Robustness of flight leadership relations in pigeons Andrea Flack a, * ,1 , Zsuzsa Ákos b, 1 , Máté Nagy a, b, c , Tamás Vicsek b, c , Dora Biro a a Department of Zoology, University of Oxford, Oxford, U.K. b Department of Biological Physics, Eötvös University, Budapest, Hungary c Statistical and Biological Physics Research Group of the Hungarian Academy of Sciences, Budapest, Hungary article info Article history: Received 8 February 2013 Initial acceptance 13 March 2013 Final acceptance 19 June 2013 Available online 24 August 2013 MS. number: 13-00098R Keywords: collective motion Columba livia group dynamics hierarchy homing leadership navigational experience pigeon Collective animal movements produce spectacular natural phenomena that arise from simple local in- teractions among group members. Flocks of homing pigeons, Columba livia, provide a useful model for the study of collective motion and decision making. During homing flights, flock members are forced to resolve potentially divergent navigational preferences in order to stay together and benefit from flying in a group. Recent work has demonstrated that some individuals consistently contribute more to the movement decisions of the flock than others do, thereby generating stable hierarchical leaderefollower networks. Yet, what attributes of a flying pigeon reliably predict leadership remains an open question. We examined the flexibility of an individual’s hierarchical leadership rank (i.e. its ordinal position when flock members are ranked according to the average time differences with which they lead or follow others) as a function of changes in its navigational knowledge. We manipulated already established hierarchical networks in three different flocks, by providing certain individuals with additional homing experience. We found that such training did not consistenly lead to an increase in birds’ leadership ranks, and that, in general, the nature of leaderefollower interactions between trained and untrained birds remained unaffected. Thus, leadership hierarchies in pigeon flocks appear resistant to changes in the navigational knowledge of a subset of their members, at least when these changes are relatively small. We discuss the implications of our results in light of the potential benefits of structural stability in decision-making networks. Ó 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved. A flock of birds circling over its roosting site is a magnificent aerial display. Theoretical work suggests that these highly syn- chronized and coordinated movements arise from simple interac- tion rules, without the need for centralized organization (Vicsek et al. 1995; Couzin et al. 2002; Vicsek & Zafeiris 2012). None the less, we are only just beginning to understand how rules imple- mented in models relate to those applied by animals. Progress in digital image processing and high temporal resolution tracking has allowed the inference of interaction rules in bird and fish species (e.g. Ballerini et al. 2008; Lukeman et al. 2010; Herbert-Read et al. 2011; Katz et al. 2011). Furthermore, in line with researchers’ increasing interest in the role of interindividual differences in shaping interactions (Conradt et al. 2009; Nakayama et al. 2012a), it has been found that flocks of homing pigeons, Columba livia, are hierarchically organized, with individuals contributing with different weights to the movement decisions of the flock (Nagy et al. 2010). Such hierarchical networks consist of transitive leaderefollower relationships in which birds consistently copy the directional choices of individuals above them in the hierarchy, while being copied by those lower in rank. Little is known about what attributes of a flying pigeon can reliably predict leadership in flocks, although it has been suggested that leadership may be related to individual navigational efficiency (Nagy et al. 2010). Empirical studies have identified a variety of traits (e.g. age, experience, social rank and motivation; Reebs 2000; King et al. 2008; McComb et al. 2011; Nakayama et al. 2012b) that can modify an in- dividual’s propensity to initiate a movement or activity change. Along similar lines, a model by Conradt et al. (2009) suggests that group movements are directed by those specific individuals for whom reaching the goal is most crucial. Several empirical studies support the findings of these models. For example, fish that are deprived of food are more likely to take front positions in shoals than those that are satiated (Krause et al. 1992), and, and lactating female zebra, Equus burchellii, initiate movements more frequently than those without dependent foals (Fischhoff et al. 2007). Furthermore, consistent leadership in group movements might be supported by the enhanced knowledge of certain individuals. In several species, including golden shiners, Notemigonus crysoleucas, bottlenose * Correspondence and present address: A. Flack, Max Planck Institute for Orni- thology, Am Obstberg 1, 78315 Radolfzell, Germany. E-mail address: afl[email protected](A. Flack). 1 These authors contributed equally. Contents lists available at ScienceDirect Animal Behaviour journal homepage: www.elsevier.com/locate/anbehav 0003-3472/$38.00 Ó 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anbehav.2013.07.005 Animal Behaviour 86 (2013) 723e732
Transcript
lable at ScienceDirect
Animal Behaviour 86 (2013) 723e732
Contents lists avai
Animal Behaviour
journal homepage wwwelsevier comlocateanbehav
Robustness of flight leadership relations in pigeons
Andrea Flack a1 Zsuzsa Aacutekos b1 Maacuteteacute Nagy abc Tamaacutes Vicsek bc Dora Biro a
aDepartment of Zoology University of Oxford Oxford UKbDepartment of Biological Physics Eoumltvoumls University Budapest Hungaryc Statistical and Biological Physics Research Group of the Hungarian Academy of Sciences Budapest Hungary
a r t i c l e i n f o
Article historyReceived 8 February 2013Initial acceptance 13 March 2013Final acceptance 19 June 2013Available online 24 August 2013MS number 13-00098R
Correspondence and present address A Flack Mthology Am Obstberg 1 78315 Radolfzell Germany
E-mail address aflackornmpgde (A Flack)1 These authors contributed equally
0003-3472$3800 2013 The Association for the Stuhttpdxdoiorg101016janbehav201307005
Collective animal movements produce spectacular natural phenomena that arise from simple local in-teractions among group members Flocks of homing pigeons Columba livia provide a useful model forthe study of collective motion and decision making During homing flights flock members are forced toresolve potentially divergent navigational preferences in order to stay together and benefit from flying ina group Recent work has demonstrated that some individuals consistently contribute more to themovement decisions of the flock than others do thereby generating stable hierarchical leaderefollowernetworks Yet what attributes of a flying pigeon reliably predict leadership remains an open questionWe examined the flexibility of an individualrsquos hierarchical leadership rank (ie its ordinal position whenflock members are ranked according to the average time differences with which they lead or followothers) as a function of changes in its navigational knowledge We manipulated already establishedhierarchical networks in three different flocks by providing certain individuals with additional homingexperience We found that such training did not consistenly lead to an increase in birdsrsquo leadership ranksand that in general the nature of leaderefollower interactions between trained and untrained birdsremained unaffected Thus leadership hierarchies in pigeon flocks appear resistant to changes in thenavigational knowledge of a subset of their members at least when these changes are relatively smallWe discuss the implications of our results in light of the potential benefits of structural stability indecision-making networks 2013 The Association for the Study of Animal Behaviour Published by Elsevier Ltd All rights reserved
A flock of birds circling over its roosting site is a magnificentaerial display Theoretical work suggests that these highly syn-chronized and coordinated movements arise from simple interac-tion rules without the need for centralized organization (Vicseket al 1995 Couzin et al 2002 Vicsek amp Zafeiris 2012) None theless we are only just beginning to understand how rules imple-mented in models relate to those applied by animals Progress indigital image processing and high temporal resolution tracking hasallowed the inference of interaction rules in bird and fish species(eg Ballerini et al 2008 Lukeman et al 2010 Herbert-Read et al2011 Katz et al 2011) Furthermore in line with researchersrsquoincreasing interest in the role of interindividual differences inshaping interactions (Conradt et al 2009 Nakayama et al 2012a) ithas been found that flocks of homing pigeons Columba livia arehierarchically organized with individuals contributing withdifferent weights to the movement decisions of the flock (Nagy
ax Planck Institute for Orni-
dy of Animal Behaviour Published
et al 2010) Such hierarchical networks consist of transitiveleaderefollower relationships in which birds consistently copy thedirectional choices of individuals above them in the hierarchywhile being copied by those lower in rank Little is known aboutwhat attributes of a flying pigeon can reliably predict leadership inflocks although it has been suggested that leadership may berelated to individual navigational efficiency (Nagy et al 2010)
Empirical studies have identified a variety of traits (eg ageexperience social rank andmotivation Reebs 2000 King et al 2008McComb et al 2011 Nakayama et al 2012b) that can modify an in-dividualrsquospropensity to initiate amovementoractivitychangeAlongsimilar lines a model by Conradt et al (2009) suggests that groupmovements are directed by those specific individuals for whomreaching the goal is most crucial Several empirical studies supportthe findings of these models For example fish that are deprived offood are more likely to take front positions in shoals than those thatare satiated (Krause et al 1992) and and lactating female zebraEquus burchellii initiate movements more frequently than thosewithout dependent foals (Fischhoff et al 2007) Furthermoreconsistent leadership in group movements might be supported bythe enhanced knowledge of certain individuals In several speciesincluding golden shiners Notemigonus crysoleucas bottlenose
by Elsevier Ltd All rights reserved
A Flack et al Animal Behaviour 86 (2013) 723e732724
dolphins Tursiops sp and meerkats Suricata suricatta it has beenshown that better informed individuals can change the action ofgroupmates using their greater knowledge about their environment(Reebs 2000 Lusseau amp Conradt 2009 Bousquet amp Manser 2011)With respect to the context of collective motion recent work hasdemonstrated that navigationally less experienced birds are likely tofollow more experienced conspecifics (Flack et al 2012) More spe-cifically the larger the difference in homing experience between twopartners the higher the likelihood that the more experienced birdwill emerge as the leader Additionally in highly experienced birdsthe accuracy with which individuals recapitulate previously estab-lished idiosyncratic routes when flying solo has been suggested topredict relative influence when flying in pairs (Freeman et al 2011)suggesting that some aspect of navigational certainty (or perhapsinflexibility) may promote leadership These findings raise newquestionsabouthowvariations innavigational knowledgepossessedby individual members influence group dynamics in pigeon flocks Ifa birdrsquos position in the hierarchy correlates positively with its ownnavigational experience we should be able to manipulate thenetwork by providing selected individuals with the opportunity toacquire additional spatial knowledge In this study we evaluatedwhether it is indeed possible to alter individualsrsquo ranks attainedduring flock homing flights by providing them with additionalhoming experience before retesting themwith their groupmates
METHODS
Subjects and Experimental Procedure
We used 30 adult homing pigeons bred at the Oxford UniversityFieldStationatWythamOxfordUK (51460583400N1190024000W)They were kept in a social group of ca 120 pigeons inside two loftsBirds normally had free access to the outside except on the dayswhen the experiments were conducted Food (a commerciallyavailablemultigrainmixture)watermineralsandgritwereprovidedad libitum throughout the study All experimental birds were be-tween 4 and 8 years old and had homing experience but had nevervisited the release site used in the current study They carried mini-ature GPS logging devices (see below) attached to their back by asmall Velcro strip glued to clipped feathers All releases were per-formed fromRadford (distance and direction to home 157 km151respectively) The experiment had three phases First we trainedthreeflocks of 10 birds (designatedgroupsA B andC) by releasing all10 birds of a flock simultaneously at the release site (Phase I grouptraining) Each flock performed eight group training flights with amaximumof two releases perdayWe then calculated for each groupa leadership hierarchy among flock members using the methodsdescribed in Nagy et al (2010) In Phase II (solo training) we allowedthree randomly chosen individuals fromeachflock to gain additionalhoming experience by performing 10 individual flights from thesamesite (oneof theseninebirdswas lost during itseighth individualtrainingflight and therefore did not participate in the third phase forgroup C) Finally in Phase III (group tests) we released each originalflock six more times to evaluate any changes in the hierarchyrsquosstructure in particular whether the additional homing experienceresulted in any changes in the ranks attained by the three individualsthat had received additional solo training Phase I was completed in10 days Phase II in 6 days and Phase III in 3 days with releasesconducted on all consecutive days when weather conditions werefavourable (dry and with winds lt7 ms)
GPS Device and Data Handling
The GPS device was based on a commercially available product(Gmsu1LP from Global Top) weighed 13 g and was capable of
logging time-stamped longitude latitude and altitude data at10 Hz The geodetic coordinates provided by the GPS were con-verted into x y and z coordinates using the Flat Earth model Thesecoordinates were smoothed by a Gaussian filter (s frac14 02 s) and weused a cubic B-spline method to fit curves onto the points obtainedwith the 01 s sampling rate Only the x and y coordinates were usedfor analysis (average number of data points recorded per bird SDwas 176107 15423) In independent tests using the devices infixed relative positions to each other the deviation between realand measured distance was 000 034 m (mean SD) This de-gree of accuracy is sufficient for calculating directional correlationdelay functions that characterize relations among the birdsrsquomovements (see Fig A1 and the Appendix for further details)
Data Analysis
To evaluate the effect of training on homing performance wecalculated homing efficiency and homing time for each flight Ef-ficiency was measured by dividing the straight-line distance be-tween the release site and the loft by the actual distance travelledby the bird to reach home Homing timewas the length of time thatelapsed between release and the bird reaching a radius of 250 mfrom the loft These two measures are of course not independentof each other although the relationship between them can vary tosome extent as a function of the birdrsquos speed In addition to mea-sure the trained birdsrsquo change in homing performance we calcu-lated the difference in efficiency and homing time between theaverage of the first two and the average of the last two solo trainingflights in Phase II
To determine leaderefollower relations inside the flock wecalculated the directional correlation delay for each pair of birds iand j (is j) The directional correlation delay of a pair isCijethsTHORN frac14 h viethtTHORN$ vjethtthorn sTHORNit where viethtTHORN is the normalized velocityof bird i at time t and vjethtthorn sTHORN is the normalized velocity of bird j attime t thorn s Note that CijethsTHORN frac14 CjiethsTHORN We then determined themaximum value of the CijethsTHORN correlation function at sij CijethsijTHORN Weidentified the corresponding sij as the directional correlation delaytime sij values focus on the relationship between specific pairingsof individuals while ignoring hierarchy changes caused by otherflock members Note also that sij frac14 sji Negative sij values meanthat the flight directional changes of bird i fall behind that of bird jand can thus be interpreted as a case of j leading To compare re-lationships among flockmembers before and after the solo trainingwe focused on pairwise sij values averaged across pre- and post-training separately For every specific pair ij we averaged those sijvalues that exhibited a CijethsijTHORN larger than 095 Because the re-lationships between specific pairings are nonindependent datapoints we used the number of individuals as our sample size forcorrelations between pre- and post-training sij values Only edgeswith values higher than 002 were retained We chose this con-servative value as our threshold to reduce the amount of errone-ously introduced edges while ensuring that there is no loss ofinformation
For the calculation of the CijethsTHORN correlation function we includedonly those pairs of data points from birds i and j where the twobirds were a maximum of 100 m apart (ie dij lt 100 m) We chosethis threshold based on the distributions of interindividual dis-tances (see Fig A2) A birdrsquos closest neighbour was less than 10 maway in 71 of all recorded data points (see inset of Fig A2)However to be able to detect potential interactions between moredistant flockmembers we used a threshold of 100 m although onlya few data points fall into this bin category
By averaging the sij values of bird i and the rest of the flock weobtained a second measure denoted si Because of full transitivityof each hierarchy this measure allowed us to resolve fully the
A Flack et al Animal Behaviour 86 (2013) 723e732 725
hierarchical order among all group members (defined as hierar-chical rank) On two occasions the si value was 34 times higherthan the standard deviation of all values (see Fig A3) in these caseswe removed the two birds from these particular flock flights andreran the analyses without them (see Table A1 for the resultsincluding the outliers) We calculated for each bird the average ofthe si values for the flights before (Phase I eight flights sprei ) andafter (Phase III six flights sposti ) the individual training period sivalues have similar properties to linear ranks (positive and negativevalues correspond to leading and following behaviour respec-tively) We tested our data for normality using a KolmogoroveSmirnov test (P lt 005) We used Pearson correlations for sampleswith equal variances (F test for equal variance) and Spearmancorrelations for those with unequal variances
RESULTS
Following the group releases of Phase I we identified fullytransitive hierarchies in each of our three flocks (Fig 1 pretraining)Besides confirming the findings of Nagy et al (2010) this initialresult also provided the necessary premise for Phases II and III
