Abstract

The reasons for conspicuous “V” and other flight formations in birds are debated. Theory and recent empirical advances show that energy saving is one important function of flight formations, but some aspects remain poorly understood. Combining theories of animal flight and sociality, we suggest that some of the variation in flight formations has its base in kin selection and reciprocation. The bird leading an acute V formation saves less energy than does the trailing participants. The disadvantage of leading is reduced in more obtuse formations, and when the longitudinal distance between neighbors is small, the leading bird can save about as much energy as others. Therefore, acute V formations are predicted to occur mainly in circumstances conducive to kin selection or reciprocity. These mechanisms seem possible, for example, in small flocks of adults with offspring, such as in swans, geese, and cranes. Inclusive fitness advantages may then favor an energetically expensive leader role for adults. In small groups, reciprocity is also possible among unrelated adults that recognize each other and take turns leading the V formation. In contrast, obtuse formations are expected in large flocks of unrelated individuals, such as spring flocks of waders migrating long distances. Possibilities for testing these ideas are discussed.

AV formation of migrating swans, geese, cranes, cormor-ants, pelicans, flamingos, or other large birds is a spectacular sight that gives rise to interesting questions. Why such regular formations? Most smaller birds that migrate in flocks do so in less ordered groups (Alerstam, 1990). What is the advantage of V formation (Figure 1), and why do mainly large birds use them? At least two hypotheses may explain such formations: energy saving and communication (for review, see Alerstam, 1990; Speakman and Banks, 1998).

Energy saving is well supported both theoretically (see Badgerow and Hainsworth, 1981; Hummel, 1995; Lissaman and Shollenberger, 1970) and empirically (see Badgerow, 1988; Cutts and Speakman, 1994; Hainsworth, 1987, 1988; Hummel, 1995; Speakman and Banks, 1998). Weimerskirch et al. (2001) showed that great white pelicans (Pelecanus onocrotalus) have lower heart and wing beat rate, glide more often, and save as much as 11–14% energy when flying in the vortex wake from another bird (Figure 2).

Flight formation may also enhance communication and orientation of the flock (see Cutts and Speakman, 1994; Gould and Heppner, 1974; Hainsworth, 1988; Hummel, 1995; Speakman and Banks, 1998). The evidence for this function is weaker than for energy saving, but both mechanisms might work together.

Still, several interesting aspects of flight formations remain poorly understood, such as their variation in occurrence, size, and form. Theory suggests that large birds make greater energy savings than do small birds by formation flight (see Alerstam, 1990). Yet, not all large long-distance migrants use formation flight. Groups of raptors often soar high together with cranes or pelicans in thermal uplifts during migration, but raptors rarely use formation flight. Other species often leave the uplift in conspicuous formation (Alerstam, 1990). Why don't raptors use flight formations?

Other questions concern formation shape. Swans, cranes, large geese, and other large birds often use acute V formation (Figure 1) (see Badgerow, 1988; Speakman and Banks, 1998). The trailing birds, in contrast with the leader, can make substantial energy savings (Hummel, 1995; Weimerskirch et al., 2001). Other species use more obtuse or bow formations (Hummel, 1995), in which the leading bird is only a little ahead of its nearest neighbors, the longitudinal distance between neighbors increasing along the arms of the formation (Figure 3). In such formations, energy savings are probably more equable (Hummel, 1995). Why is there such variation in formation shape?

We suggest that the variation is related to flock kinship structure and to reciprocity that depends on group size. Acute V formations may often include relatives, in particular parents and offspring and siblings. Gains in inclusive fitness might make parents willing to accept a less favorable lead position, if their relatives will benefit. Reciprocity, with individuals taking turns at the lead position, may also be involved.

Energetics of flight formation

In the wake of an aircraft, two counter-rotating trailing vortices create air downflow behind the wingtips, and uplift outside the wake (see Hummel, 1995; Lissaman and Shollenberger 1970) (Figure 2). The vortices are a grim reality; they can approach tangential velocities of 100 m/s and extend many kilometers behind a heavy aircraft, horizontal tornadoes with sometimes disastrous consequences for other planes that happen to fly into them. Under controlled conditions, however, a trailing plane can save much energy by suitable lateral positioning in the upwash behind the leading plane (Chichka et al., 1999; Hummel, 1973, 1995).

