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Hummingbird maneuvering performance : aerodynamic mechanisms and physiological constraints Segre, Paolo S. 2015

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HUMMINGBIRD MANEUVERING PERFORMANCE: AERODYNAMIC MECHANISMS AND PHYSIOLOGICAL CONSTRAINTS byPaolo S. SegreB.S., University of Illinois, 2003M.S., University of Montana, 2006A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Zoology)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2015© Paolo S. Segre, 2015A?᠙?ᬜ?The ability of a bird to ?aneuver in flight can deter?ine its success at avoiding 㘌edators,  catching 㘌ey, and other critical behaviors. Highly ?aneuverable ani?als, such as hu??ingbirds, are ca㘄ble of diverse behaviors but it is un㜐o?n ho? their ?aneuvering is constrained by ?ing ?otion, ?ing ?or㘪ology, and ?uscle ca?acity. The 㘬r㘅se of this dissertation ?as to deter?ine? 1) if hu??ingbird ?ings create inde㘊ndent ?a㜊s? 2) if inde?endent ?ingbeat 㜑ne?atics are used to control ?aneuvers? and 3) ho? ?aneuverability is li?ited by intrinsic features, such as ?ing ?or㘪ology, body ?ass, and 㘪ysical 㘌o㘊rties of the  air, versus facultative ca㘄city, such as ?uscle 㘅?er. The goal of cha㘔er t?o ?as to deter?ine if hu??ingbirds 㘌oduce single or bilateral vorte㬇?a㜊s using flo? visuali?ation. The goal of cha?ter three ?as to deter?ine if sustained ?aneuvers can be controlled by orienting the ?ings inde?endently of the body. I tested this hy㘅thesis by fil?ing the three di?ensional 㜑ne?atics of a hu??ingbird feeding fro? a translating feeder. The goal of cha㘔er four ?as to deter?ine if the ability to 㘊rfor? voluntary ?aneuvers ?as associated ?ith intrinsic or facultative features. I addressed this 㴬estion using a trac㜑ng syste? to record a large data set of voluntary flight tra?ectories, ?ith inde㘊ndent ?easure?ents of individual ?or㘪ology and ?a㬑?u? ?uscle ca?acity. The goal of cha㘔er five ?as to deter?ine if ?aneuvering 㘊rfor?ance declines ?ith increasing elevation and, if so, ?hether changes in o㬂gen availability or air density are ?ost res㘅nsible. I addressed these 㴬estions by ?easuring ?aneuvering 㘊rfor?ance across elevation and in an airtight cha?ber ?ith gas ?ani㘬lations. Collectively, ?y results indicate that hu??ingbirds have ?ings that o㘊rate ?ith a high degree of inde㘊ndence and that this feature influences their 㘌ecision and control. Voluntary ?aneuvers at lo? elevation are 㘌i?arily  iiinfluenced by facultative ca㘄city, s㘊cifically burst 㘅?er, and to a lesser e㬔ent by intrinsic li?its, s㘊cifically ?ing as㘊ct ratio. At higher elevations, ?aneuvering 㘊rfor?ance declines due to decreases in air density. This research de?onstrates that the re?ar㜄ble ?aneuverability of hu??ingbirds derives fro? their ability to control their ?ings inde㘊ndently and fro? high ?uscle 㘅?er reserves for generating aerodyna?ic force.iiiP???ᬜ?This doctoral dissertation is a collection of four studies that e㬶lore different as㘊cts of hu??ingbird ?aneuvering 㘊rfor?ance. I develo㘊d the central 㴬estions of these studies ?ith the hel㘇and su㘊rvision of Dr. Doug Altshuler, and I too㜇the lead in conducting the e㬶eri?ents, analy?ing the data, and ?riting the ?anuscri?ts.A version of cha㘔er t?o ?as 㘬blished in the ?ournal Experiments in Fluids (Pournazeri et al., 2012). The idea for this 㘌o?ect ?as develo㘊d ?ointly by all four authors. S. Pourna?eri and I develo㘊d the ?ethods, collected and analy?ed the data, and are co㼕irst authors on the 㘄㘊r. D.L. Altshuler and I ?rote the ?a?ority of the ?anuscri㘔. The flo? visuali?ation data ?as  su㘶le?ented ?ith 㜑ne?atic data e㬔racted fro? unanaly?ed videos of hovering hu??ingbirds ta?en by D.L. Altshuler bet?een 2003㼗006. I develo㘊d the co?㘬tational fra?e?or㜇that ?ade the e㬔raction of the 㜑ne?atic ?easure?ents 㘅ssible. This fra?e?or㜇?as additionally used in Altshuler et al. (2012), Read (2015), and cha㘔er three of this dissertation.I ?as the lead investigator for the study described in cha㘔er three. A subset of the data ca?e fro? videos collected by D.L. Altshuler ?ith the intent of ans?ering a different set of 㴬estions. I develo㘊d the central 㴬estion in cha㘔er three, re?㘬r㘅sed the videos, and develo㘊d the co?㘬tational fra?e?or㜇that ?ade the 㜑ne?atic analysis 㘅ssible. D.L. Altshuler advised during the analysis and the ?riting.  The statistical analysis ?as develo㘊d by ?.M. Middleton in a 㘌evious study (Altshuler et al., 2012). I ?as the lead investigator for the studies in cha?ters four and five. I designed the e㬶eri?ents ?ith the hel㘇of D.L. Altshuler, and conducted the? ?yself. The e㬶eri?ents ?ere based on videos fil?ed ?ith an auto?ated trac㜑ng syste? designed and 㘌ogra??ed by A.D. ivStra? for use ?ith fruit flies (Stra? et al., 2011) . I built the hard?are syste? and ?odified the soft?are to ?a㜊 it suitable for use ?ith hu??ingbirds. R.L. Da㜑n designed the statistical fra?e?or㜇used, and T.L. Reed hel㘊d ?ith the data collection and the techni㴬es used for the gas substitution 㘄rt of the study.     The 㘌ocedures used for this e㬶eri?ent ?ere a㘶roved by the UBC Ani?al Care Co??ittee (certificate 䄄10㼘223).vT???? „ ?‡???? ?Abstract............................................................................................................................................iiPreface............................................................................................................................................ivTable of contents.............................................................................................................................viList of tables....................................................................................................................................i?List of figures...................................................................................................................................?List of su㘶le?entary videos .........................................................................................................㬑iList of sy?bols and abbreviations ................................................................................................㬑iiAc㜐o?ledge?ents .......................................................................................................................㬒iDedication...................................................................................................................................㬒iii1. Introduction..................................................................................................................................11.1 Aerodyna?ics ........................................................................................................................21.2 Measure?ents of aerodyna?ic forces ...................................................................................31.3 Modulating aerodyna?ic force .............................................................................................61.䈇Redirecting aerodyna?ic forces ............................................................................................?1.5 I?㘆e?entation of s㘊cific ?aneuvers ................................................................................. ?1.6 Free㼕light ?aneuvering 㘊rfor?ance .................................................................................101.䐇Hu??ingbirds as a ?odel for studying ?aneuvering 㘊rfor?ance ...................................121.䔇Conclusions .........................................................................................................................132. Hu??ingbirds generate bilateral vorte? loo㘓 during hovering? evidence fro? flo? visuali?ation1 .................................................................................................................................152.1 Introduction.........................................................................................................................152.2 Methods...............................................................................................................................1?2.2.1 Ani?als ........................................................................................................................1?2.2.2 Flo? visuali?ation .......................................................................................................1?2.2.3 ?ingbeat 㜑ne?atics ...................................................................................................1?vi2.2.䈇Vorte? ter?inology ......................................................................................................202.3 Results.................................................................................................................................222.3.1 Flo? visuali?ation .......................................................................................................222.3.2 ?ine?atics e㬶eri?ent ................................................................................................2?2.3.3 ?a?e 㘄ttern ................................................................................................................252.䈇Discussion ...........................................................................................................................262.䈉1 Flo? visuali?ation .......................................................................................................262.䈉2 ?ingbeat 㜑ne?atics ...................................................................................................2?3. Ban㜑ng right to fly left? controlled lateral flight of hu??ingbirds2 ........................................3?3.1 Introduction.........................................................................................................................3?3.2 Methods...............................................................................................................................䈲3.2.1 Ani?als ........................................................................................................................䈲3.2.3 Fra?e of reference and 㜑ne?atic variables ................................................................䈙3.2.䈇Quasi㼓teady state analysis ..........................................................................................䈳3.2.5 Electro?yogra㘪y ....................................................................................................... 䉄3.2.6 Statistical analysis.......................................................................................................䉅3.3 Results.................................................................................................................................503.3.1 ?ingbeat 㜑ne?atics of controlled lateral flight .........................................................503.3.2 Quasi㼓teady State analysis .........................................................................................533.3.3 Motor activation............................................................................................................................................................................................................................................................553.䈇Discussion ...........................................................................................................................56䈉 Burst ?uscle 㘊rfor?ance 㘌edicts the s㘊ed, acceleration, and turning 㘊rfor?ance of hu??ingbirds ................................................................................................................................䐳䈉1 Introduction .........................................................................................................................䐳䈉2 Methods ...............................................................................................................................䑅䈉2.1 Ani?als and e㬶eri?ental trials ..................................................................................䑅䈉2.2 Trac㜑ng syste? ...........................................................................................................䑃䈉2.3 Maneuvering 㘊rfor?ance ?etrics ..............................................................................䔘䈉2.䈇Statistical analysis .......................................................................................................䕂䈉3 Results .................................................................................................................................䕄vii䈉3.1 Re㘊atability of 㘊rfor?ance ......................................................................................䕄䈉3.2 Perfor?ance in relation to burst ?uscle ca?acity ........................................................䕄䈉3.3 Perfor?ance in relation to ?or㘪ology .......................................................................䕅䈉3.䈇Effect of co??etitor on 㘊rfor?ance ...........................................................................䕅䈉䈇Discussion ........................................................................................................................... 䕃5. Mechanical constraints on burst 㘅?er reserves decrease ?aneuvering 㘊rfor?ance in hu??ingbirds ..............................................................................................................................10?5.1 Introduction.......................................................................................................................10?5.2 Materials and ?ethods ......................................................................................................1065.2.1 Trac㜑ng syste? .........................................................................................................10?5.2.2 Translocation e㬶eri?ent ..........................................................................................10?5.2.3 Gas substitution e㬶eri?ent ......................................................................................10?5.2.䈇Statistical analysis .....................................................................................................10?5.3 Results......................................................................................................................................................................................................................................................................................1115.䈇Discussion .........................................................................................................................1126. Conclusions..............................................................................................................................1216.1 Bilateral ?a㜊 structures ...................................................................................................1216.2 Constrained ?aneuvers .....................................................................................................1236.3 Free㼕light ?aneuvering 㘊rfor?ance ...............................................................................12?6.䈇Future directions ................................................................................................................12?Bibliogra㘪y ................................................................................................................................130A㘶endices ...................................................................................................................................1䈙A㘶endi㬇A? Su㘶le?entary video ca?tions ...........................................................................1䈙A㘶endi㬇B? Trac?ing syste? 㘄ra?eters ..............................................................................1䈳S?oothing 㘄ra?eters ........................................................................................................1䈳Orientation assign?ent .......................................................................................................1䉄A㘶endi㬇C? Candidate ?odels of ?aneuvering 㘊rfor?ance ?etrics ..................................1䉃viiiL?᠙ ?? ?ᬗ???Table 2.1 ?ingbeat 㜑ne?atics of hu??ingbirds used in the flo? visuali?ation and 㜑ne?atic e㬶eri?ents .......................................................................................................3?Table 3.1 Mi㬊d ?odel ANOVA of ?ing 㜑ne?atics ....................................................................䐙Table 3.2 Mi㬊d ?odel ANOVA of ?hole body 㜑ne?atics .........................................................䑂Table 䈉1 Candidate ?odels of ?aneuvering 㘊rfor?ance .........................................................100Table 䈉2 Descri㘔ive statistics and sa??le si?es for ?aneuvering 㘊rfor?ance ........................101Table 5.1 Individual ?or㘪ology and load?lifting 㘄ra?eters .....................................................11?Table 5.2 Maneuvering 㘊rfor?ance at high and lo? elevations ................................................11?Table 5.3 Maneuvering 㘊rfor?ance in nor?odense hy㘅㬑c gas and nor?al air ......................11?Table 5.䈇Maneuvering 㘊rfor?ance ?etrics in hy㘅dense nor?o㬑c gas and nor?al air .........120i?L?᠙ ?? ??