First we evaluated the effect of the training (flock and soloflights) on homing performance by examining homing efficiencyand homing time over the course of Phases I II and III (Fig 2a b)Birds improved in both measures of homing performance duringthe flock releases of Phase I Furthermore during Phase II the solotrained birds increased their efficiency by an average SD of013 006 (difference between the average of the first two and theaverage of the last two solo training flights in Phase II Fig 2c) anddecreased their homing time by 3434 s 2090 s (Fig 2d) Boththese changes differed significantly from zero (one-sample t testsefficiency t7 frac14 577 P lt 0001 time t7 frac14 465 P frac14 0002)
We next used data from Phase III to measure the stability of thehierarchies by comparing the relative ranks of the untrained birdsbefore and after solo training (sposti versus sprei ) We found a positivecorrelation between sprei and sposti (Pearson correlation group ABCtogether r20 frac14 072 P lt 0001 Fig 3a group A r6 frac14 080P frac14 0030 group B r6 frac14 087 P frac14 0011 group C r6 frac14 069P frac14 0090) which indicates the persistence of a robust hierarchicalorder among untrained flock members However the ranks of thetrained birds exhibited variability we found no correlation be-tween sprei and sposti (Pearson correlation r7 frac14 e008 P frac14 0846Fig 3a) with some birds experiencing a rise and others a drop in siAlso the changes in the birdsrsquo relative ranks did not correlate withtheir changes in homing performance (Pearson correlation effi-ciency r7 frac14 0247 P frac14 0556 time r7 frac14 0072 P frac14 0866)
We further investigated the changes the hierarchies underwentusing pairwise directional correlation time ethsijTHORN We observed apositive correlation between pre- and post-training for the un-trained birds when pooling the data from the three flocks(Spearman correlation group ABC together r20 frac14 066 P frac14 0001Fig 3b) further confirming the stability of their relationships overtime and over repeated interactions However when examining thethree flocks separately we did not find a positive correlation in twocases which might be caused by the small sample size of each flock(Spearman correlation group A r6 frac14 067 P frac14 0098 Pearson cor-relation group B r6 frac14 092 P frac14 0004 group C r6 frac14 062P frac14 0138) Moreover pairwise siTjU values enabled us to comparethe changes in pairs consisting of a trained (iT) and an untrained (jU)individual The relationship between trained and untrained pigeonsalso remained stable as evidenced by the positive correlation be-tween their pre- and post-training siTjU (Spearman correlationr28 frac14 044 P frac14 0018 Fig 3c) Despite the extra experience gatheredby certain flockmembers their positions in the hierarchy relative tountrained birds showed on average no improvement the
difference in directional correlation delay times in trainedeun-trained pairs before and after the individual training was on aver-age SEM 000 001 s and did not differ significantly from zero(one-sample t test t55 frac14 0005 P frac14 0996) Thus although theoverall hierarchical rank of the trained individuals changed slightlythe direction of these changes was not consistent In addition thechanges were small enough that across the flock as a whole theposition of the untrained birds in relation to trained flock membersremained mostly unchanged The extra training had an evensmaller effect on the positions of the untrained birds relative toeach other (Fig 1 post-training) Separate examination of the threeflocks showed that in group A two of the trained birds improvedtheir relative ranks and one maintained its position (the averagechange in sij before and after training SEM ADsij frac14 006 002 s one-sample t test t20 frac14 334 P frac14 0003Fig 1a) In group B no clear change was found (BDsij frac14 002 001 s one-sample t test t20 frac14 177 P frac14 009Fig 1b) whereas in group C the trained birds decreased theirrelative ranks (C Dsij frac14 011 002 s one-sample t testt13 frac14 530 P lt 0001 Fig 1c) An additional statistical analysismaking use of the full data set rather than per bird averages asabove further confirmed the robustness of the measured hierar-chies (see Appendix)
DISCUSSION
Previous research has shown that group decision making inpigeon flocks is hierarchically organized with certain individualsconsistently contributing with relativelymoreweight tomovementdecisions than others (Nagy et al 2010) In this study we recon-firmed the existence of such hierarchical flight dynamics demon-strating distinct leadership hierarchies in three separate flocksduring repeated homing flights Moreover we showed that addi-tional solo training given to specific group members did not affectthe overall hierarchy of the flock although trained birds increasedtheir navigational efficiency during these solo flights (thus sug-gesting that they had gained additional navigational knowledge)this increase in efficiency was not accompanied reliably byimprovement in their hierarchical position Overall pairwiseleaderefollower relations between flockmembers remained stableand thus the hierarchies themselves remained robust We use theterm lsquorobustnessrsquo to mean that the interindividual relationshipsand hence the whole systems of hierarchical leadership networkswe observed were resistant to perturbations (introduced here inthe form of experimentally changing the knowledge of certain flockmembers) Our results imply that leadership ranks within flocks donot directly relate to individual navigational experience but thatsome other intrinsic property or a combination of several proper-ties defines the organization of the hierarchy
Two possible mechanisms might allow the establishment andmaintenance of robust flight hierarchies The first requires recog-nition of conspecificsrsquo morphological physiological or behaviouralfeatures that determine leadership ranks and may be com-plemented by individual recognition and memory of previous in-teractions Flock members may have fixed leaderefollowerrelationships that are based on dominance (King et al 2008) fa-miliarity (Flack et al 2013) or individual affiliations (Jacobs et al2011) and are consequently maintained across multiple flightsAlternatively hierarchies might derive from individuals reacting inconsistent ways to other group membersrsquo movements withoutnecessarily identifying them or their status Each individual mayrespond to flockmates in a way that is defined by its own specificfeatures such as experience or motivation This would allowleadership to emerge passively as a consequence of simple inter-action rules (Vicsek et al 1995 Couzin et al 2002) In other species
002
007008 008
009
011
011
014
003
003
003002
008
003
002
006
002
005
007
003
0007
005
012006
006
005
005
006
019
004
003
008
014
009
003
015
002
002
011
004
019
005
005010
010
003
004
002003
009
003
008
003
003
004
005
0
012
006
003009
003
008
006
019
006
013
011
006
009
0 00
006
012
006
020
004
011
007
022
006
014
007
005
007
013004
010
005003
005
005
005
010
012
005
004
008
007
002
(a)
(b)
(c)
005
018006
012
017
007
005
014003
009
003
018
3
0
003
005 006
019
004
011
019
066
006
012
005
026
015
006
2
024
004
006
004
014
0090
009
011
010
016
005
004
005007
004
004 005
005
002
013
002
003
003005
004
005
014
002
016
007
007
017
0
007
0
007
002
014
3
003 006
016
008
007
014
003
003
010
023
009
013
007
004
005
022
008
010
004
007
005
019
008
003
007 016
003
006
005
003
015
010
006
013 008
016
023
013
A01
A02
Pretraining Post-training
A01
A02
A03
A04
A05
A06
A07
A08 A09
A10
A03A04
A05
A06 A07
A08
A09
A10
B01
B01B02
B03
B04
B05
B06
B07
B08
B09
B10
B02
B03
B04
B05
B06
B07
B08
B09
C01C01
C02
C03
C04
C05
C06
C07
C08
C09
C02
C03C04
C05 C06C07
C08
C09
B10
A Flack et al Animal Behaviour 86 (2013) 723e732726
0
500
1000
1500
2000
2500
Hom
ing
tim
e (s
)
0
02
04
06
08
1
41 7
Release number
Effi
cien
cy
(a) (b)
ndash01
0
01
02
03
Trained birdsndash800
ndash600
ndash400
ndash200
0
Ch
ange
in
ho
min
g ti
me
(s)
(c) (d)
41 7
41
Pretrainingflock
flights
Single training flights
Post-training
flockflights
Ch
ange
in e
ffic
ien
cy
41 7
41 7
41
10
Pretrainingflock
flights
Single training flights
Post-training
flockflights
10
Figure 2 (a) Homing efficiency (mean SEM) and (b) homing time (mean SEM) as a function of release number Data from all groups were averaged according to releasenumber Grey circles indicate phases I (N frac14 30) and III (N frac14 29) orange circles show trained individuals in Phase II (N frac14 8) (c d) Changes in (c) homing efficiency and (d) homingtime during solo flights by trained individuals Black line corresponds to mean SEM
A Flack et al Animal Behaviour 86 (2013) 723e732 727
these responses have been described as varying in line with mul-tiple factors For example fish might emerge as leaders dependingon their level of satiation (Nakayama et al 2012b) or experiencewith a foraging task (Reebs 2000) We know that in pigeons indi-vidual morphological differences like body mass do not act tostructure networks (Nagy et al 2013) Yet on which set of indi-vidual traits flight hierarchies are based remains open
The fact that we found no consistent effect of the extra trainingon birdsrsquo leadership ranks is a somewhat surprising result givenprevious suggestions of the effect of navigational experience andskill on leadership (Nagy et al 2010 Freeman et al 2011) Onepossible explanation is that solo and group homing flights affectbirds differently meaning that flying in a flock might overshadowindividually gained navigational advantages To explore the effectof experience on leadership hierarchies further one would need totest whether giving certain flock members additional grouptraining flights would cause changes in an already establishedleadership hierarchy Also the trained birdsrsquo increase in experiencemight not have been large enough to induce changes in the orga-nization of the flock Prior to the solo training each subject hadalready performed eight flock homing flights and reached highasymptotic levels of homing efficiency (Meade et al 2005) Even
Figure 1 Pre- and post-training hierarchical networks of three flocks generated using sijborders The three-digit alphanumeric codes indicate in which group the subject was testedrelations pointing from the leader to the follower (only edges where sij 002 are shown) Eas thick blue lines those that undergo a change in direction between pre- and post-trainindotted green lines Numbers on edges correspond to sij (a) (b) and (c) Pretraining and pos
though solo training did improve birdsrsquo solo homing efficiencytheir advantage over the rest of the flock remained small or wasonly temporary This interpretation is in agreement with past re-sults showing that birds with more experience will more clearlyemerge as leaders when the difference in experience between themand their flight partners is large (Flack et al 2012) Future researchshould focus on the effect of experiencewhile birds are still far fromasymptotic levels of efficiency (eg with tests run after fewerhoming flights for the most inexperienced birds) Furthermore acontrol group in which every flock member receives extra solotraining flights in Phase II would be useful as a baseline measure ofhow flock homing efficiency changes in response to training givenequally to all group members
Flack et al (2012) tested mixed-experience pairs of pigeons andfound that navigational experience had an effect on leadershipwith birds that had performed more training flights more likely toemerge as leaders In the present study using groups of 10 birds nosuch effect was detected which may indicate that influencingflockmatesrsquomovements is easier in smaller groups Recent work byHerbert-Read et al (2013) showed that individual movementcharacteristics become increasingly homogenized in larger groupssupporting the idea that the potential for an individual to affect
values Rectangles correspond to individual birds trained birds are shown with black(A B or C) and its rank during the pretraining flights Edges indicate leaderefollower
dges that have the same directionality in pre- and post-training networks are indicatedg are shown as red lines those that appear in only one of the networks are shown ast-training hierarchies of groups A B and C respectively
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash03 0 03ndash03
0
03(a) (c)(b)
τi Pretraining (s) τiUjU Pretraining (s)
τ iTj U P
ost-
trai
nin
g (s
)
τ iU
j U P
ost-
trai
nin
g (s
)
τ i P
ost
-tra
inin
g (s
)
τiTjUPretraining (s)
Figure 3 Relationship between s before and after individual training flights (mean SEM) (a) sposti as a function of sprei for solo-trained (orange circles) and untrained individuals(light grey circles) (b c) Averaged sij after individual training as a function of averaged sij before individual training for (b) untrainedeuntrained pairings and (c) trainedeuntrainedpairings
A Flack et al Animal Behaviour 86 (2013) 723e732728
collective movements diminishes with increasing group sizeInvestigating the potential link between group size and group dy-namics both empirically and theoretically is a promising avenuefor future research
Although flock dynamics can be observed without hierarchicalorganization (Xu et al 2012) hierarchical structure might bebeneficial for establishing a lsquoflight routinersquo that demands lessattention from group members The fact that hierarchies seemresistant to small changes once they are established indicates thatrather than benefitting from particular features of the leader (suchas navigational experience) their advantage might lie in the sta-bility of the structure itself Robust social structures may enhanceinformation transfer among group members thereby increasingthe accuracy of group-level decisions (Lusseau amp Conradt 2009McComb et al 2011) Recent theoretical work has found that un-derlying social structures can improve the navigational accuracy oflarge leaderless groups (Bode et al 2012) Furthermore it is sug-gested that hierarchical group dynamics could be based purely onsocial preferences (Bode et al 2011) This is in agreement with whathas been described for various species of group-living primatesKing amp Sueur (2011) suggested that leaderefollower dynamics areembedded in interindividual relationships which may result inmore efficient decision making and coordination among groupmembers Social relationships can be found between relativesfamiliar conspecifics or individuals of similar attributes such as sizepersonality or sex Hence the stability in our hierarchical networksmay arise from preferential attachments that may have developedduring early training and that may not be susceptible to changes inindividualsrsquo navigational experience
Acknowledgments
AF was supported by Microsoft Research Cambridge MN wassupported by a Royal Society Newton International Fellowship andby Somerville College Oxford DB was supported by a Royal So-ciety University Research Fellowship This work was partly sup-ported by the EU ERC COLLMOT project (grant no 227878) Wethank Benjamin Pettit for technical assistance with the GPS testsand statistical advice We are also grateful to Andrew King andthree anonymous referees for helpful comments on themanuscript
References
Baayen R H 2008 Analyzing Linguistic Data A Practical Introduction to StatisticsUsing R Cambridge Cambridge University Press
Baayen R H 2009 languageR data sets and functions with lsquoAnalyzing LinguisticData A practical introduction to statisticsrsquo R package version 0955 cranr-projectorgwebpackageslanguageRlanguageRpdf
Ballerini M Cabibbo N Candelier R Cavagna A Cisbani E Giardina ILecomte V Orlandi A Parisi G Procaccini A et al 2008 Interaction rulinganimal collective behavior depends on topological rather than metric distanceevidence from a field study Proceedings of the National Academy of SciencesUSA 105 1232e1237
Bates D amp Maechler M 2009 Package lsquolme4rsquo(Version 0999375-32) linear mixed-effects models using S4 classes cran r-project orgwebpackageslme4lme4pdf
Bode N W F Wood A J amp Franks D W 2011 The impact of social networks onanimal collective motion Animal Behaviour 82 29e38
Bode N W F Wood J A amp Franks D W 2012 Social networks improve lead-erless group navigation by facilitating long-distance communication CurrentZoology 58 329e341
Bousquet C A H amp Manser M B 2011 Resolution of experimentallyinduced symmetrical conflicts of interest in meerkats Animal Behaviour81 1101e1107
Conradt L Krause J Couzin I D amp Roper T J 2009 lsquoLeading according to needrsquoin self-organizing groups The American Naturalist 173 304e312
Couzin IDKrause J JamesRRuxtonGDampFranksNR2002Collectivememoryand spatial sorting in animal groups Journal of Theoretical Biology 218 1e11
Fischhoff I R Sundaresan S R Cordingley J Larkin H M Sellier M-J ampRubenstein D I 2007 Social relationships and reproductive state influenceleadership roles in movements of plains zebra Equus burchellii Animal Behav-iour 73 825e831
Flack A Pettit B Freeman R Guilford T amp Biro D 2012 What are leadersmade of The role of individual experience in determining leaderefollowerrelations in homing pigeons Animal Behaviour 83 703e709
Flack A Freeman R Guilford T amp Biro D 2013 Pairs of pigeons act asbehavioural units during route learning and co-navigational leadership con-flicts The Journal of Experimental Biology 216 1434e1438
Freeman R Mann R Guilford T amp Biro D 2011 Group decisions and individualdifferences route fidelity predicts flight leadership in homing pigeons(Columba livia) Biology Letters 7 63e66
Herbert-Read J E Perna A Mann R P Schaerf T M Sumpter D J T ampWard A J W 2011 Inferring the rules of interaction of shoaling fish Pro-ceedings of the National Academy of Sciences USA 108 18726e18731
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause J ampWard A J W 2013 The role of individuality in collective group movementProceedings of the Royal Society B 280 1752
Jacobs A Sueur C Deneubourg J L amp Petit O 2011 Social network influencesdecision making during collective movements in brown lemurs (Eulemur fulvusfulvus) International Journal of Primatology 32 721e736
Katz Y Tunstroslashm K Ioannou C C Huepe C amp Couzin I D 2011 Inferring thestructure and dynamics of interactions in schooling fish Proceedings of theNational Academy of Sciences USA 108 18720e18725
King A amp Sueur C 2011 Where next Group coordination and collective decisionmaking by primates International Journal of Primatology 32 1245e1267
King A J Douglas C M S Huchard E Isaac N J B amp Cowlishaw G 2008Dominance and affiliation mediate despotism in a social primate CurrentBiology 18 1833e1838
Krause J Bumann D amp Todt D 1992 Relationship between the position pref-erence and nutritional state of individuals in schools of juvenile roach Rutilusrutilus Behavioral Ecology and Sociobiology 30 177e180
Lukeman R Li Y-X amp Edelstein-Keshet L 2010 Inferring individual rules fromcollective behavior Proceedings of the National Academy of Sciences USA 10712576e12580
Lusseau D amp Conradt L 2009 The emergence of unshared consensus decisions inbottlenose dolphins Behavioral Ecology and Sociobiology 63 1067e1077
McComb K Shannon G Durant S M Sayialel K Slotow R Poole J ampMoss C 2011 Leadership in elephants the adaptive value of age Proceedings ofthe Royal Society B 278 3270e3276
Meade J Biro D amp Guilford T 2005 Homing pigeons develop local route ste-reotypy Proceedings of the Royal Society B 272 17e23
A Flack et al Animal Behaviour 86 (2013) 723e732 729
Nagy M Aacutekos Z Biro D amp Vicsek T 2010 Hierarchical group dynamics in pi-geon flocks Nature 464 890e893
Nagy M Vaacutesaacuterhelyi G Pettit B Roberts-Mariani I Vicsek T amp Biro D 2013Context-dependent hierarchies in pigeons Proceedings of the National Acad-emy of Sciences USA 110 13049e13054
Nakayama S Harcourt J L Johnstone R A amp Manica A 2012a Initiativepersonality and leadership in pairs of foraging fish PLoS ONE 7 e36606
Nakayama S Johnstone R A amp Manica A 2012b Temperament and hungerinteract to determine the emergence of leaders in pairs of foraging fish PLoSONE 7 e43747
