Buhrman 21; Seeley 23; Seeley and Visscher 23 24b). Overviews of the biology of nest-site selection are given in (Seeley and Visscher 24a; Seeley et al. 26). Beginning at the cognition unit-level (analogous to the cellular neuron-level), we build a detailed explanation of the nest-site selection process to identify the key elements and functional organization of swarm cognition. We show that the swarm has identifiable elements that correspond to neurons, action potentials, inter-neuron communications, lateral inhibition, short-term memory, neural images, and layers of processing (Kandel et al. 2). We identify functional similarities to the networks of neurons that perform certain attention, perception, and choice functions in solitary animals (Gazzaniga et al. 1998; Kandel et al. 2). Via simulations we show that the swarm s short-term memory (what we call group memory ) is on average a representation of the relative quality of the discovered nest sites that leads to good choice performance. For nest-site selection the swarm benefits by quickly choosing the best discovered nest site. Time pressure arises due to energy costs and weather risks to the exposed cluster. Also, the quality of the nest affects hive fitness. Hence, we take the view that the nest-site selection task is a type of reaction-time test studied in psychology (Luce 1986). Such tests have received significant attention in mathematical and cognitive psychology where diffusion (Ratcliff 1978), accumulator (Usher and McClelland 21), and other mathematical models (Busemeyer and Townsend 1993) have been used for behavioral-level representations of perception-selection reaction-time tests for humans and animals (see overviews and applications in (Luce 1986; Busemeyer and Townsend 1993; Ratcliff et al. 1999; Roe et al. 21; Ratcliff and Smith 24; Smith 2)). Such models have been used for studies of choice speed-accuracy trade-offs, ones studied also for social animals (Franks et al. 23; Passino and Seeley 26; Marshall et al. 25) and human groups (Karau and Kelly 1992). Here, we show that our model of swarm nest-site selection (Passino and Seeley 26) shares important features with the above-listed models for human decision making behavior, but also key differences. Moreover, we use methods from (Gazzaniga et al. 1998; Treisman and Gelade 198; Ratcliff 1978; Roe et al. 21) to show that for simulated choice tests swarms exhibit several of the same properties, and choice error characteristics, as humans and animals with neuron-based 2

3 cognition. Two categories of tests are administered in simulation: discrimination and distraction. First, we illustrate that the swarm has discrimination abilities that allow it to distinguish between two relatively close quality nest-sites. This ability is especially strong when site quality differences are large. Discrimination abilities are amplified for low quality site comparisons and are achieved in spite of significant assessment noise at the level of individual bees. Second, we show that the swarm can effectively eliminate from consideration many low quality distractor sites. However, if the distractors qualities are high enough the swarm can make many errors since the best site is essentially hidden in a field of adequate-quality sites that compete for the swarm s attention. Supporting evidence for our conclusions on swarm choice behavior is provided in the supplementary on-line information in the Appendix. Moreover, we discuss implications for group decision making in other species. 2 Process Dynamics of Nest-site Selection The model from (Passino and Seeley 26) is summarized via the flow-diagram in Figure 1. Consider a sequence of expeditions indexed by k =,1,2... by B scout bees that take on different roles in the nest-site selection process (we use B = 1). When an explorer bee finds a candidate nest site it evaluates its attributes in order to form a quality assessment. We denote the quality of nest j as N j [,1] with 1 representing a perfect site. We let the position of bee i be θ i, and J(θ) denote the landscape of nest quality, with θ = [,] the position of the cluster. We have J(θ i ) = N j if bee i is at site j, but bee i has assessment noise w i (k), and a quality threshold ǫ t =.2 below which it will ignore a site. Hence, bee i s assessment of a site is S i (k) = J(θ i (k)) + w i (k), if J(θ i (k)) + w i (k) > ǫ t, and zero otherwise. Here, w i (k) is uniformly distributed on (.1,.1) to represent up to a ±1% error in scouts nest-site quality assessment. Any bee that finds an above-threshold nest site dances for it, and hence becomes committed to that site. Bees die with a small probability p d =.16 on each expedition so that less than 1% die over the whole process. An unsuccessful explorer returns to the cluster and seeks to observe a dance. The expedition that bee i first discovers site j is kj i and if the sensed quality of the site is above the quality threshold, this is a successful explorer and it returns to the cluster and dances with a strength L ij (kj i) = γsi (kj i ) waggle runs where γ = 15. After dancing, this committed bee returns to the site, and then back to the cluster, possibly several times; however, each time it returns it dances ǫ s = 15 fewer waggle runs than the initial time. The sequence of waggle runs produced by bee i over the whole process is L i and the total number of waggle runs produced on the cluster for all sites at step k is L t (k). We call a sequence of dances by one bee for one site, from the time of the initial dance to when the dance strength goes to zero, a dance decay series. After a committed scout s dance strength has decayed to zero it rests, and rejoins the process (by seeking to observe a dance) at each step with a probability ( p m =.25. Bees that seek to observe will end up exploring with probability p e (k) = exp 1 L 2 t (k) ) 2 where σ = 4, representing that when there is not much σ 2 dancing on the cluster (small L t (k)), then there will be more exploring, and vice versa. There are B r (k) resters, B o (k) bees that seek to observe, B u (k) = B o (k) + B r (k) uncommitted bees, and B c (k) committed bees. With probability 1 p e (k) observer bees will observe dances, and with L probability p i (k) = i (k) will be recruited by the Bc(k) L i=1 i (k) ith committed dancing bee. Bees recruited to site j visit and dance for it according to their own assessment as described above. 3

