Many wrongs: the advantage of group navigation Department of Biology, College of Natural Sciences, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6 Research into the puzzling phenomena of animal navigation and aggregation has proceeded along two Experimental and observational work has refined our distinct lines. Study of navigation generally focuses on knowledge of a wide array of orientation cues that are the orientation ability of the individual without refer- available to long-distance migrants including geomag- ence to the implications of group membership. A simple netic and solar information in combination with an principle (the ’many wrongs principle’), first proposed internal circadian clock, stellar rotation, geographical by Bergman and Donner in 1964, and developed by topology, olfactory cues and complex interactions or cross- both Hamilton and Wallraff three decades ago, provides calibration of these cues (c.f. However, naviga- a link between these lines of current interest by tional imprecision has many sources. For example, suggesting that navigational accuracy increases with geomagnetic compass precision is reduced near the group size. With unprecedented scope for testing the equator and the poles; stellar rotational cues are unavail- hypotheses it generates, it is now time that the many able for much of the year in polar regions; and solar cues vary with season and location Navigation errorintroduced by limitations that are inherent to the Animal navigation has been a source of fascination to orientation cues themselves is compounded by additionalhazards such as wind drift Correction mechanisms humans for centuries. Navigation directly affects dis- serve to reduce directional bias, but add a further source of persal patterns, which influence conservation efforts as random error. Even if orientation cues were absolutely well as population and evolutionary dynamics. In spite of reliable, flawless navigation would require perfect sensory intense recent research that has improved our under- interpretation and integration of cues by individuals. This standing of the navigational tools used by animals, a inherent individual error is at the heart of the current consensus has yet to be reached on explanations for the controversy over whether orientation mechanisms, as they accuracy with which migration is accomplished In are currently understood, are sufficient to explain the a seemingly unrelated area, scientists continue to seek explanations for why animals tend to form groups, with Error rates measured on individual birds are implicitly recent work focusing on group decision making assumed to result in a corresponding dispersion of and complexity theory . Although migrating animals individuals around the target migration destination.
often occur in groups, the studies of navigation and This scatter is traditionally described (using circular aggregation have persisted as independent lines of distribution statistics) in terms of a mean migration research. A largely unnoticed idea that was first direction and directional concentration. The three focal suggested 40 years ago might hold the key to solving papers show how the failure of orientation systems to the current impasse: it could account for unexplained account for observed navigational accuracy could be the navigational accuracy and simultaneously offer an result of an unnoticed but flawed assumption about how individual error rates should determine directional scatter Bergman and Donner first made the intriguing sugges- tion that we should not expect to account for accuracy ofmigration by studying individual navigational error rates we should expect group error to be lower than that of The many wrongs principle is based on the idea that the individual members because group migration ‘increases pooling of information from many inaccurate compasses the accuracy of the orientation mechanism’ . Hamilton yields a single more accurate compass (because and Wallraff then placed the original suggestion individual orientation error is suppressed by group within a solid theoretical framework. Inadequacies in both cohesion . Renewed attention to the principle the technology for tracking migratory animals and might provide a vital step toward a fuller understanding of datasets available to test the principle might explain why the papers received little attention at the time of The simplest, or null model can be envisioned as one publication. They now offer an appropriate null model and in which there are no innate differences in accuracy general framework on which to base empirical tests of the among individuals within a flock, and individuals contribute equally to the mean flock direction. Underthis null model, expected flock accuracy is a functionof flock size; smaller flocks are expected to miss Corresponding author: Andrew M. Simons ([email protected]).
their target more often (. Recent work on the evolutionary advantage of aggregation posits superior group decisions based on consensus or democratic votecounting , and requires communication of infor- Given that it is the individual rather than the group that has tools fornavigation, it is at this level that studies of navigation have mation among individuals. The elegance of the many traditionally focused. Interindividual variation in flight paths is an wrongs principle lies in its simplicity: the navigational appropriate measure of scatter for birds in solitary flight [2,3], but flocks are cohesive units that share a single path, and groups must be viewed as random samples of n individuals drawn from the This flock size advantage can be generalized to more On the scale of linear measurements, for example, the standard complex scenarios. Variation in navigational abilities deviation of the mean (or the standard error) is given by sffi among individuals is expected, and has several sources.
error decreases as sample size, n, within each group increases.