R Development Core Team 2009 R A Language and Environment for StatisticalComputing Vienna R Foundation for Statistical Computing
Reebs S G 2000 Can a minority of informed leaders determine the foragingmovements of a fish shoal Animal Behaviour 59 403e409
Vicsek T amp Zafeiris A 2012 Collective motion Physics Reports 517 71e140Vicsek T Cziroacutek A Ben-Jacob E Cohen I amp Shochet O 1995 Novel type of
phase transition in a system of self-driven particles Physical Review Letters 751226e1229
Xu X-K Kattas G D amp Small M 2012 Reciprocal relationships in collectiveflights of homing pigeons Physical Review E 85 026120
APPENDIX
GPS Error and its Effect on the Analysis
To test the spatial and temporal error originating from the GPSdevices we performed a variety of tests Ten GPS devices (labelled0e9) were attached to a rigid 3 m long pole with an interdevicedistance of 33 cm We moved the pole along a free path in an openfield using three different orientations (1) with the polersquos orien-tation parallel to the direction of motion (GPS 0 at the front and 9 atthe back Fig A1a) (2) with the pole in a fixed orientation relativeto the field (Fig A1b) and (3) with the polersquos orientation perpen-dicular to the direction of motion (Fig A1c) Each test lasted 10 minand the pole moved between 1 and 3 ms (typical flight speed of apigeon is 18e22 ms)
An important aspect of analysing flock flights is the relativeposition of each device within a pair in relation to the movementdirection of the whole flock This is why we measured the averageforward position of each device (Fig A1def) In both the perpen-dicular and the globally fixed orientation cases we expected anaverage forward position of zero In the parallel case we wouldexpect a forward ratio of 1 for (i lt j) Any deviation from such a
Table A1Results of the sprei vs sposti correlation analysis with and without two outliers
Correlation betweensprei and sposti
Without ou
Untrained ABC r20[072 PUntrained group A r6[080 P[Untrained group B r6[087 P[Untrained group C r6frac14069 Pfrac14Trained ABC r7frac14008 P
Values in bold indicate significant correlations
value is due to noise which is lower at small interdevice distancesWe show the probability density function of this measure inFig A1gei We also measured the time a device was detected to bein front relative to the direction of motion and calculated the timeratio for the 10 min test (Fig A1jel) We also performed directionalcorrelation delay analyses for all devices (Fig A1meo) The absoluteerror of the GPS device arises from the relative error of the velocitywhich decreases as speed increases Hence our tests give an upperapproximation of the noise as each test lasted only 10 min and thepole was moved at low speeds
Additional Test of Hierarchy Robustness
We used a linear mixed-effects model to test the robustness ofthe hierarchies using as our data set the s values calculated for eachindividual in every flight of phases I and III All data were analysedusing R (R Development Core Team 2009) and the R packages lme4(Bates amp Maechler 2009) and languageR (Baayen 2008 2009) Weincluded Subject as a random effect As fixed effects we addedTraining Phase (Phase I pretraining or Phase III post-training) andTreatment Group (trained or untrained individuals) to themodel aswell as the interaction term between them
We verified that the normality of error and homogeneity ofvariance assumptions of parametric analysis were satisfied by vi-sual inspection of plots of residuals against fitted values To assessthe validity of the mixed-effects analysis we performed likelihoodratio tests comparing the model with fixed effects to the null modelwith only the random effect The model that included fixed effectsdid not differ significantly from the null model (P frac14 0222) andhence fulfilled the validation test The following P values werebased on Markov chain Monte Carlo sampling We found no sig-nificant differences between pre- and post-training s values(PMCMC frac14 0656) or trained and untrained individuals(PMCMC frac14 0203) The interaction between Training Phase andTreatment Group was not significant (PMCMC frac14 0321) Togetherthese results further confirm that the solo training had no effect onthe groupsrsquo hierarchies
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Methods
Subjects and Experimental Procedure
GPS Device and Data Handling
Data Analysis
Results
Discussion
Acknowledgments
References
Appendix
GPS Error and its Effect on the Analysis
Additional Test of Hierarchy Robustness
A Flack et al Animal Behaviour 86 (2013) 723e732724
dolphins Tursiops sp and meerkats Suricata suricatta it has beenshown that better informed individuals can change the action ofgroupmates using their greater knowledge about their environment(Reebs 2000 Lusseau amp Conradt 2009 Bousquet amp Manser 2011)With respect to the context of collective motion recent work hasdemonstrated that navigationally less experienced birds are likely tofollow more experienced conspecifics (Flack et al 2012) More spe-cifically the larger the difference in homing experience between twopartners the higher the likelihood that the more experienced birdwill emerge as the leader Additionally in highly experienced birdsthe accuracy with which individuals recapitulate previously estab-lished idiosyncratic routes when flying solo has been suggested topredict relative influence when flying in pairs (Freeman et al 2011)suggesting that some aspect of navigational certainty (or perhapsinflexibility) may promote leadership These findings raise newquestionsabouthowvariations innavigational knowledgepossessedby individual members influence group dynamics in pigeon flocks Ifa birdrsquos position in the hierarchy correlates positively with its ownnavigational experience we should be able to manipulate thenetwork by providing selected individuals with the opportunity toacquire additional spatial knowledge In this study we evaluatedwhether it is indeed possible to alter individualsrsquo ranks attainedduring flock homing flights by providing them with additionalhoming experience before retesting themwith their groupmates
METHODS
Subjects and Experimental Procedure
We used 30 adult homing pigeons bred at the Oxford UniversityFieldStationatWythamOxfordUK (51460583400N1190024000W)They were kept in a social group of ca 120 pigeons inside two loftsBirds normally had free access to the outside except on the dayswhen the experiments were conducted Food (a commerciallyavailablemultigrainmixture)watermineralsandgritwereprovidedad libitum throughout the study All experimental birds were be-tween 4 and 8 years old and had homing experience but had nevervisited the release site used in the current study They carried mini-ature GPS logging devices (see below) attached to their back by asmall Velcro strip glued to clipped feathers All releases were per-formed fromRadford (distance and direction to home 157 km151respectively) The experiment had three phases First we trainedthreeflocks of 10 birds (designatedgroupsA B andC) by releasing all10 birds of a flock simultaneously at the release site (Phase I grouptraining) Each flock performed eight group training flights with amaximumof two releases perdayWe then calculated for each groupa leadership hierarchy among flock members using the methodsdescribed in Nagy et al (2010) In Phase II (solo training) we allowedthree randomly chosen individuals fromeachflock to gain additionalhoming experience by performing 10 individual flights from thesamesite (oneof theseninebirdswas lost during itseighth individualtrainingflight and therefore did not participate in the third phase forgroup C) Finally in Phase III (group tests) we released each originalflock six more times to evaluate any changes in the hierarchyrsquosstructure in particular whether the additional homing experienceresulted in any changes in the ranks attained by the three individualsthat had received additional solo training Phase I was completed in10 days Phase II in 6 days and Phase III in 3 days with releasesconducted on all consecutive days when weather conditions werefavourable (dry and with winds lt7 ms)
GPS Device and Data Handling
The GPS device was based on a commercially available product(Gmsu1LP from Global Top) weighed 13 g and was capable of
logging time-stamped longitude latitude and altitude data at10 Hz The geodetic coordinates provided by the GPS were con-verted into x y and z coordinates using the Flat Earth model Thesecoordinates were smoothed by a Gaussian filter (s frac14 02 s) and weused a cubic B-spline method to fit curves onto the points obtainedwith the 01 s sampling rate Only the x and y coordinates were usedfor analysis (average number of data points recorded per bird SDwas 176107 15423) In independent tests using the devices infixed relative positions to each other the deviation between realand measured distance was 000 034 m (mean SD) This de-gree of accuracy is sufficient for calculating directional correlationdelay functions that characterize relations among the birdsrsquomovements (see Fig A1 and the Appendix for further details)
Data Analysis
To evaluate the effect of training on homing performance wecalculated homing efficiency and homing time for each flight Ef-ficiency was measured by dividing the straight-line distance be-tween the release site and the loft by the actual distance travelledby the bird to reach home Homing timewas the length of time thatelapsed between release and the bird reaching a radius of 250 mfrom the loft These two measures are of course not independentof each other although the relationship between them can vary tosome extent as a function of the birdrsquos speed In addition to mea-sure the trained birdsrsquo change in homing performance we calcu-lated the difference in efficiency and homing time between theaverage of the first two and the average of the last two solo trainingflights in Phase II
To determine leaderefollower relations inside the flock wecalculated the directional correlation delay for each pair of birds iand j (is j) The directional correlation delay of a pair isCijethsTHORN frac14 h viethtTHORN$ vjethtthorn sTHORNit where viethtTHORN is the normalized velocityof bird i at time t and vjethtthorn sTHORN is the normalized velocity of bird j attime t thorn s Note that CijethsTHORN frac14 CjiethsTHORN We then determined themaximum value of the CijethsTHORN correlation function at sij CijethsijTHORN Weidentified the corresponding sij as the directional correlation delaytime sij values focus on the relationship between specific pairingsof individuals while ignoring hierarchy changes caused by otherflock members Note also that sij frac14 sji Negative sij values meanthat the flight directional changes of bird i fall behind that of bird jand can thus be interpreted as a case of j leading To compare re-lationships among flockmembers before and after the solo trainingwe focused on pairwise sij values averaged across pre- and post-training separately For every specific pair ij we averaged those sijvalues that exhibited a CijethsijTHORN larger than 095 Because the re-lationships between specific pairings are nonindependent datapoints we used the number of individuals as our sample size forcorrelations between pre- and post-training sij values Only edgeswith values higher than 002 were retained We chose this con-servative value as our threshold to reduce the amount of errone-ously introduced edges while ensuring that there is no loss ofinformation
For the calculation of the CijethsTHORN correlation function we includedonly those pairs of data points from birds i and j where the twobirds were a maximum of 100 m apart (ie dij lt 100 m) We chosethis threshold based on the distributions of interindividual dis-tances (see Fig A2) A birdrsquos closest neighbour was less than 10 maway in 71 of all recorded data points (see inset of Fig A2)However to be able to detect potential interactions between moredistant flockmembers we used a threshold of 100 m although onlya few data points fall into this bin category
By averaging the sij values of bird i and the rest of the flock weobtained a second measure denoted si Because of full transitivityof each hierarchy this measure allowed us to resolve fully the
A Flack et al Animal Behaviour 86 (2013) 723e732 725
hierarchical order among all group members (defined as hierar-chical rank) On two occasions the si value was 34 times higherthan the standard deviation of all values (see Fig A3) in these caseswe removed the two birds from these particular flock flights andreran the analyses without them (see Table A1 for the resultsincluding the outliers) We calculated for each bird the average ofthe si values for the flights before (Phase I eight flights sprei ) andafter (Phase III six flights sposti ) the individual training period sivalues have similar properties to linear ranks (positive and negativevalues correspond to leading and following behaviour respec-tively) We tested our data for normality using a KolmogoroveSmirnov test (P lt 005) We used Pearson correlations for sampleswith equal variances (F test for equal variance) and Spearmancorrelations for those with unequal variances
RESULTS
Following the group releases of Phase I we identified fullytransitive hierarchies in each of our three flocks (Fig 1 pretraining)Besides confirming the findings of Nagy et al (2010) this initialresult also provided the necessary premise for Phases II and III
First we evaluated the effect of the training (flock and soloflights) on homing performance by examining homing efficiencyand homing time over the course of Phases I II and III (Fig 2a b)Birds improved in both measures of homing performance duringthe flock releases of Phase I Furthermore during Phase II the solotrained birds increased their efficiency by an average SD of013 006 (difference between the average of the first two and theaverage of the last two solo training flights in Phase II Fig 2c) anddecreased their homing time by 3434 s 2090 s (Fig 2d) Boththese changes differed significantly from zero (one-sample t testsefficiency t7 frac14 577 P lt 0001 time t7 frac14 465 P frac14 0002)
We next used data from Phase III to measure the stability of thehierarchies by comparing the relative ranks of the untrained birdsbefore and after solo training (sposti versus sprei ) We found a positivecorrelation between sprei and sposti (Pearson correlation group ABCtogether r20 frac14 072 P lt 0001 Fig 3a group A r6 frac14 080P frac14 0030 group B r6 frac14 087 P frac14 0011 group C r6 frac14 069P frac14 0090) which indicates the persistence of a robust hierarchicalorder among untrained flock members However the ranks of thetrained birds exhibited variability we found no correlation be-tween sprei and sposti (Pearson correlation r7 frac14 e008 P frac14 0846Fig 3a) with some birds experiencing a rise and others a drop in siAlso the changes in the birdsrsquo relative ranks did not correlate withtheir changes in homing performance (Pearson correlation effi-ciency r7 frac14 0247 P frac14 0556 time r7 frac14 0072 P frac14 0866)
We further investigated the changes the hierarchies underwentusing pairwise directional correlation time ethsijTHORN We observed apositive correlation between pre- and post-training for the un-trained birds when pooling the data from the three flocks(Spearman correlation group ABC together r20 frac14 066 P frac14 0001Fig 3b) further confirming the stability of their relationships overtime and over repeated interactions However when examining thethree flocks separately we did not find a positive correlation in twocases which might be caused by the small sample size of each flock(Spearman correlation group A r6 frac14 067 P frac14 0098 Pearson cor-relation group B r6 frac14 092 P frac14 0004 group C r6 frac14 062P frac14 0138) Moreover pairwise siTjU values enabled us to comparethe changes in pairs consisting of a trained (iT) and an untrained (jU)individual The relationship between trained and untrained pigeonsalso remained stable as evidenced by the positive correlation be-tween their pre- and post-training siTjU (Spearman correlationr28 frac14 044 P frac14 0018 Fig 3c) Despite the extra experience gatheredby certain flockmembers their positions in the hierarchy relative tountrained birds showed on average no improvement the
difference in directional correlation delay times in trainedeun-trained pairs before and after the individual training was on aver-age SEM 000 001 s and did not differ significantly from zero(one-sample t test t55 frac14 0005 P frac14 0996) Thus although theoverall hierarchical rank of the trained individuals changed slightlythe direction of these changes was not consistent In addition thechanges were small enough that across the flock as a whole theposition of the untrained birds in relation to trained flock membersremained mostly unchanged The extra training had an evensmaller effect on the positions of the untrained birds relative toeach other (Fig 1 post-training) Separate examination of the threeflocks showed that in group A two of the trained birds improvedtheir relative ranks and one maintained its position (the averagechange in sij before and after training SEM ADsij frac14 006 002 s one-sample t test t20 frac14 334 P frac14 0003Fig 1a) In group B no clear change was found (BDsij frac14 002 001 s one-sample t test t20 frac14 177 P frac14 009Fig 1b) whereas in group C the trained birds decreased theirrelative ranks (C Dsij frac14 011 002 s one-sample t testt13 frac14 530 P lt 0001 Fig 1c) An additional statistical analysismaking use of the full data set rather than per bird averages asabove further confirmed the robustness of the measured hierar-chies (see Appendix)
DISCUSSION
Previous research has shown that group decision making inpigeon flocks is hierarchically organized with certain individualsconsistently contributing with relativelymoreweight tomovementdecisions than others (Nagy et al 2010) In this study we recon-firmed the existence of such hierarchical flight dynamics demon-strating distinct leadership hierarchies in three separate flocksduring repeated homing flights Moreover we showed that addi-tional solo training given to specific group members did not affectthe overall hierarchy of the flock although trained birds increasedtheir navigational efficiency during these solo flights (thus sug-gesting that they had gained additional navigational knowledge)this increase in efficiency was not accompanied reliably byimprovement in their hierarchical position Overall pairwiseleaderefollower relations between flockmembers remained stableand thus the hierarchies themselves remained robust We use theterm lsquorobustnessrsquo to mean that the interindividual relationshipsand hence the whole systems of hierarchical leadership networkswe observed were resistant to perturbations (introduced here inthe form of experimentally changing the knowledge of certain flockmembers) Our results imply that leadership ranks within flocks donot directly relate to individual navigational experience but thatsome other intrinsic property or a combination of several proper-ties defines the organization of the hierarchy
Two possible mechanisms might allow the establishment andmaintenance of robust flight hierarchies The first requires recog-nition of conspecificsrsquo morphological physiological or behaviouralfeatures that determine leadership ranks and may be com-plemented by individual recognition and memory of previous in-teractions Flock members may have fixed leaderefollowerrelationships that are based on dominance (King et al 2008) fa-miliarity (Flack et al 2013) or individual affiliations (Jacobs et al2011) and are consequently maintained across multiple flightsAlternatively hierarchies might derive from individuals reacting inconsistent ways to other group membersrsquo movements withoutnecessarily identifying them or their status Each individual mayrespond to flockmates in a way that is defined by its own specificfeatures such as experience or motivation This would allowleadership to emerge passively as a consequence of simple inter-action rules (Vicsek et al 1995 Couzin et al 2002) In other species
