Three-Dimensional Analysis of Turning Within Airborne Bird Flocks

The three-dimensional structure of airborne pigeon flocks was monitored over time. Flocks changed both in overall shape, and in compactness during the execution of turns. Flight speeds of the flocks were sensitive to the vertical rather than the horizontal component of a turn. The compactness of flocks did not seem to change in relation to speed maintained during turns or sharpness of turns. The cues to which birds responded in adjusting their flight paths may be important in determining flock compactness. Birds within flocks responded to each other's position and maintained positions close to each other. In a flock groups. of birds which maintained positions close to each other were observed as a distinct physical clump of nearest neighbors only if the overall flock structure was dispersed or was expanding over time. Birds flying on very different flight paths were occasionally observed to become temporary close neighbors due to the crossing of the arcs describing the flight paths of the birds. Under such conditions birds could possibly be detected as a physical clump of close neighbors within the overall structure of the flock. Birds in flock performed aerial flight maneuvers while maintaining or increasing the compactness of the flock structure. The relative positions of birds within the flocks were not fixed. The repositioning of birds within the overall structure of turning and wheeling flocks indicates that adaptive strategies for predator avoidance could be based on a bird's ability to easily reposition within a flock, rather than on the distinctly different advantages of maintaining a peripheral or central location within the flock. Behaviorally dominant and subordinate birds did not maintain specific positions within the airborne flocks. There was a tendency for birds of dissimilar dominance rank to be nearest neighbors within the airborne flocks.

The compactness of flocks did not seem to change in relation to speed maintained during turns or sharpness of turns.

INTRODUCTION
An uneven distribution and relative scarcity of certain essential resources may promote and necessitate the gathering of birds into 1 flocks to exploit resources. Flocking aids in the location and efficient exploitation of food (Short, 1961;Morse, 1970;Murton, 1968;Hamilton and Gilbert, 1969). Turner (1964) pointed out that imitiative foraging by birds in flocks would facilitate locating and switching to new food sources. Ward and Zahavi (1973) proposed that flocks act as information centers for food finding. Birds may gain from other flock members information on where (Krebs et al., 1972;Krebs, 1973) and what to eat (Greig-Smith, 1978;Murton, 1971).
The ability of individuals in flocks to harvest food sources more radily than an equal number of birds foraging individually has been attributed to the early warning function of flocking (Lazarus, 1978). Pulliam (1973) provided a simple calculation to show that a flock will have a greater chance of detecting an approaching predator than a single bird. The probability that at least one member of the flock will detect a predator before it sets within range of attack increases with the size of the flock. Since knowledge of danger can be rapidly transmitted to other individuals either passively by orienting and escape movements or actively by alarm signals, all members of the flock can take evasive action sooner than if they were alone or in a smaller flock. Lazarus (1977) termed this the early warning function of flocking to emphasize the importance of early detecti.on in facilitating escape.
Many predators rely on surprise for their success and abandon an attack once they have been detected by the prey (Rudebeck, 1951;2 Kenward, 1978). Numerous studies using a measure of the time to take flight in response to an approaching hawk-model have procided empirical support for the early warning hypothesis. Powell (1974) found response times to a predator shorter for flocks of ten Starlings than for single birds. Siegfried and Underhill (1975)  This could be done by each individual keeping watch. The latter case would free some members of the flock for alternative behaviors. Reduced predation risk due to flock membership has been demonstrated to result in a reapportionment of flock members time budgets (Murton, 1971;Siegfried and Underhill, 1975;Inglis and Isaacson, 1978;Lazarus, 1978;Diamond and Lazarus, 1974;Lack, 1968). Powell (1974) fo\.llld that Starlings share watchfulness while feeding in flocks, while Murton (1968) and Rassa (1977) noted that subordinate individuals do a disproportionate amount of watching, and thus exhibit a reduced feeding rate. These authors also noted a spatial context to the dominant-subordinate watchfulness relationship, with dominant birds located in the center of the flock. This idea is consistent with the observation that in colonial nesting birds, dominant individuals occupy the nest sites near the colony center where predation on nests is less than at the periphery (Coulson, 1966;Patterson, 1965).