4 p probability e will explore when seek to observe c Swarm cluster B is total number of scouts B is number of committed scouts Observe dances Probability recruited by bee i, p Seek to observe dances B o observers i Waggle dances Go dance on cluster p probability rester will m seek to observe B r resters i Explorers (B total) Recruited bees (visit sites) Committed bees (after dance, revisit) Dance decay series γ S j i L (k) L (k) is dance strength of bee i ij L (k), for site j, L (k) is total γ is initial dance strength for i time bee i discovers j (k ) j ε s dance decay rate Committed scout t Explorer (successful) B = B +B is number of u o r uncommitted scouts Committed scout (that finished dancing for site) ε s e k, expedition Explorer (unsuccessful) i θ i J( θ ) N j S j i w ε t Candidate nest sites Tree Nest site 1 bee position nest-site quality landscape quality of nest j bee s assessment of j assessment noise quality threshold B d bees die at k, B dt total p is probability of death d θ2 J( θ) N j εq quorum Nest site j threshold Agreement time T a, piping, heating, lift-off θ 1 Figure 1: Nest-site selection process. Even though at any particular time the swarm of bees is spatially distributed across the environment (explorers), candidate nest sites, and the cluster, it is best to think of the process dynamics in terms of the simultaneous activities at all of these places. So, a key part of the process occurs simultaneously with the activities on the cluster via the nest-site quality assessments and quorum sensing at each candidate nest site where the bees sense the number of other bees at the site they are visiting. When the quorum threshold ǫ q is reached, bees return to the cluster, they produce piping signals that elicit heating, and then the entire swarm lifts off flies to the chosen site. Each expedition is assumed to take 3 min, and the maximum amount of time to decide is set at 32 hrs, so there are up to 64 expeditions. Due to the time pressure to decide, the possibility of close-quality alternatives, and randomness, there can be simultaneous quorum achievement at two or more sites resulting in a split decision. In this case, the process is restarted by having the swarm reform the cluster. Also, the process can fail to come to agreement before 64 expeditions are completed; this is called a no-decision failure. These failures can arise if a site of sufficient quality is not discovered early enough, one that will generate a recruitment rate that will assemble the required ǫ q bees at a nest site. 2.1 Distributed Evidence Gathering and Feedback Within the decision-making process, the evidence of the quality of a site takes two forms: dances on the cluster and bees at the sites. First, bees that are committed to a site perform a series of dances for it on the cluster to advertise it to the observers. The number of bees recruited to each site occurs in proportion to the number of waggle runs for each site at each step. If a recruit assesses 4

5 the site to be of similar quality to what its recruiter found, it will perform a similar dance decay series. A positive feedback is created since the number of recruiters and their recruited bees will grow exponentially (assuming an infinite pool of recruits). There are, however, also two types of negative feedback, one induced by dance decay rate ǫ s and the other by scout deaths as defined by p d. Since the probability of death on an expedition is low, its impact on the dynamics is small. However, the impact of the dance decay rate impact is large. Since decay rate is the same for different quality sites, the dancing for poor sites will quickly fade; hence there are few recruits to poor sites. This ensures that not too much time or too many assessors will be dedicated to poor sites. The second form of evidence of a site s quality is the number of bees assembled at the site. Assuming that the site is not independently discovered by many bees, if several bees are at a site it is due to recruitment to the site which only occurs if the site is of adequate quality. And, if there are many bees at the site, this could only occur if all those bees had judged it to be of good quality. The numbers of bees visiting each site changes dynamically as new sites are discovered and evidence is gathered by bees. Recruitment at the cluster is driven by the number of bees visiting the sites, yet the recruitment also impacts the number of bees visiting the sites. This tight coupling between activities at the cluster and candidate sites demands a broad perspective on the spatially distributed dynamics of the process, one where equal attention is given to all locations where the bees congregate, not just the cluster. Indeed, concurrent quorum sensing activities occur at all the candidate nest sites and when one or more quorum thresholds are reached, this signals that the process is complete; without the quorum sensing the process will not terminate. 