002
007008 008
009
011
011
014
003
003
003002
008
003
002
006
002
005
007
003
0007
005
012006
006
005
005
006
019
004
003
008
014
009
003
015
002
002
011
004
019
005
005010
010
003
004
002003
009
003
008
003
003
004
005
0
012
006
003009
003
008
006
019
006
013
011
006
009
0 00
006
012
006
020
004
011
007
022
006
014
007
005
007
013004
010
005003
005
005
005
010
012
005
004
008
007
002
(a)
(b)
(c)
005
018006
012
017
007
005
014003
009
003
018
3
0
003
005 006
019
004
011
019
066
006
012
005
026
015
006
2
024
004
006
004
014
0090
009
011
010
016
005
004
005007
004
004 005
005
002
013
002
003
003005
004
005
014
002
016
007
007
017
0
007
0
007
002
014
3
003 006
016
008
007
014
003
003
010
023
009
013
007
004
005
022
008
010
004
007
005
019
008
003
007 016
003
006
005
003
015
010
006
013 008
016
023
013
A01
A02
Pretraining Post-training
A01
A02
A03
A04
A05
A06
A07
A08 A09
A10
A03A04
A05
A06 A07
A08
A09
A10
B01
B01B02
B03
B04
B05
B06
B07
B08
B09
B10
B02
B03
B04
B05
B06
B07
B08
B09
C01C01
C02
C03
C04
C05
C06
C07
C08
C09
C02
C03C04
C05 C06C07
C08
C09
B10
A Flack et al Animal Behaviour 86 (2013) 723e732726
0
500
1000
1500
2000
2500
Hom
ing
tim
e (s
)
0
02
04
06
08
1
41 7
Release number
Effi
cien
cy
(a) (b)
ndash01
0
01
02
03
Trained birdsndash800
ndash600
ndash400
ndash200
0
Ch
ange
in
ho
min
g ti
me
(s)
(c) (d)
41 7
41
Pretrainingflock
flights
Single training flights
Post-training
flockflights
Ch
ange
in e
ffic
ien
cy
41 7
41 7
41
10
Pretrainingflock
flights
Single training flights
Post-training
flockflights
10
Figure 2 (a) Homing efficiency (mean SEM) and (b) homing time (mean SEM) as a function of release number Data from all groups were averaged according to releasenumber Grey circles indicate phases I (N frac14 30) and III (N frac14 29) orange circles show trained individuals in Phase II (N frac14 8) (c d) Changes in (c) homing efficiency and (d) homingtime during solo flights by trained individuals Black line corresponds to mean SEM
A Flack et al Animal Behaviour 86 (2013) 723e732 727
these responses have been described as varying in line with mul-tiple factors For example fish might emerge as leaders dependingon their level of satiation (Nakayama et al 2012b) or experiencewith a foraging task (Reebs 2000) We know that in pigeons indi-vidual morphological differences like body mass do not act tostructure networks (Nagy et al 2013) Yet on which set of indi-vidual traits flight hierarchies are based remains open
The fact that we found no consistent effect of the extra trainingon birdsrsquo leadership ranks is a somewhat surprising result givenprevious suggestions of the effect of navigational experience andskill on leadership (Nagy et al 2010 Freeman et al 2011) Onepossible explanation is that solo and group homing flights affectbirds differently meaning that flying in a flock might overshadowindividually gained navigational advantages To explore the effectof experience on leadership hierarchies further one would need totest whether giving certain flock members additional grouptraining flights would cause changes in an already establishedleadership hierarchy Also the trained birdsrsquo increase in experiencemight not have been large enough to induce changes in the orga-nization of the flock Prior to the solo training each subject hadalready performed eight flock homing flights and reached highasymptotic levels of homing efficiency (Meade et al 2005) Even
Figure 1 Pre- and post-training hierarchical networks of three flocks generated using sijborders The three-digit alphanumeric codes indicate in which group the subject was testedrelations pointing from the leader to the follower (only edges where sij 002 are shown) Eas thick blue lines those that undergo a change in direction between pre- and post-trainindotted green lines Numbers on edges correspond to sij (a) (b) and (c) Pretraining and pos
though solo training did improve birdsrsquo solo homing efficiencytheir advantage over the rest of the flock remained small or wasonly temporary This interpretation is in agreement with past re-sults showing that birds with more experience will more clearlyemerge as leaders when the difference in experience between themand their flight partners is large (Flack et al 2012) Future researchshould focus on the effect of experiencewhile birds are still far fromasymptotic levels of efficiency (eg with tests run after fewerhoming flights for the most inexperienced birds) Furthermore acontrol group in which every flock member receives extra solotraining flights in Phase II would be useful as a baseline measure ofhow flock homing efficiency changes in response to training givenequally to all group members
Flack et al (2012) tested mixed-experience pairs of pigeons andfound that navigational experience had an effect on leadershipwith birds that had performed more training flights more likely toemerge as leaders In the present study using groups of 10 birds nosuch effect was detected which may indicate that influencingflockmatesrsquomovements is easier in smaller groups Recent work byHerbert-Read et al (2013) showed that individual movementcharacteristics become increasingly homogenized in larger groupssupporting the idea that the potential for an individual to affect
values Rectangles correspond to individual birds trained birds are shown with black(A B or C) and its rank during the pretraining flights Edges indicate leaderefollower
dges that have the same directionality in pre- and post-training networks are indicatedg are shown as red lines those that appear in only one of the networks are shown ast-training hierarchies of groups A B and C respectively
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash03 0 03ndash03
0
03(a) (c)(b)
τi Pretraining (s) τiUjU Pretraining (s)
τ iTj U P
ost-
trai
nin
g (s
)
τ iU
j U P
ost-
trai
nin
g (s
)
τ i P
ost
-tra
inin
g (s
)
τiTjUPretraining (s)
Figure 3 Relationship between s before and after individual training flights (mean SEM) (a) sposti as a function of sprei for solo-trained (orange circles) and untrained individuals(light grey circles) (b c) Averaged sij after individual training as a function of averaged sij before individual training for (b) untrainedeuntrained pairings and (c) trainedeuntrainedpairings
A Flack et al Animal Behaviour 86 (2013) 723e732728
collective movements diminishes with increasing group sizeInvestigating the potential link between group size and group dy-namics both empirically and theoretically is a promising avenuefor future research
Although flock dynamics can be observed without hierarchicalorganization (Xu et al 2012) hierarchical structure might bebeneficial for establishing a lsquoflight routinersquo that demands lessattention from group members The fact that hierarchies seemresistant to small changes once they are established indicates thatrather than benefitting from particular features of the leader (suchas navigational experience) their advantage might lie in the sta-bility of the structure itself Robust social structures may enhanceinformation transfer among group members thereby increasingthe accuracy of group-level decisions (Lusseau amp Conradt 2009McComb et al 2011) Recent theoretical work has found that un-derlying social structures can improve the navigational accuracy oflarge leaderless groups (Bode et al 2012) Furthermore it is sug-gested that hierarchical group dynamics could be based purely onsocial preferences (Bode et al 2011) This is in agreement with whathas been described for various species of group-living primatesKing amp Sueur (2011) suggested that leaderefollower dynamics areembedded in interindividual relationships which may result inmore efficient decision making and coordination among groupmembers Social relationships can be found between relativesfamiliar conspecifics or individuals of similar attributes such as sizepersonality or sex Hence the stability in our hierarchical networksmay arise from preferential attachments that may have developedduring early training and that may not be susceptible to changes inindividualsrsquo navigational experience
Acknowledgments
AF was supported by Microsoft Research Cambridge MN wassupported by a Royal Society Newton International Fellowship andby Somerville College Oxford DB was supported by a Royal So-ciety University Research Fellowship This work was partly sup-ported by the EU ERC COLLMOT project (grant no 227878) Wethank Benjamin Pettit for technical assistance with the GPS testsand statistical advice We are also grateful to Andrew King andthree anonymous referees for helpful comments on themanuscript
References
Baayen R H 2008 Analyzing Linguistic Data A Practical Introduction to StatisticsUsing R Cambridge Cambridge University Press
Baayen R H 2009 languageR data sets and functions with lsquoAnalyzing LinguisticData A practical introduction to statisticsrsquo R package version 0955 cranr-projectorgwebpackageslanguageRlanguageRpdf
Ballerini M Cabibbo N Candelier R Cavagna A Cisbani E Giardina ILecomte V Orlandi A Parisi G Procaccini A et al 2008 Interaction rulinganimal collective behavior depends on topological rather than metric distanceevidence from a field study Proceedings of the National Academy of SciencesUSA 105 1232e1237
Bates D amp Maechler M 2009 Package lsquolme4rsquo(Version 0999375-32) linear mixed-effects models using S4 classes cran r-project orgwebpackageslme4lme4pdf
Bode N W F Wood A J amp Franks D W 2011 The impact of social networks onanimal collective motion Animal Behaviour 82 29e38
Bode N W F Wood J A amp Franks D W 2012 Social networks improve lead-erless group navigation by facilitating long-distance communication CurrentZoology 58 329e341
Bousquet C A H amp Manser M B 2011 Resolution of experimentallyinduced symmetrical conflicts of interest in meerkats Animal Behaviour81 1101e1107
Conradt L Krause J Couzin I D amp Roper T J 2009 lsquoLeading according to needrsquoin self-organizing groups The American Naturalist 173 304e312
Couzin IDKrause J JamesRRuxtonGDampFranksNR2002Collectivememoryand spatial sorting in animal groups Journal of Theoretical Biology 218 1e11
Fischhoff I R Sundaresan S R Cordingley J Larkin H M Sellier M-J ampRubenstein D I 2007 Social relationships and reproductive state influenceleadership roles in movements of plains zebra Equus burchellii Animal Behav-iour 73 825e831
Flack A Pettit B Freeman R Guilford T amp Biro D 2012 What are leadersmade of The role of individual experience in determining leaderefollowerrelations in homing pigeons Animal Behaviour 83 703e709
Flack A Freeman R Guilford T amp Biro D 2013 Pairs of pigeons act asbehavioural units during route learning and co-navigational leadership con-flicts The Journal of Experimental Biology 216 1434e1438
Freeman R Mann R Guilford T amp Biro D 2011 Group decisions and individualdifferences route fidelity predicts flight leadership in homing pigeons(Columba livia) Biology Letters 7 63e66
Herbert-Read J E Perna A Mann R P Schaerf T M Sumpter D J T ampWard A J W 2011 Inferring the rules of interaction of shoaling fish Pro-ceedings of the National Academy of Sciences USA 108 18726e18731
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause J ampWard A J W 2013 The role of individuality in collective group movementProceedings of the Royal Society B 280 1752
Jacobs A Sueur C Deneubourg J L amp Petit O 2011 Social network influencesdecision making during collective movements in brown lemurs (Eulemur fulvusfulvus) International Journal of Primatology 32 721e736
Katz Y Tunstroslashm K Ioannou C C Huepe C amp Couzin I D 2011 Inferring thestructure and dynamics of interactions in schooling fish Proceedings of theNational Academy of Sciences USA 108 18720e18725
King A amp Sueur C 2011 Where next Group coordination and collective decisionmaking by primates International Journal of Primatology 32 1245e1267
King A J Douglas C M S Huchard E Isaac N J B amp Cowlishaw G 2008Dominance and affiliation mediate despotism in a social primate CurrentBiology 18 1833e1838
Krause J Bumann D amp Todt D 1992 Relationship between the position pref-erence and nutritional state of individuals in schools of juvenile roach Rutilusrutilus Behavioral Ecology and Sociobiology 30 177e180
Lukeman R Li Y-X amp Edelstein-Keshet L 2010 Inferring individual rules fromcollective behavior Proceedings of the National Academy of Sciences USA 10712576e12580
Lusseau D amp Conradt L 2009 The emergence of unshared consensus decisions inbottlenose dolphins Behavioral Ecology and Sociobiology 63 1067e1077
McComb K Shannon G Durant S M Sayialel K Slotow R Poole J ampMoss C 2011 Leadership in elephants the adaptive value of age Proceedings ofthe Royal Society B 278 3270e3276
Meade J Biro D amp Guilford T 2005 Homing pigeons develop local route ste-reotypy Proceedings of the Royal Society B 272 17e23
A Flack et al Animal Behaviour 86 (2013) 723e732 729
Nagy M Aacutekos Z Biro D amp Vicsek T 2010 Hierarchical group dynamics in pi-geon flocks Nature 464 890e893
Nagy M Vaacutesaacuterhelyi G Pettit B Roberts-Mariani I Vicsek T amp Biro D 2013Context-dependent hierarchies in pigeons Proceedings of the National Acad-emy of Sciences USA 110 13049e13054
Nakayama S Harcourt J L Johnstone R A amp Manica A 2012a Initiativepersonality and leadership in pairs of foraging fish PLoS ONE 7 e36606
Nakayama S Johnstone R A amp Manica A 2012b Temperament and hungerinteract to determine the emergence of leaders in pairs of foraging fish PLoSONE 7 e43747
R Development Core Team 2009 R A Language and Environment for StatisticalComputing Vienna R Foundation for Statistical Computing
Reebs S G 2000 Can a minority of informed leaders determine the foragingmovements of a fish shoal Animal Behaviour 59 403e409
Vicsek T amp Zafeiris A 2012 Collective motion Physics Reports 517 71e140Vicsek T Cziroacutek A Ben-Jacob E Cohen I amp Shochet O 1995 Novel type of
phase transition in a system of self-driven particles Physical Review Letters 751226e1229
Xu X-K Kattas G D amp Small M 2012 Reciprocal relationships in collectiveflights of homing pigeons Physical Review E 85 026120
APPENDIX
GPS Error and its Effect on the Analysis
To test the spatial and temporal error originating from the GPSdevices we performed a variety of tests Ten GPS devices (labelled0e9) were attached to a rigid 3 m long pole with an interdevicedistance of 33 cm We moved the pole along a free path in an openfield using three different orientations (1) with the polersquos orien-tation parallel to the direction of motion (GPS 0 at the front and 9 atthe back Fig A1a) (2) with the pole in a fixed orientation relativeto the field (Fig A1b) and (3) with the polersquos orientation perpen-dicular to the direction of motion (Fig A1c) Each test lasted 10 minand the pole moved between 1 and 3 ms (typical flight speed of apigeon is 18e22 ms)
An important aspect of analysing flock flights is the relativeposition of each device within a pair in relation to the movementdirection of the whole flock This is why we measured the averageforward position of each device (Fig A1def) In both the perpen-dicular and the globally fixed orientation cases we expected anaverage forward position of zero In the parallel case we wouldexpect a forward ratio of 1 for (i lt j) Any deviation from such a
Table A1Results of the sprei vs sposti correlation analysis with and without two outliers
Correlation betweensprei and sposti
Without ou
Untrained ABC r20[072 PUntrained group A r6[080 P[Untrained group B r6[087 P[Untrained group C r6frac14069 Pfrac14Trained ABC r7frac14008 P
Values in bold indicate significant correlations
value is due to noise which is lower at small interdevice distancesWe show the probability density function of this measure inFig A1gei We also measured the time a device was detected to bein front relative to the direction of motion and calculated the timeratio for the 10 min test (Fig A1jel) We also performed directionalcorrelation delay analyses for all devices (Fig A1meo) The absoluteerror of the GPS device arises from the relative error of the velocitywhich decreases as speed increases Hence our tests give an upperapproximation of the noise as each test lasted only 10 min and thepole was moved at low speeds
Additional Test of Hierarchy Robustness
We used a linear mixed-effects model to test the robustness ofthe hierarchies using as our data set the s values calculated for eachindividual in every flight of phases I and III All data were analysedusing R (R Development Core Team 2009) and the R packages lme4(Bates amp Maechler 2009) and languageR (Baayen 2008 2009) Weincluded Subject as a random effect As fixed effects we addedTraining Phase (Phase I pretraining or Phase III post-training) andTreatment Group (trained or untrained individuals) to themodel aswell as the interaction term between them
We verified that the normality of error and homogeneity ofvariance assumptions of parametric analysis were satisfied by vi-sual inspection of plots of residuals against fitted values To assessthe validity of the mixed-effects analysis we performed likelihoodratio tests comparing the model with fixed effects to the null modelwith only the random effect The model that included fixed effectsdid not differ significantly from the null model (P frac14 0222) andhence fulfilled the validation test The following P values werebased on Markov chain Monte Carlo sampling We found no sig-nificant differences between pre- and post-training s values(PMCMC frac14 0656) or trained and untrained individuals(PMCMC frac14 0203) The interaction between Training Phase andTreatment Group was not significant (PMCMC frac14 0321) Togetherthese results further confirm that the solo training had no effect onthe groupsrsquo hierarchies
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Methods
Subjects and Experimental Procedure
GPS Device and Data Handling
Data Analysis
Results
Discussion
Acknowledgments
References
Appendix
GPS Error and its Effect on the Analysis
Additional Test of Hierarchy Robustness
A Flack et al Animal Behaviour 86 (2013) 723e732 725
hierarchical order among all group members (defined as hierar-chical rank) On two occasions the si value was 34 times higherthan the standard deviation of all values (see Fig A3) in these caseswe removed the two birds from these particular flock flights andreran the analyses without them (see Table A1 for the resultsincluding the outliers) We calculated for each bird the average ofthe si values for the flights before (Phase I eight flights sprei ) andafter (Phase III six flights sposti ) the individual training period sivalues have similar properties to linear ranks (positive and negativevalues correspond to leading and following behaviour respec-tively) We tested our data for normality using a KolmogoroveSmirnov test (P lt 005) We used Pearson correlations for sampleswith equal variances (F test for equal variance) and Spearmancorrelations for those with unequal variances
RESULTS
Following the group releases of Phase I we identified fullytransitive hierarchies in each of our three flocks (Fig 1 pretraining)Besides confirming the findings of Nagy et al (2010) this initialresult also provided the necessary premise for Phases II and III