The arguments developed so far lead to the conclusion that a flock of very large size would be maximally adaptive for detecting danger.
However, in a large flock the flock members might physically occulde the visual field of neighbors, and thus negate the benefit of increased numbers of scanners for detecting a predator. In the case of a threedimensional flock, only peripherally located inidividuals would be able to detect an approaching predator. If the shape of a typicai globular cluster flock is approximated to a sphere (Heppner, 1974)., the percentage of the total number of birds in the flock located at the surface changes predictably with flock size. The ratio of the surface area of a sphere to the volume decreases with increasingly larger spheres. Larger flocks would thus consist of a greater number of birds, but a smaller percentage of the total number would be located at the surface of the flock. Increasing the size of a cluster flight formation past some critical number of birds would not result in an increase in potential for the flock to detect and react to a predator.
Rather, there would be a decrease in the relative number of effective "watchers" in the flock, and signals from "watchers" would have to travel greater distances and to a larger number of neighbors in order for the warning ftmction of flocks to be effective.
Another problem of large flocks concerns the disrupting effect of 4 a potentially large number of false alarms (Treisman, 1975). The increase in the number of birds in a flock would result in a greater probability that at least one member of the flock would initiate a group reaction by giving a false alarm, or by inappropriate response to a neighbor. Davis (1975) studied this problem and showed that the type of response demonstrated by individuals in flocks may be a function of flock size.
He noted that the response elicited by disturbances varied systematically with the size of the flock. As flock size increased, the responses changed from taking wing, to flight intention movements, to orienting responses. This safeguard mechanism may reduce the problem of large flocks being continually perturbed and distracted.
Superior ability in detecting predators is only one potential advantage of flocking behavior. Flock members may derive protection from predators by the juxtaposition of neighbor's bodies between themselves and the predator. Williams (1964) first suggested that schooling behavior arose from a kind of defensive hiding in which a threatened fish placed itself among other fish. In doing this a fish could both reduce its conspicuousness, and place other fish between itself and the predator. Hamilton (1971) considered that an animal with near neighbors would have a smaller domain of danger. Thus, the selfish advantage to those individuals who sought cover by staying close to their neighbors might result in a tendency to aggregate. He considered it · obvious that predation on individuals outside a flock would select for centripetal behavior.
5 Pulliam (1973) pointed out that since birds on the periphery of a flock stand a greater risk of predation than solitary prey, it is to their advantage to peel away from the flock exposing a new periphery. Treisman (1975) argued that this would tend to result in the disbandment of the flock, an argument which neglects the fact that there may exist a distinct disadvantage to the first individuals to disband from a flock. The disadvantage could be twofold. Flocks are thought to offer passive structural protection from attack (Mohr, 1960;Tinbersen, 1951;Eibl-Eibesfeldt, 1962;Charnov, 1975). Individuals leavin& the flock would lose this advantage. Birds leaving the flock would also become the odd prey item in the vicinity of the predator, exposing themselves to increased hazard from predators (Mueller, 1975). Howland (1974) discussed the relative importance of speed and maneuverability to optimal strategies for predator avoidance. He suggested that zig-zagging evasive maneuvers are important to the prey, and that the timing of each individual in st~ying with the group is very important. Individuals that do not move with the flock are behaving differently, and in theory will selectively be pressed upon.
This concept is expanded in Eshel's (1978) hypothesis concerning the processes operating within groups of evasive prey. He suggested that dominant individuals may lead the group in an evasive path designed to provide themselves with structural protection and to expose the less fit individuals.
Dominant birds could gain an advantage by being located within the center of the flock structure, or in areas optimal for predator avoidance during an attack. If the positions of birds within airborne cluster flocks remain relatively fixed, a bird in the center of the flock may receive the most consistent benefit. A position on the surface of the flock could result in either minimum or maximum structural protection, depending upon the direction from which an attack occurred. The direction from which an attack occurred would also have an effect on the ability of birds to detect and respond to an attack. A position on the surface of the flock could result in a bird being the first to detect a predator, or the last bird to receive an alarm signal which travelled through the flock. Peripheral positions in a flock result in highly variable benefit both in potential for structural protection, and in timely response to predators.