2.2 Mechanisms of Selection The ability of the swarm to discriminate between sites of different quality depends on an interplay between positive and negative feedback. We illustrate this via a simple example. Assuming no assessment noise, if two bees are dancing on the cluster for two different above-threshold sites j and j with qualities N j > N j, then the difference in the number of recruits for the two cases (and hence strength of positive feedback) is proportional in a nonlinear way to the difference N j N j. As an example, first consider two low quality sites N j =.4 and N j =.2 so N j N j =.2. A bee that dances for site j does so with γn j = 15(.2) = 3 waggle runs in the first visit back to the site, and then 15 fewer, or 15 waggle runs on the second visit. Then, the dance decay series ends. The total number of runs in this case is 45. In contrast, a bee that dances for site j has a dance strength sequence of 6, 45, 3, 15, for a total of 15 waggle runs in its dance decay series. The percentage increase when quality increases from.2 to.4 is = 233%. Hence, there are many more recruits for the better site compared to the inferior site. Now, if there are two relatively high quality sites N j = 1 and N j =.8, again with N j N j =.2, the total numbers of waggle runs per dance decay series for qualities of.8 and 1 are 54 and 825 respectively. The percentage increase when quality increases from.8 to 1 is = 53%, much smaller than the above case. Hence, when site qualities are relatively low, a small difference in quality leads to a big percentage difference in the number of dances and the positive feedback gain on recruitment rate to that site. So, the swarm has a a very good ability to discriminate between nest-site qualities when they are relatively low quality sites When site qualities are higher, the same size difference in quality leads to a lower percentage difference in the number of dances and hence recruits. Hence, the swarm s site discrimination abilities for high quality sites is less than for low quality sites. At the same time, it is important to highlight that the evidence gathering dynamics have three 5

6 features that make it difficult for a swarm to always succeed at picking the best nest site. First, each bee has a noisy assessment of the quality of any site, hence all evidence is noisy. The noise is amplified by the nonlinear relationship between differential site quality and the number of recruits, which helps discriminate between sites that differ in quality. However, the quality assessment noise of each individual bee is filtered out at the group level to a significant extent by: 1. Averaging the effects of multiple dancing bees on the cluster: Some bees will assess quality low, and some high, but the relative mean number of dances per site will closely represent the relative site quality. 2. Quorum threshold effect: The proportioning of dancing on the cluster results in a proportioning of bees assessing each site in accordance with its relative quality. Since the number allocated to a site must be above the quorum threshold before it is chosen this ensures that averages are taken over a sufficient number of error-prone bees so that the swarm does not make mistakes. The second feature that conspires against the swarm making the best choice is the simple observation that evidence of the quality of a site, in the form of returning bees that dance, arrives at the cluster asynchronously. Evidence arrives randomly in time depending on the time a site is discovered and the bee returns to dance for it, and the times of occurrence of subsequent dances by recruits. Even high quality discoveries near the very end of the process will be unlikely to impact the swarm s choice since many of the scouts are apt to be committed to other sites and hence not available for recruitment. It is possible that a relatively low quality site discovered early in the process will be chosen, especially if no high quality site is found, since then there is enough time so that enough bees can be assembled at the poor site to achieve the quorum threshold. The third feature that negatively impacts accurate choice is the presence of distractor nest sites, ones of sufficient quality to be evaluated, but that should not be chosen since they are of inferior quality. Strong negative feedback due to dance decay generally enables the swarm to consider a distractor site only briefly. However, if there are many distractors the strength of the positive feedback for the best site is attenuated, perhaps even low enough that a distractor is chosen. Essentially, the swarm is too busy paying attention to many inferior sites to allow it to focus on the assessment and choice of the best site. Noise can amplify this distraction effect, but the averaging discussed above will reduce its effect at the group level. 2.3 Search-Select Phases and Dynamic Internal Coupling Nest-site selection has a search phase and a selection phase. Even though these two phases are always interleaved and simultaneous, and hence blend together, it is useful to characterize their general features. The search phase is characterized by a high value of B e (k), relatively low value of B c (k), and a small value of L t (k) since there is not much dancing on the cluster since not many bees are visiting sites. The select phase is characterized by the exact opposite of this situation so that L t (k) is higher, p e (k) is lower, not as many bees explore, and this raises the positive feedback on recruitment so that a quorum threshold ǫ q can be quickly reached and a crescendo can occur resulting in agreement at time T a. The feedback processes discussed above are modified by internal coupling (cross-inhibition) between variables associated with different candidate nest sites. Recruitment to one site means 6

7 that the recruits will not be recruited to other sites until they possibly dance for the site they are recruited to, rest, and re-enter the process as a new recruit rather than an explorer. Hence, if the total strength of dancing on the cluster and number of visitors to one site goes up, bees are inhibited from visiting other sites, and the number of visitors at other sites may even decrease (since if bees finish dancing for a poor site they will be likely to be recruited to the better one). The size of the pool of uncommitted scouts and the phase of the process (search vs. select) both impact the type of internal coupling. If there is a large amount of dancing on the dance floor, then independent of the number of bees producing the dances, the probability of exploring will go down, the probability to follow dances will go up, which then strengthens the potential for positive feedback due to recruitment. If there are many distractors, then there are generally fewer uncommitted scouts, but still a relatively low amount of total dancing, so that exploration can stay high when not