First we evaluated the effect of the training (flock and soloflights) on homing performance by examining homing efficiencyand homing time over the course of Phases I II and III (Fig 2a b)Birds improved in both measures of homing performance duringthe flock releases of Phase I Furthermore during Phase II the solotrained birds increased their efficiency by an average SD of013 006 (difference between the average of the first two and theaverage of the last two solo training flights in Phase II Fig 2c) anddecreased their homing time by 3434 s 2090 s (Fig 2d) Boththese changes differed significantly from zero (one-sample t testsefficiency t7 frac14 577 P lt 0001 time t7 frac14 465 P frac14 0002)
We next used data from Phase III to measure the stability of thehierarchies by comparing the relative ranks of the untrained birdsbefore and after solo training (sposti versus sprei ) We found a positivecorrelation between sprei and sposti (Pearson correlation group ABCtogether r20 frac14 072 P lt 0001 Fig 3a group A r6 frac14 080P frac14 0030 group B r6 frac14 087 P frac14 0011 group C r6 frac14 069P frac14 0090) which indicates the persistence of a robust hierarchicalorder among untrained flock members However the ranks of thetrained birds exhibited variability we found no correlation be-tween sprei and sposti (Pearson correlation r7 frac14 e008 P frac14 0846Fig 3a) with some birds experiencing a rise and others a drop in siAlso the changes in the birdsrsquo relative ranks did not correlate withtheir changes in homing performance (Pearson correlation effi-ciency r7 frac14 0247 P frac14 0556 time r7 frac14 0072 P frac14 0866)
We further investigated the changes the hierarchies underwentusing pairwise directional correlation time ethsijTHORN We observed apositive correlation between pre- and post-training for the un-trained birds when pooling the data from the three flocks(Spearman correlation group ABC together r20 frac14 066 P frac14 0001Fig 3b) further confirming the stability of their relationships overtime and over repeated interactions However when examining thethree flocks separately we did not find a positive correlation in twocases which might be caused by the small sample size of each flock(Spearman correlation group A r6 frac14 067 P frac14 0098 Pearson cor-relation group B r6 frac14 092 P frac14 0004 group C r6 frac14 062P frac14 0138) Moreover pairwise siTjU values enabled us to comparethe changes in pairs consisting of a trained (iT) and an untrained (jU)individual The relationship between trained and untrained pigeonsalso remained stable as evidenced by the positive correlation be-tween their pre- and post-training siTjU (Spearman correlationr28 frac14 044 P frac14 0018 Fig 3c) Despite the extra experience gatheredby certain flockmembers their positions in the hierarchy relative tountrained birds showed on average no improvement the
difference in directional correlation delay times in trainedeun-trained pairs before and after the individual training was on aver-age SEM 000 001 s and did not differ significantly from zero(one-sample t test t55 frac14 0005 P frac14 0996) Thus although theoverall hierarchical rank of the trained individuals changed slightlythe direction of these changes was not consistent In addition thechanges were small enough that across the flock as a whole theposition of the untrained birds in relation to trained flock membersremained mostly unchanged The extra training had an evensmaller effect on the positions of the untrained birds relative toeach other (Fig 1 post-training) Separate examination of the threeflocks showed that in group A two of the trained birds improvedtheir relative ranks and one maintained its position (the averagechange in sij before and after training SEM ADsij frac14 006 002 s one-sample t test t20 frac14 334 P frac14 0003Fig 1a) In group B no clear change was found (BDsij frac14 002 001 s one-sample t test t20 frac14 177 P frac14 009Fig 1b) whereas in group C the trained birds decreased theirrelative ranks (C Dsij frac14 011 002 s one-sample t testt13 frac14 530 P lt 0001 Fig 1c) An additional statistical analysismaking use of the full data set rather than per bird averages asabove further confirmed the robustness of the measured hierar-chies (see Appendix)
DISCUSSION
Previous research has shown that group decision making inpigeon flocks is hierarchically organized with certain individualsconsistently contributing with relativelymoreweight tomovementdecisions than others (Nagy et al 2010) In this study we recon-firmed the existence of such hierarchical flight dynamics demon-strating distinct leadership hierarchies in three separate flocksduring repeated homing flights Moreover we showed that addi-tional solo training given to specific group members did not affectthe overall hierarchy of the flock although trained birds increasedtheir navigational efficiency during these solo flights (thus sug-gesting that they had gained additional navigational knowledge)this increase in efficiency was not accompanied reliably byimprovement in their hierarchical position Overall pairwiseleaderefollower relations between flockmembers remained stableand thus the hierarchies themselves remained robust We use theterm lsquorobustnessrsquo to mean that the interindividual relationshipsand hence the whole systems of hierarchical leadership networkswe observed were resistant to perturbations (introduced here inthe form of experimentally changing the knowledge of certain flockmembers) Our results imply that leadership ranks within flocks donot directly relate to individual navigational experience but thatsome other intrinsic property or a combination of several proper-ties defines the organization of the hierarchy
Two possible mechanisms might allow the establishment andmaintenance of robust flight hierarchies The first requires recog-nition of conspecificsrsquo morphological physiological or behaviouralfeatures that determine leadership ranks and may be com-plemented by individual recognition and memory of previous in-teractions Flock members may have fixed leaderefollowerrelationships that are based on dominance (King et al 2008) fa-miliarity (Flack et al 2013) or individual affiliations (Jacobs et al2011) and are consequently maintained across multiple flightsAlternatively hierarchies might derive from individuals reacting inconsistent ways to other group membersrsquo movements withoutnecessarily identifying them or their status Each individual mayrespond to flockmates in a way that is defined by its own specificfeatures such as experience or motivation This would allowleadership to emerge passively as a consequence of simple inter-action rules (Vicsek et al 1995 Couzin et al 2002) In other species
002
007008 008
009
011
011
014
003
003
003002
008
003
002
006
002
005
007
003
0007
005
012006
006
005
005
006
019
004
003
008
014
009
003
015
002
002
011
004
019
005
005010
010
003
004
002003
009
003
008
003
003
004
005
0
012
006
003009
003
008
006
019
006
013
011
006
009
0 00
006
012
006
020
004
011
007
022
006
014
007
005
007
013004
010
005003
005
005
005
010
012
005
004
008
007
002
(a)
(b)
(c)
005
018006
012
017
007
005
014003
009
003
018
3
0
003
005 006
019
004
011
019
066
006
012
005
026
015
006
2
024
004
006
004
014
0090
009
011
010
016
005
004
005007
004
004 005
005
002
013
002
003
003005
004
005
014
002
016
007
007
017
0
007
0
007
002
014
3
003 006
016
008
007
014
003
003
010
023
009
013
007
004
005
022
008
010
004
007
005
019
008
003
007 016
003
006
005
003
015
010
006
013 008
016
023
013
A01
A02
Pretraining Post-training
A01
A02
A03
A04
A05
A06
A07
A08 A09
A10
A03A04
A05
A06 A07
A08
A09
A10
B01
B01B02
B03
B04
B05
B06
B07
B08
B09
B10
B02
B03
B04
B05
B06
B07
B08
B09
C01C01
C02
C03
C04
C05
C06
C07
C08
C09
C02
C03C04
C05 C06C07
C08
C09
B10
A Flack et al Animal Behaviour 86 (2013) 723e732726
0
500
1000
1500
2000
2500
Hom
ing
tim
e (s
)
0
02
04
06
08
1
41 7
Release number
Effi
cien
cy
(a) (b)
ndash01
0
01
02
03
Trained birdsndash800
ndash600
ndash400
ndash200
0
Ch
ange
in
ho
min
g ti
me
(s)
(c) (d)
41 7
41
Pretrainingflock
flights
Single training flights
Post-training
flockflights
Ch
ange
in e
ffic
ien
cy
41 7
41 7
41
10
Pretrainingflock
flights
Single training flights
Post-training
flockflights
10
Figure 2 (a) Homing efficiency (mean SEM) and (b) homing time (mean SEM) as a function of release number Data from all groups were averaged according to releasenumber Grey circles indicate phases I (N frac14 30) and III (N frac14 29) orange circles show trained individuals in Phase II (N frac14 8) (c d) Changes in (c) homing efficiency and (d) homingtime during solo flights by trained individuals Black line corresponds to mean SEM
A Flack et al Animal Behaviour 86 (2013) 723e732 727
these responses have been described as varying in line with mul-tiple factors For example fish might emerge as leaders dependingon their level of satiation (Nakayama et al 2012b) or experiencewith a foraging task (Reebs 2000) We know that in pigeons indi-vidual morphological differences like body mass do not act tostructure networks (Nagy et al 2013) Yet on which set of indi-vidual traits flight hierarchies are based remains open
The fact that we found no consistent effect of the extra trainingon birdsrsquo leadership ranks is a somewhat surprising result givenprevious suggestions of the effect of navigational experience andskill on leadership (Nagy et al 2010 Freeman et al 2011) Onepossible explanation is that solo and group homing flights affectbirds differently meaning that flying in a flock might overshadowindividually gained navigational advantages To explore the effectof experience on leadership hierarchies further one would need totest whether giving certain flock members additional grouptraining flights would cause changes in an already establishedleadership hierarchy Also the trained birdsrsquo increase in experiencemight not have been large enough to induce changes in the orga-nization of the flock Prior to the solo training each subject hadalready performed eight flock homing flights and reached highasymptotic levels of homing efficiency (Meade et al 2005) Even
Figure 1 Pre- and post-training hierarchical networks of three flocks generated using sijborders The three-digit alphanumeric codes indicate in which group the subject was testedrelations pointing from the leader to the follower (only edges where sij 002 are shown) Eas thick blue lines those that undergo a change in direction between pre- and post-trainindotted green lines Numbers on edges correspond to sij (a) (b) and (c) Pretraining and pos
though solo training did improve birdsrsquo solo homing efficiencytheir advantage over the rest of the flock remained small or wasonly temporary This interpretation is in agreement with past re-sults showing that birds with more experience will more clearlyemerge as leaders when the difference in experience between themand their flight partners is large (Flack et al 2012) Future researchshould focus on the effect of experiencewhile birds are still far fromasymptotic levels of efficiency (eg with tests run after fewerhoming flights for the most inexperienced birds) Furthermore acontrol group in which every flock member receives extra solotraining flights in Phase II would be useful as a baseline measure ofhow flock homing efficiency changes in response to training givenequally to all group members
Flack et al (2012) tested mixed-experience pairs of pigeons andfound that navigational experience had an effect on leadershipwith birds that had performed more training flights more likely toemerge as leaders In the present study using groups of 10 birds nosuch effect was detected which may indicate that influencingflockmatesrsquomovements is easier in smaller groups Recent work byHerbert-Read et al (2013) showed that individual movementcharacteristics become increasingly homogenized in larger groupssupporting the idea that the potential for an individual to affect
values Rectangles correspond to individual birds trained birds are shown with black(A B or C) and its rank during the pretraining flights Edges indicate leaderefollower
dges that have the same directionality in pre- and post-training networks are indicatedg are shown as red lines those that appear in only one of the networks are shown ast-training hierarchies of groups A B and C respectively
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash03 0 03ndash03
0
03(a) (c)(b)
τi Pretraining (s) τiUjU Pretraining (s)
τ iTj U P
ost-
trai
nin
g (s
)
τ iU
j U P
ost-
trai
nin
g (s
)
τ i P
ost
-tra
inin
g (s
)
τiTjUPretraining (s)
Figure 3 Relationship between s before and after individual training flights (mean SEM) (a) sposti as a function of sprei for solo-trained (orange circles) and untrained individuals(light grey circles) (b c) Averaged sij after individual training as a function of averaged sij before individual training for (b) untrainedeuntrained pairings and (c) trainedeuntrainedpairings
A Flack et al Animal Behaviour 86 (2013) 723e732728
collective movements diminishes with increasing group sizeInvestigating the potential link between group size and group dy-namics both empirically and theoretically is a promising avenuefor future research
Although flock dynamics can be observed without hierarchicalorganization (Xu et al 2012) hierarchical structure might bebeneficial for establishing a lsquoflight routinersquo that demands lessattention from group members The fact that hierarchies seemresistant to small changes once they are established indicates thatrather than benefitting from particular features of the leader (suchas navigational experience) their advantage might lie in the sta-bility of the structure itself Robust social structures may enhanceinformation transfer among group members thereby increasingthe accuracy of group-level decisions (Lusseau amp Conradt 2009McComb et al 2011) Recent theoretical work has found that un-derlying social structures can improve the navigational accuracy oflarge leaderless groups (Bode et al 2012) Furthermore it is sug-gested that hierarchical group dynamics could be based purely onsocial preferences (Bode et al 2011) This is in agreement with whathas been described for various species of group-living primatesKing amp Sueur (2011) suggested that leaderefollower dynamics areembedded in interindividual relationships which may result inmore efficient decision making and coordination among groupmembers Social relationships can be found between relativesfamiliar conspecifics or individuals of similar attributes such as sizepersonality or sex Hence the stability in our hierarchical networksmay arise from preferential attachments that may have developedduring early training and that may not be susceptible to changes inindividualsrsquo navigational experience
Acknowledgments
AF was supported by Microsoft Research Cambridge MN wassupported by a Royal Society Newton International Fellowship andby Somerville College Oxford DB was supported by a Royal So-ciety University Research Fellowship This work was partly sup-ported by the EU ERC COLLMOT project (grant no 227878) Wethank Benjamin Pettit for technical assistance with the GPS testsand statistical advice We are also grateful to Andrew King andthree anonymous referees for helpful comments on themanuscript
References
Baayen R H 2008 Analyzing Linguistic Data A Practical Introduction to StatisticsUsing R Cambridge Cambridge University Press
Baayen R H 2009 languageR data sets and functions with lsquoAnalyzing LinguisticData A practical introduction to statisticsrsquo R package version 0955 cranr-projectorgwebpackageslanguageRlanguageRpdf
Ballerini M Cabibbo N Candelier R Cavagna A Cisbani E Giardina ILecomte V Orlandi A Parisi G Procaccini A et al 2008 Interaction rulinganimal collective behavior depends on topological rather than metric distanceevidence from a field study Proceedings of the National Academy of SciencesUSA 105 1232e1237
Bates D amp Maechler M 2009 Package lsquolme4rsquo(Version 0999375-32) linear mixed-effects models using S4 classes cran r-project orgwebpackageslme4lme4pdf
Bode N W F Wood A J amp Franks D W 2011 The impact of social networks onanimal collective motion Animal Behaviour 82 29e38
Bode N W F Wood J A amp Franks D W 2012 Social networks improve lead-erless group navigation by facilitating long-distance communication CurrentZoology 58 329e341
Bousquet C A H amp Manser M B 2011 Resolution of experimentallyinduced symmetrical conflicts of interest in meerkats Animal Behaviour81 1101e1107
Conradt L Krause J Couzin I D amp Roper T J 2009 lsquoLeading according to needrsquoin self-organizing groups The American Naturalist 173 304e312
Couzin IDKrause J JamesRRuxtonGDampFranksNR2002Collectivememoryand spatial sorting in animal groups Journal of Theoretical Biology 218 1e11
Fischhoff I R Sundaresan S R Cordingley J Larkin H M Sellier M-J ampRubenstein D I 2007 Social relationships and reproductive state influenceleadership roles in movements of plains zebra Equus burchellii Animal Behav-iour 73 825e831
Flack A Pettit B Freeman R Guilford T amp Biro D 2012 What are leadersmade of The role of individual experience in determining leaderefollowerrelations in homing pigeons Animal Behaviour 83 703e709
Flack A Freeman R Guilford T amp Biro D 2013 Pairs of pigeons act asbehavioural units during route learning and co-navigational leadership con-flicts The Journal of Experimental Biology 216 1434e1438
Freeman R Mann R Guilford T amp Biro D 2011 Group decisions and individualdifferences route fidelity predicts flight leadership in homing pigeons(Columba livia) Biology Letters 7 63e66
Herbert-Read J E Perna A Mann R P Schaerf T M Sumpter D J T ampWard A J W 2011 Inferring the rules of interaction of shoaling fish Pro-ceedings of the National Academy of Sciences USA 108 18726e18731
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause J ampWard A J W 2013 The role of individuality in collective group movementProceedings of the Royal Society B 280 1752
Jacobs A Sueur C Deneubourg J L amp Petit O 2011 Social network influencesdecision making during collective movements in brown lemurs (Eulemur fulvusfulvus) International Journal of Primatology 32 721e736
Katz Y Tunstroslashm K Ioannou C C Huepe C amp Couzin I D 2011 Inferring thestructure and dynamics of interactions in schooling fish Proceedings of theNational Academy of Sciences USA 108 18720e18725
King A amp Sueur C 2011 Where next Group coordination and collective decisionmaking by primates International Journal of Primatology 32 1245e1267
King A J Douglas C M S Huchard E Isaac N J B amp Cowlishaw G 2008Dominance and affiliation mediate despotism in a social primate CurrentBiology 18 1833e1838
Krause J Bumann D amp Todt D 1992 Relationship between the position pref-erence and nutritional state of individuals in schools of juvenile roach Rutilusrutilus Behavioral Ecology and Sociobiology 30 177e180
Lukeman R Li Y-X amp Edelstein-Keshet L 2010 Inferring individual rules fromcollective behavior Proceedings of the National Academy of Sciences USA 10712576e12580
Lusseau D amp Conradt L 2009 The emergence of unshared consensus decisions inbottlenose dolphins Behavioral Ecology and Sociobiology 63 1067e1077
McComb K Shannon G Durant S M Sayialel K Slotow R Poole J ampMoss C 2011 Leadership in elephants the adaptive value of age Proceedings ofthe Royal Society B 278 3270e3276
Meade J Biro D amp Guilford T 2005 Homing pigeons develop local route ste-reotypy Proceedings of the Royal Society B 272 17e23
A Flack et al Animal Behaviour 86 (2013) 723e732 729
Nagy M Aacutekos Z Biro D amp Vicsek T 2010 Hierarchical group dynamics in pi-geon flocks Nature 464 890e893
Nagy M Vaacutesaacuterhelyi G Pettit B Roberts-Mariani I Vicsek T amp Biro D 2013Context-dependent hierarchies in pigeons Proceedings of the National Acad-emy of Sciences USA 110 13049e13054