If the positions of birds within a flock were not fixed, birds could place themselves in specific parts of a flock, or at random positions, and attempt to relocate within the structure if the flock was attacked. Some degree of structural reorganization is common to the response of many flocks to a predator (Nichols, 1931;Tinbersen, 1951;Mohr, 1960;Dill and Majo~ 1978 Heppner (1974) summarized the principal characteristics of true flocks. He noted that the activities of flock-members tend to be synchronized such that birds head in the same direction and maintain even spacing. Heppner also differentiated between organized flocks in which birds fly in single file or columns (linear flocks), and flocks which have a three-dimensional structure (cluster flocks). Birds which fly in the cluster configuration include Starlings, many shorebirds, and Pigeons. This study presents the behavior of birds flying in cluster flocks.
Two dimensional analyses of certain structural attributes of flocks have been attempted using both radar (Williams et al., 1976) and photographic techniques (Miller and Stephen, 1966;van Tets, 1966;Nachtisall, 1970;Gould and Heppner, 1974) . Dill and Major (1977)  Previous studies have filmed birds in straight and level flight.
Such flocks are in the polarized state of group organization (Shaw, 1978), in which individuals in the group face in the same direction, proceed at the same rate of speed, and maintain precise position relative to each other. Birds in the flocks I monitored maintained a compact flock structure, but may not have been in the polarized state. Breder (1976) presented a detailed model of the optimum geometric relationships between individuals in schools or flocks in the polarized state. He noted that because of the need for some type of locomotion by group members, it is necessary that a certain amount of space be maintained by each individual (Breder, 1965;van Olst and Hunter, 1970). Each individual, and a spherical shell of space around it, is thus considered as a unit sphere. Flocing or schooling can therefore be considered as a packing together of these spheres. Various three-dimensional lattices, and the maximum packing of unit spheres therein are described. 9 Functionally, the model states that no individual in the group has another individual to either side or directly above or below it. The spatial relationships between individuals in a single layer of such a packed group approximate a diamond shape (Weins, 1973). Threedimensional analyses of the distribution of fish in schools have demonstrated this type of deployment (Cullen et al., 1965;Hunter, 1966;Pitcher, 1973). The applicability of the model to globular flight formation is shown in Dill and Major's (1978) nearest neighbor analysis of Starling and Dunlin flocks.
An interesting aspect of the above model is the restriction on the potential directions of travel available to group members when the formation is turning. Breder (1976) noted that a tighter packing of individuals would require a more precise deployment of group members.
With individuals distributed in a precise geometric pattern, certain areas of the flock or school represent forbidden paths of direction of travel. These forbidden sectors would require too close a mutual approach of individuals while turning. The size and position within the group of these critical areas is a function of the density of the group. Functionally stated, a group must expand to make a sharp turn, and as the group compacts the potential for individuals to redistribute themselves within the overall structure quickly diminishes. Hunter (1966) demonstrated this phenomenon in fish schools, noting that periods of high angular deviation in the headings of fish always resulted in an expansion of the school structure. Individuals in such a group would be more or less fixed into place once the structure started to become compact, and for as long as the compact structure was maintained.
A bird on the outside of such a structure would not be able to reposition itself to the center or "safe side" of the flock in response to a predator. The deployment of the cameras was orthogonal. The cameras were mounted on tripods, raised to the same elevation, and aligned such that the interaction of their optical axes formed an angle of 90°.
When viewed from above, the cameras would be located on opposite ends of a diagonal bisecting a square of dimension 60.8 m per side.
Both cameras pointed at a coIImlOn third corner of the box. The Kodak Panatomic-X film was used in the still cameras. Film was exposed at Fl.8 (1/1000) and developed according to manufacturer's instructions. Developed film rolls were viewed at !OX through a modified microfilm reader (Eastman Kodak model C) to check the quality of the negatives. Film pair sequences found usable were printed on 8 X 10 RC paper.
