Supplementry Figure y (m) x (m) prllel perpendiculr Distnce (m) Bird Stndrd devition for distnce (m) c 6 prllel perpendiculr 4 doi:.8/nture99 SUPPLEMENTARY FIGURE Confirmtion tht movement within the flock is not result of potentil logger mesurement error. The red circles () represent the positions of the irds, for ll irds nd ll times, with respect to the flock centroid. From this, the shortest distnce (red lines) to the 4 degree line (lue line) ws clculted nd the position ws projected on the 4 degree line, nd then the distnce etween projected position nd green dot (the centroid) ws clculted (). The stndrd devitions (SD) re from the lue perpendiculr line rther thn the solute distnce, nd represent how much the position vries with respect to the line. A men SD ws then clculted for ech perpendiculr/prllel reltionship (,c). The positioning of ll individuls vries more long the line thn out from the line (c). If the chnges in position were logger mesurement error lone, the vrition in perpendiculr nd prllel distnce nd position would e expected to e equl. Insted, there is greter vriility long the 4 line, indicting pprent motions within the V formtion where not merely logger error rtefct. Bird W W W. N A T U R E. C O M / N A T U R E
RESEARCH In sptil phse; wingpths mtch φ sptil In sptil phse; wingpths mtch Sptil ntiphse φ sptil Sptil ntiphse SUPPLEMENTARY FIGURE Medin sptil phse ounded y 9% confidence intervls (grey shding) for flying in the most populted m squre (V formtion,, n=6 ird-ird pirs) or in. m region directly ehind for 4 m stremwise (, n=6 ird-ird pirs). Temporl phse of following ird - - - 4 Distnce ehind focl ird (m) Temporl phse of following ird - - - 4 Distnce ehind focl ird (m) SUPPLEMENTARY FIGURE Alterntive representtion of Fig. plots in Crtesin coordintes. The lck line indictes the predicted temporl phse (directly upwrd eing in phse - flpping t the sme time) s function of distnce from reltive hed ird (indicted y rdil distnce). The temporl phse is predicted from ) the medin sptil phse t the most populted m x m region (V formtion, ) or the region directly ehind ech hed ird (. m cross, 4 m ehind, ), nd ) the men mesured wvelength etween irds for. m x. m re long trnsect in line with the most populted region () or directly stremwise, nose-to-til (). Medin mesured vlues for ech re within ech trnsect (grey dots; grey curves denote 9% confidence intervls of the medin) rodly mtch prediction up to 4 m etween irds. WWW.NATURE.COM/NATURE
Supplementry Figure 4 RESEARCH Temporl phse of following ird - - - Idel wingpth mtch (zero sptil phse) 4 6 8 Distnce ehind focl ird (m) N Bird-Bird pirs 4 8 6 4 4 6 8 N Flp-Flp interctions Distnce ehind focl ird (m) Temporl phse of following ird - - - Idel wingpth mismtch (+/- π sptil phse) 4 6 8 Distnce ehind focl ird (m) N Bird-Bird pirs 4 8 6 4 4 6 8 N Flp-Flp interctions Distnce ehind focl ird (m) SUPPLEMENTARY FIGURE 4 Phse dt s for Fig. nd Supplementry Fig., ut for n extended stremwise rnge, lso indicting the numer of ird-ird pirs of flp-flp interctions hs histogrms, either in line with the V fvoured position (), or directly stremwise, nose-to-til (). Note tht the WWW.NATURE.COM/NATURE