Nakayama S Harcourt J L Johnstone R A amp Manica A 2012a Initiativepersonality and leadership in pairs of foraging fish PLoS ONE 7 e36606
Nakayama S Johnstone R A amp Manica A 2012b Temperament and hungerinteract to determine the emergence of leaders in pairs of foraging fish PLoSONE 7 e43747
R Development Core Team 2009 R A Language and Environment for StatisticalComputing Vienna R Foundation for Statistical Computing
Reebs S G 2000 Can a minority of informed leaders determine the foragingmovements of a fish shoal Animal Behaviour 59 403e409
Vicsek T amp Zafeiris A 2012 Collective motion Physics Reports 517 71e140Vicsek T Cziroacutek A Ben-Jacob E Cohen I amp Shochet O 1995 Novel type of
phase transition in a system of self-driven particles Physical Review Letters 751226e1229
Xu X-K Kattas G D amp Small M 2012 Reciprocal relationships in collectiveflights of homing pigeons Physical Review E 85 026120
APPENDIX
GPS Error and its Effect on the Analysis
To test the spatial and temporal error originating from the GPSdevices we performed a variety of tests Ten GPS devices (labelled0e9) were attached to a rigid 3 m long pole with an interdevicedistance of 33 cm We moved the pole along a free path in an openfield using three different orientations (1) with the polersquos orien-tation parallel to the direction of motion (GPS 0 at the front and 9 atthe back Fig A1a) (2) with the pole in a fixed orientation relativeto the field (Fig A1b) and (3) with the polersquos orientation perpen-dicular to the direction of motion (Fig A1c) Each test lasted 10 minand the pole moved between 1 and 3 ms (typical flight speed of apigeon is 18e22 ms)
An important aspect of analysing flock flights is the relativeposition of each device within a pair in relation to the movementdirection of the whole flock This is why we measured the averageforward position of each device (Fig A1def) In both the perpen-dicular and the globally fixed orientation cases we expected anaverage forward position of zero In the parallel case we wouldexpect a forward ratio of 1 for (i lt j) Any deviation from such a
Table A1Results of the sprei vs sposti correlation analysis with and without two outliers
Correlation betweensprei and sposti
Without ou
Untrained ABC r20[072 PUntrained group A r6[080 P[Untrained group B r6[087 P[Untrained group C r6frac14069 Pfrac14Trained ABC r7frac14008 P
Values in bold indicate significant correlations
value is due to noise which is lower at small interdevice distancesWe show the probability density function of this measure inFig A1gei We also measured the time a device was detected to bein front relative to the direction of motion and calculated the timeratio for the 10 min test (Fig A1jel) We also performed directionalcorrelation delay analyses for all devices (Fig A1meo) The absoluteerror of the GPS device arises from the relative error of the velocitywhich decreases as speed increases Hence our tests give an upperapproximation of the noise as each test lasted only 10 min and thepole was moved at low speeds
Additional Test of Hierarchy Robustness
We used a linear mixed-effects model to test the robustness ofthe hierarchies using as our data set the s values calculated for eachindividual in every flight of phases I and III All data were analysedusing R (R Development Core Team 2009) and the R packages lme4(Bates amp Maechler 2009) and languageR (Baayen 2008 2009) Weincluded Subject as a random effect As fixed effects we addedTraining Phase (Phase I pretraining or Phase III post-training) andTreatment Group (trained or untrained individuals) to themodel aswell as the interaction term between them
We verified that the normality of error and homogeneity ofvariance assumptions of parametric analysis were satisfied by vi-sual inspection of plots of residuals against fitted values To assessthe validity of the mixed-effects analysis we performed likelihoodratio tests comparing the model with fixed effects to the null modelwith only the random effect The model that included fixed effectsdid not differ significantly from the null model (P frac14 0222) andhence fulfilled the validation test The following P values werebased on Markov chain Monte Carlo sampling We found no sig-nificant differences between pre- and post-training s values(PMCMC frac14 0656) or trained and untrained individuals(PMCMC frac14 0203) The interaction between Training Phase andTreatment Group was not significant (PMCMC frac14 0321) Togetherthese results further confirm that the solo training had no effect onthe groupsrsquo hierarchies
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Methods
Subjects and Experimental Procedure
GPS Device and Data Handling
Data Analysis
Results
Discussion
Acknowledgments
References
Appendix
GPS Error and its Effect on the Analysis
Additional Test of Hierarchy Robustness
002
007008 008
009
011
011
014
003
003
003002
008
003
002
006
002
005
007
003
0007
005
012006
006
005
005
006
019
004
003
008
014
009
003
015
002
002
011
004
019
005
005010
010
003
004
002003
009
003
008
003
003
004
005
0
012
006
003009
003
008
006
019
006
013
011
006
009
0 00
006
012
006
020
004
011
007
022
006
014
007
005
007
013004
010
005003
005
005
005
010
012
005
004
008
007
002
(a)
(b)
(c)
005
018006
012
017
007
005
014003
009
003
018
3
0
003
005 006
019
004
011
019
066
006
012
005
026
015
006
2
024
004
006
004
014
0090
009
011
010
016
005
004
005007
004
004 005
005
002
013
002
003
003005
004
005
014
002
016
007
007
017
0
007
0
007
002
014
3
003 006
016
008
007
014
003
003
010
023
009
013
007
004
005
022
008
010
004
007
005
019
008
003
007 016
003
006
005
003
015
010
006
013 008
016
023
013
A01
A02
Pretraining Post-training
A01
A02
A03
A04
A05
A06
A07
A08 A09
A10
A03A04
A05
A06 A07
A08
A09
A10
B01
B01B02
B03
B04
B05
B06
B07
B08
B09
B10
B02
B03
B04
B05
B06
B07
B08
B09
C01C01
C02
C03
C04
C05
C06
C07
C08
C09
C02
C03C04
C05 C06C07
C08
C09
B10
A Flack et al Animal Behaviour 86 (2013) 723e732726
0
500
1000
1500
2000
2500
Hom
ing
tim
e (s
)
0
02
04
06
08
1
41 7
Release number
Effi
cien
cy
(a) (b)
ndash01
0
01
02
03
Trained birdsndash800
ndash600
ndash400
ndash200
0
Ch
ange
in
ho
min
g ti
me
(s)
(c) (d)
41 7
41
Pretrainingflock
flights
Single training flights
Post-training
flockflights
Ch
ange
in e
ffic
ien
cy
41 7
41 7
41
10
Pretrainingflock
flights
Single training flights
Post-training
flockflights
10
Figure 2 (a) Homing efficiency (mean SEM) and (b) homing time (mean SEM) as a function of release number Data from all groups were averaged according to releasenumber Grey circles indicate phases I (N frac14 30) and III (N frac14 29) orange circles show trained individuals in Phase II (N frac14 8) (c d) Changes in (c) homing efficiency and (d) homingtime during solo flights by trained individuals Black line corresponds to mean SEM
A Flack et al Animal Behaviour 86 (2013) 723e732 727
these responses have been described as varying in line with mul-tiple factors For example fish might emerge as leaders dependingon their level of satiation (Nakayama et al 2012b) or experiencewith a foraging task (Reebs 2000) We know that in pigeons indi-vidual morphological differences like body mass do not act tostructure networks (Nagy et al 2013) Yet on which set of indi-vidual traits flight hierarchies are based remains open
The fact that we found no consistent effect of the extra trainingon birdsrsquo leadership ranks is a somewhat surprising result givenprevious suggestions of the effect of navigational experience andskill on leadership (Nagy et al 2010 Freeman et al 2011) Onepossible explanation is that solo and group homing flights affectbirds differently meaning that flying in a flock might overshadowindividually gained navigational advantages To explore the effectof experience on leadership hierarchies further one would need totest whether giving certain flock members additional grouptraining flights would cause changes in an already establishedleadership hierarchy Also the trained birdsrsquo increase in experiencemight not have been large enough to induce changes in the orga-nization of the flock Prior to the solo training each subject hadalready performed eight flock homing flights and reached highasymptotic levels of homing efficiency (Meade et al 2005) Even
Figure 1 Pre- and post-training hierarchical networks of three flocks generated using sijborders The three-digit alphanumeric codes indicate in which group the subject was testedrelations pointing from the leader to the follower (only edges where sij 002 are shown) Eas thick blue lines those that undergo a change in direction between pre- and post-trainindotted green lines Numbers on edges correspond to sij (a) (b) and (c) Pretraining and pos
though solo training did improve birdsrsquo solo homing efficiencytheir advantage over the rest of the flock remained small or wasonly temporary This interpretation is in agreement with past re-sults showing that birds with more experience will more clearlyemerge as leaders when the difference in experience between themand their flight partners is large (Flack et al 2012) Future researchshould focus on the effect of experiencewhile birds are still far fromasymptotic levels of efficiency (eg with tests run after fewerhoming flights for the most inexperienced birds) Furthermore acontrol group in which every flock member receives extra solotraining flights in Phase II would be useful as a baseline measure ofhow flock homing efficiency changes in response to training givenequally to all group members
Flack et al (2012) tested mixed-experience pairs of pigeons andfound that navigational experience had an effect on leadershipwith birds that had performed more training flights more likely toemerge as leaders In the present study using groups of 10 birds nosuch effect was detected which may indicate that influencingflockmatesrsquomovements is easier in smaller groups Recent work byHerbert-Read et al (2013) showed that individual movementcharacteristics become increasingly homogenized in larger groupssupporting the idea that the potential for an individual to affect
values Rectangles correspond to individual birds trained birds are shown with black(A B or C) and its rank during the pretraining flights Edges indicate leaderefollower
dges that have the same directionality in pre- and post-training networks are indicatedg are shown as red lines those that appear in only one of the networks are shown ast-training hierarchies of groups A B and C respectively
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash03 0 03ndash03
0
03(a) (c)(b)
τi Pretraining (s) τiUjU Pretraining (s)
τ iTj U P
ost-
trai
nin
g (s
)
τ iU
j U P
ost-
trai
nin
g (s
)
τ i P
ost
-tra
inin
g (s
)
τiTjUPretraining (s)
Figure 3 Relationship between s before and after individual training flights (mean SEM) (a) sposti as a function of sprei for solo-trained (orange circles) and untrained individuals(light grey circles) (b c) Averaged sij after individual training as a function of averaged sij before individual training for (b) untrainedeuntrained pairings and (c) trainedeuntrainedpairings
A Flack et al Animal Behaviour 86 (2013) 723e732728
collective movements diminishes with increasing group sizeInvestigating the potential link between group size and group dy-namics both empirically and theoretically is a promising avenuefor future research
Although flock dynamics can be observed without hierarchicalorganization (Xu et al 2012) hierarchical structure might bebeneficial for establishing a lsquoflight routinersquo that demands lessattention from group members The fact that hierarchies seemresistant to small changes once they are established indicates thatrather than benefitting from particular features of the leader (suchas navigational experience) their advantage might lie in the sta-bility of the structure itself Robust social structures may enhanceinformation transfer among group members thereby increasingthe accuracy of group-level decisions (Lusseau amp Conradt 2009McComb et al 2011) Recent theoretical work has found that un-derlying social structures can improve the navigational accuracy oflarge leaderless groups (Bode et al 2012) Furthermore it is sug-gested that hierarchical group dynamics could be based purely onsocial preferences (Bode et al 2011) This is in agreement with whathas been described for various species of group-living primatesKing amp Sueur (2011) suggested that leaderefollower dynamics areembedded in interindividual relationships which may result inmore efficient decision making and coordination among groupmembers Social relationships can be found between relativesfamiliar conspecifics or individuals of similar attributes such as sizepersonality or sex Hence the stability in our hierarchical networksmay arise from preferential attachments that may have developedduring early training and that may not be susceptible to changes inindividualsrsquo navigational experience
Acknowledgments
AF was supported by Microsoft Research Cambridge MN wassupported by a Royal Society Newton International Fellowship andby Somerville College Oxford DB was supported by a Royal So-ciety University Research Fellowship This work was partly sup-ported by the EU ERC COLLMOT project (grant no 227878) Wethank Benjamin Pettit for technical assistance with the GPS testsand statistical advice We are also grateful to Andrew King andthree anonymous referees for helpful comments on themanuscript
References
Baayen R H 2008 Analyzing Linguistic Data A Practical Introduction to StatisticsUsing R Cambridge Cambridge University Press
Baayen R H 2009 languageR data sets and functions with lsquoAnalyzing LinguisticData A practical introduction to statisticsrsquo R package version 0955 cranr-projectorgwebpackageslanguageRlanguageRpdf
Ballerini M Cabibbo N Candelier R Cavagna A Cisbani E Giardina ILecomte V Orlandi A Parisi G Procaccini A et al 2008 Interaction rulinganimal collective behavior depends on topological rather than metric distanceevidence from a field study Proceedings of the National Academy of SciencesUSA 105 1232e1237
Bates D amp Maechler M 2009 Package lsquolme4rsquo(Version 0999375-32) linear mixed-effects models using S4 classes cran r-project orgwebpackageslme4lme4pdf
Bode N W F Wood A J amp Franks D W 2011 The impact of social networks onanimal collective motion Animal Behaviour 82 29e38
Bode N W F Wood J A amp Franks D W 2012 Social networks improve lead-erless group navigation by facilitating long-distance communication CurrentZoology 58 329e341
Bousquet C A H amp Manser M B 2011 Resolution of experimentallyinduced symmetrical conflicts of interest in meerkats Animal Behaviour81 1101e1107
Conradt L Krause J Couzin I D amp Roper T J 2009 lsquoLeading according to needrsquoin self-organizing groups The American Naturalist 173 304e312
Couzin IDKrause J JamesRRuxtonGDampFranksNR2002Collectivememoryand spatial sorting in animal groups Journal of Theoretical Biology 218 1e11
Fischhoff I R Sundaresan S R Cordingley J Larkin H M Sellier M-J ampRubenstein D I 2007 Social relationships and reproductive state influenceleadership roles in movements of plains zebra Equus burchellii Animal Behav-iour 73 825e831
Flack A Pettit B Freeman R Guilford T amp Biro D 2012 What are leadersmade of The role of individual experience in determining leaderefollowerrelations in homing pigeons Animal Behaviour 83 703e709
Flack A Freeman R Guilford T amp Biro D 2013 Pairs of pigeons act asbehavioural units during route learning and co-navigational leadership con-flicts The Journal of Experimental Biology 216 1434e1438
Freeman R Mann R Guilford T amp Biro D 2011 Group decisions and individualdifferences route fidelity predicts flight leadership in homing pigeons(Columba livia) Biology Letters 7 63e66
Herbert-Read J E Perna A Mann R P Schaerf T M Sumpter D J T ampWard A J W 2011 Inferring the rules of interaction of shoaling fish Pro-ceedings of the National Academy of Sciences USA 108 18726e18731
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause J ampWard A J W 2013 The role of individuality in collective group movementProceedings of the Royal Society B 280 1752
Jacobs A Sueur C Deneubourg J L amp Petit O 2011 Social network influencesdecision making during collective movements in brown lemurs (Eulemur fulvusfulvus) International Journal of Primatology 32 721e736
Katz Y Tunstroslashm K Ioannou C C Huepe C amp Couzin I D 2011 Inferring thestructure and dynamics of interactions in schooling fish Proceedings of theNational Academy of Sciences USA 108 18720e18725
King A amp Sueur C 2011 Where next Group coordination and collective decisionmaking by primates International Journal of Primatology 32 1245e1267
King A J Douglas C M S Huchard E Isaac N J B amp Cowlishaw G 2008Dominance and affiliation mediate despotism in a social primate CurrentBiology 18 1833e1838
Krause J Bumann D amp Todt D 1992 Relationship between the position pref-erence and nutritional state of individuals in schools of juvenile roach Rutilusrutilus Behavioral Ecology and Sociobiology 30 177e180
Lukeman R Li Y-X amp Edelstein-Keshet L 2010 Inferring individual rules fromcollective behavior Proceedings of the National Academy of Sciences USA 10712576e12580
Lusseau D amp Conradt L 2009 The emergence of unshared consensus decisions inbottlenose dolphins Behavioral Ecology and Sociobiology 63 1067e1077
McComb K Shannon G Durant S M Sayialel K Slotow R Poole J ampMoss C 2011 Leadership in elephants the adaptive value of age Proceedings ofthe Royal Society B 278 3270e3276
Meade J Biro D amp Guilford T 2005 Homing pigeons develop local route ste-reotypy Proceedings of the Royal Society B 272 17e23
A Flack et al Animal Behaviour 86 (2013) 723e732 729
Nagy M Aacutekos Z Biro D amp Vicsek T 2010 Hierarchical group dynamics in pi-geon flocks Nature 464 890e893
Nagy M Vaacutesaacuterhelyi G Pettit B Roberts-Mariani I Vicsek T amp Biro D 2013Context-dependent hierarchies in pigeons Proceedings of the National Acad-emy of Sciences USA 110 13049e13054
Nakayama S Harcourt J L Johnstone R A amp Manica A 2012a Initiativepersonality and leadership in pairs of foraging fish PLoS ONE 7 e36606
Nakayama S Johnstone R A amp Manica A 2012b Temperament and hungerinteract to determine the emergence of leaders in pairs of foraging fish PLoSONE 7 e43747
R Development Core Team 2009 R A Language and Environment for StatisticalComputing Vienna R Foundation for Statistical Computing
Reebs S G 2000 Can a minority of informed leaders determine the foragingmovements of a fish shoal Animal Behaviour 59 403e409
Vicsek T amp Zafeiris A 2012 Collective motion Physics Reports 517 71e140Vicsek T Cziroacutek A Ben-Jacob E Cohen I amp Shochet O 1995 Novel type of
phase transition in a system of self-driven particles Physical Review Letters 751226e1229
Xu X-K Kattas G D amp Small M 2012 Reciprocal relationships in collectiveflights of homing pigeons Physical Review E 85 026120
APPENDIX
GPS Error and its Effect on the Analysis
To test the spatial and temporal error originating from the GPSdevices we performed a variety of tests Ten GPS devices (labelled0e9) were attached to a rigid 3 m long pole with an interdevicedistance of 33 cm We moved the pole along a free path in an openfield using three different orientations (1) with the polersquos orien-tation parallel to the direction of motion (GPS 0 at the front and 9 atthe back Fig A1a) (2) with the pole in a fixed orientation relativeto the field (Fig A1b) and (3) with the polersquos orientation perpen-dicular to the direction of motion (Fig A1c) Each test lasted 10 minand the pole moved between 1 and 3 ms (typical flight speed of apigeon is 18e22 ms)
An important aspect of analysing flock flights is the relativeposition of each device within a pair in relation to the movementdirection of the whole flock This is why we measured the averageforward position of each device (Fig A1def) In both the perpen-dicular and the globally fixed orientation cases we expected anaverage forward position of zero In the parallel case we wouldexpect a forward ratio of 1 for (i lt j) Any deviation from such a