As the exact magnification involved in making each print was used in the analytical procedure for calculating the positions of birds, a non-standard printing procedure was required. The negatives were held in place in the enlarger between two thin plates of achromatic glass, rather than by a standard negative holder. This allowed for the entire 24 nun by 36 nun area of the exposed negative, and the area around it which included the sprocket holes in the film, to be printed ABSOLUTE POSITION: Information derived from the 8 X 10 prints was first used to establish where in three-dimensional space each bird in the flock was located at each of the points in time at which photographic samples were taken. A Cartesian coordinate system was defined for this point in space analysis. The X and Y axes of the system were perpendicular, and crossed at the point of intersection of the optical axes of the two 35 mm cameras. The plane of the X-Y axis was level with the ground. The Z, or vertical, axis of · the system was defined as perpendicular to the X-Y plane. The elevation (Z axis), and that bird's displacement along the horizontal grid system (X-Y plane) were the real space coordinates of the bird. Real Mean separation distance between all flock members was calculated for all times at which the flock was photographed. This distance is the average of all unique combinations of between-bird distances within the flock. Nearest neighbor distance is not sensitive to fragmentation of a flock into subgroups. Mean separation distance is sensitive to such changes in structure, and is thus a true measure of flock compactness (Hunter, 1966). Plots of changes in the relative values of these two parameters over time were used to study internal flock structure. The resulting series of plots of birds' relative positions on the X-Y (flock as viewed from above) and X-Z (flock was viewed from the side) planes yielded information on left, right, above, and below.
These plots were used to ascertain whether the integrity of the positional relationships between birds was maintained as the flock flew through the air.
A premise basic to the study was that the negatives produced by the two cameras were exposed at exactly the same time. To test for synchrony of film exposure the cameras were mounted in tendem such that they both faced the screen of a high speed digital readout timing device (Berkeley model 500B). Shutter speeds of both cameras were set at 1/1000. The cameras were electrically activated from the common control unit at 500 msec intervals until the ends of the 36 exposure rolls of film were reached. Analysis of the exposed negatives indicated that the two cameras consi-tently fired at exactly the same time (~ msec), and the time period between firing remained 500 msec (+1.5 msec) for the entire 36 frames (Appendix B).
A field simulation was conducted to determine empirically the accuracy and precision of the photographic and digitizing methods employed in the study. A three-dimensional test "flock" in which the distances and angular relationships between "birds" were known was constructed from wood dowels and Styrofoam "birds".
The test flock was suspended from a helium-filled balloon. Two assistants on the ground used tether lines to "fly" the apparatus through the filming area. Analyses of the sequence of photograph pairs taken of the model provided an estimate of the error term for the experimental method. The calculated distances between "birds" and angular relationships between "birds" differed from the actual Each observation period lasted 90 minutes, with 45 minutes spent at each end of the loft. Two observation areas were used to minimize site-dependent dominance (Brown, 1975).
Agonistic encounters between birds and the act of supplanting were used to establish a win/loss matrix for each observation 20 period. Three sunnnary matrices, each representing six observation periods, were formulated and used to establish dominant and subordinate birds in each of the airborne flocks analyzed. As Pigeons do not form linear dominance hierarchies (Brown, 1965), data from the dominance matrices were used to investigate whether individuals of either extreme rank behaved differently than other birds in the flock.  Table 1 shows the composition of the flocks for each of the seven trials. Three types of information are given for each trial. Assigned numbers were trial specific labels used to distinguish birds in the series of photographs for a trial. Identification numbers were given to each bird and used throughout the duration of the study to identify specific individuals (Appendix A). All members of airborne flocks which could be identified have entries in Table I for the associated dominance rank of that individual.