For example, adult and juvenile raptors differ in their Variation among flight trajectories must be measured on an angular ability to compensate for wind drift Similarly, rather than linear scale because orientation is a compass directionthat is taken from a circular distribution that has neither true zero, nor naı¨ve migrants might orient correctly but only true high or low values. Analogously to the linear scale, it is the experienced individuals can adjust this vector naviga- angular sampling distribution of flock means rather than that of tion if displaced from the correct route. When differ- individuals that determines directional scatter [12,24]. Therefore, all ences in ability are recognized by fellow flock members, else being equal, individuals flying within larger flocks will arrive navigational responsibility might be weighted unequ- more reliably at their destination than will individuals within smallerflocks, because of the declining relationship between flock size and ally among individuals. The effective sample size of a standard error of flight trajectories (Figure I). Thus, the assumption flock for navigation would then be smaller than the that error rates of flight trajectories are given by individual error rates bird count, but the correct expectation for directional is erroneous when individuals navigate in groups constrained by scatter among groups must still consider the general their cohesiveness to follow a single trajectory.
The sampling distribution of flocks converges on that of individuals only if a single individual assumes exclusive navigational responsibility for an entire flock. However, even at this logical extreme, flocks will show little scatter ifexperienced individuals lead the flocks. Thus, the use of individual error to predict directional scatter is reasonable only for solitary flight or under the unreasonable assump-tion that a single individual of average navigational abilityleads.
Tests and implicationsThus far, the scant references to the original papers,with few exceptions, do not directly test the naviga-tional advantage of aggregation. Important exceptionsdo exist. A comparison of orientation ability in homingpigeon Columba livia pairs that were manipulated todiffer in orientation abilities shows that the trajectoryof the flock of two birds is a result of a compromisebetween the paths that the birds would have takenindividually . Randomly assembled flocks of three –six directional scatter and homing times compared withsingle birds although, in another study comparingone- and four-member pigeon flocks, no significantgroup accuracy increases with flock size in the skylark Alauda arvensis providing support for the many Figure I. The advantageous effect of large group size on navigational accu- racy. Shaded areas depict 95% confidence intervals of trajectories for With the development of tracking technology and groups of 1, 10, 100, and 1000 individuals of equal navigational ability.
the accumulation of large datasets, several testable The trajectory of a cohesive group is given by the angular mean of theindividual navigators comprising the group as calculated using angular predictions based on the automatic grouping advantage statistics [24]. The mean angular deviation is given by s ¼ 1808 should provide fruitful avenues for research. The most where r, the angular concentration, is given by the length of the mean vec- basic prediction is that, within species, directional tor. The 95% angular confidence interval of group orientation is then cal-culated as 2s. Here, a fixed value chosen for r results in an angular scatter among groups will decrease with increasing deviation s ¼ 10.368 for animals navigating alone; s ¼ 3.438 when partici- group size. Furthermore, if the ’correct’ direction can pating in groups of size 10; s ¼ 1.078 in groups of 100; and s ¼ 0.348 ingroups of 1000. In a manner analogous to this simultaneous vector sum- be inferred, larger flocks will deviate less from the mation for many individuals, accuracy can also be gained from sequential correct direction than will smaller flocks. Species trajectory summation (c.f. [25]) if a trajectory is chosen only at the begin- characterized by small group sizes are predicted to ning of each stage of a migration that occurs in multiple stages.
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and J.E. Yack for comments and suggestions. This paper benefited from comments by H. Wallraff, T. Alerstam and two anonymous reviewers.
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The Wilson Journal of Ornithology 120(4):725–731, 2008LESSER SNOW GEESE AND ROSS’S GEESE FORM MIXEDFLOCKS DURING WINTER BUT DIFFER IN FAMILY´ N EINAR JO´NSSON1,2,4 AND ALAN D. AFTON3ABSTRACT.—Smaller species are less likely to maintain families (or other forms of social groups) than largerspecies and are more likely to be displaced in competition with larger species. We observed mix

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