Table A1Results of the sprei vs sposti correlation analysis with and without two outliers
Correlation betweensprei and sposti
Without ou
Untrained ABC r20[072 PUntrained group A r6[080 P[Untrained group B r6[087 P[Untrained group C r6frac14069 Pfrac14Trained ABC r7frac14008 P
Values in bold indicate significant correlations
value is due to noise which is lower at small interdevice distancesWe show the probability density function of this measure inFig A1gei We also measured the time a device was detected to bein front relative to the direction of motion and calculated the timeratio for the 10 min test (Fig A1jel) We also performed directionalcorrelation delay analyses for all devices (Fig A1meo) The absoluteerror of the GPS device arises from the relative error of the velocitywhich decreases as speed increases Hence our tests give an upperapproximation of the noise as each test lasted only 10 min and thepole was moved at low speeds
Additional Test of Hierarchy Robustness
We used a linear mixed-effects model to test the robustness ofthe hierarchies using as our data set the s values calculated for eachindividual in every flight of phases I and III All data were analysedusing R (R Development Core Team 2009) and the R packages lme4(Bates amp Maechler 2009) and languageR (Baayen 2008 2009) Weincluded Subject as a random effect As fixed effects we addedTraining Phase (Phase I pretraining or Phase III post-training) andTreatment Group (trained or untrained individuals) to themodel aswell as the interaction term between them
We verified that the normality of error and homogeneity ofvariance assumptions of parametric analysis were satisfied by vi-sual inspection of plots of residuals against fitted values To assessthe validity of the mixed-effects analysis we performed likelihoodratio tests comparing the model with fixed effects to the null modelwith only the random effect The model that included fixed effectsdid not differ significantly from the null model (P frac14 0222) andhence fulfilled the validation test The following P values werebased on Markov chain Monte Carlo sampling We found no sig-nificant differences between pre- and post-training s values(PMCMC frac14 0656) or trained and untrained individuals(PMCMC frac14 0203) The interaction between Training Phase andTreatment Group was not significant (PMCMC frac14 0321) Togetherthese results further confirm that the solo training had no effect onthe groupsrsquo hierarchies
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Methods
Subjects and Experimental Procedure
GPS Device and Data Handling
Data Analysis
Results
Discussion
Acknowledgments
References
Appendix
GPS Error and its Effect on the Analysis
Additional Test of Hierarchy Robustness
0
500
1000
1500
2000
2500
Hom
ing
tim
e (s
)
0
02
04
06
08
1
41 7
Release number
Effi
cien
cy
(a) (b)
ndash01
0
01
02
03
Trained birdsndash800
ndash600
ndash400
ndash200
0
Ch
ange
in
ho
min
g ti
me
(s)
(c) (d)
41 7
41
Pretrainingflock
flights
Single training flights
Post-training
flockflights
Ch
ange
in e
ffic
ien
cy
41 7
41 7
41
10
Pretrainingflock
flights
Single training flights
Post-training
flockflights
10
Figure 2 (a) Homing efficiency (mean SEM) and (b) homing time (mean SEM) as a function of release number Data from all groups were averaged according to releasenumber Grey circles indicate phases I (N frac14 30) and III (N frac14 29) orange circles show trained individuals in Phase II (N frac14 8) (c d) Changes in (c) homing efficiency and (d) homingtime during solo flights by trained individuals Black line corresponds to mean SEM
A Flack et al Animal Behaviour 86 (2013) 723e732 727
these responses have been described as varying in line with mul-tiple factors For example fish might emerge as leaders dependingon their level of satiation (Nakayama et al 2012b) or experiencewith a foraging task (Reebs 2000) We know that in pigeons indi-vidual morphological differences like body mass do not act tostructure networks (Nagy et al 2013) Yet on which set of indi-vidual traits flight hierarchies are based remains open
The fact that we found no consistent effect of the extra trainingon birdsrsquo leadership ranks is a somewhat surprising result givenprevious suggestions of the effect of navigational experience andskill on leadership (Nagy et al 2010 Freeman et al 2011) Onepossible explanation is that solo and group homing flights affectbirds differently meaning that flying in a flock might overshadowindividually gained navigational advantages To explore the effectof experience on leadership hierarchies further one would need totest whether giving certain flock members additional grouptraining flights would cause changes in an already establishedleadership hierarchy Also the trained birdsrsquo increase in experiencemight not have been large enough to induce changes in the orga-nization of the flock Prior to the solo training each subject hadalready performed eight flock homing flights and reached highasymptotic levels of homing efficiency (Meade et al 2005) Even
Figure 1 Pre- and post-training hierarchical networks of three flocks generated using sijborders The three-digit alphanumeric codes indicate in which group the subject was testedrelations pointing from the leader to the follower (only edges where sij 002 are shown) Eas thick blue lines those that undergo a change in direction between pre- and post-trainindotted green lines Numbers on edges correspond to sij (a) (b) and (c) Pretraining and pos
though solo training did improve birdsrsquo solo homing efficiencytheir advantage over the rest of the flock remained small or wasonly temporary This interpretation is in agreement with past re-sults showing that birds with more experience will more clearlyemerge as leaders when the difference in experience between themand their flight partners is large (Flack et al 2012) Future researchshould focus on the effect of experiencewhile birds are still far fromasymptotic levels of efficiency (eg with tests run after fewerhoming flights for the most inexperienced birds) Furthermore acontrol group in which every flock member receives extra solotraining flights in Phase II would be useful as a baseline measure ofhow flock homing efficiency changes in response to training givenequally to all group members
Flack et al (2012) tested mixed-experience pairs of pigeons andfound that navigational experience had an effect on leadershipwith birds that had performed more training flights more likely toemerge as leaders In the present study using groups of 10 birds nosuch effect was detected which may indicate that influencingflockmatesrsquomovements is easier in smaller groups Recent work byHerbert-Read et al (2013) showed that individual movementcharacteristics become increasingly homogenized in larger groupssupporting the idea that the potential for an individual to affect
values Rectangles correspond to individual birds trained birds are shown with black(A B or C) and its rank during the pretraining flights Edges indicate leaderefollower
dges that have the same directionality in pre- and post-training networks are indicatedg are shown as red lines those that appear in only one of the networks are shown ast-training hierarchies of groups A B and C respectively
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash03 0 03ndash03
0
03(a) (c)(b)
τi Pretraining (s) τiUjU Pretraining (s)
τ iTj U P
ost-
trai
nin
g (s
)
τ iU
j U P
ost-
trai
nin
g (s
)
τ i P
ost
-tra
inin
g (s
)
τiTjUPretraining (s)
Figure 3 Relationship between s before and after individual training flights (mean SEM) (a) sposti as a function of sprei for solo-trained (orange circles) and untrained individuals(light grey circles) (b c) Averaged sij after individual training as a function of averaged sij before individual training for (b) untrainedeuntrained pairings and (c) trainedeuntrainedpairings
A Flack et al Animal Behaviour 86 (2013) 723e732728
collective movements diminishes with increasing group sizeInvestigating the potential link between group size and group dy-namics both empirically and theoretically is a promising avenuefor future research
Although flock dynamics can be observed without hierarchicalorganization (Xu et al 2012) hierarchical structure might bebeneficial for establishing a lsquoflight routinersquo that demands lessattention from group members The fact that hierarchies seemresistant to small changes once they are established indicates thatrather than benefitting from particular features of the leader (suchas navigational experience) their advantage might lie in the sta-bility of the structure itself Robust social structures may enhanceinformation transfer among group members thereby increasingthe accuracy of group-level decisions (Lusseau amp Conradt 2009McComb et al 2011) Recent theoretical work has found that un-derlying social structures can improve the navigational accuracy oflarge leaderless groups (Bode et al 2012) Furthermore it is sug-gested that hierarchical group dynamics could be based purely onsocial preferences (Bode et al 2011) This is in agreement with whathas been described for various species of group-living primatesKing amp Sueur (2011) suggested that leaderefollower dynamics areembedded in interindividual relationships which may result inmore efficient decision making and coordination among groupmembers Social relationships can be found between relativesfamiliar conspecifics or individuals of similar attributes such as sizepersonality or sex Hence the stability in our hierarchical networksmay arise from preferential attachments that may have developedduring early training and that may not be susceptible to changes inindividualsrsquo navigational experience
Acknowledgments
AF was supported by Microsoft Research Cambridge MN wassupported by a Royal Society Newton International Fellowship andby Somerville College Oxford DB was supported by a Royal So-ciety University Research Fellowship This work was partly sup-ported by the EU ERC COLLMOT project (grant no 227878) Wethank Benjamin Pettit for technical assistance with the GPS testsand statistical advice We are also grateful to Andrew King andthree anonymous referees for helpful comments on themanuscript
References
Baayen R H 2008 Analyzing Linguistic Data A Practical Introduction to StatisticsUsing R Cambridge Cambridge University Press
Baayen R H 2009 languageR data sets and functions with lsquoAnalyzing LinguisticData A practical introduction to statisticsrsquo R package version 0955 cranr-projectorgwebpackageslanguageRlanguageRpdf
Ballerini M Cabibbo N Candelier R Cavagna A Cisbani E Giardina ILecomte V Orlandi A Parisi G Procaccini A et al 2008 Interaction rulinganimal collective behavior depends on topological rather than metric distanceevidence from a field study Proceedings of the National Academy of SciencesUSA 105 1232e1237
Bates D amp Maechler M 2009 Package lsquolme4rsquo(Version 0999375-32) linear mixed-effects models using S4 classes cran r-project orgwebpackageslme4lme4pdf
Bode N W F Wood A J amp Franks D W 2011 The impact of social networks onanimal collective motion Animal Behaviour 82 29e38
Bode N W F Wood J A amp Franks D W 2012 Social networks improve lead-erless group navigation by facilitating long-distance communication CurrentZoology 58 329e341
Bousquet C A H amp Manser M B 2011 Resolution of experimentallyinduced symmetrical conflicts of interest in meerkats Animal Behaviour81 1101e1107
Conradt L Krause J Couzin I D amp Roper T J 2009 lsquoLeading according to needrsquoin self-organizing groups The American Naturalist 173 304e312
Couzin IDKrause J JamesRRuxtonGDampFranksNR2002Collectivememoryand spatial sorting in animal groups Journal of Theoretical Biology 218 1e11
Fischhoff I R Sundaresan S R Cordingley J Larkin H M Sellier M-J ampRubenstein D I 2007 Social relationships and reproductive state influenceleadership roles in movements of plains zebra Equus burchellii Animal Behav-iour 73 825e831
Flack A Pettit B Freeman R Guilford T amp Biro D 2012 What are leadersmade of The role of individual experience in determining leaderefollowerrelations in homing pigeons Animal Behaviour 83 703e709
Flack A Freeman R Guilford T amp Biro D 2013 Pairs of pigeons act asbehavioural units during route learning and co-navigational leadership con-flicts The Journal of Experimental Biology 216 1434e1438
Freeman R Mann R Guilford T amp Biro D 2011 Group decisions and individualdifferences route fidelity predicts flight leadership in homing pigeons(Columba livia) Biology Letters 7 63e66
Herbert-Read J E Perna A Mann R P Schaerf T M Sumpter D J T ampWard A J W 2011 Inferring the rules of interaction of shoaling fish Pro-ceedings of the National Academy of Sciences USA 108 18726e18731
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause J ampWard A J W 2013 The role of individuality in collective group movementProceedings of the Royal Society B 280 1752
Jacobs A Sueur C Deneubourg J L amp Petit O 2011 Social network influencesdecision making during collective movements in brown lemurs (Eulemur fulvusfulvus) International Journal of Primatology 32 721e736
Katz Y Tunstroslashm K Ioannou C C Huepe C amp Couzin I D 2011 Inferring thestructure and dynamics of interactions in schooling fish Proceedings of theNational Academy of Sciences USA 108 18720e18725
King A amp Sueur C 2011 Where next Group coordination and collective decisionmaking by primates International Journal of Primatology 32 1245e1267
King A J Douglas C M S Huchard E Isaac N J B amp Cowlishaw G 2008Dominance and affiliation mediate despotism in a social primate CurrentBiology 18 1833e1838
Krause J Bumann D amp Todt D 1992 Relationship between the position pref-erence and nutritional state of individuals in schools of juvenile roach Rutilusrutilus Behavioral Ecology and Sociobiology 30 177e180
Lukeman R Li Y-X amp Edelstein-Keshet L 2010 Inferring individual rules fromcollective behavior Proceedings of the National Academy of Sciences USA 10712576e12580
Lusseau D amp Conradt L 2009 The emergence of unshared consensus decisions inbottlenose dolphins Behavioral Ecology and Sociobiology 63 1067e1077
McComb K Shannon G Durant S M Sayialel K Slotow R Poole J ampMoss C 2011 Leadership in elephants the adaptive value of age Proceedings ofthe Royal Society B 278 3270e3276
Meade J Biro D amp Guilford T 2005 Homing pigeons develop local route ste-reotypy Proceedings of the Royal Society B 272 17e23
A Flack et al Animal Behaviour 86 (2013) 723e732 729
Nagy M Aacutekos Z Biro D amp Vicsek T 2010 Hierarchical group dynamics in pi-geon flocks Nature 464 890e893
Nagy M Vaacutesaacuterhelyi G Pettit B Roberts-Mariani I Vicsek T amp Biro D 2013Context-dependent hierarchies in pigeons Proceedings of the National Acad-emy of Sciences USA 110 13049e13054
Nakayama S Harcourt J L Johnstone R A amp Manica A 2012a Initiativepersonality and leadership in pairs of foraging fish PLoS ONE 7 e36606
Nakayama S Johnstone R A amp Manica A 2012b Temperament and hungerinteract to determine the emergence of leaders in pairs of foraging fish PLoSONE 7 e43747
R Development Core Team 2009 R A Language and Environment for StatisticalComputing Vienna R Foundation for Statistical Computing
Reebs S G 2000 Can a minority of informed leaders determine the foragingmovements of a fish shoal Animal Behaviour 59 403e409
Vicsek T amp Zafeiris A 2012 Collective motion Physics Reports 517 71e140Vicsek T Cziroacutek A Ben-Jacob E Cohen I amp Shochet O 1995 Novel type of
phase transition in a system of self-driven particles Physical Review Letters 751226e1229
Xu X-K Kattas G D amp Small M 2012 Reciprocal relationships in collectiveflights of homing pigeons Physical Review E 85 026120
APPENDIX
GPS Error and its Effect on the Analysis
To test the spatial and temporal error originating from the GPSdevices we performed a variety of tests Ten GPS devices (labelled0e9) were attached to a rigid 3 m long pole with an interdevicedistance of 33 cm We moved the pole along a free path in an openfield using three different orientations (1) with the polersquos orien-tation parallel to the direction of motion (GPS 0 at the front and 9 atthe back Fig A1a) (2) with the pole in a fixed orientation relativeto the field (Fig A1b) and (3) with the polersquos orientation perpen-dicular to the direction of motion (Fig A1c) Each test lasted 10 minand the pole moved between 1 and 3 ms (typical flight speed of apigeon is 18e22 ms)
An important aspect of analysing flock flights is the relativeposition of each device within a pair in relation to the movementdirection of the whole flock This is why we measured the averageforward position of each device (Fig A1def) In both the perpen-dicular and the globally fixed orientation cases we expected anaverage forward position of zero In the parallel case we wouldexpect a forward ratio of 1 for (i lt j) Any deviation from such a
Table A1Results of the sprei vs sposti correlation analysis with and without two outliers
Correlation betweensprei and sposti
Without ou
Untrained ABC r20[072 PUntrained group A r6[080 P[Untrained group B r6[087 P[Untrained group C r6frac14069 Pfrac14Trained ABC r7frac14008 P
Values in bold indicate significant correlations
value is due to noise which is lower at small interdevice distancesWe show the probability density function of this measure inFig A1gei We also measured the time a device was detected to bein front relative to the direction of motion and calculated the timeratio for the 10 min test (Fig A1jel) We also performed directionalcorrelation delay analyses for all devices (Fig A1meo) The absoluteerror of the GPS device arises from the relative error of the velocitywhich decreases as speed increases Hence our tests give an upperapproximation of the noise as each test lasted only 10 min and thepole was moved at low speeds
Additional Test of Hierarchy Robustness
We used a linear mixed-effects model to test the robustness ofthe hierarchies using as our data set the s values calculated for eachindividual in every flight of phases I and III All data were analysedusing R (R Development Core Team 2009) and the R packages lme4(Bates amp Maechler 2009) and languageR (Baayen 2008 2009) Weincluded Subject as a random effect As fixed effects we addedTraining Phase (Phase I pretraining or Phase III post-training) andTreatment Group (trained or untrained individuals) to themodel aswell as the interaction term between them
We verified that the normality of error and homogeneity ofvariance assumptions of parametric analysis were satisfied by vi-sual inspection of plots of residuals against fitted values To assessthe validity of the mixed-effects analysis we performed likelihoodratio tests comparing the model with fixed effects to the null modelwith only the random effect The model that included fixed effectsdid not differ significantly from the null model (P frac14 0222) andhence fulfilled the validation test The following P values werebased on Markov chain Monte Carlo sampling We found no sig-nificant differences between pre- and post-training s values(PMCMC frac14 0656) or trained and untrained individuals(PMCMC frac14 0203) The interaction between Training Phase andTreatment Group was not significant (PMCMC frac14 0321) Togetherthese results further confirm that the solo training had no effect onthe groupsrsquo hierarchies
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Methods
Subjects and Experimental Procedure
GPS Device and Data Handling
Data Analysis
Results
Discussion
Acknowledgments
References
Appendix
GPS Error and its Effect on the Analysis
Additional Test of Hierarchy Robustness