enough good sites of sufficient quality have been found. If a large number of uncommitted bees is available, then recruiters can achieve their maximum recruitment rate which will tend to focus the swarm on a single great site and inhibit consideration of relatively low quality sites. Hence, in the beginning of the process (during the search phase) there is a type of flexibility in that many alternatives are often considered, but their consideration is coupled in complex ways depending on discovery times and qualities. The nature of the coupling changes as the phase switches from search to selection. Near the end of the process, the coupling is such that there is a strong tendency of the swarm not to consider new evidence. Normally, the relatively low quality alternatives have become significantly less visited due to dance decay, and the best one gets many more recruits and the crescendo occurs. Hence, the cross-inhibition helps to avoid having oscillations between different alternative choices, at least when there are clear quality differences. 2.4 Dynamics Create a Speed-Accuracy Trade-off There is a trade-off between speed and accuracy of choice (Passino and Seeley 26) that is a direct consequence of the dynamics. Generally, error rate reduction typically costs more time T a or more dances, or both. The time when agreement is reached, T a, is a random variable that is affected by the pattern of times of discovery of sites, their qualities, and indeed all aspects of the dynamics described above. Let L t denote the total amount of dances that have been performed by time T a. The agreement time is in a sense controlled by the swarm: the swarm will reach agreement when it has evaluated enough alternatives of sufficient quality to make it likely that it picks the best one. Natural selection will favor reducing L t so that the swarm invests less time and energy in scouting and dancing to achieve a decision. Also, it will favor reducing T a so that the swarm can lift off, fly to the new nest, and quickly establish its new home. Generally, choice errors are made in trying to minimize T a and L t. The main mechanism that tries to make the decision occur quickly is the positive feedback aided by cross-inhibition that forces discrimination and a quick transition from the search to select phases. Correspondingly, the negative feedback tends to slow the process. The balance between the two, mediated by coupling and randomness in assessments and discovery times, leads to the agreement time. Specific scenarios serve to highlight how the dynamics affect the speed-accuracy trade-off. First, if there are no sites discovered for a period of time, or only low quality sites are discovered, then the positive feedback is not strong enough to completely switch from a search to a select phase, which is good since the swarm needs more time to find a sufficiently high quality site. There can also be an increase in T a due to the presence of similar quality sites that require more deliberation time (coupled dynamic interactions that inhibit each other from achieving a sufficient recruitment 7

8 rate and hence a quorum), which normally costs more dances (i.e., an increased L t ). Such extra deliberation time can even result from the need to distinguish between inferior distractors of different quality. When luckily a great nest site is found quickly, both T a and L t can be relatively low and the error rate can be low. 3 Features of Swarm Cognition If N j [,1] is the quality of nest site j, its relative quality is N j / j Nj. For nest site j, let d j be the distance from the hive to site j and let φ j be the angle to site j for a coordinate system with origin at the cluster and the x axis pointing to an appropriate reference point, the one used in bee dance communication on the cluster. Let i Lij (k) denote the total number of waggle runs for site j at step k; hence i denotes the sum over all bees dancing with (d j,φ j ). The total number of waggle runs for site j up to T a is denoted by k i Lij (k). Its mean over many nestsite selection processes is E[ k i L ij (k)]. This expectation is a measure of the total amount of signaling (advertisement) for site j. For plotting purposes we will consider the relative mean total amount of dancing for site j, which is E[ k i Lij (k)]/( j E[ k i Lij (k)]). Let B(j,k) be the number of bees that visit site j at step k. Then, max k B(j,k) denotes the maximum number of bees that visited site j up to T a. Its mean over many nest-site selection processes is E[max k B(j,k)]. This expectation is a measure of the maximum number of bees that a site can muster before the agreement is reached when its value reaches quorum for some j (the chosen site). For plotting purposes, we use the relative mean E[max k B(j,k)]/( j E[max k B(j,k)]) for each site j. 3.1 Interconnected Cognition Units An individual scout bee is the fundamental unit of cognition (analogous to a neuron). The unit can change its role and location. It can sense, act, and communicate with other units. The swarm s sensory process is the sum of the sensory processes of all the scout bees. The swarm s spatial field of view (Kandel et al. 2) is dynamically modulated by scout bee choices (e.g., during exploration or site assessment) to appropriately span many square kilometers and possibly many candidate nest sites. Dances by bee i of strength L ij for site j are analogous to action potentials (Kandel et al. 2). For this, there is an assessment of quality relative to threshold ǫ t before such dancing is activated (analogous to activation thresholds (Kandel et al. 2) in neurons). The dances play a special role in that they act as signals between different units. If we view bees as nodes and bee-to-bee dance communications as directed arcs, a time-varying random graph can describe the dynamic interconnection topology of the inter-bee communications on the swarm cluster. The form of the graph is driven by where bees dance on the cluster and which bees happen to be present and observe this dancing. If another graph is used to represent the union of all communications until the agreement time, there would be arcs clustered around bees that discovered relatively high quality sites, and arcs pointing from the bee that first discovered each site on a path (of recruiting recruits) to the last bee recruited for that site. Hence, while it is not a fixed network of communicating units as is often the case for neural networks, the interconnection topology for bee cognition units has a structure with some predictable properties. 8