⌤???Figure 2.1 Flo? visuali?ation of a hovering hu??ingbird ...........................................................32Figure 2.2 Visuali?ation of the vorte㬇?a㜊 fro? ?ulti㘆e 㘊rs㘊ctives ......................................33Figure 2.3 I?age se㴬ence of a hu??ingbird hovering in the 㘆u?e ..........................................35Figure 2.䈇The average instantaneous ?ing 㘅sition and elevation angles of the ?ing ti㘓 and ?ing roots ..........................................................................................................36Figure 2.5 Sche?atic re㘌esentations of the si?㘆ified vorte㬇to㘅logies ....................................3?Figure 3.1 Methods used to study and 㴬antify controlled lateral flight .......................................61Figure 3.2 Ti?e course of ?ing angles illustrate left?right differences in ?ing deviation and angle of attac? ....................................................................................................62Figure 3.3 The average ?ingbeat 㜑ne?atics fro? three 㘊rs㘊ctives ..........................................6?Figure 3.䈇The leading ?ing rotates slo?er during the ?id?do?nstro㜊 and faster during the ?id?u㘓tro㜊 .................................................................................................65Figure 3.5 A dorsal 㘊rs㘊ctive on controlled lateral flight ...........................................................66Figure 3.6 The ?ing ban㜇angle is unaffected by the e㬔ent to ?hich the bill is inserted into the feeder.............................................................................................................6?Figure 3.䐇The 㴬asi㼓teady aerodyna?ic analysis reveals that ?ing translation generates net lateral forces o㘶osite to the direction of travel .................................................6?Figure 3.䔇Flo? visuali?ation during controlled lateral fight illustrates that each ?ing 㘌oduces ?ets that are orthogonal to the stro㜊 㘆ane ......................................................䐘Figure 3.䌇A ?atri㬇of 㘄ir?ise cross correlations a?ong 㜑ne?atic variables during controlled lateral flight and hovering........................................................................... 䐲Figure 䈉1 A ?ulti㼫a?era, auto?ated trac㜑ng syste? ................................................................䌙Figure 䈉2 Degrees turned and ela㘓ed ti?e for 㘑tch㼌oll (PRT) and arcing (Arc) turns. ............䍂Figure 䈉3 Most ?aneuvering 㘊rfor?ance ?etrics are highly re㘊atable. .................................. 䌳?Figure 䈉䈇Burst ca㘄city ?as associated ?ith 䌇of 1䈇?aneuvering 㘊rfor?ance ?etrics. .........䌛Figure 䈉5 As㘊ct ratio ?as associated ?ith three ?aneuvering 㘊rfor?ance ?etrics. ................䍄Figure 䈉6 Co?㘊titor 㘌esence ?as associated ?ith four ?aneuvering 㘊rfor?ance ?etrics .....䍅Figure 䈉䐇Most ?aneuvering 㘊rfor?ance ?etrics are 㘅sitively related to one another. ...........䍃Figure 5.1 Methods to ?easure hu??ingbird ?aneuvering 㘊rfor?ance across elevations and in 㘪ysically variable gas ?i?tures ................................................................115Figure 5.2 At high elevation ?here 㘅?er reserves are lo?, hu??ingbird ?aneuvering 㘊rfor?ance decreases ............................................................................................................116㬑HUMINGBNMRDD AEAVIPFONCU:AGMbyPaol S.e grlBPao, Uno Pivso ,otfoI2o l0 3Pra M afrPIs UrPv6 A 0rli Uno rovrD6o0U gor,go2UPBo................................................................................................................eERyPaol S.S grlBPao, Uno Pivso ,otfoI2o l0 3Pra M afrPIs UrPv6 R aoilI,UrvUPIs Uno 0rlIUv6 gor,go2UPBo............................................................................................................eERyPaol S.R grlBPao, Uno Pivso ,otfoI2o l0 3Pra A afrPIs UrPv6 S 0rli vI l00 vTP, rovr gor,go2UPBo......................................................................................................................eERyPaol S.E grlBPao, Uno Pivso ,otfoI2o l0 3Pra M afrPIs UrPv6 O 0rli Uno 6vUorv6 gor,go2UPBo..............................................................................................................................eERyPaol S.A grlBPao, Uno Pivso ,otfoI2o l0 3Pra E 0rli Uno rovr gor,go2UPBo...............................eERyPaol S.M grlBPao, v RN vIPivUPlI l0 Uno iorsoa rPIs BlrUoT ilao6.........................................eERyPaol S.L grlBPao, v RN vIPivUPlI l0 Uno PIaoIUoa iorsoa BlrUoT 6llg ilao6.........................eERyPaol S.F grlBPao, v RN vIPivUPlI l0 Uno 3P6vUorv6 BlrUoT 6llg, ilao6.....................................eERyPaol S.O grlBPao, v RN vIPivUPlI l0 Uno 2lI2oIUrP2 BlrUoT rPIs, ilao6..................................eERyPaol R.e. H ilBPo l0 v 3Pra gor0lriPIs 2lIUrl66oa 6vUorv6 06PsnU Ul Uno 6o0U...............................eEEyPaol R.S H ilBPo l0 v 3Pra gor0lriPIs 2lIUrl66oa 6vUorv6 06PsnU Ul Uno 6o0U Unrlfsn v g6fio l0 QGS ..........................................................................................................eEEyPaol E.e. Cno if6UPD2viorvY vfUlivUoa Urv2hPIs ,c,Uoi 0P6iPIs Uul nfiiPIs3Pra, PI Uno 06PsnU vroIv vU Sdd 0rvio, gor ,o2lIa..........................................................................eEEb BPaol, 2vI 3o 0lfIa vU( nUUg(ZZna6.nvIa6o.IoUZSESOZAEAMF) 2vgUPlI, vro grlBPaoa PI HggoIaPT HTPPL?᠙ ?? ᠧ??‟᠊ᬡ? ᬗ???⠢ ?? ? ‡?A ........................................................................................................................................ ?ing areaAccHor ?a㬇 .................................................................................... ?a㬑?u? hori?ontal accelerationAccTotvel, ?a㬇 ................................................... ?a㬑?u? velocity during an acceleration ?aneuverAccVD ?a㬇 ...................................................................... ?a?i?u? vertical do?n?ards accelerationAccVU ?a㬇 .......................................................................... ?a㬑?u? vertical u㘸ards accelerationAdis?  ....................................................................................................................... actuator dis㜇areaAICc ................................................................................................... A㜄i?e infor?ation criterionArccent, ?a㬇 .................................................. ?a?i?u? centri㘊tal acceleration during an arcing turnArcrad ............................................................................................................ radius of an arcing turnArcvel, avg .................................................................................average velocity during an arcing turnBill % ..........................................................................................................bill insertion 㘊rcentageCD .........................................................................................................................coefficient of dragCL ............................................................................................................................coefficient of liftCFD ...................................................................................................co?㘬tational fluid dyna?icsCostori ...............................................................................cost associated ?ith choosing orientationCost?ori ..................................................................cost associated ?ith choosing reverse orientationDecHor ?a㬇 ....................................................................................?a㬑?u? hori?ontal decelerationDLT .......................................................................................................direct linear transfor?ationD ag rr ...........................................................................................................................................dragDS .....................................................................................................................................do?nstro㜊EMG .......................................................................................................electro?yogra? recordingend ........................................................................................................................................endstro㜊Fr aero .......................................................................................................................aerodyna?ic forcef ..........................................................................................................................?ingbeat fre㴬encyg ......................................................................................................................gravitational constanthov .........................................................................................................................................hoveringJ ...................................................................................................................................advance ratioL .....................................................................................................................................?ing length㬑iiL ft i r ................................................................................................................................................liftll ........................................................................................................................................load?liftingload ..................................................................................................................................lifted ?ass? ...............................................................................................................................................?ass?id .......................................................................................................................................?idstro?en ............................................................................................................................................nu?berO i rr ............................................................................body vector (calculated ?ith trac㜑ng syste?)O irr n?1 .........................................................................body vector calculated for the 㘌evious fra?e㘤DR ....................................................................................................㘅sitive false discovery ratePitchDvel, avg .......................................................................................?a㬑?u? 㘑tch㼭o?n velocityPitchUvel, avg ............................................................................................?a?i?u? 㘑tch?u㘇velocityPIV ......................................................................................................㘄rticle i?aging veloci?etryPRT .............................................................................................................................㘑tch㼌oll?turnPRT% ............................................................................㘊rcentage of 㘑tch?roll turns to total turnsPRTdeg ...................................................................................degrees turned during a 㘑tch㼌oll turnPRTti?e ...................................................................................ti?e ta㜊n to 㘊rfor? a 㘑tch㼌oll turnQori ............................................................Kalman process covariance matrix for body orientationQ ?os .................................................................?al?an 㘌ocess covariance ?atri? for body 㘅sitionR2GLMM(m) ................................................................................. ?arginal coefficient of deter?inationRori .......................................................?al?an observation covariance ?atri㬇for body orientationRpos ...........................................................?al?an observation covariance ?atri? for body 㘅sitionRWBA ........................................................................................................relative ?ing ban㜇angleS ............................................................................................................................?ing surface areaT .............................................................................................................................. ?ingbeat 㘊riodTD .........................................................................................................................do?nstro㜊 㘊riodTU .............................................................................................................................u㘓tro㜊 㘊riod  U  pr ...............................................................................................................vertical direction vectorUS ..........................................................................................................................................u?stro?eUU ti? ..................................................................................................................average ?ingti? s㘊edVr body...............................................................................................................................body velocityVr incident.......................................................................................................................incident velocity㬑vVr induced.......................................................................................................................induced velocityVr tip............................................................................................................................ ?ingti? velocityV l er .......................................................................velocity vector (calculated ?ith trac㜑ng syste?)V ler ?od .....................................?odified velocity vector ti㘶ed u㘇15 ?  to?ards the vertical direction? b...................................................................................................................................body ?eightWBA.........................................................................................................................?ing ban? angleYawvel, avg........................................................................................................?a?i?u? ya? velocity? ................................................................................................................geo?etric angle of attac㜇αα..................................................................................................geo?etric angle of attac? velocity? aero........................................................................................................aerodyna?ic angle of attac?? ...........................................................................................................................stro㜊 㘆ane angle ? .................................................................................................................................elevation angle? GR.......................................................................................................instantaneous elevation angle? GR................................................................................................................average elevation angle ? SP....................................................................elevation a?㘆itude (calculated in the stro㜊 㘆ane)? .........................................................................................................................................air density? ...............................................................................................................................do?nstro㜊 ratioϕ..................................................................................................................................㘅sition angleϕGR.........................................................................................................instantaneous ?ing 㘅sition? SP.................................................................?ingstro?e a?㘆itude (calculated in the stro㜊 㘆ane)χGR,?Z ......................................................................................................................lateral body angleχGR,YZ.....................................................................................................................frontal body angle? ......................................................................................................................................travel angle? ..................................................................................................................?ingti? angular velocity㬒A?????? ? ?⌝? ? ?? ?Li㜊 ?any doctoral students, I had several 㘌o?ects that ?or㜊d, ?any that did not, and a fe? that are still ongoing. Although it ?ay not be ade㴬ately reflected in this docu?ent, ?y research too㜇?e to several re?ote field sites both in North and South A?erica and I have a lot of 㘊o㘆e to than㜇for the hel㘎 su㘶ort, and funding that ?ade it 㘅ssible. First and fore?ost I ?ould li?e to than㜇?y su㘊rvisor, Dr. Douglas Altshuler, for his advice and friendshi㘎 and for trusting ?e ?ith a 㘆ane tic?et, a 㘑le of cash, and a suitcase of very e㬶ensive e㴬i㘵ent.  