Photographs of the wake of birds flying in clouds of helium bubbles also show that birds leave two trailing vortices (see Pennycuick, 1989; Spedding, 1987). The birds in a flock can therefore fly more cheaply in V formation, saving energy in the uplift from the frontal neighbor (see Hummel, 1995; Lissaman and Shollenberger, 1970; for review, see Alerstam, 1990; Norberg, 1990; Speakman and Banks, 1998). Lateral distance strongly influences energy savings (Chichka et al., 1999; Hummel, 1995; Lissaman and Shollenberger, 1970). Theory suggests that the lateral distance, d, between the centres of the two trailing vortices is less than the wingspan, b (Figure 2), the approximate relation being d = bπ/4 = 0.78b (Badgerow and Hainsworth, 1981). In theory, a bird gains the greatest benefits if its wingtip overlaps laterally with that of the bird in front (Figure 2), as described by the optimal wingtip spacing (negative, as the wings overlap): Sopt = (0.78bb)/2 = −0.11b (Badgerow and Hainsworth, 1981). Energy saving decreases rapidly with increasing lateral distance (Badgerow and Hainsworth, 1981; Hummel, 1973, 1995).

The longitudinal distance between individuals that minimizes the total energy expended by the flock is debated (see Hainsworth, 1987; Higdon and Corrsin, 1978; Speakman and Banks, 1998), but it is probably less critical than lateral distance (Chichka et al., 1999; Hummel, 1995; Speakman and Banks, 1998). For individual birds, however, energy saving can vary strongly depending on longitudinal distances (Figure 3). In an acute V with long distances, the leading bird makes little or no energy saving (Hummel, 1973, 1995; Weimerskirch et al., 2001). A mathematical model of energy savings in relation to lateral and longitudinal position (Hummel, 1973) shows that energy savings are more equable in bow formation, in which trailing neighbors are closer to the leader (Figure 3). As there is a slight upwash preceding each bird, with short longitudinal distances the leader can benefit from lift generated by the trailing neighbors.

Owing to longitudinal variation in the “concertina-wake” from wing strokes (see Pennycuick, 1989; Spedding, 1987), and to potential effects of phase relationships between neighbors, it seems likely that longitudinal position is more critical in birds than in fixed-wing aircraft (see Hainsworth, 1987). This may be why there are often longitudinal distances of several bird lengths between neighbors in an acute V formation, although such long distances are probably unfavorable for the leader. A follower may fly most cheaply at some optimal point up to several bird lengths behind the neighbor ahead, at least in large species with high flight speed, slow wing beats, and long distance between successive equal-phase wake points. This aspect may be testable in wind tunnels (see Pennycuick et al. 1997) in species such as red knot (Calidris canutus) (Kvist et al., 2001; Piersma et al., 1990).

Theory suggests that if formation members differ in size, energy savings will be particularly high for small light individuals, for example, juveniles, or females in species with sexual size dimorphism (Hummel, 1995).

Not all flock migrants use regular V formations or echelons (see Alerstam, 1990; Heppner, 1974). In passerines and other birds with short relative wing length, their rapid, large-amplitude wing strokes create complex wake patterns that may prevent energy saving by formation flight (Hummel, 1995).

Kin selection and reciprocity

We suggest that kin selection (Hamilton, 1964) plays a role in flight formations of related birds. Although the leading position in acute V formation is energetically more expensive than are other positions, the leader may gain inclusive fitness if the followers are close relatives such as offspring or siblings. Likely candidates are small flocks of geese, swans, cranes, or other large birds that migrate in family groups of parents and young (see Alonso and Alonso, 1993; Ely, 1993; Prevett and MacInness, 1980; Scott, 1980). The behavior of the leading bird may then be a form of aerial parental care. The advantage for young can be large if they are smaller and lighter than are adults (see above), as is usually the case (see Cramp and Simmons, 1977).

Kin selection may also occur in flocks of several families migrating together. In waterfowl with female-biased philopatry (Anderson et al., 1992), related females often breed near each other, and there is evidence that mothers, daughters, and sisters can recognize each other as adults (see Andersson and Åhlund, 2000; van der Jeugd et al., 2002). In some arctic geese, wintering adults and offspring in extended family groups may contain members from more than two generations (Ely, 1993). Migrating flocks of swans or geese may consist of several related females and their mates, plus offspring from several years (Warren et al., 1993).

