| Recruitment,
Search Behavior, and Flight Ranges of Honey Bees* * An Invited Review Paper for the Division of Invertebrate Zoology. |
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ADRIAN M. WENNER AND DANIEL
E. MEADE SYNOPSIS. During the past three decades, considerable evidence has been gathered in attempts to understand more fully honey bee recruitment to food sources. Those efforts also apply directly to two long-standing and competing recruitment hypotheses: odor search vs. "dance language" communication. However, whereas most researchers have focused on individual interactions and behavior, the colony can also be viewed as a unit. A review of evidence from a colony perspective reveals that colony members range an average distance from their home base, whether while foraging on food sources, while collecting water, or while relocating as swarms. Those averages, based on the logarithm of the distance from the colony, vary with the type of resource exploited and size of the odor field. Such a mathematical correspondence between distances travelled from parent colonies may well agree with an odor-search recruitment model, but is hardly reconcilable with the "dance language" hypothesis. INTRODUCTION Any assessment of what might
be true changes constantly, since science is a process rather
than a "thing" or an accomplishment (Hull, 1988). An
example of that process is the ongoing question of how honey
bees (Apis mellifera) might forage and recruit hivemates
to resources. During the past 45 years one opinion ("language"
use) has prevailed; more recently, a second interpretation (odor
use) has been regaining credibility. Few realize that, throughout
recorded history, those who have studied honey bee exploitation
of food sources have embraced either one or the other of those
interpretations (Wenner and Wells, 1990:chap. 4).
We found that this earlier
model outlined by von Frisch meshed better with the observed
behavior of searching recruits (e.g., Friesen, 1973; Rosin,
1990; Wenner and Wells, 1990) than did the dance language hypothesis
proposed by von Frisch (e.g., 1947, 1967). Since the first
formal presentation of our odor-search model (Wenner, 1974),
based largely on research by Friesen (1973), we have improved
our understanding of the behavior of recruited honey bees during
our search for feral honey bee colonies on Santa Cruz Island
off the coast of Santa Barbara, California (Wenner et al.,
1990).
The odor-search hypothesis gained support from some of the results gathered by Esch and Bastian (1970), by Gould et al. (1970), and by Friesen (1973). When Esch and Bastian relocated a familiar station to a new site, a few of the foragers found the new location and danced upon their return to the colony; however, only 14 of the 70 bees attending the dances of foragers found the new location. Twenty others attended dances and left the hive but failed to arrive at the transposed station. The remaining 36 former foragers did not contact the dancers. Ten of the 14 "successful" recruits in the Each and Bastian experiments required between two and nine exploratory flights (after repeated contacts with the dances of regular foragers between flights) before they finally located the station. Only four of the 14 successful recruits located the food on the first flight, with search times of 56, 58, 90, and 360 seconds. By contrast, experienced foragers would have expended less than 30 seconds flying on their "beeline" flight paths between hive and food (Wenner, 1963). In the Gould et al. (1970) experiments, 277 different bees left the hive after having attended 155 observed dances. Of those 277 recruits, only 37 found either of the two stations located 120 m from the hive (the fate of the other 240 recruits was undetermined). Twenty-five of the searching bees ended up at a station in the "correct" direction, but 12 of them ended up at a station in the opposite direction that had not been "indicated" in the dance maneuver. Search times for recruited bees in those experiments were even more revealing (Fig. 2). Whereas the outgoing flight time between colony and food source for experienced foragers was less than 20 seconds (see Wenner, 1963), recruit bees searched for up to 75 minutes (median time of 8 min) for the stations, even if they had later arrived at the station in the "correct" direction, as supposedly indicated by information contained in the dance maneuver. Friesen (1973) measured the elapsed time between hive departure and arrival at a feeding station. Maximum search times for recruits that found a downwind station were more than 24 min but slightly less than 9 min for an upwind station. The dance language hypothesis H. Eltringham, Fellow of the Royal Society in London, translated Julian Francon's book, The Mind of the Bees, and wrote a preface to that English edition. Francon (1939) had proposed a sophisticated "language" hypothesis for recruitment of honey bees, and Eltringham felt that Francon had gained convincing evidence that "the original bee can, in some way unknown to us, give to the assistant bees the most precise and accurate instructions." Experiments by von Frisch followed shortly thereafter; he concluded on the basis of those experiments (von Frisch, 1947, p. 5): "Today, after two years of experimenting, I have come to realise that these wonderful beings can, in a manner hitherto undreamt of, give each other exact data about the source of food." He later wrote (at various times):