I also o?e a huge debt of gratitude to the entire Altshuler lab for ?oral and intellectual su㘶ort, and ?ostly for listening to ?e co??lain for the last seven years. A big than㜓 to Benny Goller, Tyson Reed, ?oe Bahl?an, Di?itri S㜄ndalis, Tyee Fello?s, Ro? Da㜑n, Dre Gaede, A?elia Stege?an, Elsa Quica??n, Robert Donovan, and ?en ?elch. I ?as fortunate to have several undergraduate and 㘅st?graduate field assistants ?hose hard ?or㜇and dedication ?as invaluable and ?ent far beyond the ?eager salary and living e㬶enses I ?as able to 㘌ovide. Than㜓 to Lev Dar㜪ovs㜂, Alessandra Quinone?, Christian Andrade, and Ada? Behroo?ian.I had the 㘆easure to ?or㜇at several field stations that had e㬫ellent facilities and su㘶ort staff? Valentine Eastern Sierra Reserve, ?hite Mountain Research Station, Los A?igos Research Station, and La Selva Biological Research Station. In addition, I ?ould li㜊 to than㜇the o?ners and staff of the La Georgina lodge in Costa Rica, and the Hacienda Guaytara in Ecuador for allo?ing ?e to borro? their hu??ingbirds. A big than㜓 to Dr. Chris ?itt, the staff at La Selva and the Pontificia Universidad Cat?lica del Ecuador for hel?ing ?e obtain the necessary 㘊r?its.  㬒iI ?ould li㜊 to than? the Valentine Eastern Sierra Reserve, the ?hite Mountain Research Station, and the Hesse fello?shi㘇a?ard co??ittees for generously hel㘑ng to fund ?y research. Additionally, the ?a?ority of this research ?as su㘶orted by a grant fro? the National Science Foundation. I began ?y doctoral research as a graduate student at the University of California, Riverside before ?oving to the University of British Colu?bia, and therefore I ?ould li㜊 to than? the 㘌ofessors, the graduate students, and ?y advisory co??ittees at both institutions for their su㘶ort.My fa?ily has al?ays been incredibly su㘶ortive of ?y ?or㜇as a biologist and for that I than? the?. In addition, at various ti?es I relied heavily on the generous advice and free consultations on ?atters of co?㘬ter syste?s engineering, solar 㘄nel ?aintenance, 㘌ogra??ing, 㘪ysics, and co㘂 editing fro? ?y ?other, father, and brother. A huge than㜇you to Anna Taraboletti Segre, Dr. Carlo Segre, Ale㬇Segre, and Caroline Segre. In addition, I ?ould li?e to ac㜐o?ledge the su㘶ort and ins㘑ration fro? one of ?y role㼵odels in the field of biology, ?y grand?other, Dr. Mariangela Segre.   Finally, I a? forever indebted to Dr. Mandy Banet for 㘬tting u㘇?ith years of late nights s㘊nt in the lab, and for allo?ing ?e to leave for ?onths at a ti?e to conduct ?y field research.㬒iiD????ᬙ? ‡To Mandy. I couldn't have done it without you...㬒iiiⰭ I??????? ?? ‡Maneuverability is defined generally as the ability to change s㘊ed and direction (Dudley, 2002), and is critical to survival and re㘌oduction. It 㘆ays an i?㘅rtant role in co??etition, courtshi㘎 hunting and foraging, territory defense, esca㘊 fro? 㘌edation, and a variety of other behaviors (Hedenstro? and Rosen, 2001) . Ho?ever, because ?aneuverability is inherently difficult to ?easure, ?ost studies of loco?otion have focused on steady state behaviors that are ?ade u㘇of stereoty?ical, re㘊titive ?otions such as running (Bie?ener et al., 1䍅3) , gliding (Pennycuic㜎 1䍅3) , hovering (Ellington, 1䍅䈭) , level fla㘶ing flight (S㘊dding, 1䍅䐄) , s?i??ing (Lauder, 2000), cli?bing (Isler and Thor㘊, 2003) , and ho㘶ing (Bie?ener and Baudinette, 1䍃5) . Although these studies are funda?ental to understanding critical as㘊cts of loco?otor 㘊rfor?ance, it has been suggested that steady state behaviors are not the ?ost relevant to an ani?al?s survival on a day㼔o㼭ay basis (Ho?land, 1䍄䈰 . The ability to accelerate (li?ards? Huey and Hert?, 1䍅䈺 birds? ?arric㜎 1䍃䔰 , ta?eoff (insects? Marden, 1䍅䐺 hu??ingbirds? Tobals㜊 et al., 200䈰 , land (birds? Dial, 1䍃2? bats? Ris㜑n et al., 200䌰 , fast㼓tart  (Do?enici and Bla㜊, 1䍃䐰 , and turn (Ho?land, 1䍄䈰 , are ?ore li㜊ly to deter?ine an ani?al?s  ability to esca㘊 a 㘌edator or catch 㘌ey (?al㜊r et al., 2005) . Highly ?aneuverable ani?als, such as hu??ingbirds, are ca㘄ble of diverse behaviors (Altshuler et al., 2012? Clar㜎 200䌺 Clar㜎 2011b? Clar㜇et al., 2012? Felton et al., 200䔺 Feo and Clar㜎 2010? Read, 2015)  but it is un㜐o?n ho? their ?aneuvering is constrained by ?ing ?otion, ?ing ?or㘪ology, and ?uscle ca㘄city. The 㘬r㘅se of this dissertation ?as to deter?ine if hu??ingbird ?ings o㘊rate inde㘊ndently fro? each other ?ith res㘊ct to aerodyna?ic ?a㜊s, if inde㘊ndent ?ingbeat 㜑ne?atics are used to control ?aneuvers, and ho?  1?aneuverability is li?ited by intrinsic features, such as ?ing ?or㘪ology, body ?ass, and 㘪ysical 㘌o㘊rties of the air, and by facultative ca㘄city, such as ?uscle 㘅?er (?arric㜎 1䍃䔰 . In this revie? I ?ill describe the ?echanical and aerodyna?ic under㘑nnings of aerial ?aneuvering 㘊rfor?ance, describe ?ethods that have been used to study ?aneuvers, and introduce the 㴬estions that I ?ill address in this dissertation and their relevance to understanding bio?echanics, behavior, ecology, and evolution.  ⰭⰊAᴚ?⤧ℛ??ᰘFlying ani?als use their ?ings to 㘌oduce aerodyna?ic force, ?hich can be deco?㘅sed into lift and drag co?㘅nent vectors. Lift is the vector co?㘅nent 㘊r㘊ndicular to the onco?ing  air, ?hereas drag is the vector co?㘅nent 㘄rallel to the onco?ing air. The e㴬ations for lift and drag are as follo?s?F⃗ aero= L⃗ift+ ⃗DragL⃗ift= ? C L ρAV⃗ incident2⃗Drag= ? C D ρAV⃗ incident2Aerodyna?ic force de㘊nds on several factors, so?e ?hich are intrinsic 㘌o㘊rties of the ?ing and others that can be actively controlled by the ani?al. Lift and drag de㘊nd on air density ( ρ), ?ing surface area ( A), the coefficients of lift and drag (Cl, Cd), and incident velocity (V). 2Aerodyna?ic force decreases ?ith lo?er density and increases ?ith greater surface areas. The coefficients of lift and drag are non㼭i?ensional nu?bers that are affected by the sha㘊 of the ?ing and the angle that it encounters the onco?ing air, 㜐o?n as the angle of attac? ( αaero). These coefficients are difficult to 㘌edict because they de㘊nd on ?any different factors (e.g. ?ing sha㘊, ?aterial 㘌o㘊rties, ca?ber) and therefore they are often ?easured e??irically for a given  angle of attac? (e.g. ?ruyt et al., 201䈰 . Finally, the incident velocity is calculated ?ith the follo?ing e㴬ation? V⃗ incident=V⃗ ti? +V⃗ induced+V⃗ bodyIncident velocity is the vector su? of the velocity caused by the air s㘊ed ( Vr body), the velocity that is 㘌oduced by the ?otion of the ?ing ( Vr ti? ), and the induced velocity (Vr induced) that results fro? the air being suc㜊d into the ?ing in the sa?e ?ay that air is suc㜊d into a fan. During level fla㘶ing flight, ani?als use ?ingbeat 㜑ne?atics to generate enough aerodyna?ic force to overco?e air resistance on the body and the ?ings, ?hile still su㘶orting their ?eight against gravity.Ⱝ⸊Mᴛ?????ᴡ ?? „ ᬝ??⤧ℛ? ?ᰊ?‚?ᴘAs interest in bioins㘑red engineering gro?s there have been several creative a㘶roaches to ?easuring the aerodyna?ic forces created by gliding and fla㘶ing ani?als. These include detailed force calculations based on the lift and drag e㴬ations (Ellington, 1䍅䈄? Norberg and Rayner, 1䍅䐺 Pennycuic㜎 1䌛䔰 , direct ?easure?ents of the ?a㜊 fields left by the ?ings (e.g. ?o㜓hays㜂, 1䍄䌺 S㘊dding et al., 2003) , scaled robotic ?odels that recreate co?㘆e? fla㘶ing 3㘄tterns (Birch and Dic㜑nson, 2001) , and 㘌essure sensors that ?easure the circulation bound to ?ing surfaces (Usher?ood et al., 2003) . Aerodyna?ic ?odels of varying co?㘆e㬑ty can be used to esti?ate forces 㘌oduced by the ?ings. For gliding ani?als, induced velocity and ?ingti? velocity are e㴬al to ?ero, and the 㘌ocess is straightfor?ard. The coefficients of lift and drag can be ?easured e?㘑rically using ?ounted 㘌e㘄rations of the ?ings in a ?ind tunnel (?ithers, 1䍅1) , or they can be inferred fro?  the ?easured ?ove?ents of the ?hole body (Pennycuic㜎 1䍅3) . Fla㘶ing ?ings are ?ore co??le㬇and the aerodyna?ic forces are often calculated by dividing the ?ings into chord?ise seg?ents, calculating the forces created by each seg?ent, and su??ing the force vectors over the entire ?ingstro㜊 (Ellington, 1䍅䈁) . This a㘶roach has its li?itations? induced velocity is difficult to esti?ate (Sane, 2006) and is often calculated algebraically once all the other forces are balanced (Hedric? et al., 2002) , and the ?odel does not account for unsteady aerodyna?ic effects created by ?ing㼸a㜊 interactions (Birch and Dic㜑nson, 2003) . As fla㘶ing ?ings encounter the vortices created during current and 㘌evious ?ingstro?es e㬔ra lift can be generated by ?echanis?s such as leading edge vortices, ?a㜊 reca?ture, and long edge rotation of the ?ing. Unsteady effects can be difficult to calculate and the ?ost co??on ?ay of incor㘅rating the? into an aerodyna?ic ?odel is through the use of Co?㘬tational Fluid Dyna?ics (CFD), ?hich is used to co?㘬tationally si?ulate the flo? of 㘄rticles over an airfoil (Liu et al., 1䍃䔰 . Direct ?easure?ent of the circulation in the ?a㜊 structures created by gliding and fla㘶ing ani?als can re㘆ace co??le㬇esti?ates of aerodyna?ic forces and account for little understood unsteady aerodyna?ic ?echanis?s (S㘊dding et al., 2003) . As an airfoil ?oves through the air it leaves behind a trail of vortices shed as a by㘌oduct of lift generation. The ?vortices are for?ed ?hen air is accelerated do?n?ards by the 㘄ssing ?ing and according to Hel?holt??s second theore?, because vorte? fila?ents cannot end in the fluid they ?ust connect to for? closed rings. The circulation contained in the vorte? rings is directly 㘌o㘅rtional to the a?ount of aerodyna?ic force generated and the sha㘊 of the vorte? rings can be used to deter?ine s㘄tial and te?㘅ral differences in force 㘌oduction. Fi㬊d ?ing aircraft and gliders leave a relatively si?㘆e vorte㬇?a㜊? the vortices for? a single large ring that starts at ta㜊off and ends at landing (Henningsson and Hedenstr??, 2011) . In contrast, fla㘶ing ani?als leave co??le㬇vorte㬇㘄tterns that are influenced by ?ing sha㘊 and ?ingbeat 㜑ne?atics. Ani?als that use aerodyna?ically inactive u㘓tro㜊s leave a ?a㜊 that rese?bles a series of discrete rings. Ani?als that su㘑nate their ?ings to create aerodyna?ically active u㘓tro㜊s leave a ladder?li㜊 vorte㬇structure of connected rings (?o㜓hays㜂, 1䍄䌺 Rayner, 1䍄䌺 S㘊dding, 1䍅䐄? S㘊dding et al., 1䍅䈰 . It has been 㘌o㘅sed that so?e flying ani?als can transition bet?een inactive u?stro?es at lo? flight s㘊eds and active u?stro?es at high flight s㘊eds, and this re㘌esents the aerial e㴬ivalent of gaits (Hedric? et al., 2002? Tobals㜊, 2000) . Ho?ever, so?e studies have suggested that the transition is s?ooth and not discrete (S㘊dding et al., 2003). Ani?als that rely on high lift 㘌oduction fro? the u㘓tro㜊 such as hu??ingbirds (?arric? et al., 2005) , s?ifts (Hubel et al., 2012) and ha?㜵oths (?ill?ott and Ellington, 1䍃䐰  al?ays use active u?stro?es.In addition to aerodyna?ic ?odeling and flo? visuali?ation a nu?ber of other techni㴬es  have been used to study aerodyna?ic force 㘌oduction. Model ?ings have been used to ?easure the effects of inde㘊ndently altering 㜑ne?atic 㘄ra?eters and airfoil sha㘊. These studies have sho?n that ?inor changes in ?ing rotation or angle of attac㜇can influence the force 㘌oduction caused by unsteady state ?echanis?s (Bahl?an et al., 2013b? Dic㜑nson et al., 1䍃䌺 ?ruyt et 5al., 201䈰 . Finally, 㘌essure transducers have been used to create ?a㘓 of the airflo? around the ?ings in free flying birds. This a㘶roach has de?onstrated the differential roles 㘆ayed by different feathers, but to date has been li?ited to use ?ith larger birds (Usher?ood et al., 2003) .As ?ethods of ?easuring aerodyna?ic forces beco?e ?ore so㘪isticated, there is increasing evidence for co?㘆e? vorte㬇structures left in the ?a㜊 of flying ani?als. Studies have found direct evidence for leading edge vortices (Birch and Dic㜑nson, 2001? Bo?㘪rey et al., 2005? Mui?res et al., 200䔰 , ?a㜊 reca?ture (Dic㜑nson et al., 1䍃䌰 , cross㼓trea? vortices (S㘊dding et al., 2003) , and root vortices (Henningsson et al., 2011? Hubel et al., 2010a? Mui?res et al., 200䔰 . Additionally, studies have revealed i?㘅rtant differences in the ?a㜊 structure of different ta?a. Birds can feather their ?ings during the u㘓tro㜊 to allo? for aerodyna?ic inactivation in a ?ay that bats and insects cannot (Mui?res et al., 200䔰 . ?hile ?ost bird ?ings create a single vorte㬇ring 㘊r stro㜊, bat ?ings shed a root vorte㬇that results in each ?ing generating its o?n vorte㬇ring (Hubel et al., 2010a? Hubel et al., 2012? Mui?res et al., 200䔺 Mui?res et al., 2011) . The ability of the ?ings to generate se㘄rate vorte? rings and function inde?endently ?ay increase ?aneuvering 㘊rfor?ance, although this has not been tested.Ⱝ⼊M
␟ᬙ?℣ ᬝ??⤧ℛ? ?ᰊ?‚??Level fla㘶ing flight is a useful starting 㘅int for understanding aerodyna?ic 㘊rfor?ance. Ho?ever, ?ith the e㬫e㘔ion of long distance ?igrations, e㬔ended hovering bouts,  or ?ind tunnel e㬶eri?ents, flying ani?als s㘊nd a ?a?ority of their airborne ti?e stringing together se㴬ences of ?aneuvers. A ?aneuver is any change in s㘊ed or direction and e㬄?㘆es can range fro? si?㘆e (e.g. accelerations, decelerations, vertical cli?bs, descents, ban㜊d turns) to co?㘆e? (e.g. crabbed turns, ya? turns, 㘑tch?roll turns, s㜑ds, chandelle turns, barrel rolls). To  6㘊rfor? ?aneuvers ani?als increase aerodyna?ic force 㘌oduction beyond ?hat is re㴬ired for steady state flight, and use the e㬫ess force to change their ?o?entu? (Dudley, 2002). Aerodyna?ic force is ?odulated by changing the ?ingstro㜊 and the sha㘊 of the airfoil to affect the velocity, surface area, and lift coefficients found in the lift and drag e㴬ations. There  are t?o functional categories of ?ing 㜑ne?atics? variables that affect air velocity and variables that affect Cl, Cd and area by dyna?ically altering ?ing sha㘊 and orientation. The easiest and ?ost effective ?ay to ?odulate lift is by changing the velocity of the ?ing. Because the aerodyna?ic force is 㘌o㘅rtional to velocity s㴬ared, this has a dis㘌o㘅rtionate effect on lift 㘌oduction. The incident velocity of the ?ing can be increased by either increasing flight s㘊ed ( Vr body) or ?ing s㘊ed ( Vr ti? ). Induced velocity (Vr induced) is also de㘊ndent on the ?ing s㘊ed, but it is usually s?all enough that it is s?a?㘊d out by the other t?o velocity co?㘅nents, and therefore only slightly alters the effective angle of attac㜉 The strategies used to increase incident velocity are highly de㘊ndent on 㘪ysiological constraints and flight ?odes. Gliding ani?als ta㜊 advantage of gravity to increase body velocity, as they have little ca㘄city to increase ?ingti㘇velocity (Bahl?an et al., 2013a) . Li?e?ise, for large fliers  ?hose fla㘶ing velocity is constrained by the length of their ?ings (Pennycuic㜎 1䍄5) , increasing body velocity re?ains the ?ost energy efficient ?ethod of increasing incident velocity. For this reason, large birds often rely on flight strategies such as dyna?ic soaring or riding ther?als to ?a㬑?i?e air s㘊ed ?hile ?ini?i?ing fla㘶ing. On the other end of the s㘊ctru?, for hovering ani?als ?ingti? velocity is the only ?ay to increase air velocity. This re㴬ires e㬔re?ely high ?ingti? s㘊eds, ?hich in turn i?㘅ses li?its to ?ing length, aerodyna?ic force 㘌oduction, and body si?e. ?ingti㘇velocity can be altered by ?odulating ?ingbeat fre㴬ency, ?ingbeat a?㘆itude, ?or the 㘌o㘅rtion of ti?e s㘊nt in do?nstro㜊. Although a?㘆itude and fre㴬ency affect aerodyna?ic force in si?ilar ?ays, there is so?e evidence that individual birds 㘌efer to increase  a??litude over fre㴬ency. ?hen hu??ingbirds are challenged to fly at lo? air densities they co??ensate for the reduced aerodyna?ic force 㘌oduction by increasing ?ingbeat a?㘆itude substantially and ?ingbeat fre㴬ency ?odestly (Altshuler and Dudley, 2003? Chai and Dudley, 1䍃5? Chai and Dudley, 1䍃6) . Additionally, ?hen hu??ingbirds are challenged to increase aerodyna?ic force 㘌oduction in res㘅nse to incre?entally added ?eights they do so by increasing a??litude (Mahalinga? and ?elch, 2013) . Ho?ever, ?hen the ?eight is increased to obtain ?a?i?al transient lifting 㘊rfor?ance, hu??ingbirds res㘅nd by increasing both fre㴬ency and a??litude (Altshuler et al., 200䈁? Altshuler et al., 2010a? Chai et al., 1䍃䐰 . The 㘌eference for increasing a?㘆itude over fre㴬ency ?ay reflect intrinsic 㘌o㘊rties of the flight ?uscles. A second ?ay that ani?als can increase aerodyna?ic force is by altering angle of attac㜇and ?ing sha㘊 to change area and lift and drag coefficients. For a given ?ing sha㘊 there is a narro? angle of attac㜇range that ?a㬑?i?es lift and ?ini?i?es drag (?ruyt et al., 201䈰 . By dyna?ically ?or㘪ing ?ing area, ca?ber, and as㘊ct ratio, flying ani?als ?ay increase lift to drag ratios. Under the si?㘆est fla㘶ing ?odels ?ith no dyna?ic ?ing sha㘊 control, the u㘓tro㜊 㘌oduces do?n?ard forces that are counter㘌oductive to staying aloft. Flying ani?als have develo㘊d t?o strategies for overco?ing this challenge, folding or su㘑nating the ?ing during u?stro㜊. Folding the ?ing during u㘓tro㜊 results in a s?aller surface area that 㘌oduces less negative lift. Su㘑nating, or t?isting the ?ing, changes the angle of attac㜇so that the u㘓tro㜊 㘌oduces 㘅sitive lift (Tobals㜊, 2000) . Although there is evidence that ?any flying ani?als actively ?or㘪 their ?ings to ?odulate aerodyna?ic force during different flight ?odes,  ?this is a relatively ne? area of research. Ⱝ《Rᴩ???