9 3.2 Group Memory The group of bees committed to nest site j is a population of units (analogous to a population of neurons (Kandel et al. 2)) that can accumulate quality evidence for the site. The set of such groups for each discovered site serves as a short-term group memory for the swarm. The group memory is an internal model of the pattern of nest-site qualities currently in the swarm s field of view (analogous to a neural image (Kandel et al. 2)). The group memory is spatially distributed across the cluster and the candidate sites with the distribution defined by the current locations of the committed scouts in the populations for each site j: 1. Group memory at the cluster: Group memory on the cluster can be decoded from the cluster surface where dances are performed. For each dancing bee, the value of (d j,φ j ) can be found. Then the populations of bees can be formed for each nest site j. The dancing on the cluster at any step k < T a is a representation of the cluster s current estimate of the nest-site quality landscape. Mathematically, when j i Lij (k) > j i Lij (k) i Lij (k) is the relative total amount of waggle runs for site j at step k, the cluster s internal model of N j / j Nj at time k. If a site has not been found it will not be in the representation. The representation becomes more accurate as more bees visit the site (the averaging filters the noise due to individual assessment errors). 2. Group memory at the candidate nest sites: The component of group memory distributed across the nest-sites is composed of the number of bees at each candidate site B(j,k). We call B(j, k) the current swarm preference level for each nest site j. When swarm preference for site j reaches the quorum threshold, site j is chosen. For examples of the dynamical time evolution of the cluster internal model estimate and swarm preferences see (Passino and Seeley 26) or for corresponding experimental data see (Seeley et al. 26). The swarm s distributed group memory is distinct from the internal neural-based memory of each individual bee. What is known by the swarm is actually far more than the sum of what is known by the individual bees since the swarm s knowledge includes what is in the bees brains and information coded in the locations of the bees and their actions. No bee can know all the locations and activities for all other bees. But this information is coded at the swarm level and, as discussed below, is explicitly used in swarm decision making. 3.3 Layered Early/Late Processing at the Cluster and Nest Sites Individual bees can sense group level variables and memory, but with noise, and this provides for layered processing of information via parallel and converging paths as found in neural systems (Kandel et al. 2; Gazzaniga et al. 1998). There are three forms of sampling of group memory variables: 1. Allocation to exploration vs. recruitment: By sensing delays in finding dancers, bees can estimate the total number of dancing bees, i.e., a current group memory value. They can 9

10 use such a value to make decisions about whether to explore or get recruited. The individual decisions can be error-prone (e.g., by being unlucky and not seeing any dancers even though there are many), but on average the group of bees that use this cue can make a correct decision. Indeed, as the sizes of groups of committed scouts increase, as is the case for relatively high quality sites, the variance on the groups sample will decrease. Hence, group memory is in a sense more accurate for better sites. 2. Proportionate recruitment: Even though a bee cannot measure the sizes of the individual groups dancing for the candidate sites, they can be influenced directly by these values in that they are proportionally recruited according to the proportion of dancing for each site. Hence cluster-based group memory is used by the swarm to allocate the cognition units to nest sites. Again, the key is that while the individual cannot estimate the proportions of bees dancing for each site, the group of observers can. Moreover, they will do it more accurately for higher quality sites. 3. Nest-site bee assembly: At each nest site the assembly of bees provides a group memory of the number of bees that have assessed (or is assessing) its quality. Via the simultaneous and self-referential process of quorum sensing, the bees take actions based on this group-level memory by deciding when the process should be terminated. Thus there is a layering of processing in the swarm, with bees playing roles in the early processing of sensory signals and dancing, and roles in late processing where the overall level of dance activity, proportions of committed bees, or numbers of bees assembled at sites are used. 3.4 Functional Relationships to Attention, Perception, and Choice Key functionalities of neuron-based attention, perception, and choice processes (Gazzaniga et al. 1998) are found in swarm decision making. For attentional systems, the group memory sets the overall relative level of attention paid to site j at step k. More attention will be paid to higher quality sites when they are found. Distractor nest sites will enter into swarm s field of view, but they will be purged from the memory by low average quality assessments and dance decay. There is a coupling between late and early attentional processes where via recruitment, swarm resources are directed to the more interesting (higher quality) points in the spatial field of view of the swarm. Distractors require swarm resources and hence can degrade the quality of the focusing process. Focusing dynamics are slowed by a cluttered field