In contrast to these statements by von Frisch, proponents of the dance language hypothesis today no longer seem to have a clear notion of what one should expect from that hypothesis. COLONY FORAGING, A UNIFYING PRINCIPLE Research has focused primarily on individual foragers and searching recruits, but the colony can also be studied as a unit (e.g., Wheeler's 1923 "super-organism" concept). However, while individual bees may range far and wide, simple energetics would impose a limit on the distances at which colonies could effectively exploit resources. An early study by Eckert (1933) reviewed previous work on colony foraging. Eckert found, as Gowland (1927) had found earlier, that colonies concentrated on food sources in certain regions near the hive and that colonies too far removed from resources steadily lost weight. Other reviews have covered work since that time (Waddington, 1983; Seeley, 1985; Winston, 1987). Visscher and Seeley (1982) extracted distance and direction information from dance maneuvers of foragers in an observation hive and also found that their colonies concentrated on food sources in particular areas. Foraging patterns changed through time; they attributed those changes to the discovery of richer food sources and recruitment thereafter by means of "dance language" use. They did not consider other possible explanations for their results, such as changes in fragrance concentration and dispersal or changes in wind direction. Roubik (1989) recognized that the Visscher and Seeley (1982) results obtained in New York for the distances bees foraged from their colonies bore a striking resemblance to results Vergara (1983) obtained in Panama. Roubik proposed an area exploitation model for colonies; however, his model 1) implied a mechanistic foraging pattern rather than the use of dance maneuver information and 2) did not fit either the Visscher and Seeley (1982) or the Vergara (1983) results especially well. Wenner (1967) earlier had proposed that an expanded binomial pattern could explain the eventual arrival of recruits at equaliy attractive stations located at various distances from a colony. Experiments with a scented computer-driven mechanical bee (Michelsen et al., 1989), provided a pattern of results similar to that obtained by Visscher and Seeley (1982) and to that obtained by Vergara (1983). Moreover, the results Michelsen et al. (1989) obtained admittedly did not mesh closely with expectations of the von Frisch dance language hypothesis. The similarity of results obtained from studies in Wyoming, New York, California, Panama, and Europe to one another all suggest that a unifying principle exists. These various studies of colony foraging patterns, as covered below, also provide new insight into the applicability of the two competing honey bee recruitment hypotheses. DISTANCES HONEY BEES RANGE FROM THEIR COLONIES Researchers usually use one of three methods to estimate the distances honey bees travel to resources or to new home sites: 1) they interpret the information contained in forager or scout dances executed within the colony or on the surface of swarms, 2) they sample bee visitation at different distances from a colony to determine the density of foragers known to be from that colony, and/or 3) they mark bees in the field and recover them later at the parent colonies. Accuracy of distance information in waggle dances The straight run portion of the dance maneuver is apparently the most consistent of available measures if one wishes to determine distances travelled by foragers (Wenner, 1962; von Frisch, 1967, p. 104) and is best delineated by the sounds emitted by dancing bees during the staight run portion of their dance (Wenner, 1962:fig. 1). However, researchers at best obtain only imprecise distance information from waggle dances. Appreciable variability occurs both for repeated runs of the dance maneuver performed by individual bees (i.e., within bee variation) and for dances executed by different bees (between bee variation) travelling to any given site. Table II and figure 5 in Wenner, 1962 provide an analysis of variance, based on the results obtained from 86 different bees and 629 straight