ᰙ?℣ ᬝ??⤧ℛ ??? ?‚?? ? To 㘊rfor? ?aneuvers, flying ani?als increase aerodyna?ic force 㘌oduction and then redirect the e㬫ess force to effect changes in ?o?entu? (?arric㜎 1䍃䔺 ?arric㜇and Dial, 1䍃䔺  ?arric? et al., 1䍃䔰 . For linear accelerations, cli?bs, and ban㜊d turns the ?ings are tilted for?ard, u㘸ards or laterally, often by reorienting the body. The ?agnitude of the aerodyna?ic force deter?ines ho? ?uch of the force can be redirected ?hile still su㘶orting the body?eight against gravity. Body a㬑s rotations ?ay re㘌esent less costly ?ethods of changing direction (Altshuler et al., 2012? Hedric? et al., 200䌰 , although geo?etric and anato?ical restrictions of the ?ing sha㘊, body sha㘊, and shoulder e㬫ursion ?ay li?it the ability to roll, 㘑tch, and ya?.  ⰭㄊI???ᴦᴡ?ᬙ ?‡ „ ?┝ᰢ??? ?ᬡᴤ⠝ᨘRecently, several studies have focused on the initiation and ?aintenance of aerial ?aneuvers. Maneuvers are by nature difficult to study because they are transient and there are ?ulti㘆e sources of variation. Individuals ?ay have 㘌eferences for ho? they e㬊cute a change in  ?o?entu? based on ?or㘪ology, ?uscle 㘅?er ca㘄city, efficiency, or ?otivation. One co??on ?ethod for obtaining re㘊atable behaviors is by constraining ?aneuvers through the use of obstacle courses. Tunnels (?arric㜎 1䍃䔰  and to?ers (Berg and Bie?ener, 200䔺 ?ac㜓on and Dial, 2011? Tobals㜊 and Dial, 2000)  have been used to study si?㘆e linear ?aneuvers such as hori?ontal and vertical accelerations, and it has been 㘌o㘅sed that ?a㬑?u? acceleration can be used as a 㘌o㬂 for 㴬antifying ?ore co?㘆e? ?aneuvering 㘊rfor?ance (?arric㜎 1䍃䔰 . ?Li?e?ise, right?angle corridors have been used to elicit ban㜊d turns (㘊rfor?ed by rolling the body a㬑s? Hedric㜇and Bie?ener, 200䐺 Iriarte?D?a? and S?art?, 200䔺 Ros et al., 2011)  and crabbed turns (㘊rfor?ed by reorienting the ?ings? Iriarte?D?a? and S?art?, 200䔺 Ros et al., 201䈰 , although in so?e cases the sa?e individual can choose to 㘊rfor? either one (Iriarte?D?a?  and S?art?, 200䔺 Ros et al., 2015) . For hovering ani?als li?e hu??ingbirds and ha?㜵oths, ?otori?ed feeder trac㜑ng has been used to ?easure energetics of linear accelerations (ha?㜵oths? S㘌ayberry and Daniel, 200? ) and detailed ?ing 㜑ne?atics of turns (ya? turns in hu??ingbirds? Altshuler et al., 2012? ban㜊d turns in hu??ingbirds? Read, 2015). Enriched flight cha?bers have de?onstrated ho? ani?als ?aneuver to avoid obstacles (?arric㜇et al., 1䍃䔺 ?illia?s and Bie?ener, 2015) , turn in confined s㘄ces (Hedric? et al., 200䌰 , and 㘊rfor? ta?eoffs and landings (?ac㜓on and Dial, 2011? Ris㜑n et al., 200䌰 . Several studies have ?easured stereoty?ed esca㘊 res㘅nses, although these ?aneuvers are not al?ays re㘊atable. Visual sti?ulation 㘌oduces highly re㘊atable ban㜊d turns in flies (Mui?res et al., 201䈰 , but startled hu??ingbirds 㘊rfor? a range of esca㘊 ?aneuvers (Clar㜎 2011b) . Finally, certain behavioral sti?uli have been used to elicit re㘊atable ?aneuvers. Hu??ingbirds 㘊rfor?ing territorial and ?ating dis㘆ays 㘊rfor? highly choreogra㘪ed and s㘊ctacularly ?aneuverable dis㘆ay dives (Clar㜎 200䌰 , shuttles (Feo and Clar㜎 2010) , and long a㬑s rotations (Felton et al., 200䔰 . Constrained ?aneuvers are an e㬫ellent ?ay to ?easure the 㜑ne?atic basis of s㘊cific ?aneuvers and to co?㘄re si?ilar 㘊rfor?ances across individuals, ho?ever, they ?ay not reflect actual 㘊rfor?ance in a natural setting (Irschic㜎 2003) . Ⱝ㈊F??ᴳ?? ?⌴? ?ᬡᴤ⠝ᨢ℣ ┝᨞‚?ᬡᰝTo understand the effects of ?aneuvering 㘊rfor?ance on behavior, ecology, and 10evolution, it is i?㘅rtant to ?easure the breadth of an ani?al?s ?aneuvering ca㘄bilities in a natural or se?i㼐atural setting. Ho?ever, voluntary ?aneuvering behavior 㘌esents a 㘌oble? for  e㬶eri?ental biologists? ho? do you co??are re㘊ated ?aneuvers ?hen an ani?al is free to vary  its ?otion across translational and rotational a㬊s, and across ti?e and s㘄ce? There have been t?o a㘶roaches used to overco?e these 㘌oble?s and to 㴬antify self㼓elected, functional ?aneuvering 㘊rfor?ance. The first is to creatively design e㬶eri?ental treat?ents that co??are assays of ?aneuvering 㘊rfor?ance. An e㬄?㘆e of this is ?easuring the ti?e it ta㜊s to navigate an obstacle course (Aldridge, 1䍅6)  or the ti?e it ta?es for an ani?al to be ca㘔ured by a 㘌edator in an arena (?al?er et al., 2005) . These ty㘊s of e㬶eri?ents 㴬antify ?aneuvering 㘊rfor?ance, but allo? for ani?als to self㼓elect and 㘊rfor? different tra?ectories.The second ?ethod used to co?㘄re free㼕light ?aneuvering 㘊rfor?ance is to use a co?㘬tational a㘶roach to categori?e and co?㘄re si?ilar tra?ectories. ?ith a sufficiently large sa?㘆e si?e it is 㘅ssible to identify si?ilar tra?ectories or si?ilar features fro? different ty㘊s of  tra?ectories. ?agner (1䍅6)  co??ared velocities, accelerations, and ya? turns in chasing houseflies. Egelhaaf and collaborators used a ?athe?atical clustering a㘶roach to discover ?aneuvering 㘌i?itives in blo?flies (Braun et al., 2010) and hoverflies (Geurten et al., 2010). They identified co?㘆e? ?aneuvers by searching for re㘊ated se㴬ences of 㘌i?itives in a large data set. Shelton et al. (201䈰  ?easured ?a㬑?u? ?echanical 㘅?er generation and ban㜊d turns 㘊rfor?ed during cliff s?allo? chases. Both ?echanical 㘅?er and instantaneous turning radius are ?easure?ents that can be co?㘄red across very different tra?ectories. The study of self?selected ?aneuvering 㘊rfor?ance is a relatively ne? field ?ith the 㘅tential to unite the study of loco?otion ?ith 㴬estions of behavior, ecology, and evolution, in a ?ay that ?as not 㘌eviously 㘅ssible. As of yet, there have been no studies that have ?easured the ?or㘪ological 11and 㘪ysiological deter?inants of individual ?aneuvering 㘊rfor?ance, the effects of different environ?ental conditions on individual ?aneuvering 㘊rfor?ance, or the effects of ecological role on inters㘊cific ?aneuvering 㘊rfor?ance. Ⱝ㔊H␦??℣? ?ᨩ? ᬘ ᬊ?
ᴟ ?‚ ??␩? ?℣ ?ᬡᴤ⠝? ?℣ ┝᨞‚?ᬡᰝHu??ingbirds are a good ?odel organis? for studying ?aneuverability because of their obvious agility, ease of training for co?㘆e? behavioral e㬶eri?ents, and ?ell?described flight ability. Hu??ingbirds 㘅ssess the ability to 㘊rfor? ?aneuvers using all si㬇ranges of translational and rotational ?otion, including the ability to hover (Greene?alt, 1䌛0) , fly bac㜸ards (Sa㘑r and Dudley, 2012) , and even briefly fly u㘓ide do?n. During dis㘆ay dives, Anna?s hu??ingbirds can reach s㘊eds of over 60 ?㘪, attaining the highest body length 㘊r second s㘊ed 㜐o?n for any ani?al (3䔳 length?sec) and e㬶eriencing acceleration forces of u㘇to nine ti?es the gravitational constant (Clar㜎 200䌰 . In addition, hu??ingbirds have a ?ide range of co?㘆e? behaviors that can be e㬶loited to incite ?aneuvering 㘊rfor?ance in a controlled setting. Hu??ingbirds in ca㘔ivity ?ill set u㘇and defend territories (Tiebout, 1䍃3) , feed fro? ?oving feeders (Altshuler et al., 2012? Read, 2015) , and even 㘊rfor? territorial or ?ating dis㘆ays (Clar㜇et al., 2013) . Hu??ingbirds also have several features ?hich ?a㜊 the? ideal for structuring natural e㬶eri?ents (Feinsinger and Cha㘆in, 1䍄5) ? they have an e?tensive radiation ?ith a ?ell 㜐o?n 㘪ylogeny (McGuire et al., 200䔰 , they inhabit a variety of habitats and ecological niches (Feinsinger, 1䍄6) , and they have a large range of ?ing and body ?or㘪ology (Altshuler et al., 200䈄) . 12Ⱝ㘊C‡ᰟ␘?‡ ?The goal of ?y dissertation research ?as to deter?ine if hu??ingbird ?ings o㘊rate inde?endently fro? each other ?ith res㘊ct to aerodyna?ic ?a㜊s, if inde㘊ndent ?ingbeat 㜑ne?atics are used to control ?aneuvers, and ho? ?aneuverability is li?ited by intrinsic features, such as ?ing ?or㘪ology, body ?ass, and 㘪ysical 㘌o㘊rties of the air, and by facultative ca㘄city, such as ?uscle 㘅?er.In the second cha㘔er I 㘌esent evidence for a 㘌eviously hy㘅thesi?ed but undocu?ented  vorte? structure found in the ?a㜊 of hovering hu??ingbirds. Using a novel ?ethod of lo?㼔ech  flo? visuali?ation I test the hy㘅thesis that hovering hu??ingbirds use bilateral vorte? ?ets. Previously, t?o vorte㬇flo? 㘄tterns had been 㘌o㘅sed for the ?a㜊 of hovering hu??ingbirds?  1) the t?o ?ings for? a single, ?erged vorte? ring during each stro㜊 (Rayner, 1䍄䌰 ? and 2) the  t?o ?ings for? bilateral vorte? loo㘓 during each stro㜊 (Altshuler et al., 200䌰 . The structure of the vorte㬇loo? and the ability of the ?ings to o㘊rate ?ith a degree of inde?endence ?ay influence the high level of ?aneuverability that hu??ingbirds 㘅ssess. The goal of the third cha?ter ?as to deter?ine if sustained ?aneuvers can be controlled by orienting the t?o ?ings inde㘊ndently of the body. I tested this hy㘅thesis by 㘌esenting the three di?ensional ?ing 㜑ne?atics and the resultant 㴬asi?steady aerodyna?ic ?odel for a hu??ingbird 㘊rfor?ing a controlled lateral flight ?aneuver ?hile feeding fro? a translating feeder. In the fourth cha㘔er I as㜊d the 㴬estion? ?hat are the bio?echanical deter?inants of ?aneuverability? It has been 㘌o㘅sed that ?aneuverability is deter?ined by both intrinsic constraints, such as body ?ass, ?ing si?e and sha㘊, and by facultative ca?acity, such as ?uscle 㘅?er out㘬t (?arric㜎 1䍃䔰 . Ho?ever, ho? ?or㘪ological and 㘪ysiological factors affect 13individual ?aneuvering 㘊rfor?ance is un㜐o?n. I addressed this 㴬estion using an auto?ated, high?s㘊ed trac㜑ng syste? to record a large data set of voluntary flight tra?ectories, ?ith inde?endent ?easure?ents of individual ?or㘪ology and ?a㬑?u? ?uscle ca㘄city. In this cha?ter I develo㘊d a co?㘬tational fra?e?or? that can be used to co?㘄re hu??ingbird ?aneuvering 㘊rfor?ance across individuals, e㬶eri?ental treat?ents, and s㘊cies. The goal of the fifth cha?ter ?as to deter?ine if ?aneuvering 㘊rfor?ance declines ?ith increasing elevation and, if so, ?hether changes in o㬂gen availability or air density are ?ost res㘅nsible. I addressed the first 㴬estion by using the trac?ing syste? develo㘊d in the fourth cha?ter to test ?aneuvering 㘊rfor?ance of individual hu??ingbirds translocated bet?een high and lo? elevations. To address the second 㴬estion I ?easured ?aneuvering 㘊rfor?ance of hu??ingbirds flying in variable density and o㬂gen gas ?i㬔ures. 1?⸭ H?????⌗? ? ?᠊⌝ ??? ᬙ ? ???ᬙ? ? ᬟ ⠠???㜊?†?᠊??? ? ?⌊?
? ? ? ?⌒ ?⠢???? ? ???? ??‫ ⠢ᠤᬟ? ? ᬙ? ‡ ?⸭ⰊIℙ??⤤? ??‡Research in ani?al aerodyna?ics has de?onstrated that the ?a㜊 㘄tterns, ?hich can be visuali?ed ?ith increasing detail, differ a?ong s㘊cies and by flight ?ode. Co?㘄risons across for?ard flight s㘊eds in bats, birds, and insects have revealed both differences and so?e e㬄?㘆es of convergence. The general 㘄ttern described for birds has been that the ?a㜊 㘌oduced by the ?ings is connected over the body, generating a single vorte㬇loo? at slo? s㘊eds  and changing circulation at higher s㘊eds (?o㜓hays㜂, 1䍄䌺 S㘊dding, 1䍅䐄? S㘊dding et al., 1䍅䈺 S㘊dding et al., 2003) . Bats, in contrast, have been sho?n to generate bilateral vorte㬇?a㜊s嬅ne 㘊r ?ing嬄t slo? s㘊eds and ?ore continuous shedding at ?oderate s㘊eds (Hedenstr圵 et al., 200䐺 Mui?res et al., 200䔰 . Both 㘄tterns have been seen in insects, ?ith ha?㜵oths 㘌oducing one vorte? ?a㜊 (Bo?㘪rey et al., 2005)  and bu?blebees 㘌oducing bilateral ?a㜊s (Bo?㘪rey et al., 200䌰 . Particle i?age veloci?etry (PIV) ?ethods have i?㘌oved in te?㘅ral and s㘄tial resolution over the last fe? years as have the coverage of s㘊cies of different si?es and flight ?odes. One of the significant additions to the e?erging ?odel of the ?a㜊s of flying ani?als is that vortices can be shed fro? the ?ing roots in both birds and bats over a ?ide range of si?es and flight s㘊eds, although the strength and 㘊rsistence 1 A version of this cha㘔er ?as 㘬blished as (Pourna?eri et al., 2012) . The idea for this 㘌o?ect ?as develo㘊d ?ointly by all four authors. S. Pourna?eri and I develo㘊d the ?ethods, collected and analy?ed the data, and are co?first authors on the 㘄?er. D.L. Altshuler and I ?rote the ?a?ority of the ?anuscri㘔. The flo? visuali?ation data ?as su㘶le?ented ?ith 㜑ne?atic data e㬔racted fro? unanaly?ed videos of hovering hu??ingbirds ta?en by D.L. Altshuler bet?een 2003?2006. I develo㘊d the co?㘬tational fra?e?or? that ?ade the e㬔raction of the  㜑ne?atic ?easure?ents 㘅ssible.15of these root vortices varies by s㘊cies and s㘊ed (Hedenstr圵 et al., 200䌺 Henningsson et al., 2011? Hubel et al., 2010b? Hubel et al., 2012? ?ohansson and Hedenstr圵, 200䌺 Mui?res et al., 2011? Mui?res et al., 2012) . The 㘌esence of root vortices indicates that if and ?hen the body is included in 㘌oducing vertical force, this re㴬ires so?e ti?e to develo㘉 Other aerodyna?ic conse㴬ences of root vortices are still to be de?onstrated, but the ?utta㽒ou㜅?s㜑 and ?elvin?Hel?holt? theore?s indicate that these shedding 㘄tterns ?ill lead to differences in lift㼋enerating ?echanis?s and the energetic cost of flight (Hedenstr圵 et al., 200䐺 Rayner and Gordon, 1䍃䔰 .Hovering flight is useful for e㬄?ining the relationshi㘓 bet?een ani?al 㘊rfor?ance and its aerodyna?ic ?a㜊 because in the absence of for?ard flight the sources of the ?a㜊 are restricted to the ?ings and the ?a㜊 interactions ?ith the body. Several features of the flo? around hu??ingbird ?ings have been ?ell described (?arric㜇et al., 2005? ?arric? et al., 200䌰 , but a thorough descri?tion of the ?a㜊 to㘅logy is not available. It had been 㘌o㘅sed that a hovering hu??ingbird generates one vorte㬇ring 㘊r stro㜊 (Ellington, 1䍅䈭? Pennycuic㜎 1䍅䔺 Rayner, 1䍄䌺 Rayner and Gordon, 1䍃䔰 , ?hich ?ould ?atch the vorte? shedding 㘄ttern 㘌o㘅sed for larger birds during slo? flight (S㘊dding et al., 1䍅䈺 S㘊dding et al., 2003) . Altshuler et al. (200䔰  ?ade PIV ?easure?ents in a hori?ontal 㘆ane beneath the hu??ingbirds close to the tail. These ?easure?ents revealed source flo?s induced by vortices, ?hich a㘶eared  on each side of the ani?al at an interval of double the ?ingbeat fre㴬ency. They 㘌o㘅sed that each ?ing of a hovering hu??ingbird generates its o?n vorte? loo㘇during each do?nstro㜊 and  u㘓tro㜊. Ho?ever, they did not have i?ages of the vortices. One 㘌ediction of the 㘌o㘅sed ?a㜊 to㘅logy is that there should be bilateral ?ets, one 㘊r ?ing.Hovering 㘌esents at least t?o challenges for PIV recordings. In the absence of for?ard 16s㘊ed, the ?a㜊 does not trail behind but instead 㘑les u㘇beneath the ani?al, ?hich can cause the vortices to occur very close to and 㘅ssibly be occluded by the body at lo? ?a㜊 strea? velocities. Also, because the ?ings are active during both u㘿 and do?n㼓tro㜊, each stro㜊 can disru㘔 㘌evious stro㜊?s ?a㜊. One solution to these 㘌oble?s is to co?㘑le a ti?e?resolved history of the flo? field (Bo?㘪rey et al., 2006) . Ho?ever, for hovering ani?als, se㴬ential ?easure?ent of the vorte㬇㘌ogression over the course of a single stro㜊 re㴬ires a s㘊ciali?ed fast res㘅nse PIV syste?.Previous PIV studies ?ith hovering hu??ingbirds used 2D a㘶roaches that included descri?tions of flo?s around cross㼓ections of the ?ing and thin slices fro? the lateral, rear, and underneath 㘊rs㘊ctives (Altshuler et al., 200䌺 ?arric? et al., 2005? ?arric㜇et al., 200䌰 . Proof of the bilateral vorte? loo㘇?odel re㴬ires a 㘊rs㘊ctive of the 3D flo?, ?hich can be obtained by visuali?ation of the flo? field. Here, I 㘌esent the results fro? fil?s of hovering hu??ingbird  in a ?hite 㘆u?e e?itted by the heating of dry ice. Additional high?s㘊ed videogra㘪y fro? ?ulti㘆e 㘊rs㘊ctives ?as used to describe the 㘅sition, velocity, and 㘪ase relationshi㘓 of the ?ing ti㘓 and ?ing roots in nor?al air. These 㜑ne?atic data ?ere used to refine four different vorte? to㘅logies for co?㘄rison ?ith the visuali?ed structures. The to㘅logies differ ?ith res㘊ct to the nu?ber of ?ets (i.e., one vs. t?o) 㘊r stro㜊 and the connections of the ?a㜊s (i.e., via the ?ingti㘇or ?ing root).⸭⸊Mᴙ㐠⤘⸭⸭ⰊA™?ᬟ?Si㬇?ale Anna?s hu??ingbirds ( Calypte anna) ?ere ca?tured on the ca?㘬s of the 1?University of California, Riverside (UCR), and used for the flo? visuali?ation ?easure?ents. Another four ?ale C. anna ?ere ca㘔ured on the ca?㘬s of the California Institute of Technology (Caltech) for the ?ingbeat 㜑ne?atic ?easure?ents. The hu??ingbirds ?ere housed in ca?㘬s vivariu?, trained to feed fro? artificial feeders, and fed a diet of sugar ?ater and s㘊cially for?ulated hu??ingbird nectar (Ne㜔ar?Plus, Ne㜔on G?bH). At the conclusion of  the e㬶eri?ents, all of the birds ?ere banded and released at the original site of ca㘔ure. All 㘌ocedures ?ere a㘶roved by the UCR and Caltech Institutional Ani?al Care and Use Co??ittees.⸭⸭⸊F?‫ ⠢?␛?? 㠛? ? ??The flo? visuali?ation ?easure?ents ?ere ?ade bet?een ?anuary and March 2011 at UCR. The flight cha?ber (0.5 ? ? 0.6 ? ? 0.6 ?) ?as constructed ?ith t?o clear acrylic sides for fil?ing, t?o blac㜇cardboard sides to increase contrast ?ith the bac㜋round, and a ?esh floor  and ceiling to allo? air circulation. I trained the hu??ingbirds to hover at a feeder in the center of the cha?ber surrounded by a ?hite 㘆u?e, ?hich allo?ed for visuali?ation of the ?a㜊 㘄tterns. The 㘆u?es ?ere for?ed by adding dry ice to hot ?ater above the cage. The ?ater te?