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash04 ndash02 0 02 04ndash04
ndash02
0
02
04
ndash03 0 03ndash03
0
03(a) (c)(b)
τi Pretraining (s) τiUjU Pretraining (s)
τ iTj U P
ost-
trai
nin
g (s
)
τ iU
j U P
ost-
trai
nin
g (s
)
τ i P
ost
-tra
inin
g (s
)
τiTjUPretraining (s)
Figure 3 Relationship between s before and after individual training flights (mean SEM) (a) sposti as a function of sprei for solo-trained (orange circles) and untrained individuals(light grey circles) (b c) Averaged sij after individual training as a function of averaged sij before individual training for (b) untrainedeuntrained pairings and (c) trainedeuntrainedpairings
A Flack et al Animal Behaviour 86 (2013) 723e732728
collective movements diminishes with increasing group sizeInvestigating the potential link between group size and group dy-namics both empirically and theoretically is a promising avenuefor future research
Although flock dynamics can be observed without hierarchicalorganization (Xu et al 2012) hierarchical structure might bebeneficial for establishing a lsquoflight routinersquo that demands lessattention from group members The fact that hierarchies seemresistant to small changes once they are established indicates thatrather than benefitting from particular features of the leader (suchas navigational experience) their advantage might lie in the sta-bility of the structure itself Robust social structures may enhanceinformation transfer among group members thereby increasingthe accuracy of group-level decisions (Lusseau amp Conradt 2009McComb et al 2011) Recent theoretical work has found that un-derlying social structures can improve the navigational accuracy oflarge leaderless groups (Bode et al 2012) Furthermore it is sug-gested that hierarchical group dynamics could be based purely onsocial preferences (Bode et al 2011) This is in agreement with whathas been described for various species of group-living primatesKing amp Sueur (2011) suggested that leaderefollower dynamics areembedded in interindividual relationships which may result inmore efficient decision making and coordination among groupmembers Social relationships can be found between relativesfamiliar conspecifics or individuals of similar attributes such as sizepersonality or sex Hence the stability in our hierarchical networksmay arise from preferential attachments that may have developedduring early training and that may not be susceptible to changes inindividualsrsquo navigational experience
Acknowledgments
AF was supported by Microsoft Research Cambridge MN wassupported by a Royal Society Newton International Fellowship andby Somerville College Oxford DB was supported by a Royal So-ciety University Research Fellowship This work was partly sup-ported by the EU ERC COLLMOT project (grant no 227878) Wethank Benjamin Pettit for technical assistance with the GPS testsand statistical advice We are also grateful to Andrew King andthree anonymous referees for helpful comments on themanuscript
References
Baayen R H 2008 Analyzing Linguistic Data A Practical Introduction to StatisticsUsing R Cambridge Cambridge University Press
Baayen R H 2009 languageR data sets and functions with lsquoAnalyzing LinguisticData A practical introduction to statisticsrsquo R package version 0955 cranr-projectorgwebpackageslanguageRlanguageRpdf
Ballerini M Cabibbo N Candelier R Cavagna A Cisbani E Giardina ILecomte V Orlandi A Parisi G Procaccini A et al 2008 Interaction rulinganimal collective behavior depends on topological rather than metric distanceevidence from a field study Proceedings of the National Academy of SciencesUSA 105 1232e1237
Bates D amp Maechler M 2009 Package lsquolme4rsquo(Version 0999375-32) linear mixed-effects models using S4 classes cran r-project orgwebpackageslme4lme4pdf
Bode N W F Wood A J amp Franks D W 2011 The impact of social networks onanimal collective motion Animal Behaviour 82 29e38
Bode N W F Wood J A amp Franks D W 2012 Social networks improve lead-erless group navigation by facilitating long-distance communication CurrentZoology 58 329e341
Bousquet C A H amp Manser M B 2011 Resolution of experimentallyinduced symmetrical conflicts of interest in meerkats Animal Behaviour81 1101e1107
Conradt L Krause J Couzin I D amp Roper T J 2009 lsquoLeading according to needrsquoin self-organizing groups The American Naturalist 173 304e312
Couzin IDKrause J JamesRRuxtonGDampFranksNR2002Collectivememoryand spatial sorting in animal groups Journal of Theoretical Biology 218 1e11
Fischhoff I R Sundaresan S R Cordingley J Larkin H M Sellier M-J ampRubenstein D I 2007 Social relationships and reproductive state influenceleadership roles in movements of plains zebra Equus burchellii Animal Behav-iour 73 825e831
Flack A Pettit B Freeman R Guilford T amp Biro D 2012 What are leadersmade of The role of individual experience in determining leaderefollowerrelations in homing pigeons Animal Behaviour 83 703e709
Flack A Freeman R Guilford T amp Biro D 2013 Pairs of pigeons act asbehavioural units during route learning and co-navigational leadership con-flicts The Journal of Experimental Biology 216 1434e1438
Freeman R Mann R Guilford T amp Biro D 2011 Group decisions and individualdifferences route fidelity predicts flight leadership in homing pigeons(Columba livia) Biology Letters 7 63e66
Herbert-Read J E Perna A Mann R P Schaerf T M Sumpter D J T ampWard A J W 2011 Inferring the rules of interaction of shoaling fish Pro-ceedings of the National Academy of Sciences USA 108 18726e18731
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause J ampWard A J W 2013 The role of individuality in collective group movementProceedings of the Royal Society B 280 1752
Jacobs A Sueur C Deneubourg J L amp Petit O 2011 Social network influencesdecision making during collective movements in brown lemurs (Eulemur fulvusfulvus) International Journal of Primatology 32 721e736
Katz Y Tunstroslashm K Ioannou C C Huepe C amp Couzin I D 2011 Inferring thestructure and dynamics of interactions in schooling fish Proceedings of theNational Academy of Sciences USA 108 18720e18725
King A amp Sueur C 2011 Where next Group coordination and collective decisionmaking by primates International Journal of Primatology 32 1245e1267
King A J Douglas C M S Huchard E Isaac N J B amp Cowlishaw G 2008Dominance and affiliation mediate despotism in a social primate CurrentBiology 18 1833e1838
Krause J Bumann D amp Todt D 1992 Relationship between the position pref-erence and nutritional state of individuals in schools of juvenile roach Rutilusrutilus Behavioral Ecology and Sociobiology 30 177e180
Lukeman R Li Y-X amp Edelstein-Keshet L 2010 Inferring individual rules fromcollective behavior Proceedings of the National Academy of Sciences USA 10712576e12580
Lusseau D amp Conradt L 2009 The emergence of unshared consensus decisions inbottlenose dolphins Behavioral Ecology and Sociobiology 63 1067e1077
McComb K Shannon G Durant S M Sayialel K Slotow R Poole J ampMoss C 2011 Leadership in elephants the adaptive value of age Proceedings ofthe Royal Society B 278 3270e3276
Meade J Biro D amp Guilford T 2005 Homing pigeons develop local route ste-reotypy Proceedings of the Royal Society B 272 17e23
A Flack et al Animal Behaviour 86 (2013) 723e732 729
Nagy M Aacutekos Z Biro D amp Vicsek T 2010 Hierarchical group dynamics in pi-geon flocks Nature 464 890e893
Nagy M Vaacutesaacuterhelyi G Pettit B Roberts-Mariani I Vicsek T amp Biro D 2013Context-dependent hierarchies in pigeons Proceedings of the National Acad-emy of Sciences USA 110 13049e13054
Nakayama S Harcourt J L Johnstone R A amp Manica A 2012a Initiativepersonality and leadership in pairs of foraging fish PLoS ONE 7 e36606
Nakayama S Johnstone R A amp Manica A 2012b Temperament and hungerinteract to determine the emergence of leaders in pairs of foraging fish PLoSONE 7 e43747
R Development Core Team 2009 R A Language and Environment for StatisticalComputing Vienna R Foundation for Statistical Computing
Reebs S G 2000 Can a minority of informed leaders determine the foragingmovements of a fish shoal Animal Behaviour 59 403e409
Vicsek T amp Zafeiris A 2012 Collective motion Physics Reports 517 71e140Vicsek T Cziroacutek A Ben-Jacob E Cohen I amp Shochet O 1995 Novel type of
phase transition in a system of self-driven particles Physical Review Letters 751226e1229
Xu X-K Kattas G D amp Small M 2012 Reciprocal relationships in collectiveflights of homing pigeons Physical Review E 85 026120
APPENDIX
GPS Error and its Effect on the Analysis
To test the spatial and temporal error originating from the GPSdevices we performed a variety of tests Ten GPS devices (labelled0e9) were attached to a rigid 3 m long pole with an interdevicedistance of 33 cm We moved the pole along a free path in an openfield using three different orientations (1) with the polersquos orien-tation parallel to the direction of motion (GPS 0 at the front and 9 atthe back Fig A1a) (2) with the pole in a fixed orientation relativeto the field (Fig A1b) and (3) with the polersquos orientation perpen-dicular to the direction of motion (Fig A1c) Each test lasted 10 minand the pole moved between 1 and 3 ms (typical flight speed of apigeon is 18e22 ms)
An important aspect of analysing flock flights is the relativeposition of each device within a pair in relation to the movementdirection of the whole flock This is why we measured the averageforward position of each device (Fig A1def) In both the perpen-dicular and the globally fixed orientation cases we expected anaverage forward position of zero In the parallel case we wouldexpect a forward ratio of 1 for (i lt j) Any deviation from such a
Table A1Results of the sprei vs sposti correlation analysis with and without two outliers
Correlation betweensprei and sposti
Without ou
Untrained ABC r20[072 PUntrained group A r6[080 P[Untrained group B r6[087 P[Untrained group C r6frac14069 Pfrac14Trained ABC r7frac14008 P
Values in bold indicate significant correlations
value is due to noise which is lower at small interdevice distancesWe show the probability density function of this measure inFig A1gei We also measured the time a device was detected to bein front relative to the direction of motion and calculated the timeratio for the 10 min test (Fig A1jel) We also performed directionalcorrelation delay analyses for all devices (Fig A1meo) The absoluteerror of the GPS device arises from the relative error of the velocitywhich decreases as speed increases Hence our tests give an upperapproximation of the noise as each test lasted only 10 min and thepole was moved at low speeds
Additional Test of Hierarchy Robustness
We used a linear mixed-effects model to test the robustness ofthe hierarchies using as our data set the s values calculated for eachindividual in every flight of phases I and III All data were analysedusing R (R Development Core Team 2009) and the R packages lme4(Bates amp Maechler 2009) and languageR (Baayen 2008 2009) Weincluded Subject as a random effect As fixed effects we addedTraining Phase (Phase I pretraining or Phase III post-training) andTreatment Group (trained or untrained individuals) to themodel aswell as the interaction term between them
We verified that the normality of error and homogeneity ofvariance assumptions of parametric analysis were satisfied by vi-sual inspection of plots of residuals against fitted values To assessthe validity of the mixed-effects analysis we performed likelihoodratio tests comparing the model with fixed effects to the null modelwith only the random effect The model that included fixed effectsdid not differ significantly from the null model (P frac14 0222) andhence fulfilled the validation test The following P values werebased on Markov chain Monte Carlo sampling We found no sig-nificant differences between pre- and post-training s values(PMCMC frac14 0656) or trained and untrained individuals(PMCMC frac14 0203) The interaction between Training Phase andTreatment Group was not significant (PMCMC frac14 0321) Togetherthese results further confirm that the solo training had no effect onthe groupsrsquo hierarchies
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Methods
Subjects and Experimental Procedure
GPS Device and Data Handling
Data Analysis
Results
Discussion
Acknowledgments
References
Appendix
GPS Error and its Effect on the Analysis
Additional Test of Hierarchy Robustness
A Flack et al Animal Behaviour 86 (2013) 723e732 729
Nagy M Aacutekos Z Biro D amp Vicsek T 2010 Hierarchical group dynamics in pi-geon flocks Nature 464 890e893
Nagy M Vaacutesaacuterhelyi G Pettit B Roberts-Mariani I Vicsek T amp Biro D 2013Context-dependent hierarchies in pigeons Proceedings of the National Acad-emy of Sciences USA 110 13049e13054
Nakayama S Harcourt J L Johnstone R A amp Manica A 2012a Initiativepersonality and leadership in pairs of foraging fish PLoS ONE 7 e36606
Nakayama S Johnstone R A amp Manica A 2012b Temperament and hungerinteract to determine the emergence of leaders in pairs of foraging fish PLoSONE 7 e43747
R Development Core Team 2009 R A Language and Environment for StatisticalComputing Vienna R Foundation for Statistical Computing
Reebs S G 2000 Can a minority of informed leaders determine the foragingmovements of a fish shoal Animal Behaviour 59 403e409
Vicsek T amp Zafeiris A 2012 Collective motion Physics Reports 517 71e140Vicsek T Cziroacutek A Ben-Jacob E Cohen I amp Shochet O 1995 Novel type of
phase transition in a system of self-driven particles Physical Review Letters 751226e1229
Xu X-K Kattas G D amp Small M 2012 Reciprocal relationships in collectiveflights of homing pigeons Physical Review E 85 026120
APPENDIX
GPS Error and its Effect on the Analysis
To test the spatial and temporal error originating from the GPSdevices we performed a variety of tests Ten GPS devices (labelled0e9) were attached to a rigid 3 m long pole with an interdevicedistance of 33 cm We moved the pole along a free path in an openfield using three different orientations (1) with the polersquos orien-tation parallel to the direction of motion (GPS 0 at the front and 9 atthe back Fig A1a) (2) with the pole in a fixed orientation relativeto the field (Fig A1b) and (3) with the polersquos orientation perpen-dicular to the direction of motion (Fig A1c) Each test lasted 10 minand the pole moved between 1 and 3 ms (typical flight speed of apigeon is 18e22 ms)
An important aspect of analysing flock flights is the relativeposition of each device within a pair in relation to the movementdirection of the whole flock This is why we measured the averageforward position of each device (Fig A1def) In both the perpen-dicular and the globally fixed orientation cases we expected anaverage forward position of zero In the parallel case we wouldexpect a forward ratio of 1 for (i lt j) Any deviation from such a
Table A1Results of the sprei vs sposti correlation analysis with and without two outliers
Correlation betweensprei and sposti
Without ou
Untrained ABC r20[072 PUntrained group A r6[080 P[Untrained group B r6[087 P[Untrained group C r6frac14069 Pfrac14Trained ABC r7frac14008 P
Values in bold indicate significant correlations
value is due to noise which is lower at small interdevice distancesWe show the probability density function of this measure inFig A1gei We also measured the time a device was detected to bein front relative to the direction of motion and calculated the timeratio for the 10 min test (Fig A1jel) We also performed directionalcorrelation delay analyses for all devices (Fig A1meo) The absoluteerror of the GPS device arises from the relative error of the velocitywhich decreases as speed increases Hence our tests give an upperapproximation of the noise as each test lasted only 10 min and thepole was moved at low speeds
Additional Test of Hierarchy Robustness
We used a linear mixed-effects model to test the robustness ofthe hierarchies using as our data set the s values calculated for eachindividual in every flight of phases I and III All data were analysedusing R (R Development Core Team 2009) and the R packages lme4(Bates amp Maechler 2009) and languageR (Baayen 2008 2009) Weincluded Subject as a random effect As fixed effects we addedTraining Phase (Phase I pretraining or Phase III post-training) andTreatment Group (trained or untrained individuals) to themodel aswell as the interaction term between them
We verified that the normality of error and homogeneity ofvariance assumptions of parametric analysis were satisfied by vi-sual inspection of plots of residuals against fitted values To assessthe validity of the mixed-effects analysis we performed likelihoodratio tests comparing the model with fixed effects to the null modelwith only the random effect The model that included fixed effectsdid not differ significantly from the null model (P frac14 0222) andhence fulfilled the validation test The following P values werebased on Markov chain Monte Carlo sampling We found no sig-nificant differences between pre- and post-training s values(PMCMC frac14 0656) or trained and untrained individuals(PMCMC frac14 0203) The interaction between Training Phase andTreatment Group was not significant (PMCMC frac14 0321) Togetherthese results further confirm that the solo training had no effect onthe groupsrsquo hierarchies
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Figure A2 Histogram illustrating the frequency distribution of distances (bin frac14 1 m) to the first nearest neighbour of all three groups and flock flights (before and after solotraining) pooled Inset shows probability density functions of distances (bin frac14 025 m) to the first second third and fourth nearest neighbours in groups A B and C in red solidgreen dashed and blue dotted lines respectively (data shown only up to the fourth nearest neighbours for better visibility)
Figure A1 Spatial and temporal error of the GPS trajectories and the directional correlation delay method for parallel globally fixed and perpendicular orientation tests The pole(illustrated as coloured lines) was moved along a path (black line) in (a) parallel (b) globally fixed and (c) perpendicular orientation relative to the movement direction (def)Relative position of each device in a pair relative to the direction of motion as a function of its actual position (d) shows only one value of each pair (i lt j) (e) and (f) show bothvalues (gei) Probability density function (PDF) of the measured forward position of graphs (def) (g) The deviation between measured and actual position for each pair (jel)Forward ratio defined as the time ratio a device was detected to be at front relative to the motion direction (j) shows only one value of each pair (i lt j) (k) and (l) show both values(meo) Directional correlation function (Cij(s)) between GPS 0 and all other devices (per) The directional correlation delay time (sij) of each pair
A Flack et al Animal Behaviour 86 (2013) 723e732 731
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
Methods
Subjects and Experimental Procedure
GPS Device and Data Handling
Data Analysis
Results
Discussion
Acknowledgments
References
Appendix
GPS Error and its Effect on the Analysis
Additional Test of Hierarchy Robustness
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
Cij(τ
ij)
ndash2 ndash1 0 1 208
085
09
095
1
τi (s)
ndash2 ndash1 0 1 208
085
09
095
1(a) (b)
(c) (d)
Figure A3 Scatter plot of the relationship between an individualrsquos CijethsijTHORN value and si for groups (a) A (b) B and (c) C for each flight Red circles in (b) indicate si outliers with lowcorrelation values (d) The recalculated CijethsijTHORN si value pairs for group B after excluding these two outliers
A Flack et al Animal Behaviour 86 (2013) 723e732732
Robustness of flight leadership relations in pigeons