runs performed by foragers. In those studies, between bees and within bees variance combined increased steadily with increasing distance travelled by foragers from their colony (Wenner, 1962:fig. 5b). Distance experiments run by von Frisch Von Frisch (1967, pp. 88-97) summarized the results from several experiments designed to test the ability of recruits to find a station located at a particular distance from the colony after they had contacted a dancing bee visiting that same station. The results in his summary permit us to address the question: How accurately did recruits in the von Frisch experiments perform compared to any distance information they could have obtained from the dance maneuver? We can also ask: 2) How well did searching recruits in the Michelsen et al. mechanical bee experiments perform compared to the performance of recruited bees in the von Frisch experiments? By extracting information from figures 1 and 5 in Wenner (1962), one also can derive histograms illustrating between-bee variation in distance information, as contained in the dance maneuver, for any particular distance from the colony. That is, one can estimate the expected distribution of recruited bees in the field if they would be able to use distance information without error that they had extracted from dancing bees. Figure 3 provides a triple comparison: 1) the best results that could be expected for distance recruitment on the basis of dance maneuver information (Fig. 3A), 2) results obtained by von Frisch in his experiments (Fig. 3B), and 3) results obtained by Michelsen and co-workers in their studies of recruitment with a mechanical bee (Fig. 3C). The examples chosen are for feeding stations placed at about 1 km from the colony. The searching recruits in von Frisch's 1,050 m experiment (Fig. 3B) performed much better than expected on the basis of dance maneuver information (Fig. 3A). Furthermore, recruited bees should have exhibited, on average, some error on their outward flight and performed even less well than indicated by the distance information present in dance maneuvers. When von Frisch was informed about the inaccuracy of dance maneuver information, he resorted to an ad hoc modification of his hypothesis and proposed that recruit bees "averaged" the information from several dances of the attended bee before they left the hive. However, averaging the information, as he proposed, would only reduce within-bee variance, not between-bee variance (Wenner, 1962). Von Frisch (1967) had many more foragers travelling between colony and feeding station when his feeding stations were at greater distances than when they were closer to the colony. The resultant larger aerial pathway for greater distances would provide a stronger odor trail for stations more remote from the hive. He also did not refer to his earlier mention (von Frisch, 1937) of the long time required for searching: "The farther [the stations] were the longer time it took. . . . In the last experiment they were found after 4 hours in a meadow a full kilometer from the hive. . . ." Another factor von Frisch did not consider fully was the importance of odors during recruitment, both those provided by regular foragers and by odors peculiar to the station locality. Others (e.g., Gould, 1975, p. 686) eventually realized that von Frisch did not have adequate controls against odor artifacts. The Michelsen and co-workers 1,000 m results In the distance experiments (100, 250, 500, 1,000 m) run by Michelsen et al. (1989), both the within - and between - bee variances should have been negligible. That is, they should have been able to provide a rather precise signal for distance of a food source (mean of means), since they would not have to contend with the natural variation present in dances by real bees. In three of the Michelsen et al. experiments, test stations were located at distances similar to those employed by von Frisch (1967, p. 88-97), including one experiment with a target station at about 1,000 m. In none of their mechanical bee experiments did results correspond with those obtained by von Frisch for the same distance (e.g., Fig. 3C). Almost all recruits in mechanical bee experiments ended up at stations closer to the colony than at the one presumably indicated by the programmed dance maneuver. Michelsen and co-workers also obtained results completely at variance with the dance language hypothesis (and with von Frisch's results for a 450 m station) when they had two real foragers visiting a station 500 m from the colony (Fig. 4A). Once again more recruits arrived at stations closer to the colony than at the station presumably indicated by forager dances. A recurring lognormal pattern Instead of supporting the notion that recruits use "dance language" information as they search for food sources exploited by