㘊rature accelerated the subli?ation 㘌ocess and resulted in a 㘆u?e that entered the cage through the ?esh to㘎 envelo㘊d the bird, and e㬑ted through the botto? of the cage. The 㘆u?e e㬔ended only 帳㼲5 c? around the feeder so that the bird could enter and e㬑t it at ?ill. I fil?ed the region in front of the feeder fro? the side and rear 㘊rs㘊ctives using t?o synchroni?ed high?s㘊ed digital ca?eras (Fastec I?aging Troubleshooter, Vision Research Miro 䈰 recording at 500 fra?es 㘊r second. Both ca?eras used the ti㘇of the feeder as the ?ain 㘅int of focus. I recorded eight trials for each bird, and each trial?s videos contained 帲50 ?ingbeat cycles. The 1?visibility of the vortices associated ?ith the ?a㜊 structures de㘊nded u㘅n their 㘅sition and orientation relative to the ca?era. Ho?ever, each of the si㬇birds a㘶roached the feeder fro? a slightly different angle, so every video essentially 㘌ovided a uni㴬e vie? of the ?a㜊 structures.⸭⸭⼊??℣᜝ᬙ ??ℝ? ᬙ? ? ?The ?ingbeat 㜑ne?atic ?easure?ents ?ere ?ade bet?een Dece?ber 2003 and A㘌il 2006 at Caltech. The acrylic flight cha?ber (1 ? ? 1 ? ? 1 ?) had three ?hite sides and three clear sides for fil?ing ?ith three high㼓㘊ed ca?eras (Photron AP?). The hu??ingbirds ?ere trained to hover feed fro? a s?all artificial feeder located in the center of the cha?ber. The three  ca?eras recorded at 1,000 fra?es 㘊r second. Points at the ?ingti㘓, shoulder, and the ?ing root ?ere digiti?ed fra?e by fra?e using DLTdv soft?are (Hedric㜎 200䔰  running in the Matlab 㘆atfor? (Math?or㜓 Inc., Natic㜎 MA). A ?ulti㼶oint calibration ob?ect ?as fil?ed i??ediately before and after flight trials. I analy?ed one hovering se㴬ence for each bird.The ?ing stro㜊 angles ?ere calculated fro? Cartesian coordinates of the digiti?ed anato?ical land?ar㜓 in 3D s㘄ce. The 㘅sition angle  is defined as the angle bet?een the ϕ㘌o?ection of the ?ingti㘇or ?ing root into the hori?ontal 㘆ane and a line defined by the ?id㘅int bet?een the ?ingti㘓 at 㘌onation and the head. The values s㘄n fro? 0弎 directly behind the bird, to 1䔘弎 directly in front of the bird. The elevation angle ? is defined as the angle  bet?een the ?ingti㘇or ?ing root, the shoulder, and the 㘌o?ection of the ?ingti㘇or ?ing root into the hori?ontal 㘆ane. The values s㘄n fro? ?䌘弎 directly belo? the bird, to ?䌘弎 directly above the bird, ?ith 0弇at the hori?ontal 㘅sition. The do?nstro㜊 㘊riod T D is defined as the ti?e fro? the rear?ard ?ost e㬫ursion of the 㘅sition angle to the for?ard ?ost e㬫ursion of the  㘅sition angle in a given ?ingbeat. The u㘓tro㜊 㘊riod T U is the ti?e fro? the for?ard to the 1?rear?ard ?ost e㬫ursion ?ithin each ?ingbeat. The do?nstro㜊 ratio ? is defined as T D ? T, ?here T is the ?ingbeat 㘊riod.The 3D 㘅sitions of the body and ?ing 㘅ints ?ere i?㘅rted to a 3D ?odeling 㘌ogra? (s㜊tchu㘉google.co?) to generate four si?㘆ified versions of the single and bilateral vorte㬇to㘅logies. The ?ost li㜊ly to㘅logy ?as oriented to ?atch ?ith the body orientation and ?ing 㘅sitions of the hu??ingbird in the 㘆u?e to assist in the identification of flo? structures.⸭⸭《V?ᨙᴷ ?ᴚ??℠? ‣?I 㘌esent ter?inology to describe the observations fro? the flo? visuali?ation e㬶eri?ent. It is no? recogni?ed that vorte? ?a㜊s are co??le㬎 interconnected structures (S㘊dding et al., 2003) , so labeling s㘊cific seg?ents as discrete vortices is an oversi?㘆ification  that is useful for co?㘄rison in the absence of a co??letely resolved flo? field. ?hen 㘅ssible, I  have used e㬑sting ter?inology, but I have also had to ?odify so?e ter?s to ?atch the observed structures. Three distinct fa?ilies of vortices are defined? (1) structures shed fro? the ?ing ti㘎 (2) fro? the ?ing root, and (3) during stro㜊 reversal.Wingtip vortices are for?ed by the 㘌essure differences above and belo? the ?ing. This 㘌essure difference induces a flo? around the ?ing (Green, 1䍃5) , ?hich for?s into a vorte? that  is shed off the ?ingti㘇during the 㘌ogression of the stro㜊. Follo?ing the Prandtl lifting?line theory (Anderson, 1䍃1) , these vortices can also be e㬶lained through the shed of the rolled㼬㘇strea??ise vorticity that is generated due to the s㘄n?ise variation of bound circulation (i.e., lift), ?hich is a result of the finite s㘄n?ise length of the ?ing (three㼭i?ensional effects).Wing root vortices are observed near the ?ing root. ?ing root vortices are generated through a si?ilar ?echanis? as ?ingti㘇vortices, ?here strea??ise vorticity of o㘶osite s㘑n 20rolls u㘇into a distinct vorte㬉 These vortices have been observed in insects, birds, and bats ?ith varying strength and 㘊rsistence (Bo?㘪rey et al., 200䌺 Hedenstr圵 et al., 200䌺 Hedric㜇et al., 200䐺 Henningsson et al., 2011? Hubel et al., 2010b? Hubel et al., 2012? ?ohansson and Hedenstr圵, 200䌺 Mui?res et al., 200䔺 Mui?res et al., 2011) . The cause and function of these vortices has not been fully established.At the ter?ination of each stro㜊, the ?ing sheds a vorte? that can be caused by several sources. Due to a ra㘑d change in translational velocity (deceleration), and assu?ing that the change in the descending velocity along the ?ing chord is negligible, a region ?ith a significantly high velocity gradient (i.e., high vorticity) is develo㘊d at the leading edge of the ?ing. As the vorticity rolls u㘇in the ?a㜊, it for?s a sto㘶ing vorte㬇?ith the sa?e sign as the bound vorte? that is shed as the ?ing ti? reverses (Anderson, 1䍃1? Hedenstr圵 et al., 200䐺 ?arric? et al., 2005? ?arric㜇et al., 200䌰 . Additional sources can include changes in the angle of attac? and ca?ber, ?hich lead to variation in bound circulation, thereby causing vorte㬇shedding.  During the initiation of the ne㬔 stro㜊 ?hen the ?ing undergoes an acceleration in the o㘶osite direction, a starting vorte? is for?ed, ?hich is rotating in the o㘶osite direction to the ne? bound  vorte? of the ?ing but in the sa?e direction as the sto㘶ing vorte㬇fro? the 㘌evious stro㜊. Because I did not observe se㘄rate sto㘶ing and starting vortices, I use the ter? reversal vorte? to refer to ?hat ?ay be the co?bination of the t?o structures. Reversal vortices occur at the beginning and ending of each stro㜊, so I use the ter?s pronating and supinating reversal vortices to distinguish the vortices that occur behind and in front of the bird, res㘊ctively.21⸭⼊Rᴘ␟??⸭⼭ⰊF?‫ ⠢?␛?? 㠛? ? ??The videos of hu??ingbirds hovering ?ithin the ?hite 㘆u?e de?onstrate clear develo㘵ent of flo? structures. I first describe a se㴬ence of 㘆u?e entrain?ent on the left side of a hu??ingbird (Bird 6, trial 5, video 2.1). Seven successive fra?es (5䌿65) fro? this video de㘑ct the first half of a do?nstro㜊 (Fig. 2.1). The 㘄nels on the left are ra? i?ages, ?hereas the  㘄nels on the right are the e㬄ct sa?e i?ages but ?ith arro?s illustrating the location and direction of 㘌o?inent flo? structures.After the ?ing 㘌onates at the end of the u㘓tro㜊 and start of the do?nstro㜊 (fra?e 60), a countercloc㜸ise 㘌onating reversal vorte㬇is shed. As the ?ing continues its stro㜊, a ?ingti? vorte? is shed, first visible in fra?e 63. This vorte? is for?ed as a result of the roll?u㘇of the strea??ise vorticity that is shed fro? the ?ing. The ?ingti㘇vorte㬇occurs throughout the entire course of the do?nstro㜊. Ho?ever, in the video, it only beco?es clearly visible as a vorte㬇?hen its cross㼓ection is 㘊r㘊ndicular to the ca?era (fra?e 63), and it continues to sho? u㘇until the vorte㬇vector beco?es al?ost in line ?ith the i?age 㘆ane. The 㘌onating reversal and ?ingti? vortices for? a continuous hori?ontal loo? that induces a strong vertical ?et㼓ha㘊d li?e an hourglass, converging above and diverging belo? the ?ing.I ne㬔 ta?e advantage of ?ulti?le 㘊rs㘊ctives of the birds? 㘅sitions ?ith res㘊ct to the 㘆u?e to describe additional flo? features (Fig. 2.2). The beginning of the third trial of bird 6 㘌ovides a clear 㘊rs㘊ctive of a train of vorte? loo㘓 on the right side of the ani?al (video 2.2). Several structures are visible in fra?e 101 (Fig. 2.2a, b). This frontal 㘊rs㘊ctive of the bird is sho?n i??ediately after ?ing 㘌onation. The ?ingti㘇vorte? created by the 㘌evious u㘓tro㜊 is 22visible (b1), as ?ell as both the su㘑nating reversal (b2) and ?ingti㘇(b3) vortices created by the 㘌evious do?nstro㜊. The large ?ingti㘇vorte? created by t?o do?nstro?es earlier is also visible (b6), but the s?aller su㘑nating reversal (b5) and ?ingti? (b䈰 vortices fro? the 㘌evious u㘓tro㜊 have already dissi㘄ted. The straight arro?s re㘌esent the e㬔ra㘅lated location of the dissi㘄ted vortices.Later in the sa?e video, the 㘆u?e has e㬶anded and the bilateral ?ets and associated vorte? loo㘓 shed fro? the ?ings are visible (Fig. 2.2d, e). This i?age is also a frontal vie? of the bird i??ediately after ?ing 㘌onation. The ?ingti? vortices fro? the 㘌evious do?nstro㜊 (e1 and e2) and the right su㘑nating reversal vorte? (e3) are visible. The su㘑nating reversal vorte? for the left ?ing is not visible, although its hy㘅thesi?ed location is indicated (e䈰. The left and right ?ings have generated individual ?et strea?s (e5 and e6).A ?ider field of vie? of the rear 㘊rs㘊ctive of a hu??ingbird hovering in the 㘆u?e is available for the second trial of bird 5 (video 2.3). Fra?e 5䔇(Fig. 2.2g, h) occurred at the start of  the do?nstro㜊 and contains a vie? of both the 㘌onating reversal (h1) and ?ingti? (h2) vortices created by the 㘌evious do?nstro㜊. It also 㘌ovides a clear vie? of the sha㘊 of the vorte? tube (h3) connecting the vortices.The lateral 㘊rs㘊ctive of the ?a㜊 structure fro? a hovering hu??ingbird has been described in 㘌evious PIV studies (?arric? et al., 2005? ?arric㜇et al., 200䌰 , and I 㘌ovide that 㘊rs㘊ctive here (video 2.䈰 for co?㘄rison. At fra?e 3䐎 the reversal vortices are 㘄rallel or nearly so ?ith res㘊ct to the ca?era 㘆ane and, therefore, not visible. The ?ingti? vortices fro? both the u㘓tro㜊 and the do?nstro㜊 are visible. T?o sets of vortices can be observed at stro㜊 transition? 㜲 is the ?ingti㘇vorte? shed at the beginning of the current u㘓tro㜊, and 㜗 is the ?ingti? vorte? shed at the end of the 㘌evious do?nstro㜊 (Fig. 2.2?, 㜰. At the 㘌evious 23u㘓tro㜊?do?nstro㜊 transition, there is a single vorte? (㜙), ?hich is li?ely to contain the ?ingti? vortices that have either ?erged by this 㘅int or are too close to be resolved. At the 㘌evious do?nstro㜊㼬㘓tro㜊 transition, the ?ingti㘇vorte? fro? the do?nstro㜊 is still 㘌o?inent (㜳), but the ?ingti㘇vorte? fro? the u?stro㜊 has ?ust disa㘶eared. The red arro? indicates its hy㘅thesi?ed 㘅sition (㝂). The 㘌evious u㘓tro㜊?do?nstro㜊 vorte㬇(㜛) has no? dissi㘄ted.⸭⼭⸊? ? ℝ? ?? ? ᰘ ᴷ┝ᨢ? ᴡ?The ?ing stro㜊 a?㘆itude (?), ?ingbeat fre㴬ency ( f), and do?nstro㜊 ratio (?) of the hu??ingbirds fro? both e㬶eri?ents are 㘌esented in Table 1. The hu??ingbirds in the 㜑ne?atics e㬶eri?ent e㬪ibited values for these variables that are si?ilar to ?hat has 㘌eviously  been re㘅rted for ?ale C. anna during hovering (Altshuler et al., 2010b). On average, the hu??ingbirds in the flo? visuali?ation e㬶eri?ent used lo?er stro㜊 a?㘆itudes and higher ?ingbeat fre㴬encies, but the individual birds ?ere also ?ore variable. Bird 䈎 for e㬄?㘆e, used  a stro㜊 a?㘆itude??ingbeat fre㴬ency co?bination that ?as nearly identical to the average values for the 㜑ne?atics e㬶eri?ent. An i?age se㴬ence of flo? develo㘵ent on the left side of  the bird is 㘌esented in Fig. 2.3 and in video 2.5. The vorte? di㘅le in fra?e 351 consists of a ?ingti? vorte? on the left and either a reversal or ?ing root vorte㬇on the right. Fro? this 㘊rs㘊ctive of the bird, both are 㘅ssible because the 㘅sition at ?hich 㘌onation occurred ?as nearly 㘊r㘊ndicular to the i?age 㘆ane of the ca?era.The average instantaneous 㘅sition ( ) and elevation (?) angles of the left and right ?ing ϕti㘓 and ?ing roots are de㘑cted in Fig. 2.䈇The 㘅sition angles of the ?ingti㘓 and ?ing roots have si?ilar a?㘆itudes, but ?ith the ?ingti㘓 leading at all stages of the stro㜊. The elevation 2?traces e㬪ibit a double har?onic 㘄ttern, but again ?ith the ?ing ti㘓 leading at all 㘪ases. Thus,  the ?ing root reverses in both 㘅sition and elevation after the ?ing ti㘉 The left and right ?ings follo?ed nearly identical 㘄tterns.⸭⼭⼊??⨝ ┛??ᴚ?The ?ingbeat 㜑ne?atics and flo? visuali?ations ?ere used to visuali?e four 㘅tential to㘅logies for hovering hu??ingbirds. These ne? but still si??lified ?odels are based u㘅n 㘌evious hy㘅theses of the single (Rayner, 1䍄䌰  and bilateral (Altshuler et al., 200䌰  vorte㬇loo㘓 and other 㘅ssible e㬶lanations for the flo? 㘄tterns observed here (Fig. 2.5). The ?ing stro㜊 is assu?ed to i?㘄rt the sa?e do?n?ard ?o?entu? to the vortices in all four ?odels. The do?n?ard velocity ?as esti?ated by tracing ?ingti㘇vortices over se㴬ences of i?ages in the flo? visuali?ation e㬶eri?ent. The i?ages ?ere calibrated using a ruler that ?as 㘆aced vertically ne㬔 to the feeder and fil?ed i??ediately after the e㬶eri?ent. The calibration ?as then a㘶lied to the flo? visuali?ation i?ages and analy?ed using I?age?. The average descent velocity based on 60 ?ingbeats fro? si㬇individuals ?as 2.6 ??s (?0.2 ??s SD). This velocity is a coarse a㘶ro㬑?ation and ?as not used to calculate aerodyna?ic force and efficiency.The outer 㘄ths of the ?odels follo? the 㘄ths of the ?ing ti㘓 over the stro㜊 a?㘆itudes  recorded during hovering flight in the 㜑ne?atics ?easure?ents. For the ?erged vorte? ring ?odel (Fig. 2.5a), the ?ingti? vorte㬇㘄th follo?s an e㬔ra㘅lated ?ingti? tra?ectory to ?erge the  left and right sides. The indented ?erged vorte? loo㘇?odel is a version of the single loo㘇?odel that includes reversal vortices. It assu?es that the connection bet?een the left and right sides occurs near the body, ?hich 㘌oduces an hourglass㼓ha㘊d loo? (Fig. 2.5b). The bilateral vorte? loo㘓 ?odel accounts for the reversal vortices by assu?ing that these are connected by root 25vortices (Fig. 2.5c). Because I did not observe se㘄rate starting and sto㘶ing vortices, these are assu?ed to either ?erge or a㘶ear very close together in this and the indented ?erged vorte㬇loo? ?odel. The bilateral vorte? loo㘓 ?odel ?as oriented to ?atch each of the bird 㘅sitions in Fig. 2.2, ?here it is 㘌esented in the right colu?n. The concentric vorte㬇rings ?odel is 㘌esented  for the scenario in ?hich the stro㜊 a?㘆itude is close to 1䔘弎 and the ?ingti㘓 and ?ing roots each for? closed loo㘓 unifying the left and right sides (Fig. 2.5d). Three?di?ensional ani?ations of the four to㘅logies are available in the videos 2.6㼗.䌉⸭《D??ᰤ? ??‡⸭〭ⰊF?‫ ⠢?␛?? 㠛? ? ??Previous PIV ?easure?ent of the hori?ontal 㘆ane underneath hovering Anna?s hu??ingbirds, C. anna, 㘌ovided vector to㘅logies that i?㘆icated the 㘌esence of bilateral vorte? loo㘓 in the ?a㜊 (Altshuler et al., 200䌰 . Ho?ever, only the source flo?s caused by the ?ets could be distinguished and not the associated vortices. Here, I ?ade high㼓㘊ed i?age se㴬ences of the ?a㜊 structures for?ed by C. anna hovering in ?hite 㘆u?es. Videos recorded fro? rear (Figs. 2.1, 2.2g) and frontal (Fig. 2.2a, d) 㘊rs㘊ctives revealed the 㘌esence of bilateral ?ets and associated vortices, ?hich dis㘌oves the ?erged vorte㬇ring ?odel (Fig. 2.5a), at least for this s㘊cies of hu??ingbird. There are t?o 㘅tential to㘅logies that can account for observations by the 㘌evious PIV study (Altshuler et al., 200䌰  and the current flo? visuali?ation? an indented ?erged vorte㬇loo? (Fig. 2.5b) and the bilateral vorte㬇loo? ?odels (Fig. 2.5c).The difference bet?een the ?odels that include bilateral ?ets is the 㘌esence or absence of  26root vortices. Vorte㬇di㘅les surrounding the bilateral ?ets ?ere shed during both u㘿 and do?n㼓tro㜊s. Ho?ever, because of the 㘌o㬑?ity and align?ent of the root and reversal vortices  at the start and end of the stro㜊, it is not certain ?hich structure ?as visuali?ed in each fra?e. Assu?ing that there are no root vortices, the ?ost co??on ?a㜊 structure e㬶ected ?ould be the to㘅logy suggested by (S㘊dding et al., 2003)  ?here the body is included in the lift generation. This can be valid in for?ard flight. Ho?ever, the distinct feature of hovering flight co??ared to other flight ?odes is the absence of for?ard flight s㘊ed, ?hich essentially e㬫ludes  the body fro? the lift generation. The flo? s㘊ed across the ?ing ?ill increase ?ith distance fro? the body but should be ?ero at the ?ing㼁ody ?unction. This decrease in flo? s㘊ed, ?hich is also a decrease in circulation to?ard the body, should be acco?㘄nied by a vorte㬇shed close to the root. The total e㬫ursion of the ?ing root during nor?al hovering is considerably less than the length of the body, ?a㜑ng it highly i?㘆ausible that the vortices shed fro? the left and right ?ing roots connect to each other. Rather, this root vorte? should connect the su㘑nating and 㘌onating vortices fro? the sa?e ?ing. This ?ill for? a closed loo? and lead to a bilateral vorte?  ?a㜊 structure.The t?o 㘅tential to㘅logies ?ith bilateral ?ets (Fig. 2.5b,c) include the assu?㘔ion that the vortices 㘌oduced by each stro㜊 for? connected strea?s rather than se㘄rate structures. I did not discern se㘄rate sto㘶ing and starting vortices, ?hich is consistent ?ith the flo? 㘄tterns generated at the do?nstro㜊?u?stro㜊 transition (su㘑nation), but not of the u㘓tro㜊?do?nstro㜊 transition (㘌onation) re㘅rted for rufous hu??ingbirds, Selasphorus rufus (Warrick et al., 2009) (see ?arric? et al., 200䌇 su㘶le?entary ?aterial, Fig. 6). Because the transition at both su㘑nation and 㘌onation occurs very fast relative to the descent rate of the flo? 