Reciprocation (Trivers, 1971) can occur in flight formations if individuals take turns as leader, sharing the energetic disadvantage of the front position. Reciprocity can most easily evolve in small groups in which individuals interact repeatedly over long time (Axelrod and Hamilton, 1981; Boyd and Richerson, 1988; Trivers, 1971; for review, see Dugatkin, 1997). Large group size tends to favor defecting individuals that avoid costly behavior (Boyd and Richerson, 1988). Acute formations and reciprocity are therefore expected mainly in small stable groups with individual recognition. Recognition facilitates punishment of a free-loader that avoids taking the expensive lead position, for example, by mobbing it in the air or, perhaps more likely, at stopover sites. Reciprocity and kin selection can have strong synergistic effects in small groups (Axelrod and Hamilton, 1981; Boyd and Richerson, 1988) and may be particularly likely in migrating flocks of extended families. Such flocks may be teams in the sense of Anderson and Franks (2001).

In large flocks of unrelated individuals, acute formation shape that saves little energy for the leader may not be stable. If the nearest neighbors lag behind at positions that benefit them but not the leader, it may easily reduce flight speed so far below the optimum that the trailing neighbors will catch up. The leader therefore has an easy means of achieving a more egalitarian obtuse formation. This applies also for other birds in the formation relative to their nearest followers. Such adjustments of longitudinal distances may contribute to the dynamic nature of large formations of migrating eiders (Somateria mollissima) and Branta geese, which may have several local and varying leading points. Such points may perhaps also contain related or familiar birds among which kin selection or reciprocity can operate locally within the larger flock.

The scope for leader adjustment of the distance to followers may be a major reason why obtuse V, echelon, or bow formations occur in many birds flying in large flocks, for instance, arctic geese (Branta and Chen), sea ducks such as eiders (Alerstam, 1990), and also many waders (Piersma et al., 1990). During the many 1000 km nonstop migrations over open ocean by some waders (Piersma and Gill, 1998), energy saving is probably crucial for each individual. Large flocks of such long-distance migrants are therefore expected to fly in energetically equable, obtuse formations (Figure 1) or bows in which all individuals make similar energy savings (Figure 3).

No raptors use V formation, perhaps because selection for hunting efficiency prevents dense flocking and therefore also formation flight. But raptors do not migrate in formations, not even when leaving thermal uplifts at great height on migration, when hunting is probably no option. Lack of flight formation in raptors may in part depend on their lack of kin-related social structure after the breeding season, when they lead solitary lives.

Alternative explanations

The angle of a V formation may be related to relative neck length for reasons of optical contact, long-necked birds such as cranes and geese using acute formations, and short-necked species using more obtuse formations (Hummel, 1995). Neck length and communication, however, do not seem to explain the longitudinal distances between neighbors in, for example, geese, which are often much longer than a bird length (see Speakman and Banks, 1998).

Small birds will probably save relatively less energy by V formation than do large birds, in which flight formations are more common (see Alerstam, 1990). But there is no obvious reason why small birds might not benefit as much from coordination and orientation by formation flight as do larger birds. The lack of V formations in small flock-migrating passerines therefore suggests that communication is not the major function of formation flight.

Formation shape may depend on body size if the slower wing strokes of large birds permit closer approach to optimal positions in a formation (see Hummel, 1995), perhaps explaining why acute V formation may be more common in, for example, large geese than in small geese (Badgerow and Hainsworth, 1981; Speakman and Banks, 1998). Another possible reason is that smaller species tend to occur in larger flocks, in which kin selection or reciprocity seem less likely to favor individuals that accept an expensive leader role.

Predictions and possibilities for tests

The previous ideas predict that small flocks containing relatives will often use acute formations in which the leader saves little or no energy. Energetically more equable obtuse or bow-shaped formations are predicted when there is little possibility for kin selection or reciprocity among individuals that recognize each other.

These ideas are testable by analysis of the occurrence and shape of flight formations in relation to flock size and kinship structure. Formation shape is expected to differ between flocks of small to moderate size, especially those containing related individuals (e.g., geese and cranes) (Alonso and Alonso, 1993; Prevett and MacInnes, 1980), and larger flocks of mostly unrelated individuals, such as spring-migrating waders and arctic geese (see Alerstam, 1990; Piersma et al., 1990). To critically test these ideas, quantitative observations of formation shape are needed, which may be possible to obtain at suitable migration stations or in overwintering areas (see Speakman and Banks, 1998).

Age and sex distribution are expected to influence formation shape. Homogeneity in age, sex, and body size is expected to favor more egalitarian formations than do mixed flocks of, for example, adults and young. Offspring of the year are often smaller than parents and may be less able to maintain as high speed in lead position as larger adults can. Being smaller, juveniles can also make greater energy savings by following larger adults than vice versa (see above). Juveniles are therefore expected not to lead acute V formations. In contrast, a larger parent might help its offspring (see above) and increase flock speed by taking the lead position in an acute V. If, however, the birds are unrelated and adults have markedly higher optimal flight speed (Hedenström and Alerstam, 1995) than juveniles, adults may obtain higher fitness by forming their own flocks.