regular foragers, the pattern of results obtained by Michelsen et al. (1989) matched the patterns Roubik (1989) relied upon (Visscher and Seeley, 1982; Vergara, 1983) to develop his area exploitation model. Actually, all three of those patterns appear to be lognormal (i.e., random) and thereby hardly consistent with the "language" hypothesis. Figure 4B depicts as a histogram all the Michelsen et al. data for both mechanical and real bees, plotted against a theoretical lognormal distribution for the same distance. A simple test of lognormality for such results can be run. The results can be cumulated, converted to percentiles, and plotted as a function of distance on lognormal probability graph paper. One can then fit a straight line as closely as possible, percentage-wise, to all of the points so plotted (Siegel, 1956). A Kolmogorov-Smirnov test can then be applied to indicate whether the straight line fit is significantly different, statistically, from the results obtained (Siegel, 1956; Zar, 1984). Michelsen et al. (1989) had in fact obtained a distribution for their searching recruits that did not differ statistically from a random and mathematically predictable lognormal distribution (D = 0.40; P> 0.20). A re-interpretation of the 1967 Wenner results Johnson (1967), Wenner (1967), and Johnson and Wenner (1970) recognized that the von Frisch distance experiments lacked an important control and that he did not demonstrate searching bees use dance maneuver information. Wenner then repeated a key von Frisch distance experiment with the original experimental protocol. With a feeding station at 400 m from the colony and with three scented control stations at 200 m, 300 m, and 500 m, recruits arrived, as in the von Frisch experiments, predominantly at the 400 m distance (Wenner and Wells, 1990:fig. 9.2). After Wenner had provided bee visitation from another colony at two of the other scented stations as well (200 and 300 m), hereby having bee odor at three stations, the recruit arrival pattern from the experimental colony altered dramatically (Wenner, 1967:table 1, experiment 2). Most recruits from the experimental colony now arrived at the 200 and 300 m stations (as in the experiments by Michelsen et al., 1989). That result occurred despite the fact that only 400 m distance information was present in the dance maneuvers of foragers in the hive. Wenner (1967) concluded that the distribution of recruits at the three now more nearly equivalent stations matched a binomial distribution (1:2:1). However, a lognormal fit matches the same set of results (D = 0.25, P > 0.20) better than does a binomial distribution. We re-examined the experimental results that Wenner obtained with a feeding station at a site 500 m distant from the colony, on the possibility that the correlation observed above was spurious. When bees from the experimental colony visited only a station located 500 m from the colony, as in the von Frisch protocol, once again nearly all recruits ended up at that station and ignored a station at 350 m (Wenner and Wells, 1990:fig. 9.3). However, when bee visitation was provided at three control stations located closer to the colony as well as at the 500 m experimental station, a very different distribution emerged for recruitment from the experimental colony (Wenner, 1967:table 1, experiment 3). Then, very few of the recruits arrived at the 500 m station presumably indicated by dance maneuvers in the experimental colony; nearly all recruits arrived instead at stations closer to the experimental colony. At the time, Wenner had concluded that the distribution of searching recruits was similar to what one would expect from an expanded binomial distribution (1:3:3:1). However, statistical tests revealed that the results were not as close to a 1:3:3:1 ratio as they were to a lognormal fit (D = 0.20; P > 0.20). The Cornell and Panama patterns Consider now the two sets of patterns upon which Roubik based his area model for distance foraging. Whereas Roubik (1989:fig. 2.24) combined the Visscher and Seeley (1982) data gathered at different times during the season, we recognized that the mid-July segment of their original data (see Fig. 5) did not differ from a lognormal pattern (D = 0.25; 0.20 > P > 0.10). The close fit to a single lognormal distribution might imply that one or at most two food sources dominated input of resources to the colony at that time. The other results gathered by Visscher and Seeley did not form unimodal lognormal patterns but were polymodal lognormal. The data gathered in mid-June, for example, fell into four quite distinct lognormal modes (by application of techniques outlined by Cassie (1954). The Vergara results for the foraging pattern of African bees in Panama (Roubik, 1989:fig. 2.24) were not statistically different from a lognormal