㘄ssing the bird, these vortices are s㘄tially very close and, it a㘶ears, ?erge to for? a single vorte㬉 The ?a㜊 2?created by a hovering C. anna should, therefore, consist of a vertically connected vorte? ladder rather than se㘄rated vorte㬇loo㘓. It is un㜐o?n ?hether the ?ing㼸a㜊 interactions at stro㜊 transition include strong co?㘅nents of ?ing rotation and ?a㜊 ca?ture (Dic㜑nson et al., 1䍃䌰 .The vorte? structure influences the lift generated by the ?ings. The ?a㜊 㘄tterns of Blac㜫a㘓 ( Sylvia atricapilla, ?ohansson and Hedenstr圵, 200? ) include ?ing root vortices that could be either o㘶osite or sa?e sign relative to the ?ingti? vortices. The u㘸ash and do?n?ash  induced by these vortices can reduce or enhance the lift, res㘊ctively (?ang and ?u, 2010) . In the 㘌esent study, I observed vorte㬇di㘅les under each ?ing ?ith the outer (?ingti㘰 㘅le al?ays  of o㘶osite sign to the inner (reversal or ?ing root) 㘅le. This suggests that a ?ing root vorte? generates u㘸ash directly beneath the hu??ingbird. This structure can be seen in i?age se㴬ences 㘌esented here (e.g., Fig. 2.2d, e), and its signature also e㬑sts in PIV results 㘌esented in Altshuler et al. (200䌰  as a sin㜇flo? behind the bird body (e.g., their Fig. 䔰. Although the u㘸ash bet?een the bilateral loo㘓 is relatively ?ea㜎 it can slightly reduce the total lift by generating a local negative lift. Thus, ?hen all else is e㴬al, the single vorte㬇loo? ?ill 㘌oduce higher aerodyna?ic force due to the larger do?n?ash area, absence of the u㘸ash, and inclusion  of the body in lift generation. For a hovering ani?al, the vertical force ?ust by definition balance  the body ?eight regardless of ?a㜊 to㘅logy, but the single vorte? ring ?a㜊 ?ill be ?ore aerodyna?ically efficient (Mui?res et al., 2012? Norberg et al., 1䍃3) .Ani?als atte??ting to ?a㬑?i?e lift should e㬶and the area of do?n?ash, ?hereas ani?als ai?ing to ?ini?i?e 㘅?er e㬶enditure ?ould benefit fro? 㘌oducing the ?a㜊 that ?eets the aerodyna?ic re㴬ire?ents for the s?allest ?uscle out㘬t. A 㘅tential advantage of each ?ing 㘌oducing a vorte㬇loo? is that differences in the si?e and orientation of the ?a㜊 could confer enhanced ability to 㘌oduce left?right asy??etries in aerodyna?ic force 2?(Bo?㘪rey et al., 200䌰 . This level of control ?ould be advantageous for ?aneuverability (Henningsson et al., 2011), 㘅tentially at the e㬶ense of stability.The original vorte㬇?odel for hovering in hu??ingbirds (Fig. 2.5a) ?as based on early ?easure?ents fro? a tro㘑cal hu??ingbird ( Florisuga fuscus) that used a relatively high stro㜊 a??litude and close to hori?ontal stro㜊 㘆ane (Stol㘊 and Zi??er, 1䌙䌰 . Although necessarily si?㘆istic, this ?odel of a ?erged vorte? ring (Ellington, 1䍃䌺 Pennycuic㜎 1䍅䔺 Rayner, 1䍄䌺  Rayner and Gordon, 1䍃䔰 , such as that 㘌oduced by helico㘔ers, allo?ed for consideration of ho? aerodyna?ics could influence the ?etabolic costs of hovering flight (E㘔ing and Casey, 1䍄3)  and related ecological and biogeogra㘪ical constraints (Feinsinger and Cha㘆in, 1䍄5? Feinsinger and Col?ell, 1䍄䔺 Feinsinger et al., 1䍄䌰 . An e㬫iting 㘌os㘊ct of the ne? to㘅logy of the hovering ?a㜊 is that this ?ay also contribute to ne? understanding of hu??ingbird 㘪ysiological ecology.⸭〭⸊??℣᜝ᬙ ??ℝ? ᬙ? ? ??hen hovering in nor?al air, hu??ingbirds used an average ?ing stro㜊 a??litude of 153.6弎 but the average stro㜊 a?㘆itude of the birds studied in the ?hite 㘆u?es ?as only 12䌉䕟. It has been de?onstrated that hu??ingbirds ?ill ?odulate stro㜊 a?㘆itude and ?ingbeat fre㴬ency under a variety of conditions (Ortega??i?ene? and Dudley, 2012)  and can ?atch the lift re㴬ire?ents for different environ?ental and e㬶eri?ental conditions. Across ta㬄,  high?elevation hu??ingbirds use higher stro㜊 a??litudes during hovering than lo?㼊levation ta?a (Altshuler and Dudley, 2003? Altshuler et al., 2010a) . Measure?ents of the sa?e ta㬄 at different elevations reveal that hovering stro㜊 a?㘆itudes can increase by as ?uch as 2䉟 over a 1,000㼵 gain in elevation (Buer?ann et al., 2011) . During e㬶eri?ental reduction of air density, 2?hovering Ruby㼔hroated hu??ingbirds Archilochus colubris increase stro㜊 a?㘆itude fro? 帲55弇to a geo?etric li?it near 1䔘弇 (Chai and Dudley, 1䍃5) . Hu??ingbirds challenged to hover ?hen loaded ?ith ?eights increase their stro㜊 a?㘆itudes u㘇to the 帲䔘弇li?it fro? hovering values that are bet?een 22弇and 䈘弇lo?er de㘊nding on the s㘊cies (Altshuler and Dudley, 2003? Chai and Millard, 1䍃䐺 Chai et al., 1䍃䐰 . Although it is reasonable to assu?e that hu??ingbirds ?ill have bilateral vorte㬇loo㘓 ?hen using stro㜊 a??litudes ty㘑cal of hovering in nor?al air, this flo? 㘄ttern could change as the ?ing stro㜊 a?㘆itude a㘶roaches 1䔘弉 The vortices shed fro? the t?o ?ings ?ill a㘶roach each other as the stro㜊 a?㘆itude increases and ?ay cancel each other out ?hen the 㘄rallel reversal vortices collide. Under such circu?stance, I hy㘅thesi?ed that the ?a㜊 to㘅logy could consist of a root vorte? ring, 㘅sitioned ?ithin a ?ing ti? vorte㬇ring (Fig. 2.5d).?hen hovering in the 㘆u?e, the hu??ingbirds used lo?er stro㜊 a?㘆itudes but higher ?ingbeat fre㴬encies on average. ?hat could cause such an obvious change in ?ingbeat 㜑ne?atics? I tested one hy㘅thesis that the 㘆u?e could be influencing the air density by co??aring the recorded fre㴬ency of a Galton ?histle (after Dudley 1䍃5)  in air and ?ithin the 㘆u?e, as ?ell as ?ithin larger clouds of dry ice, and ?ithin an airtight cha?ber. I did not detect any changes in air density greater than 1按 It is also 㘅ssible that a higher concentration of CO 2 could influence ?ingbeat 㜑ne?atics by co?㘌o?ising o㬂gen ?etabolis?. Ho?ever, the higher ?ingbeat fre㴬encies ?ithin the 㘆u?e ?ust derive fro? an increase in the contractile fre㴬encies of the o㬂gen㼭e?anding 㘅?er ?uscles, ?hich does not su㘶ort this hy㘅thesis. Instead, reductions in o㬂gen availability cause decrease in ?ingbeat fre㴬ency ?ithout a consistent effect on ?ing stro㜊 a??litude during hovering flight in hu??ingbirds (Altshuler and Dudley, 2003). Thus, the cause of the lo?er stro㜊 a?㘆itudes is 㘌esently un㜐o?n, but I 30㘌o㘅se that the higher ?ingbeat fre㴬ency ?ay be a behavioral ad?ust?ent to allo? for a ra㘑d esca㘊 fro? an environ?ent ?ith reduced visibility and that ?aintaining vertical 㘅sition ?ith an elevated ?ingbeat fre㴬ency ?ill necessarily re㴬ire lo?er stro㜊 a?㘆itude.31AlFrame:065BLKJIHCDEFGMN Frame:065Frame:064Frame:064Frame:063 Frame:063Frame:062Frame:062Frame:061 Frame:061Frame:060Frame:060Frame:059 Frame:05932Figure 2.1. Flow visualization of a hovering hummingbird from the rear- left perspective, demonstrating sequential development of a vortex loop on the left side during a downstroke. The time interval between frames is 2 ms and sequence runs from top to bottom. The panels on the left are unmanipulated images. The panels on the right are the same images but with the bird outlined in white and key features of the flows indicated by color: blue (downstroke wing tip vortex), purple (reversal vortex), green (air jet). This image sequence comes from frames 59–65 (labeled in the lower right of each panel) of the video (2.1) of trial #5 from bird 6.33Video S3: bird 5, trial 2Video S2: bird 6, trial 3 Video S2: bird 6, trial 3ILVideo S4: bird 6, trial 92431K56A326 541B CD153 4 26E F231G101165 16558 5837 37101HJF?⌤?? ⸭⸭ V???ᬟ??ᬙ ?‡ „ ᤴ? ⠠?ᤝ㜊? ᬪ ? Ḛ?☊☤?ᤢ? ?? ????? ??? ?⠝? ⴊ Un?ani㘬lated i?ages are 㘌esented in the left 㘄nels. The central 㘄nels contain the sa?e i?ages ?ith the bird outlined in ?hite and 㜊y features of the flo?s indicated by color? blue (do?nstro㜊 ?ingti? vorte㬰, red (u㘓tro㜊 ?ingti㘇vorte㬰, 㘬r㘆e (reversal vorte㬰, green (air ?et). Straight arro?s indicate the hy㘅thesi?ed locations or structures that are no longer 㘌esent. The nu?bers build fro? ?ost recent (1) to oldest (highest nu?ber) shedding events. The acco?㘄nying video na?es, bird nu?bers, and trial are 㘌ovided underneath the left 㘄nels. The bilateral vorte㬇?odel has been 㘆aced in si?ilar orientations for co?㘄rison in the right 㘄nels. The frontal 㘊rs㘊ctive is 㘌esented after a su㘑nating rotation (A, B) and then again at the beginning of do?nstro㜊 (D, E). An off㼄㬑s rear 㘊rs㘊ctive ?ith a ?ide field of vie? is 㘌esented for a ?ing at the initiation of a do?nstro㜊 (G搖). A lateral vie? is 㘌esented at ?id?do?nstro㜊 ?ith the ?ingti? 㘄ths during the do?n㼇and u㘿stro㜊s indicated in blue and red, res㘊ctively (G搣).3?35347 348 349350 351 352353 354 355Figure 2.3. Image sequence of a hummingbird hovering in the plume with wingbeat frequency and wing stroke amplitude values that fall within the range of birds hovering in normal air. The development and progress of a jet including shed wing tip and either reversal or wing root vortices during the downstroke is visible on the left side of the animal. The vortices are indicated by blue arrows in frame 351. The amplitude of this specific downstroke was 146°.3601800LeftRight10 ms-2020-80Wing tipWing rootdown upϕ(°)θ(°)Figure 2.4. The average instantaneous wing position (ϕ) and elevation (θ) angles of the wing tips and wing roots from free-flight measurements of four male Anna’s hummingbirds (Calypte anna) during hovering flight. The downstroke phase is indicated in light blue and the upstroke is in light red. The mean stroke kinematic pattern is presented twice in succession for viewing the stroke transitions. 37indented merged vortexbilateral vortex concentric vorticesmerged vortexA BDCFigure 2.5. Schematic representations of the simplified vortex topologies. For all four topologies, the downstrokes are indicated in blue and upstrokes are indicated in red. The merged vortex ring model (A) is similar to the structures shed from a helicopter. The indented, merged vortex loop model (B) can account for wingtip and reversal vortices (purple), but has a junction at the proximal region of the latter in place of root vortices. The bilateral vortex loop model (C) accounts for wingtip, wing root, and reversal vortices. The concentric vortices model (D) may occur at wing stroke amplitudes approaching 180°.T???? ⸭Ⱝ ???⌗?ᬙ ????☛ᤢ ?? „ ??☦?? ⌗ ??? ? ???? ?? ??? ḟ‫ ⠢??ᬟ? ?ᬙ?‡ ᬡ? ????☛ᤢ? ?㜥???? ?? ?? ⴊ The sa?㘆e si?es ( n) refer to the nu?ber of ?ingbeats analy?ed to deter?ine the ?ing stro㜊 a?㘆itude ( ? , in degrees), ?ingbeat fre㴬ency ( f, in hert?), and do?nstro㜊 ratio (?, in 挰. For the flo? visuali?ation ?easure?ents, the sa?㘆e si?e of ?ingbeats analy?ed ?as lo?er for the stro㜊 a?㘆itude than for the other variables. The e㬶eri?ent average by ty㘊 of ?easure?ent is indicated by average ?ith standard errors in 㘄rentheses. Ro?s ?ith bird nu?bers contain individual ?eans ?ith standard errors in 㘄rentheses.F?‫ V???ᬟ ??ᬙ?‡? ??? 䄊 n ? ?  㵃㸊 nf? ? f 㴁?? ? 㵅㸊3 10 116.32 (1.03) 33 䈲.56 (0.3䐰 䉂.䍅 (0.63) 䈇 10 15䈉0䔇(0.䍅) 26 3䔉51 (0.2䌰 䈛.䈳 (0.3䐰 5 10 121.55 (0.䔛) 21 䉂.䐙 (0.33) 䈳.䌗 (0.䈲) 6 10 12䐉05 (1.0䌰 21 3䌉55 (0.3䌰 50.3䐇(0.6䈰 average 䈲.0䌇(1.3䐰 䈛.䌙 (1.1䔰 12䌉䐳 (䔉䈘) ??? ?☛ᤢ ??? ??? 䄊 n ?  㵃㸊 f 㴁?㸊 ? 㵅㸊䐇 15 1䉅.䍂 (1.1䐰 3䌉0䔇(0.20) 50.00 (0.3䈰 䔇 11 16䈉3䔇(0.䌲) 3䔉62 (0.31) 䈛.2䌇(0.䈙) 䌇 1䈇 1䉃.36 (0.䌛) 3䔉05 (0.1䔰 䉃.䐗 (0.䉅) 10 1䈇 151.65 (0.5䈰 3䔉2䐇(0.26) 䉄.26 (0.33) average 153.5䔇(3.65) 3䔉51 (0.22) 䉅.32 (0.䌲) 3?⼭ Bᬡ???⌊? ?⌴? ? ?? ✊?? ??: ?‡???? ? ? ? ?ᬙ???? ???⌴? ?? ????? ?⌗?? ?? ?⼭ⰊIℙ??⤤? ??‡Hu??ingbirds and ?any insects are ca?able of sustained hovering flight, as ?ell as a suite of related steady?state ?aneuvers such as ya? turns (Altshuler et al., 2012), vertical ascents (Vance et al., 201䈰 , bac㜸ards flight (Sa㘑r and Dudley, 2012) , and lateral flight. These ?aneuvers can be incor㘅rated in co?㘆e? behaviors such as feeding and se㬬al dis㘆ays. For e㬄?㘆e, hu??ingbirds are ca㘄ble of doc㜑ng at flo?ers and artificial feeders ?oving bac? and  forth in the ?ind (㘊rsonal observation), and both lateral flights and ya? turns have been described during dis㘆ays to fe?ales (Felton et al., 200䔺 Hurly et al., 2001) . Lateral flight has also been observed for brief 㘊riods in freely flying fruit flies (Ristro㘪 et al., 200䌺 van Breugel and Dic㜑nson, 201䈰 , hoverflies (Collett and Land, 1䍄5) , blo?flies (Nachtigall, 1䍄䌰 , and houseflies (?agner, 1䍅6a) , but the ?ing 㜑ne?atics and aerodyna?ic ?echanis?s that enable the ?aneuver are not fully understood. Lateral flight is of 㘄rticular bio?echanical interest because it is a translational ?aneuver that in 㘌inci㘆e only re㴬ires a force asy??etry bet?een the left and right ?ings for initiation and steady㼓tate control (Zhang and Sun, 2011).Previous studies that docu?ented lateral flight raised the 㴬estion of ?hat is the 㜑ne?atic source for force in the lateral direction. T?o hy㘅thesis have been 㘌o㘅sed, ?hich are  aerodyna?ically si?ilar but 㜑ne?atically distinct. The 㜊y assu?㘔ion underlying both 2 A subset of the data used for this cha㘔er ca?e fro? videos collected by D.L. Altshuler ?ith the intent of ans?ering a different set of 㴬estions. I develo㘊d the central 㴬estion, re?㘬r㘅sed the videos, and develo㘊d the co?㘬tational fra?e?or? that ?ade the 㜑ne?atic analysis 㘅ssible. D.L. Altshuler advised during the analysis and the ?riting.  The statistical analysis ?as develo㘊d by ?.M. Middleton in a 㘌evious study.  3?hy㘅theses is that fla㘶ing ?ings function li㜊 the actuator disc of a helico㘔er, ?eaning that the ti?e?averaged out㘬t force is nor?al to the stro㜊 㘆ane (?eis?Fogh, 1䍄2) . The first hy㘅thesis is that the actuator disc (stro㜊 㘆ane) is essentially fi㬊d to the body, and it is necessary to reorient the body to direct force into the direction of travel (force vectoring). This hy㘅thesis is derived fro? studies ?ith insects including tethered fruit flies (G圔?, 1䌛䔺 Vogel, 1䌛6) , and free?flying fruit flies (David, 1䍄䔰  and house flies (?agner, 1䍅6b) . A second hy㘅thesis is that the actuator disc, and therefore the out㘬t force, can be reoriented off the body a㬑s. Thus, the ani?al tilts its stro㜊 㘆ane in the direction of ?otion ?hile ?aintaining a constant body 㘅sture ?ith res㘊ct to the ground. This hy㘅thesis ?as 㘌o㘅sed as a 㘅ssible e㬶lanation for the lateral  flights observed in blo?flies (Blondeau, 1䍅1? Nachtigall, 1䍄䌰 . ?agner (1䍅6b)  argued against this second hy㘅thesis and 㘌o㘅sed that force vectoring can e㬶lain the strong lateral ?ove?ents observed in hoverflies  (Collett and Land, 1䍄5)  and blo?flies  (Nachtigall, 1䍄䌰 , assu?ing that the ani?als roll about their longitudinal body a㬑s during the ?aneuver. These studies did not include detailed ?easure?ents of ?ingbeat 㜑ne?atics due to li?ited availability of ?ulti?ca?era, high㼓㘊ed videogra㘪y. Recent studies ?ith detailed ?ingbeat 㜑ne?atics of ra㘑d ?aneuvers 㘊rfor?ed by freely  flying insects (Fry et al., 2003? Mui?res et al., 201䈰  and birds (Hedric? et al., 200䐺 Ros et al., 2011) su㘶ort the force vectoring hy㘅thesis? ti?e?averaged out㘬t force is orthogonal to the stro㜊 㘆ane, and the stro㜊 㘆ane is oriented by redirecting the body a㬑s. Asy??etries in stro㜊 a??litude, angle of attac㜇and ?ing deviation ?ere observed for at least so?e ?ingbeats during these brief turning ?aneuvers. Ho?ever, one study ?ith fruit flies indicates that asy??etries in ?ingbeat 㜑ne?atics can lead to an orientation of aerodyna?ic forces that contradicts the assu?㘔ion of the actuator disc (Ristro㘪 et al., 200䌰 . During t?o ?aneuvers, the tilt of the 䈘stro㜊 㘆ane did not fully account for the ?agnitude of the lateral acceleration. The authors 㘌o㘅sed that the lateral force ?as further su㘶le?ented by a drag㼁ased ?echanis? caused by differences in the ti?e of ?ing rotation (fli㘰 bet?een the left and right ?ings.The original ai? of the 㘌esent study ?as to e㬄?ine the neuro?uscular and bio?echanical control of sustained lateral flight as hu??ingbirds fed continuously fro? a translating feeder. Initial e㬄?ination of the digiti?ed data revealed a sur㘌ising result? hu??ingbirds 㘊rfor?ed controlled lateral flight by ban㜑ng the stro㜊 㘆ane off the body a㬑s, but o㘶osite to the direction of travel. This indicates that 1) hu??ingbirds can control lateral flight using a ?echanis? other than force vectoring, and 2) that controlled lateral flight 㘊rfor?ed at a feeder involves forces not 㘌edicted by the tilt of the stro㜊 㘆ane. Here I 㘌esent this result and focus ?y analysis on e㬶laining these t?o une㬶ected results. ⼭⸊Mᴙ㐠⤘⼭⸭ⰊA™?ᬟ?Si㬇adult ?ale Anna?s hu??ingbirds ( Calypte anna) ?ere ca?tured near the ca?㘬s of the California Institute of Technology and t?o additional ?ale Anna?s hu??ingbirds ?ere ca?tured near the ca?㘬s of the University of British Colu?bia using dro㘿door tra㘓 (Russell and Russell, 2001). The hu??ingbirds ?ere housed in individual cages and fed ad libitum ?ith a  solution of artificial nectar (Ne㜔ar?Plus, Ne㜔on, Pfor?hei?, Ger?any) and sugar ?ater. Before the e㬶eri?ents, the birds ?ere allo?ed to accli?ate to the flight cha?ber. The 㘌ocedures ?ere a㘶roved by the Institutional Ani?al Care and Use Co??ittee of the California Institute of Technology and the Ani?al Care Co??ittee at the University of British Colu?bia.䈲3.2.2 E㬶eri?ental setu㘇and trainingE㬶eri?ents ?ere 㘊rfor?ed in an acrylic cube (0.䌇? 3) ?ith three clear sides and three ?hite sides to 㘌ovide bac㜋rounds for fil?ing (Fig. 3.1a). The birds ?ere trained to feed fro? an artificial feeder ?ade out of a 25 ?l syringe ?ounted on a 䈳c? linear slide table 㘅?ered by  a ste㘶er ?otor (?1䔇and MD2b, Arric? Robotics, Tyler T?). The feeder ?as oriented hori?ontally and 䌘弇to the a㬑s of table ?otion so that the hu??ingbird could 㘊rfor? 