A complete analysis will be presented for three trials representative of the different behaviors observed within the airborne flocks. The first trial presented (trial 7) demonstrates the types of information available from the study. Summary data for five trials are shown for flock speeds, compatness, and turning arc, as well as for distributions of distances to first, second, and third neighbors. Dominance data are summarized for all seven trials. Table II shows        TRIAL 2: Trial two shows a flock of dispersed individuals and subgroups which merged to form a single, core group. Figure 14 shows the flock of 14 birds viewed from above at six instants in time. Step increases in distances to neighbors, a situation suggesting the existence of clumped distribution of birds, exist at times three and four. The step distribution is not seen at times five or six, indicating that the subgroups have merged into a single, core flock. Note the decrease in distance to all neighbors at times five and six, which also suggests the merging of subgroups to form a single flock.
The processes described above are apparent in Figure 17. Nearest neighbor pairs do exist at time two. Figure 17

DISCUSSION
A type of compact cluster flock commonly observed is the spherical ball reaction of some species of birds to predators (Mohr, 1960;Tinbersen, 1951;Dill and Major, 1977).

32
The mean distance to first nearest neighbor for the flocks in this study (153.8 cm) is similar to those reported by Dill and Major (1978) for Dunlin (70.0 cm) and Starling (145.0 cm). flocks. Absolute distances to nearest neighbor as a measure of the density or compactness of a flock is not sensitive to the size of the birds which are spacing themselves apart in the flock. One can take into account the size of the birds in a flock by computing the ratio of distance 33 to first nearest neighbor to the average size of flock members. The range of values for the ratio in the present study go from approximately 4:1 which is close to the 3.25:1 ratio of tightly packed Dunlin flocks, to 8.5:1 which is slightly higher than the 71.:1 ratio reported for Starling flocks (Dill and Major, 1978).
The distance distributions for first, second, and third neighbors in the seven flocks of this study also resemble those reported by Dill and Major (1977)  The distances between fish in schools relative to the size of fish indicates that there is much less internal or empty space in schools than in bird cluster flocks. Hl.lllter (1966Hl.lllter ( , 1969 and van Olst and Hl.lllter (1970) demonstrated that spacing between fish in four species of jack mackeral was approximately equal to one-half the body lengths of individual fish. Pitcher (1973) Hunter (1966) studied the communication of velocity changes in· schools of jack mackeral. He demonstrated that responding fish may be quicker to sense alteration in a neighbor's behavior if the neighbor occupies a particular area of the visual field. Gould and Heppner (1974) suggested that the Vee formation of geese is such that neighbors are in the center of the visual field of following birds. It is very common for pairs or small groups of birds to break away from and then rejoin cluster flocks, a situation which would occur if birds followed specific neighbors within the flock resulting in pockets of response. Localized pockets of response have been observed to form within schools of fish that are turning (Shaw, 1978).
Two aspects of turning in cluster flocks have been discussed.

37
The first involves the potential for birds to change relative position within an airborne flock. A spherical flock structure involving relatively fixed positions of individuals would offer distinctively different advantages to peripherally and centrally located birds.
My study indicates that turning and wheeling cluster flocks are in a constant state of structural reorganization, and that adaptive strategies for reducing the risk of predation could be based on the phenomena of relocation rather than maintaining a fixed position in the flock.
A bird would not necessarily have to peel off from the surface of the flock (Pulliam, 1973)  These two aspects of turning in cluster flocks may act to influence how the potential for flocks to offer passive structural protection (Mohr, 1960;Charnov, 1975) and the selection of odd prey by predators (Mueller, 1975)  The continual redistribution of birds within turning flocks has bearing also on several current hypotheses of the aerodynamics of flocking behavior. It has been proposed that birds in flight formations could theoretically achieve an aerodynamic advantage by flying in the updrafts created by their neighbors (Lissaman and Shollenbeger, 1979;Higdon and Carrson, 1978;May, 1979). Models The birds within the flocks of Dill and Major's (.1978) study were deployed in a manner which would result in an aerodynamic advantage to flock members. It is interesting to note that the flocks filmed in their study were in the process of traveling between roosting and feeding areas, or migrating through the study area. Birds of the same species respond to predators by flying in compact, turning and wheeling cluster flocks (Dill and Major, 1977). Under the latter conditions the adaptive strategies of flocking relate to each individual's ability to protect itself rather than aerodynamic advantages. Some of the benefits of each type of flock configuration and behavior are exclusive to one type of flock. It would seem very likely however, that birds can easily and rapidly switch from an aerodynamic flock formation to a flock configuration in which Several results from this study may have bearing on future investigations of three-dimensional flocks. Two potential problems exist with the present dominance study. The first concerns the fact that pigeons do not form linear dominance hierarchies (Brown, 1975) so that dominance rank may be useful for establishing two distinct classes of individuals at either end of the hierarchy, but not for linear analyses. The second problem is that of site dependent dominance (Brown, 1975). A dominance relationship established under certain circumstances or areas may not b.e absolute. The problem in this study was that a pigeon's dominance rank as observed at the loft may only apply in the loft. Dominance rank established in the loft may not carry over to interaction within the airborne flocks.