of close quality sites. Cross-inhibition between site variables affects focusing dynamics. Relative to neural perception and choice systems, there are receptive fields (Kandel et al. 2) set by individual bees. Lateral inhibition (Kandel et al. 2) is closely related to what we call cross-inhibition above and it defines coupling in the process due to: (i) individual bees not comparing dances, (ii) abandonment via dance decay of relatively poor sites, (iii) the finite size of the pool of potential recruits, and (iv) since sites winning recruits inhibit other sites from getting recruits. Cross inhibition is driven by the distance between alternatives as in neural systems (Kandel et al. 2), but distance in this case is not, for instance, physical distances between nest sites, but is defined via (i) relative site quality, (ii) closeness in times of discovery, and (iii) the random interconnectedness of all site variables via the dance floor. There is a type of two-point discrimination process (see above discussion) that is due to on-center, off-surround feature found in neural perceptual systems (Kandel et al. 2; Gazzaniga et al. 1998). There is a process of 1

11 feature detection (Kandel et al. 2) that occurs in what can be viewed as the later processing by the swarm. The feature that is detected in this late processing is the best-of-n discovered sites. There is a type of winner-take-all process that emerges via the quorum threshold achievement, agreement, and lift-off and it is analogous to ones in neural systems (Gazzaniga et al. 1998). 3.5 Simulation: Group Memory Quality and Impact on Choice Performance For the model in (Passino and Seeley 26) we use 1 simulation runs where sites 1-6 have qualities of.5,.6,.7,.8,.9, 1, respectively ( case 2 from (Passino and Seeley 26)). This is a representative, yet challenging quality landscape since, for instance, the sites of low quality will distract the swarm, and it will be difficult to discriminate between the sites of close quality. Consider the top-right plot in Figure 2. This shows that group memory as measured by the relative mean total amount of dancing for site j (cluster-portion, white bars) and relative mean maximum number of bees visit site j (nest-site portion, light gray bars) is skewed per the relative site quality (black bars). The skewing is seen as you scan from site 1 (low quality), to site 6 (high quality), where the white and light gray bars increase more than relative nest-site quality. The swarm s group memory (both at the cluster and nests) views relatively low quality sites as worse than they are (see site 1). The swarm s group memory views relatively high site qualities (site 6) as better than they are. The swarm s group memory is used to make choices. The skew represents that the swarm forms good memory for the task at hand; the skew helps the swarm discriminate between sites. This shows that on average the swarm develops a useful group memory of the quality landscape. Next, consider the top- and bottom-left plots. The probability distribution of T a shows that it never decides too fast, or too slow (there were zero no-decision failures). The distribution is heavytailed which means that long agreement times are not highly unlikely. Early decisions are reached via quick discovery of a great site, and few or no other good discoveries, so that a maximum level of positive feedback is achieved and the quorum is reached quickly. Longer T a times result from slow discoveries and long deliberation times in trying to discriminate between sites. The distribution for Lt has similar characteristics and is also somewhat heavy-tailed. Finally, the bottom-right plot shows that almost no bees dance for two or more sites which illustrates that the swarm choice has little dependence on bees switching from dancing for one site to another (i.e., choice is a group-level phenomenon). 4 Swarm Choice Tests Viewing the swarm as a superorganism, in this section we evaluate its choice performance. We use the values of the behavioral parameters validated in (Passino and Seeley 26), and consider performance for several types of nest-site quality landscapes. For each landscape quality pattern we use 1 nest-site selection processes that terminate with a single site chosen. 4.1 Discrimination To test discrimination, let all sites have zero quality, except sites 5 and 6, which both start out at a quality of N 6 = N 5 =.75 and differentially move to.5 and 1. The results are shown in Figure 3. 11

12 Number of times per T a bin Vert lines=2.5,25,5,75,97.5% quantiles #splits=286; #no dec= RelQual(blk);Cluster(wht) Sites(ltgray);RelChoice(dkgray) 5 1 T a, hrs Nest site Number of times per Σ L t bin Mean=gray dotted vert line Σ L t x 1 4 At T a :MeanB c =51.88;MeanB e =18.634;Mean p e =.3687 #Bees2.5,25,5,75,97.5%quant #Nest sites visited Figure 2: Simulation results, case 2 quality landscape. Top-left: Number of times terminated at T a with vertical lines the indicated quantiles (e.g., 2.5% of the cases terminated with a T a less than the left-most vertical bar) with the mean indicated by the gray-dotted line. Bottom-left: Similar to top-left, but number of times terminated at T a with L t. Top-right: horizontal is site no., vertical: black (relative site quality, N j / j Nj ), white (relative mean total amount of dancing for site j, i Lij (k)]/( j E[ k i Lij (k)])), light gray (relative mean maximum number of bees visit E[ k site j, E[max k B(j,k)]/( j E[max k B(j,k)])), dark gray (proportion times chosen). Bottom-right: quantile plot of number of bees that dance for zero, one, two, etc. sites. Before interpreting the results, note that besides the horizontal axes, labeling of all plots in the remainder of this paper is the same. To interpret the results in Figure 3 note that ideally, once the two sites have different qualities the swarm should always choose the best one. However, the results show that many errors are committed by the swarm, especially for low values of differential quality. The swarm can, however, amplify the quality differences (at a rate of increase higher than the relative quality of the two sites) and often make the correct choice, with choice performance increasing as the differential site quality increases. The slope of the curves in the top-right plot are positively correlated with the level of discrimination ability. The slope of the choice percentage curve for the best site (site 6) is about (1-.5)/.4=5/4; we will compare other values to this one (e.g., in the Appendix). When 12