㘬re lateral flight ?hile feeding during feeder ?ove?ent. The birds ?ere trained to feed on co??and once every 20 ?inutes (Altshuler et al., 2012). Si㬇birds ?ere fil?ed during hovering and ?hile ?oving laterally at 0.15 ??s in both the left and right directions.The trials ?ere recorded using three internally synchroni?ed high㼓㘊ed ca?eras (Photron  AP?, San Diego CA? f?s? 1000 fra?es?sec, shutter? 1?6000sec). The ca?eras ?ere 㘆aced dorsally, laterally and above the bird. Calibration ?as 㘊rfor?ed using direct linear transfor?ation (DLT) ?ith a 2䐿㘅int calibration ob?ect in DLTdv5 soft?are (Hedric㜎 200䔰 . Eight 㘅ints ?ere digiti?ed on each hu??ingbird? right shoulder, left shoulder, right ?ing ti㘎 left ?ing ti㘎 right 5th 㘌i?ary, left 5th 㘌i?ary, to? of the head, and the ti㘇of the ?iddle tail feather. The 2D 㘅ints ?ere transfor?ed to 3D coordinates that ?ere filtered ?ith a ?ero?㘪ase, fourth?order lo?㼶ass Butter?orth filter. The filter cut㼅ff fre㴬encies ?ere si㬇ti?es the ?ingbeat fre㴬ency for the shoulders and tail, eight ti?es the ?ingbeat fre㴬ency for the ?ingti?  and 5th 㘌i?ary, and t?ice the ?ingbeat fre㴬ency for the head. To co?㘄re ?ingbeat 㜑ne?atics ?ith electro?yogra㘪y data, the filtered 㜑ne?atic data ?ere u㘓a?㘆ed fro? 1000 sa?㘆es?sec to 10,000 sa?㘆es?sec using a cubic s㘆ine (inter㘅late 㘄c?age, Scientific Tools for Python). I defined the 㘌onation ti?e for each ?ing as the ti?e of ?ini?u? e㬫ursion in the stro㜊 㘆ane and the su㘑nation ti?e as the ti?e of the ?a㬑?u? e㬫ursion. 䈗The flo? visuali?ation trials ?ere 㘊rfor?ed ?ith t?o birds using a different ste㘶er ?otor and linear actuator (M㼭rive 23 Motion Control, Schneider Electric, Marlborough CT). The birds ?ere fil?ed 㘊rfor?ing controlled lateral flight at 15c??s and 30c??s ?hile flying through a 㘆u?e of CO 2 created by dro㘶ing dry ice cubes into hot ?ater. This ?ethod is described in detail in Pourna?eri et al. (2012). The trials ?ere fil?ed fro? the dorsal 㘊rs㘊ctive using a single ca?era (M120, Vision Research, ?ayne N?, USA? f㘓? 1000 fra?es?sec, shutter? 1?1110 sec) ⼭⸭⼊Fᨛ?ᴊ?? ???? ??ℜ? ᬡ⤊??ℝ? ?? ? ? ⠛ᨢ?ᜟ? ?To co?㘄re the 㜑ne?atics across ?ingbeats, I used t?o fra?es of reference defined by the 㘅sition of the ?ings at the start and end of do?nstro㜊 and u㘓tro㜊? one gravitational and one stro㜊㼫entered. The fra?es of reference and ?ost of the 㜑ne?atic variables are described in  detail else?here (Altshuler et al., 2012). Fro? these t?o fra?es of reference I calculated 1䈇㜑ne?atic variables for each do?nstro㜊 and u?stro㜊. Seven variables ?ere calculated in the gravitational fra?e of reference? average ?ingti? s㘊ed ( Uti? ), lateral body angle (χGR,?Z ), frontal body angle (χGR,YZ), instantaneous 㘅sition angle ( ϕGR), instantaneous elevation angle (? GR), average elevation angle (? GR), and the stro㜊 㘆ane angle (䤰. The stro㜊 㘆ane angle is calculated  solely fro? the ? and Z coordinates of the ?ingti㘓, and therefore only ?easures the angle relative to the hori?ontal 㘆ane fro? the lateral 㘊rs㘊ctive. It does not describe other features of the stro㜊 㘆ane. In the stro㜊㼫entered fra?e of reference I calculated the ?ingstro㜊 a??litude (? SP) and elevation a?㘆itude (? SP). I calculated several ne? ?easure?ents co?㘄red to Altshuler et al. (2012) to assess lateral flight 㘊rfor?ance. The ?ing ban㜇angle ( WBA) is defined as the difference in the average 䈙elevation angle bet?een the left and right ?ings, divided by 2. By convention, ?hen the left ?ing is elevated and the right ?ing is de㘌essed the WBA is 㘅sitive, and ?hen the right ?ing is elevated and the left ?ing is de㘌essed the WBA is negative. The relative ?ing ban? angle (RWBA) is a ?easure of the ?ing ban㜇relative to the frontal body a㬑s and is calculated as the absolute value of the su? of the WBA and χGR,YZ. ?hen the ?ings are 㘊r㘊ndicular to the body a㬑s the RWBA is ?ero.  The geo?etric angle of attac㜇( ?)  is calculated as the angle bet?een the 㘆ane of the ?ing and the hori?ontal for a given ?ing elevation (Fig. 3.1b). By this convention, a geo?etric angle of 0弇signifies that the ?ing is oriented 㘄rallel to hori?ontal, and at 䌘弇the ?ing is oriented vertically. The 㘆ane of the ?ing ?as defined by three 㘅ints? the shoulder, the ?ingti㘎 and the ti㘇of the 5th 㘌i?ary feather. This ?easure of the hu??ingbird geo?etric angle  of attac? is calculated in the gravitational fra?e of reference and therefore differs fro? analogous ?easures in the body㼫entered fra?e of reference (?ruyt et al., 201䈺 Tobals㜊 et al., 200䐰 . The ?ing rotation velocity ( ) is calculated as the derivative of the geo?etric angle of ααattac? and the ?ingti㘇angular velocity (儰 is calculated ?ith the s㘪erical la? of cosines for the ?ing 㘅sition and deviation angles. The travel angle (?)  re㘌esents ho? the bird is oriented ?ith res㘊ct to the feeder (Fig. 3.1c,d) and is defined as the angle bet?een the feeder, ?hich defines the 㬿a㬑s, and the ?ingti? 㘄th dividing line. The latter is defined as a line connecting the ?id㘅ints bet?een the ?ingti㘓 at the u㘓tro㜊?do?nstro㜊 transition and do?nstro?e?u㘓tro㜊 transition (Altshuler et al., 2012). The travel angle is 㘅sitive ?hen the bird is facing the direction of ?otion, as sho?n in figure 3.1d, and negative ?hen the bird is facing a?ay fro? the direction of ?otion. The bill insertion (Bill 挰 is the 㘊rcentage of the e㬶osed cul?en inside the  artificial feeder, calculated using I?age? soft?are. The fra?e of reference transfor?ations and the calculations of the 㜑ne?atic variables ?e re ?ade using custo? soft?are ?ritten in Python 䉂(Python Soft?are Foundation).⼭⸭《? ␛?? ? ?? ᴛ⤧ ??ᬙᴊᬡᬟ ✘? ?I used a Quasi㼓teady state aerodyna?ic analysis based on the blade?ele?ent ?odel develo㘊d by ?eis㼤ogh (1䍄3)  and e?㘆oyed by others (e.g., Fry et al., 2005? ?ruyt et al., 201䈰 . This a㘶roach integrates the instantaneous lift and drag forces occurring along chord??ise  sections (blades) of the ?ing over the ti?e course of the ?ingstro㜊. By definition, 㴬asi?steady state aerodyna?ic ?odels do not include rotational lift generating ?echanis?s that are 㜐o?n to act on reci㘌ocating ?ings (Altshuler et al., 2005). The instantaneous, 㴬asi?steady lift and drag acting on each fla㘶ing ?ing are calculated as?L⃗ift= ? C LρS R22 V⃗ incident2⃗Drag= ? C DρS R33 V⃗ incident2?here ?  is the air density (1.225 㜋 ? ?3 ), S is the surface area of the ?ing (6.䑅E ??  ? 2) and R2 and R3 are the second and third ?o?ents of the ?ing (.䉃䌇and .552 res㘊ctively). The ?ing and body ?ass ?easure?ents used in the ?odel are s㘊cies㼄veraged values for C. anna that ?ere re㘅rted in a 㘌evious study (?ruyt et al., 201䈰 . CL and CD are the coefficients of lift and drag, res㘊ctively, ?hich ?ere calculated using the aerodyna?ic angle of attac㜇( ? aero, 弰, defined as the angle of attac㜇of the ?ing relative to the incident velocity ( Vincident)?CL, do㠐 =0.0031+1.5䕂2 ×cos(0.0301αaero+ 䈉䐲2? )䈳CD, do㠐 = 䔉31䐲 + 䔉1䌘? ×cos(0.00䐙 αaero+3.1䈲6 )CL, u? =0.002? +1.1251×cos(0.0332(αaero−1?0 )+ ?.6?63 )CD, u? =1.1䍃3 +1.0䌙? ×cos(0.02䔲 (αaero−1䔘 )+3.12䑄 )These e㴬ations ?ere e?㘑rically derived for C. anna ?ings and 㘌esented in ?ruyt et al. ( 201? ), and differ here only in the sign convention of ? aero ?ith res㘊ct to the u㘿 and do?n㼇stro㜊s . The incident velocity ?as calculated as?V⃗ incident=V⃗ ti? +V⃗ induced+V⃗ body?here Vr ti?  is the velocity of the ?ingti? calculated fro? the ?otion of the ?ing, Vr body is the velocity of the bird (0 for hovering, 0.15?s ?1  for lateral flight), and Vr induced is the velocity of the air induced by the ?otion of the ?ings. The induced velocity ?as esti?ated using the Ran㜑ne㼤roude ?odel ?hich assu?es a flat stro㜊 㘆ane and a do?n?ard directed velocity. Pennycuic㜇 (1䌛䔰  derives t?o e㴬ations for induced velocity, one for hovering and one for for?ard flight at s㘊eds greater than 1?s ?1 . Because the s㘊ed of the controlled lateral flight trials  ?as ?uch less than 1?s ?1  I use the hovering e㴬ation for all of ?y calculations?V⃗ induced=√ mg2ρ Adis?䈛?here ? is the ?ass (0.0䈛䔇㜋), g is the gravitational constant, and Adis㜇 is the area s?e㘔 out by the actuator dis㜎 esti?ated by the e㴬ation?Adis? =( 11䔘 )ΦSPπ L2?here ? s?  is the calculated stro㜊 a??litude, and L is the ?ing length (0.0525?). To calculate Vr ti?  and ? aero I used the average ?ingbeat 㜑ne?atics, assu?ing a 3䌇H? ?ingbeat fre㴬ency for hovering and a 䈲 H? ?ingbeat fre㴬ency for lateral flight, as ?ell as a do?nstro㜊?u㘓tro㜊 ratio of 䉅?52 for both hovering and lateral flight. The lift acts in the direction of the vector obtained by ta㜑ng the cross 㘌oduct of the leading edge of the ?ing and Vr incident, in the 㘅sitive vertical direction, ?hereas the drag acts in the direction of Vr incident. The instantaneous forces ?ere calculated for 200 e㴬ally s㘄ced ti?e 㘅ints during the course of the ?ingbeat and then the average forces in the global vertical, for?ard, and lateral directions ?ere calculated.⼭⸭ㄊE?ᴜ? ??? ✠⌚ᬥ㐧The 㘌ocedures for ?a㜑ng electro?yogra㘪ic recordings (EMGs) in hu??ingbirds are described in detail else?here (Altshuler et al., 2010b? Altshuler et al., 2012) . Briefly, u㘇to four 㘄irs of double㼁onded 䍃.䍃指silver ?ires se㘄rately insulated ?ith heavy 㘅lyi?ide (HML, bifilar, California Fine ?ire, Grover Beach, CA, USA) ?ere inserted in the pectoralis major and pronator superficialis ?uscles. An atte??t ?as ?ade to insert one ?ire 㘄ir into each ?uscle on the left and right sides, but not all insertions ?ere successful. During surgeries, birds ?ere 䉄anestheti?ed ?ith isoflourane and ?ires ?ere inserted by for?ing a hoo㜇?ith a hy㘅der?ic needle and then using the needle to insert the ?ire into the ?uscle. A force㘓 ?as used to hold the ?ire in 㘆ace ?hile re?oving the needle and then ?oving the ?ire slightly to secure it to a bundle of fibers. A fifth insertion ?as ?ade for the ground electrode, ?hich consisted of a single silver ?ire ?ith HML insulation. All ?ires ?ere attached first to the s㜑n and then to the intervertebral fascia using suture. The signals fro? the EMG ?ires ?ere a?㘆ified 1000? (?odel 1䐘0, A㼚 Syste?s, Se㴬i?, ?A, USA) and digitally ac㴬ired (Digidata 1䉂0, Molecular Devices, Sunnyvale, CA, USA) along ?ith the ca?era trigger signal for synchroni?ation ?ith the ?ingbeat 㜑ne?atics. The online filters ?ere set ?ide o㘊n at 0.1 H? (high?㘄ss) and 10 㜥? (lo?㼶ass), and subse㴬ent filtering and analyses ?ere conducted offline using custo? scri㘔s ?ritten in Matlab (Math?or㜓 Inc., Natic㜎 MA, USA). All EMG signals ?ere 㘌ocessed using a fourth㼅rder Butter?orth filter at bet?een 3 and 12 ti?es the ?ingbeat fre㴬ency. A ti?ing and an intensity ?easure for each activation burst ?ere analy?ed. Recordings fro? the pectoralis major had one burst 㘊r cycle ?hereas recordings fro? the pronator superficialis has t?o bursts 㘊r cycle.⼭⸭㈊S?????? ? ᰛ? ᬡᬟ✘??To 㴬antify the changes in 㜑ne?atic and ?uscle activation features I used a ?i?ed㼵odel ANOVA ?ith ?ing 㘅sition (leading ?ing, hovering ?ing, trailing ?ing) as the fi㬊d effect and bird as rando? effect. The 㜑ne?atic and electro?yogra㘪ic ?easure?ents for the leading ?ings ?ere averaged for both left and right lateral flights and li㜊?ise for the trailing  ?ings. The hovering ?ingbeat 㜑ne?atics are an average of the left and right ?ings. The do?nstro㜊 and u㘓tro㜊 㘄ra?eters ?ere analy?ed se㘄rately. For ?odels ?ith significant 䉅overall ANOVAs (alpha ? 0.05), a 㘅st hoc analysis ?as used to test for significant differences bet?een leading ?ing and hovering ?ing, trailing ?ing and hovering ?ing, and leading ?ing and  trailing ?ing using general linear hy㘅thesis tests corrected for ?ulti㘆e co?㘄risons (Hothorn et al., 200䔰 . Si?ilarly, for the body 㜑ne?atics I used a ?i?ed㼵odel ANOVA ?ith direction of travel (right lateral, hover, left lateral) as the fi?ed effect and bird as rando? effect, and ?hen the  results ?ere significant ( alpha ? 0.05) I 㘊rfor?ed the three 㘅st hoc co?㘄risons to test for significant differences bet?een right lateral flight and hovering, left lateral flight and hovering, and right and left lateral flight.Analysis of the cross㼫orrelations bet?een 㜑ne?atic and electro?yogra㘪ic ?easure?ents largely follo? Altshuler et al. (2012). Briefly, I considered 㘄ir?ise cross㼫orrelations a?ong 㜑ne?atic ?easure?ents and bet?een 㜑ne?atic and electro?ygra㘪ic ?easure?ents each for a series of 16 consecutive ?ingbeats. I included lag values of 㼗, 㼲, 0, 1, and 2, corres㘅nding to ?ingbeat lags of 㼲, 㼲?2, 0, 1?2 , and 1. Significance of cross㼫orrelations  ?as deter?ined analytically using 10,000 rando?i?ations for each variable 㘄ir, because rando?ly 㘊r?uted data can sho? significant a㘶arent cross㼫orrelation (Altshuler et al., 2012). To aid in visuali?ation of cross㼫orrelation analysis result, I colori?ed 㘑vot?tables of P㼒alues according to significance level.Because I carried out ?any statistical tests on closely related data (䔘 hy㘅thesis tests in Table 3.1 and Table 3.2, co?bined ?ith 2,3䈘 in the cross㼫orrelation analysis), correction for ?ulti㘆e co??arisons ?as necessary to 㘌event inflation of fa?ily??ise error rate overall (Curran?Everett, 2000) .  I 㘊rfor?ed a 㘅sitive false discovery rate (㘤DR) analysis, ?ith the goal of controlling fa?ily?ise error rate at 0.05 (i.e., no ?ore than 5指?false 㘅sitives?? Storey, 2002). The ?s?oother? o㘔ion in the R (v. 3.1.0? R Foundation for Statistical Co?㘬ting) 䉃㘄c?age 㴒alue  (v. 1.3䔉0) ?as used to deter?ine an ad?usted ? level for the statistical tests. The results of this analysis, ?hich uses the e?㘑rical distribution of P㼒alues to esti?ate the rate of true null hy㘅theses indicates that at alpha ? 0.01䐎 fa?ily㼸ise error rate is controlled at 5按 Therefore, I use this ?odified al㘪a level for inferences (Table 3.1 and Table 3.2).⼭⼊Rᴘ␟??⼭⼭Ⰺ??℣᜝ᬙ ??ℝ? ᬙ? ? ? „ ᰠ?? ??? ? ᴩ ???ᴚᬟ ???⌴?Si㬇?ale Anna?s hu??ingbirds ( Calype anna) ?ere fil?ed during both hovering and controlled lateral flight at 15 c??s ?hile feeding fro? a translating, artificial feeder. This s㘊ed ?as the ?a㬑?u? that could be steadily achieved by the ste㘶er ?otor and linear slide. I later fil?ed t?o additional C. anna ?ales for flo? visuali?ation  using a different ?otor and slide, ?hich could achieve s?ooth ?otion at faster s㘊eds. These t?o birds ?ere able to easily feed fro? a feeder ?oving at 30 c??s. Feeder ?ove?ents began ?ith a brief acceleration 㘪ase and ended ?ith a brief deceleration 㘪ase, but only se㴬ences ?ith constant velocity ?ere analy?ed.Ignoring defor?ations, the instantaneous ?ing ?otion of a hu??ingbird can be described using three angles in the gravitational fra?e of reference (Fig. 3.2). ?ing 㘅sition angles (ϕGR) ?ere sinusoidal and highly re㘊atable for both ?ings across all three treat?ents. Elevation angles (? GR) follo?ed a si?ilar ti?e course for the left and right ?ing during hovering but differed during lateral flight. The leading ?ing ?as elevated relative to the trailing ?ing during ?ost of the ?ingbeat but ?as lo?er than the trailing ?ing during su㘑nation. This 㘄ttern ?as observed in every bird in al?ost all ?ingbeats and is readily a㘶arent in 㘆ots of the average ?ingstro㜊s overlaid onto bird silhouettes (Fig. 3.3).50During lateral flights, the t?o ?ings also differed in the ti?e course of the geo?etric angle of attac? ( ? ) for ?ost of the ?ingbeat (Fig. 3.2). On average, the change in the angle of attac? (?ing rotation) ?as delayed in the leading ?ing and advanced in the trailing ?ing during the transition fro? do?nstro㜊 to u?stro㜊 (su㘑nation). The t?o ?ings ?ere ?ore synchroni?ed during the transition fro? u?stro?e to do?nstro㜊 (㘌onation). Ho?ever, the ti?e course of the angle of attac? ?as ?ore variable than the other ?ing angles ?ithin and bet?een birds. The derivative of the angle of attac㜎 the rotational velocity ( αα), also differed bet?een the t?o ?ings during lateral flight (Fig. 3.䈰. The leading ?ing rotated slo?er during the last half of the do?nstro㜊 and faster during the first half of the u㘓tro㜊, relative to the trailing ?ing. The ?ingti? angular velocity (? ) ?as si?ilar bet?een the leading and trailing ?ings. The t?o online su㘶le?entary videos of left?ard lateral flights fro? the dorsal 㘊rs㘊ctive de?onstrate the differences in elevation angle and angle of attac? bet?een leading and trailing ?ings. Individual fra?es fro? video 3.1 of 㘌onation, ?id㼭o?nstro㜊, su㘑nation, and ?id㼬㘓tro㜊 fro? a single  ?ingbeat are sho?n in figure 3.5.To analy?e the differences in the ?ingstro㜊 㘄tterns observed during hovering and controlled lateral flight, I defined stro㜊?s㘊cific 㜑ne?atic 㘄ra?eters that are co?㘄rable to other studies of ani?al flight (Table 3.1). Generally, during lateral flight the stro㜊 㘆ane angle (䤰 of the leading ?ing increased, ?hereas the stro㜊 㘆ane angle of the trailing ?ing decreased relative to hovering. I ?as unable to statistically analy?e the stro㜊 㘆ane angle using a linear ?i?ed ?odel because this variable had a bi?odal distribution. During lateral flight the stro㜊 a??litude (? SP) ?as lo?er than hovering flight, ho?ever there ?as no significant difference bet?een leading and trailing ?ings. The average ?ingti? s㘊ed ( Uti? ) ?as faster during the do?nstro㜊 co??ared to the u㘓tro㜊, but there ?as no significant difference bet?een the 51leading and trailing ?ings during lateral flight. I 㘌esent t?o ?easures to describe the deviation of the ?ing fro? the body and the stro㜊 㘆ane, the average elevation angle ( ? GR) and the elevation a?