distribution (D = 0.25, P > 0.20). Gould 315 m "misdirection" experimental results In his book on honey bee ecology, Seeley selected the results of one of Gould's "misdirection" experiments (Seeley, 1985:fig. 7.2) to illustrate the apparent success of those experiments in directing bees to a site at a given distance from the colony. However, an analysis of Gould's data once again yielded a distribution that did not differ significantly from a random lognormal distribution (D = 0.15; P > 0.20). Magnetic retrieval of metal tagged bees Gary et al. (1978) collected thousands of foraging bees in the field, some of them from common Italian colonies and some of them from hybrid bee colonies. They tagged them with metal discs that were later recovered with the aid of bar magnets attached to the parent colony entrances. From their paper (Gary et al., 1978:fig. 2, table 2), we recovered the original data for distances routinely travelled by foragers. The combined data for the two strains of bees did not differ from a lognormal distribution (D = 0.37; P > 0.20). Hybrid bees ranged a lognormal average distance of 75 m from their colonies (D = 0.22; P > 0.20). Forager distribution for Italian bees was bimodal lognormal, with 70 percent of them foraging only slightly further than the average distance travelled by the hybrid bees. The other 30% of the Italian foragers travelled a somewhat greater average distance, a distance that can be determined readily by separating modes (Cassie, 1954). Swarm relocation behavior Schmidt and Thoenes (1990) tallied the distances that swarms moved from their parent colonies by placing a set of concentric rings of empty swarm hives (scented with pheromones) around the experimental colonies. They already knew that swarms are more likely to occupy these specifically designed cavities than natural cavities (Schmidt, 1990). The distances that swarms relocated from their parent colonies did not differ from a lognormal pattern (Fig. 6; D = 0.40, P > 0.20). Coincidentally, the distances Schmidt and Thoenes selected for their placement of scented empty swarm hives matched those distances chosen by Michelsen and co-workers for placement of test stations in their mechanical bee experiments. Both patterns were approximately logarithmic and matched one another. Both Lindauer (1955) and Seeley and Morse (1977) tallied distance information provided by foragers on the surfaces of swarm clusters to determine likely sites those swarms would move after having exited from their parent colonies. The distance distribution patterns gathered in both studies were quite similar to one another. The combined set of results (Seeley and Morse, 1977:fig. 1) did not differ from a lognormal pattern (D = 0.33; 0.10 > P > 0.05). Water gathering Colonies usually exist close to a water source (e.g., Columella, ~50 A.D.). During our honey bee removal project on Santa Cruz Island, California (Wenner, 1989; Wenner et al., 1990), we gathered data on the distances from colonies where we found bees at water. The pattern we obtained from data gathered for 53 colonies was binomial lognormal (Fig. 7A), with ~80% of the colonies exploiting water sources closer than 400 m (lognormal mean of ~160 m). The other 20% of the colonies gathered water from a greater distance (Fig. 7B), apparently forced to do so because of the prolonged drought in Southern California these past few years. DIRECTION EXPERIMENTS Experiments testing the presumed "use" of direction information, as interpreted from dance maneuvers, pose even greater problems than those testing "use" of distance information. First, we seem to have no good measures of the degree of variation present in direction information contained in dance maneuvers, compared to what is known for variation in distance information in dances (Wenner, 1962 and above). Second, stations set out to test the "use" of direction information have almost always been placed in an arc at one distance from the colony, without an equivalent arc of stations placed in the opposite direction from the colony. Earlier Wenner (1962) warned against use of that station arrangement, because that procedure generates an odor field in only one direction from the colony and a consequent "odor center" problem. Third, very little attention has been paid to wind speed and direction in those experiments designed to measure effectiveness of "direction communication." Yet, odors (as physical particles) can only travel downwind, and stations must be scented or one gets no recruits (e.g., von Frisch, 1937; Wenner et al., 1969; Wells and Wenner, 1971). In areas with prevailing wind directions, as on Santa Cruz Island, one can also readily perceive that bees forage primarily upwind from their colonies (Wenner et al., 1990). Recruit distribution: A center of odor field phenomenon Whereas