RESEARCH stremwise rnge, lso indicting the numer of ird-ird pirs of flp-flp interctions hs histogrms, either in line with the V fvoured position (), or directly stremwise, nose-to-til (). Note tht the underlying (grey) line is not the sme s shown (lck line) in Fig. nd Supplementry Fig.. In this cse, it shows the phse predicted to e optiml through theoreticl, supported y numericl modelling. Mximum enefit would e chieved in line with the V fvoured position if the following ird wings exctly followed the triling wingtip vortices nd so, pproximtely, the wingtip pth of the ird hed; the wings should e in sptil phse, or in temporl phse every whole-integer wvelength ehind the ird hed. Minimum detriment due to downwsh for ird flying directly ehind nother if the wingpths were out of phse; the wings should flp in temporl ntiphse every whole-integer wvelength ehind the ird hed. Distnce (km) 8 6 4 4 Distnce (km) Speed (m/s) Flp frequency (Hz) c 6 4 SUPPLEMENTARY FIGURE Three pnelled figure focusing on 4 minutes of one migrtory flight for the 4 Northern ld iises, detiling: () GPS trce of the 4 irds, the close proximity of the individuls precluding the identifiction of single trces. An exmple of single flight trce, imposed over Google Erth TM (Lndst), cn e seen in Supplementry Photo s KML file. Further detils cn e found in Supplementry Fig. 6. () verge speed (± SD) nd, (c) verge flp frequency (± SD). The shded grey re refers to the 7 minute section of cler V formtion flight used for susequent nlysis (see Fig., nd Supplementry Fig. 6). 4 WWW.NATURE.COM/NATURE
RESEARCH Distnce (km).8.6.4..... 4 4. Distnce (km) Speed (m/s) Flp frequency (Hz) c 6 4 4 Verticl ccelertion (m/s ) Verticl ccelertion (m/s ) 4 d - - - -4 4 e originl filtered - -.... 4 4. SUPPLEMENTARY FIGURE 6 Highlight of the grey shded re in Supplementry Fig., highlighting WWW.NATURE.COM/NATURE
Durtion (s) RESEARCH the 7 minute V formtion section of migrtory flight for the 4 Northern ld iises, detiling: () GPS trce of the 4 irds. An exmple of single flight trce, imposed over Google Erth TM (Lndst), cn e seen in Supplementry Photo s KML file. The lue line represents the pth of the prplne contining the foster prent. () verge speed (± SD) nd (c) verge flp frequency (± SD). (d) exmple dorsl ccelertion trce tken from the Hz Inertil Mesurement Unit. The lck ox positioned t s refers to the zoomed in section displyed in (e), which demonstrtes how ech flp ws detected vi our pek detect nlysis (see Supplementry Methods). The red line denotes the rw trce, nd the lue line the filtered dt. The circles highlight position of identified peks. Distnce to centroid (m) Distnce to centroid (m) SUPPLEMENTARY FIGURE 7 Loction histogrm of the 7 minute flight section, showing position of individul iis within the V formtion, mesured vi Hz GPS dt logger. The grey scle refers to the durtion (s) ird ws present in ech. m x. m grid. The outer red line denotes the flock shpe for the entire 4 minutes durtion of the flight, superimposed round the 7 minute section (See Fig. ). The red line encloses 9% of ville dt points. 6 WWW.NATURE.COM/NATURE
RESEARCH SUPPLEMENTARY FIGURE 8 Photogrph (T. Huel) of Northern ld iis, showing dt logger ttchment vi Velcro TM fstening to plte, which in turn is ttched to hrness. WWW.NATURE.COM/NATURE 7
RESEARCH SUPPLEMENTARY TABLE. P Vlue Averge Phse Lower 9% CI Upper 9% CI Temporl V Fvoured Ryleigh test (men).8.87.9.9 Hodges-Ajne. - - - Medin -.78 -.44.86 Sptil V Fvoured Ryleigh test (men). -. -.77 -.4 Hodges-Ajne.4 - - - Medin - -.7 -.79. Temporl Stremwise Ryleigh test (men). -.97 -.67 -.878 Hodges-Ajne.6 - - - Medin - -.74 -. -.49 Sptil Stremwise Ryleigh test (men).494 -.9 - - Hodges-Ajne. - - - Medin - -.897-4.49 -.4 Sttisticl prmeters nd summry for circulr sttisticl nlysis of wing-et phsing (see Supplementry Informtion Text). P <. indictes significnt directionl preference. When flying in fvoured V position, irds exhiit significnt temporl nd sptil phsing of their wing-ets, which is sent when in stremwise position. For the fvoured V position, 6 ird-ird pirs were nlysed, which incorported 86 flp-flp interctions. For the stremwise position, 6 ird-ird pirs were nlysed, incorporting flp-flp interctions. 8 WWW.NATURE.COM/NATURE