13 Marker(site): *(6),o(5),sq(4),dia(3),tU(2),tR(1) 1 T a, hrs %choice(blk);%qual(gray) x 1 4 Split(x),no dec(o)(right) 14 Marker(#sites):x(6)*(5)o(4)sq(3)dia(2)tU(1)tR() Mean (.)/std(+)σ L t Mean#Bees visit MeanB c (x)meanb e (+) Differential quality Differential quality Figure 3: Discrimination effect, linear differential quality. Top-left: middle line in each box is the median value of T a, boxes with notches that do not overlap represent that the medians of the two groups differ at the 5% significance level, whiskers (dashed lines) represent 1.5 times the interquartile range, and outliers are designated with a +. Top-right: percentage of times each nest site is chosen (black lines), with site 1 designated by ( tr represents triangle right, a right-pointing triangle), site 2 by ( tu represents triangle up ), site 3 by ( dia ), site 4 by ( sq ), site 5 by, and site 6 by. The gray lines with markers show the relative site qualities, N j / j Nj. Bottom-left: left-vertical axis and the black lines show the mean L t (solid line, dots), and its standard deviation (dash-dot line, + marker), while gray lines and right-vertical axis show the number of split decision ( ) and no-decision ( ) cases that occur for the 1 nest site selection processes that terminate with a single choice. Bottom-right: left-vertical axis and the black lines show the mean number of bees out of the 1 total that visit sites (designated with ), 1 site ( ), 2 sites ( ), 3 sites ( ), 4 sites ( ), 5 sites ( ), and 6 sites ( ), and right-vertical axis shows via the gray lines the mean number B c of committed scouts ( ) and mean number of explorers B e (+) at the agreement time T a. the differential site quality is close to zero the swarm generalizes and treats the two sites as having the same quality. Note that there is uniformly distributed noise in individual bee quality assessments on (.1,.1), yet the swarm can often discriminate (due to filtering with multiple bee assessments) two sites with less then a.1 quality difference. There is little change in the median 13

14 T a or mean L t for a change in differential quality. For low values of differential quality there are many split decision cases due to the build-up of bees at each of the sites being similar due to the close quality sites. The number of no-decision cases is higher for lower differential quality simply because in that case there are no obviously superior sites for the swarm to pick. The number of bees that visit no sites is around half the bees; these bees explore or rest. Of the bees that visit sites, most visit only one. Of the bees that do visit sites, the relative mean number of bees visiting 2 sites is about 6/4=15% for all cases, which demonstrates that there is some coupling between site variables via dance decrease to zero and then reentry to the process via recruitment to a different site. The mean number of bees that are committed to sites and explore is relatively constant. 4.2 Distraction To test distraction, let N 6 = 1, N 1 =, a distractor quality variable D = N 5 = N 4 = N 3 = N 2, and consider D [,1]. See Figure 4. The key feature is that the swarm his very effective at evaluating then discarding from consideration distractors so long as they are of a quality D <.4 since for this range the swarm always makes the correct choice. As the distractor quality D gets closer to one, more errors are made. In fact, at about D =.55 the percentage of times the correct site is chosen is about 8% as in (Seeley and Buhrman 21). The percent of correct choices quickly decreases for D >.55 where by about D =.8 the percentage of times the swarm picks the best site is close to that for the distractors, even though the best site is markedly better. The median value of T a decreases significantly representing that the errors are made fast, yet the value of the mean of L t increases since the swarm tries to discriminate between many distractors and the best site and this requires many dancers. For high distractor quality there are many split decisions and the relatively high coupling in the process decreases and this is why the bees lock in on incorrect decisions. The bees are busy discriminating between sites, but this reduces the coupling and hence the number of correct decisions in this case. Indeed, the number of explorers decreases significantly for high distractor quality since bees quickly find and recruit to all the sites and this leads to a reduction in cross-inhibition between site variables so that there is no clear winner. In the Appendix we study the impact of the number of distractors via a Treisman-type test (Treisman and Gelade 198), several interactions between discrimination and distraction effects, context-dependent effects, the effect of individual bee assessment noise magnitude, and cognition mechanism adaptation. 5 Discussion This synthesis paper provides evidence that bee-based swarms have a cognition process that shares key features with neuron-based brains, both at the level of the neuron/bee and at the level of the brain/swarm. 5.1 Relations to Neuroscience and Psychology In Section 3, we noted numerous similarities between swarms and brains in their functional organization for information processing. This entailed showing close relationships to key ideas from neuroscience (Kandel et al. 2; Gazzaniga et al. 1998), including analogs to: early sensory processing (field of view, receptive fields), neurons (bees), activation levels (quality thresholds), action 14