The difference between physical clumps and CFSs suggested by this study provides the following guideline for requirements of sampling. A single sample of a flock can establish the geometric construct that exists at a particular time, but is insensitive to CFSs in a flock. The movement and redistribution of birds within a turning flock render analyses based solely on detecting physical clumps, or analyses based on nearest neighbor data from a single sample of a flock, of questionable value for establishing the processes responsible for maintenance of flock stability and structure. The above type of nearest neighbor analyses may establish artitrary associtions such as temporary neighbor pairs resulting from birds whose flight paths approach or cross at a point in time.    Fig. 2a shows a level flight path in which bird A is directly in front of bird B. Fig. 2b shows a flight path involving a dive. In this case bird A is in front of and above bird B. over time. Figure 4a shows the flock in trial seven as seen from above for each point in time at which photographic samples were taken. The deployment of birds in the horizontal plane is readily seen. Arrows indicate the mean direction of travel of the flock. Figure 4b shows the changes in elevation of the geometric center of the flock. Note that the X-Y plane was elevated approximately 150 cm above ground level.

Spatial analyses for clumped versus uniform or
. B th Distances to first through N neighbor within the flock are plotted for each of the time periods at which the flock in trial seven was photographed. Figure 6a shows the neighbor distance distribution for time one, while Figure 6f shows the distances at time six. The solid line in each plot connects the mean values of the distributions. The dashed line in all but the connecting mean values at time one, and appears so that changes in distributions over time may be more readily seen. . .  Figure 9. Summary information on flock movements over time. Figure 9a shows the flock in trial eight as seen from above for the eight points in time at which the flock was photographed. Arrows indicate the direction of travel of the flock. Figure 9b shows the changes in elevation of the geometric center of the flock over time. Note that the X-Y plane was elevated approximately 150 cm above ground level.    ..       Figure 14. Summary information on flock movements over time. Figure 14a shows the flock in trial two as seen from above for the seven points in time at which the flock was photographed. Arrows indicate the direction of travel of the flock. Figure 14b shows the changes in elevation of the geometric center of the flock over time. Note that the X-Y plane was elevated approximately 150 cm above ground level.  th Distances to first through N neighbor within the flock are plotted for each of the time periods at which the flock in trial two was photographed. Figure 16a shows the neighbor distance distribution for time one, while Figure 16f shows the distances at time six. The solid line in each plot connects the mean values of the distributions. The dashed line in all but the first plot is a trace of the line which connects mean values at time one, and appears so that changes in distributions over time may be more readily seen. ...• t S . GQ Figure 17. Relative positions, shown from two viewpoints, of flock members in trial two at five periods in time for which relative positions could be calculated. Assigned numbers of birds are shown as seen from above (left plot) and as seen from the side (right plot). The X-Y axis has been centered at the geometric center of the flock in each of the plots. The arrow the right of the X axis indicates the direction of travel of the flock. . : ., .. i-o: . .:.:: •.::

APPENDIX D
Distances between birds at the six time periods (Frames) in trial seven. Mean separation distance, and the mean distance to first nearest neighbor are shown for each time period. Identification numbers of birds forming nearest neighbor pairs, and associated distances, are also listed.