Some of these predictions can be tested in species in which juveniles differ markedly in coloration from adults, for instance, swans and pelicans. Flight formation structure can be measured in photographs taken by a vertically directed camera (Speakman and Banks, 1998). Kin structuring may be detectable by analysis of the positions of adults and juveniles in formations, to see if there are suggestive nonrandom patterns, for example, with adults helping offspring to energy-saving positions. Family structuring seems likely if the formation is led by one or two adults followed by a number of juveniles, then one or two adults again followed by juveniles, etc. General differences in flock kinship structure between species, and between parts of the year within species, may also be revealing.

Field studies have greatly clarified formation structure and function, corroborating the hypothesis of energy savings (see Badgerow, 1988; Cutts and Speakman, 1994; Hainsworth, 1987, 1988; Speakman and Banks, 1998; Weimerskirch et al., 2001). There are observations of changes in position near the formation front (see Hummel, 1995), but quantitative data on shifts in leader position and on distances between individuals are needed. Observations on roles in flight formation in relation to age, sex, season, and other aspects are also desirable.

A possible test of the relative roles of kin selection and reciprocity is to see if parents always take the expensive lead position in single-family flocks, or if there are shifts between parents and offspring or siblings. In the latter cases, there is reciprocation, although kin selection is probably also involved. Such tests might be possible with flocks of birds trained to follow a car, boat, or light aircraft (see Weimerskirch et al., 2001).

Whether reciprocation alone, without kin selection, suffices for development of acute leader-expensive formations may be tested during spring migration in some species. For example, spring flocks of waders (Piersma et al., 1990) seem less likely to contain a high proportion of close relatives than, for example, autumn-migrating small groups of geese, swans, and cranes. Kin selection may therefore be negligible in wader flocks in spring (but this needs to be tested). Reciprocation probably requires small groups in which individuals recognize each other (see above). If, therefore, large flocks of adult waders use equable flight formations but small flocks use leader-expensive acute formations, this suggests that reciprocation may suffice for development of acute flight formations.

Figure 1

V formation flights, the upper one with an obtuse formation angle, α >90°. In the lower figure, the greater spacing between birds in the longitudinal (flight) direction leads to an acute formation angle, α < 90°

Figure 1

V formation flights, the upper one with an obtuse formation angle, α >90°. In the lower figure, the greater spacing between birds in the longitudinal (flight) direction leads to an acute formation angle, α < 90°

Figure 2

A vortex is formed in the wake of each wingtip, creating downflow behind the wing and uplift outside the wake, as indicated at the tip of the right wing of the right-hand bird. A trailing bird can take energetic advantage of this uplift by flying at a suitably lateral position relative to the bird ahead. Theory suggests that the optimal wingtip overlap for the trailing bird is about one tenth of the wingspan b. A distance of about 0.78b separates the centres of the two trailing vortices from a bird or aircraft

Figure 2

A vortex is formed in the wake of each wingtip, creating downflow behind the wing and uplift outside the wake, as indicated at the tip of the right wing of the right-hand bird. A trailing bird can take energetic advantage of this uplift by flying at a suitably lateral position relative to the bird ahead. Theory suggests that the optimal wingtip overlap for the trailing bird is about one tenth of the wingspan b. A distance of about 0.78b separates the centres of the two trailing vortices from a bird or aircraft

Figure 3

Energy savings are unequally distributed among individuals in an acute V formation (top), the leading bird expending more energy than the others. A bow-shaped formation (bottom) is more egalitarian, and the frontal birds owing to uplift from their neighbors can make similar energy savings as the birds farther back in the formation. The average energy gain is similar for both formations, as the number of birds and the distance between wingtips are similar (modified from Hummel, 1995)

Figure 3

Energy savings are unequally distributed among individuals in an acute V formation (top), the leading bird expending more energy than the others. A bow-shaped formation (bottom) is more egalitarian, and the frontal birds owing to uplift from their neighbors can make similar energy savings as the birds farther back in the formation. The average energy gain is similar for both formations, as the number of birds and the distance between wingtips are similar (modified from Hummel, 1995)

We thank Donald Blomqvist, Frank Götmark, Henk van der Jeugd, and two referees for helpful suggestions on the manuscript, and the Swedish Research Council for funding (M.A.).

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