recruitment and foraging at different distances from a colony fit a lognormal pattern, a different mathematics applies when stations are all at the same distance from a colony. This topic is already treated fully in Wenner and Wells (1990:chap. 5, excursus PN) and will be covered only briefly here. An expanding spiral flight pattern (e.g., Fig. 1) would result in many searching bees ending up downwind from scented food. Von Frisch did not recognize the potential consequences of the geometry of unevenly placed stations in his experiments (e.g., Wenner, 1962). Instead, when he conducted his "fan" experiments, he always placed his experimental station behind the central portion of an arc of stations. The geometry of station placement could then dictate the results (e.g., Johnson, 1967). Goncalves (1969) later placed test stations in all directions from the colony and obtained recruitment in all directions, rather than only in the direction indicated in the dance maneuver. A downwind station bias in his results was explained by Friesen's (1973) results. Despite the fact that Johnson (1967) pointed out the unacceptability of arc station placement, others continued to employ that flawed design (e.g., Stephen and Schricker, 1970; Gould, 1975; Michelsen et al., 1989). In one case, Michelsen and co-workers placed an arc of three stations in one direction from the colony and a single station in the opposite direction. They then attempted to direct recruits to the central station of the arc; their results seemed compatible with the notion of use of direction information provided by their mechanical bee (Fig. 8A). However, their results also closely match what one might expect if recruits ended up at the various stations in inverse proportion to the distance of all stations from the center of them all (Fig. 8B; see also Wenner and Wells, 1990:excursus PN). A PRACTICAL APPLICATION We successfully apply our knowledge of odor-search behavior in our research project on Santa Cruz Island (Santa Barbara County, California). We treat colonies as foraging units while we locate and remove all feral colonies from that 25,000 hectare mountainous terrain (Wenner, 1989; Wenner et al., 1990). Our perception, as shown in part in Figure 1, permits us to find colonies in only a few hours instead of the days formerly required (e.g., Visscher and Seeley, 1989). We have now located more than 120 colonies in only four seasons. The canyon topography and uniform Mediterranean climate on Santa Cruz Island most of the year results in wind moving past most colonies from only one direction all summer. That circumstance provides opportunity to study foraging patterns. In the seasonal drought circumstances prevailing on that island, most colonies are very small, numbering only a few thousand individuals. Average distances foragers travel upwind apparently vary with quality of crop, but those distances in any case have not been very great. The maximum distances noted so far have been only upwind to introduced European weed patches, such as 1,500 m to horehound (Marrubium vulgare) and yellow mustard (Brassica species) and 2,500 m to sweet fennel (Foeniculum vulgare). By contrast, as Friesen (1973) found earlier in studies of recruitment, we have found that island colonies forage only a few hundred meters downwind, regardless of the type or quality of crops that might be in that direction. Studies of pollen gathered by colonies, in conjunction with Steve Buchmann at the USDA bee laboratory in Tucson, have just begun. These studies will reveal the maximum distances travelled for various plant species. Fortunately, the island vegetation has already been mapped and, aside from natural changes (e.g., fire), will change only in a prescribed and planned manner (e.g., removal of foreign exotics), because Santa Cruz island is now a portion of the Channel Islands National Park. PERSPECTIVE A recurring pattern is evident in the average distances that bees range from their colonies, a pattern found so far in four different circumstances: 1) distribution of searching honey bees at test stations in field experiments, 2) distances foragers travel to food sources, 3) distances bees travel to water, and 4) distances swarms relocate from their parent colonies. The distributions, based on the logarithm of the distance (i.e., lognormal), indicate that honey bee colonies function as units. The lognormal pattern applies to the two extant hypotheses concerning honey bee recruitment to food sources. These two persistent and competing hypotheses, with us for centuries, may both be considered to be supported by any given set of experimental results; however, neither should have become a "ruling theory" (Chamberlin, 1890). The question is not which hypothesis is the correct one, but which hypothesis is most applicable (i.e., which