15 Marker(site): *(6),o(5),sq(4),dia(3),tU(2),tR(1) 1 T a, hrs %choice(blk);%qual(gray) x 14 Split(x),no dec(o)(right) 57 Marker(#sites):x(6)*(5)o(4)sq(3)dia(2)tU(1)tR() Mean (.)/std(+)σ L t Mean#Bees visit MeanB c (x)meanb e (+) Distractor quality Distractor quality Figure 4: Distractor effect, four distractors (see Figure 3 caption for axes explanation). potentials (dances), neuron populations (groups of dancing bees), neural network structure and communications (bee-to-bee communications on a random topology), neural image and short-term memory (spatially distributed internal model, group memory), lateral inhibition (cross-inhibition), late processing based on group memory (for explore/get recruited allocation, proportional allocation of recruits, and quorum sensing), and parallel and converging paths (simultaneous assessment of multiple sites, yet late processing for agreement on the best-of-n). The study of group memory accuracy in Section 3.5 showed that group memory on average provides the swarm with a representation of the relative nest-site qualities under consideration that enhances its choice performance. Identification and evaluation of these cognition elements allowed us to relate swarm cognition to well-studied attention-perception-choice tasks from cognitive neuroscience (Gazzaniga et al. 1998). We explained at a conceptual level the surprising similarities to attentional systems with a view of the swarm as eliminating distractors from consideration, and simultaneously focusing on the best sites. Similarly, for perception-choice tasks we explained how the swarm considers its field of view, develops a representation of its problem domain, and then uses that to choose. The series of behavioral tests we administer in simulation for the swarm borrowed from ideas in neuroscience and psychology (Gazzaniga et al. 1998; Treisman and Gelade 198; Ratcliff 1978; Roe et al. 21). First, we performed discrimination tests and showed that in spite of significant 15

16 individual assessment noise the swarm was able to discriminate between close quality sites. In the Appendix we show that the ability to discriminate depends not only on the differential quality, but the absolute quality. In particular, discrimination performance improves for lower quality sites. Next, we studied the impact of distractor sites. First, we showed that multiple distractors can be effectively eliminated from consideration provided their quality is relatively low. However, when distractors are of higher quality, fast but erroneous choices are made. It is as if the best site is hidden by the set of distractors. In the Appendix we administer a version of a Treisman feature search test (Treisman and Gelade 198). This shows that choice performance only degrades slightly if relatively low quality distractors are added to the task of finding the best quality site. The original idea that this provides evidence of parallel processing in the brain (Treisman and Gelade 198) clearly also holds for the swarm. Moreover, we show that if the high quality site is removed, the swarm takes much longer to decide which site to choose. It was proposed that this was due to a switch in humans to a sequential search mode (see discussion in (Treisman and Gelade 198; Gazzaniga et al. 1998)). Here, however, the delay is clearly induced by the dynamics of the process that leads to deliberation. This provides an alternative way to interpret the delays that occur in reaction time tests and this may be useful to infer mental dynamics and structure in other species. To gain more insights into discrimination and distraction effects we report additional studies in the Appendix. First, we show that distractors can attenuate the ability of the swarm to discriminate. Second, we show how discrimination mechanisms try to overcome the negative impacts of distractors. Third, we study whether swarms exhibit irrational choice behavior commonly found in human decision making (Luce and Suppes 1965; Huber et al. 1982; Tversky 1972; Simonson 1989; Simonson and Tversky 1992) in the presence of context-dependent effects (i.e., certain patterns of choice alternatives that can conspire to mislead the decision-maker). Context-dependence has also been studied for human group decision making (Steiner 1966; Laughlin and Ellis 1986; Laughlin 1999; Kerr and Tindale 24; Hastie and Kameda 25) as summarized in (Hinsz et al. 1997). We use an approach like in (Ratcliff et al. 1999; Ratcliff and Smith 24; Roe et al. 21; Busemeyer and Townsend 1993) where humans are subjected to reaction-time tests. For a very wide variety of nest-site quality patterns, our simulations show that the swarm cannot be tricked into misordering its choice percentages in relation to the nest-site quality pattern. This implies that violations of strong stochastic transitivity (Luce and Suppes 1965), the similarity effect (Tversky 1972), and the comparison effect (Simonson 1989; Simonson and Tversky 1992) will not occur. Finally, we show that for a special nest-site quality pattern (where a discrimination-distraction interaction is induced) the attraction effect (Huber et al. 1982) can occur. However, this leads to improved choice performance. Diffusion, accumulator, and other models of reaction-time tests (Ratcliff 1978; Luce 1986; Ratcliff et al. 1999; Usher and McClelland 21; Ratcliff and Smith 24; Roe et al. 21; Busemeyer and Townsend 1993; Smith 2) have a number of similarities to our model of nest-site selection (Passino and Seeley 26). For instance, they have representations of the time evolution of preference based on probabilistic arrival of evidence regarding multiple alternatives. There is internal coupling between the dynamical evolution of the preferences and preference thresholds that trigger choice. Moreover, a range of speed-accuracy trade-offs have been discovered with these models as also found by Passino and Seeley (26). In spite of these broad similarities, direct use of these models to represent the nest-site selection process is not possible since: (i) unique nonlinearities exist in the swarm (e.g., due to dance decay and explorer allocation); (ii) swarm cognition is a distributed process which leads to a significantly different information structure (i.e., when and how 16