fits the largest body of facts now) and/or which is most useful for explaining foraging patterns. The new lognormal concept opens research possibilities, and one should note that many different researchers contributed to its formulation. Roubik (1989) took an important step toward breaking the long-standing impasse, not because the model he proposed fit the examples of distance foraging results he chose especially well, but because he introduced a mathematical model to explain the regular pattern of forager distributions. The mechanistic approach that Roubik used, in contrast to the vitalism attitude (functionalism) that has prevailed these past 45 years (see Rosin, 1980), is the same type of approach that led to rapid advances in other areas of biology (e.g., molecular biology and genetics). As Visscher and Seeley stressed (and as others have noted), the distribution of resources is patchy in nature. The lognormal recruitment patterns observed are certainly not what one would expect if bees could use a "dance language." This new perspective has really been a joint effort. Esch and Bastian (1970), Gould et al. (1970), and Friesen (1973) provided accurate data on time taken for recruits to reach a station and on the percentage of success for those searching recruits. Wenner, Wells, and Johnson (reviewed in Wenner and Wells, 1990) made the test stations more nearly equal to one another, demonstrated that the dance language model no longer fit the results, and quantified the importance of odor to searching recruits. Friesen (1973) thoroughly documented the importance of wind direction for recruit success. Michelsen and co-workers, by having either none or only two bees visit a test station, also made their test stations more nearly equal to one another. Their results did not agree with expectations of the dance language hypothesis; however, by having their stations placed at unequal distances from one another (with no concentration of stations near the test station as von Frisch had done), they obtained a recognizable lognormal pattern. Visscher and Seeley gathered ample data on how far foragers ranged from large colonies in a natural setting and thereby provided an opportunity for a comparison of the results that Michelsen et al. obtained with few stations and with only two bees, to that which might happen for a colony foraging as a unit. Vergara studied African bee foraging; his find of a similar pattern to that obtained by Visscher and Seeley opened the way for Roubik to recognize the similarity between the two patterns and possible implications of that similarity. What factors contribute to the average lognormal distance that bees range from their colony or relocate as swarms? The expanding spiral flight of naive bees as they leave their colony has been reported by students of bee behavior from the time of Columella (~50 A.D.) to Southwick (1991). Nor is the "Golden Section" pattern a rare phenomenon in nature (Cook, [1914] 1979; Ghyka, [1946] 1977). The radius of an expanding spiral (perhaps logarithmic) would differ somewhat for each departing recruit, and searching bees would end up at varying distances from their colony on their first flight out. Furthermore, several factors would influence the length of that radius at any given time; richness of food, strength of odor cues, size of odor field, wind speed, relative abundance of stores in the colony, and colony size are a few examples. Aside from the above general statement about direction orientation (and stressing the importance of wind direction), we do not cover here problems that arise when colonies forage in different directions. That is because a different mathematics applies; our mechanistic odor-search model (Fig. 1) is but a start. We note that nearly all direction experiments have been run with stations at a single distance. Once all stations are made equal in attractiveness, the geometry of station placement apparently dictates the results one can obtain (e.g., Johnson, 1967; Wenner and Wells, 1990:excursus PN). Friesen's 1973 paper could have provided an important lead for investigating that direction orientation further, but wind speed and direction were ignored by others at that time and have been largely ignored in publications since that time. So, also, have others ignored the importance of odor drifting downwind from the aerial pathway of foragers flying their beelines (e.g., Friesen, 1973; Wenner, 1974). That omission is striking, since everyone knows odor is important for successful recruitment and that odors travel only downwind. In any event, the way is now open for some giant strides in the study of honey bee foraging ecology. We now perceive that searching behavior in honey bees is much like that exhibited by other flying insects. 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