㘆itude (? SP). During lateral flight the leading ?ing ?as elevated and had a lo? elevation a?㘆itude, and the trailing ?ing ?as lo?ered and had a high elevation a??litude, co??ared to hovering. The geo?etric angle of attac? ?as analy?ed statistically at four 㜊y 㘅sitions? the ?iddle ( ? ?id ) and the end (? end) of the do?nstro㜊 and the u?stro㜊. The leading ?ing angle of attac? ?as si?ilar to hovering ?ings during the do?nstro㜊 but ?as significantly shallo?er co?㘄red to hovering ?ings during the ?iddle of the u㘓tro㜊. The trailing ?ing had a  stee?er angle of attac㜇during the do?nstro㜊, but ?as si?ilar to hovering during the u㘓tro㜊. The angles of attac? at the end of the u?stro?e ?ere si?ilar for all flight ?odes. ?hole body 㜑ne?atic ?easure?ents are 㘌esented in Table 3.2. The 㘊rcentage of the bill inserted into the feeder (Bill ? ) did not differ significantly a?ong treat?ents. The do?nstro㜊 ?as significantly faster during lateral flight than hovering. Birds tended to face the direction of travel during lateral flight, but I did not analy?e this ?ith a ?i?ed ?odel because travel angle (? ) has no ?eaning during hovering flight. The body angle fro? the lateral 㘊rs㘊ctive ( χGR,?Z ) did not differ significantly across treat?ents. Fro? the frontal 㘊rs㘊ctive (χGR,YZ), the hu??ingbirds? bodies ?ere significantly tilted to the right during flight to left but ?ere close to vertical (䌘弰 during hovering and flight to the right. During controlled lateral flight the bird used a ?ing ban? angle ( WBA) that ?as tilted o㘶osite to the direction of ?otion, and the bird did not ?aintain a 㘊r㘊ndicular ?ing ban㜇angle ( RWBA) bet?een ?ings and the dorsal body a㬑s. These 㘄tterns held for both do?nstro㜊 and u㘓tro㜊.The hu??ingbirds did not orient their stro㜊 㘆ane into the direction of travel during sustained lateral flight. To discard the 㘅ssibility that these counterintuitive ?ingbeat 㘄tterns 52?ere a result of the bird being dragged by the ?oving feeder, I ?easured the 㘊rcentage of the bill inserted into the feeder. This nu?ber had a broad range? the ?a?i?u? value ?as 5䉣 and the ?ini?u? value ?as only 2指(Fig. 3.3a,d?e). Bill insertion 㘊rcentage did not vary consistently ?ith flight ?ode (Fig. 3.6b). Bill insertion 㘊rcentage ?as unrelated to the ?ing ban? angle (Fig. 3.6c), and individuals that ?aintained a lo? insertion also tilted their ?ings o㘶osite to the direction of travel. Additionally, ?hen the feeder ?as ?odified so that there ?as no 㘅ssibility of tethering, the ?ings re?ained ban㜊d o㘶osite to the direction of travel (Fig. 3.6f). Collectively, these results do not suggest that the bird is being 㘬lled along by the feeder.⼭⼭⸊? ␛?? ? ?? ᴛ⤧ S???ᴊᬡᬟ ✘? ?The observed 㜑ne?atic 㘄tterns during lateral flight indicate that hu??ingbirds generate a net force that is not nor?al to the ?ing stro㜊 㘆ane. This observation is inconsistent ?ith the actuator disc ?odel 㘌o㘅sed by ? eis㼤ogh (1䍄2) . Broadly s㘊a㜑ng, there are t?o 㘅ssible e㬶lanations for this 㘄ttern. The first is that a ?ore co?㘆e㬎 blade?ele?ent ?odel, incor㘅rating left?right differences in ?ing deviation and angle of attac㜎 can lead to a net force that is not nor?al to the average stro㜊 㘆ane. This hy㘅thesis can be evaluated using a 㴬asi?steady aerodyna?ic analysis. An alternative hy㘅thesis is that unsteady ?echanis?s are generating the force co?㘅nents to 㘌o㘊l hu??ingbirds in the direction of travel.The 㴬asi?steady forces in the vertical, thrust, and lateral co?㘅nents are 㘌esented for the average ?ingbeat 㘄ttern during left lateral, hovering, and right lateral flight (Fig. 3.䐄㼫). These force co?㘅nents are e㬶ressed in a bird centered fra?e of reference. The 㴬asi?steady analysis for hovering flight largely su㘶orts observations fro? other studies such as left㼌ight sy??etry for the vertical and thrust co?㘅nents, asy??etry in force out㘬t bet?een the 53do?nstro㜊 and u㘓tro㜊, and 66指?eight su㘶ort (0.66? b) (Fry et al., 2003? ?ruyt et al., 201䈺 ?arric? et al., 2005) . There ?as an une㬶ected asy??etry bet?een bac㜸ards and for?ards thrust for all three flight ?odes. During left lateral flight, the net thrust ?as 0.0䌸 b in the for?ard direction. Net thrust ?as 0.11? b of body ?eight in the for?ard direction during hovering  and right lateral flight. This result ?as 㘌obably due to ?ing t?ist. The 㘌o㬑?al section of the ?ing had a very high angle of attac? and the distal section had a ?uch lo?er angle of attac㜎 but the ?easure of ? ?as based on a flat 㘆ane that incor㘅rated both sections. This led to a high esti?ate for drag and for?ard thrust during the u?stro㜊.The left and right ?ings 㘌oduce o㘶osite lateral forces, ?hich essentially su? to ?ero over the course of the full hovering ?ingbeat (0.0䐸 b to?ards the left). During lateral flight, the net vertical and thrust co?㘅nents are si?ilar to hovering flight, but the lateral co?㘅nents do not su? to ?ero. Ho?ever, the net lateral forces are oriented o㘶osite to the direction of travel. During lateral flight to the left, the average lateral force is 0.0?? b to?ards the right, and during lateral flight to the right, the average lateral force is 0.06? b to the left. Because the birds had non㼼ero travel angles (21.䍟 during left lateral flights and 10.3弇during right lateral flights), I also calculated the 㴬asi?steady force in the direction of travel, ?hich ?as 0.03? b to the right during left lateral flight and 0.0?? b to the left during right lateral flight. It is i?㘅rtant to note that if the for?ard thrust co?㘅nent during the u㘓tro㜊 is inflated (see above), then the 㴬asi?steady forces o㘶osite to the direction of travel ?ill be even stronger. This analysis therefore indicates that although asy??etries in ?ingbeat 㜑ne?atics are sufficient to generate lateral forces, the observed 㜑ne?atic 㘄tterns are not consistent ?ith a 㴬asi㼓teady ?echanis? for controlling lateral flight in hu??ingbirds.5?I ne㬔 used flo? visuali?ation via subli?ation of dry ice to e㬄?ine the orientation of the ?ets caused by the ?ings. This visuali?ation a㘶roach ?or㜓 best for the i?㘬lse ?ets caused by the fla㘶ing of the ?ings and is therefore another ?ethod to describe the feasibility of 㴬asi?steady ?echanis?s.  Controlled lateral flight through the s?o㜊 revealed the 㘌esence of t?o ?ets, one under each of the leading and trailing ?ings (Fig. 3.䔰. The 㘌i?ary flo?s generated  during ?id㼓tro㜊s ?ere oriented  in the direction of travel and the resulting ?o?entu? i?㘬lse is o㘶osite to the direction of travel. This result is in agree?ent ?ith the 㴬asi㼓teady analysis.⼭⼭⼊M’‚ ᬜ??⠛? ? ‡Muscle activation 㘄tterns derived fro? electro?yogra? recordings of 㘊ctoral and ?ing ?uscles ?ere analy?ed in ter?s of ti?ing and intensity. As ?as the case for a 㘌evious study of ya? turns in Anna?s hu??ingbirds (Altshuler et al., 2012), I found no statistically significant relationshi㘓 bet?een ?uscles activations and flight treat?ents. Because feeder trac?ing involves a se㴬ence of ?ingbeats, I further analy?ed the ?ing㼇and body㼓㘊cific variables and EMG variables using cross㼫orrelation analysis. Most of the 㜑ne?atic variables sho?ed significant associations ?ith other 㜑ne?atic variables, and ?ost of these associations 㘊rsisted over ?ulti?le ti?e lags (?1 ?ingbeat, Fig. 3.䌰. Ho?ever, several 㜑ne?atic variables including frontal travel angle, bill 㘊rcent, body angle, and stro㜊 a?㘆itude had fe?, if any, associations ?ith other variables. There ?ere no significant associations bet?een EMG and 㜑ne?atic variables.55⼭《D??ᰤ? ??‡ Hu??ingbirds 㘊rfor?ing controlled lateral flight ?hile feeding fro? a translating feeder 㘌oduced asy??etrical ?ingbeats ?ith substantial differences in the ti?e course of the instantaneous elevation angle and geo?etric angle of attac㜇(Fig 3.2). Analyses on stro㜊?averaged 㜑ne?atics revealed a nu?ber of significant differences in ?ing ?otion bet?een  the leading and trailing ?ings. The average elevation angle of the leading ?ing ?as higher, and of the trailing ?ing ?as lo?er, relative to the hovering ?ingbeat 㘄ttern (Fig. 3.3, 3.5). The leading ?ing also had a lo?er elevation a??litude and stee?er stro㜊 㘆ane angle relative to the trailing ?ing (Table 3.1). Again, the hovering ?ingbeat had inter?ediate values. The overall result of this e㬶eri?ent is that the ?ings of Anna?s hu??ingbirds are ban㜊d a?ay fro? the direction of travel during sustained lateral flight, although the birds ?aintained a vertical body orientation as in hovering. Thus, the tilt of the stro㜊 㘆ane during steady lateral ?otion ?as not generated by a reorientation of the body fra?e, but rather a change in 㜑ne?atics relative to the body. This 㘄ttern ?as unaffected by the e㬔ent of insertion of the bill in the feeder (Fig. 3.6). Collectively, these results suggest that controlled lateral flight 㘊rfor?ed at a feeder involves forces not 㘌edicted by the tilt of the stro㜊 㘆ane.There are at least four 㘅ssible sources for the lateral force in the direction of travel, including? 1) doc㜑ng to the ?oving feeder, 2) bilateral asy??etries during the translational 㘪ases of the stro㜊, 3) bilateral differences in ?ing㼸a㜊 interaction during stro㜊 reversal, and 䈰 inter?ittent ?ingbeats ban㜊d to?ards the direction of travel. The analysis of feeder doc㜑ng does not suggest that the feeder itself is the lateral force ?echanis? but it ?ay be that slight contact bet?een the bill and feeder, even as little as 2挎 is indeed sufficient to 㘬ll the bird. If true, this re㘌esents rather re?ar㜄ble behavior that could e㬶lain ho? hu??ingbirds are able to  56㘌ecisely feed fro? flo?ers ?oving in the ?ind.  I did observe consistent differences in ?ing elevation, angle of attac㜇and rotation velocity bet?een the leading and trailing ?ings. Aerodyna?ic ?echanis?s o㘊rating during the translational 㘪ases of the stro㜊 ?ay be accurately a㘶ro㬑?ated fro? a 㴬asi㼓teady analysis, ?hich indicates that the ?ing asy??etries do generate significant lateral force (Fig. 3.䐰. Indeed,  the esti?ated lateral forces ?ere oriented o㘶osite to the direction of travel. Flo? visuali?ation sho?ed that the induced flo? through the vorte? structures created by each of the ?ings is nor?al to the stro㜊 㘆ane and slightly inclined in the direction of lateral ?otion (Fig. 3.䔰. If this  coarse flo? structure is inter㘌eted as re㘌esenting the ?o?entu? i?㘄rted to the fluid during the translational 㘪ases of the stro㜊, then these results are consistent ?ith the 㴬asi㼓teady analysis. Another 㘅ssible e㬶lanation for the direction of lateral ?otion is the force 㘌ovided by unsteady aerodyna?ic ?echanis?s that are not ca?tured by either the 㴬asi㼓teady ?odel or the flo? visuali?ations. Because the advance ratio is so lo? ( J ? 0.01䈇and 0.030 for the 㜑ne?atic analysis and s?o㜊 visuali?ation, res㘊ctively), one 㘅tential source of force results fro? the interaction of the ?ing ?ith the ?a㜊 of the 㘌evious stro㜊 (Altshuler et al., 2005? Birch, 2003? Dic㜑nson et al., 1䍃䌰 . Although it has not been for?ally evaluated, the force due to ?ing㼸a㜊 interactions ?ay have large lateral co?㘅nents because the surface of each ?ing, ?hich is a coarse 㘌edictor for the direction of any net 㘌essure force, is oriented 㘊r㘊ndicular to the direction of travel. I also observed a bilateral asy??etry in the 㘌ogression of the angle of attac? bet?een the leading and trailing ?ings, ?hich led to differences in the ?ing rotation velocity and  in the ti?ing of ?ing su㘑nation. These differences ?ay cause unsteady aerodyna?ic effects that are sufficient to o㘶ose and overco?e the lateral forces generated by the ban㜊d ?ings to drive 5?the lateral flight in the direction observed. Although I cannot directly test this hy㘅thesis ?ith ?y  data (or li?ely any data collected fro? live ani?als), this hy㘅thesis could be evaluated using a dyna?ically㼓caled robot or an accurate CFD ?odel.Finally, it is 㘅ssible that inter?ittent ?ingbeats ban㜊d to?ards the direction of travel are sufficient to 㘌ovide lateral force but do not have a strong influence on the average ?ingstro㜊 㘄ttern. If this is true, then 㘌ecise lateral velocity is ?odulated ?ith a se㴬ence of alternating ?ingbeats used to accelerate and brea㜎 as o㘶osed to a single, stereoty㘊d ?ingstro㜊. This intriguing 㘅ssibility could be tested ?ith a ti?eseries analysis of long stretches  of controlled lateral flight.Another une㬶ected finding of this study is that a s㘊cific co?bination of 㜑ne?atic features used by hu??ingbirds 㘊rfor?ing controlled lateral flight are also observed during asy??etric ?aneuvers described in other studies. The elevated ?ing has a lo?er elevation a??litude and delayed rotation during su㘑nation, relative to hovering. The lo?ered ?ing has a higher elevation a?㘆itude and advanced rotation during su㘑nation, relative to hovering. The sa?e co?bination ?as observed in the 椓ashay椇and 椭odge? lateral flight ?aneuvers of fruit flies (Ristro㘪 et al., 200䌰 , although they used a different a㘶roach for describing the 㜑ne?atic 㘄tterns. Ho?ever, to 㘊rfor? these ?aneuvers, flies elevated the trailing ?ing, in contrast to laterally flying hu??ingbirds ?hich elevated the leading ?ing. A 㘌evious study e㬄?ined the ?ingbeat 㜑ne?atics that Anna?s hu??ingbirds e?㘆oyed to ?a㜊 ya? turns, ?hich is another ?aneuver involving asy??etry bet?een the left and right ?ings (Altshuler et al., 2012). In that study, the geo?etric angle of attac㜇?as not ?easured, but the association bet?een ?ing elevation and elevation a?㘆itude ?as observed during ya? turns ?here the outside ?ing ?as elevated. Given that the association a?ong ?ing elevation, ?ing elevation a?㘆itude, and ?ing 5?rotation ti?ing has no? been observed for t?o ta㬄 during four asy??etrical ?aneuvers, an obvious 㴬estion for future research is ?hether this association is driven by ?or㘪ological constraints, ti?ing constraints, or aerodyna?ic efficiency?Controlled lateral flight is slo? and steady, re㴬iring 㘌ecision in lateral acceleration and balancing of all ?o?ents. In contrast, the free㼕light ?aneuvers that have been studied in detail for insects and birds (Fry et al., 2003? Hedric㜇et al., 200䐺 Iriarte?D?a? and S?art?, 200䔺 Mui?res et al., 201䈰  ?ere fast and transient, and it ?ay be ?ore difficult to control accelerations and balance ?o?ents ?hen using force vectoring. Ho? often is controlled lateral found in nature? Hu??ingbirds have been 㜐o?n to use lateral flight to 㘊rfor? a variety of different tas㜓 including esca?e behaviors (Clar㜎 2011b) , co?㘊titive interactions, aerial insect ca?ture (Yanega and Rubega, 200䈰 , feeding fro? ?oving flo?ers or feeders, and a ?ide variety of shuttle dis㘆ays (Clar㜎 2011a? Clar? et al., 2012? Hurly et al., 2001) . The ?ing 㜑ne?atics of these behaviors have not been studied in?de㘔h, but it is li?ely that ?any of the? are significantly different than those used for controlled lateral flight. Esca㘊 behaviors and co??etitive interactions re㴬ire high levels of agility but a lo?er level of 㘌ecision co?㘄red to feeder trac?ing. ?hen the 㘌i?ary goal is to esca㘊 or hit an o㘶onent, this can be acco?㘆ished ?ith a series of i?㘬lsive darts and dodges. Li㜊?ise, aerial insect ca㘔ure re㴬ires high levels of agility, but using an e㬔re?e bill ga㘊 hel㘓 reduce the levels of control and 㘌ecision needed (Yanega and Rubega, 200䈰 . For all three of these behaviors it is e㬶ected that hu??ingbirds ?ould 㘌i?arily use force vectoring 㜑ne?atics. The 㘌ecision to feed fro? flo?ers and feeders ?oving in ?indy conditions ?ay lead birds to use a strategy ?ore si?ilar to controlled lateral flight, although at high s㘊eds they ?ay change to a for? of force vectoring. Hu??ingbird courtshi? dis㘆ays are highly varied and s㘊cies㼓㘊cific and ?ay be 㘊rfor?ed ?ith either 5??ethod de㘊nding on the flight features that are being 㘬t on dis㘆ay. A dis㘆ay that sho?cases accelerations and changes in direction is li㜊ly 㘊rfor?ed by force vectoring ?hereas a dis㘆ay that involves stability, control, and 㘌ecision ?ay use ?echanis?s si?ilar to those used in controlled lateral flight. The increased 㘅rtability of high㼓㘊ed ca?eras should allo? for ?ore e㬔ensive docu?entation of ho? lateral flight is 㘊rfor?ed in natural settings.6061+_CamerasAmplifier100 mmShoulder to WingtipHorizontalA BDCX axisY axisΨbill %Figure 3.1. Methods used to study and quantify controlled lateral flight. (A) Hummingbird feeder tracking was studied in an acrylic flight chamber. The feeder was moved left and right using a stepper motor and linear slide. Three high-speed cameras were placed orthogonally and filmed the bird during hovering and lateral flight. Trailing EMG electrodes were connected to an extracellular amplifier just outside of the chamber. (B) The kinematic variables are presented in Altshuler et al. (2012), and one new variable, the geometric angle of attack α, is introduced here. α is calculated relative to a plane defined by the shoulder to wingtip vector and the horizontal. (C) A top view of a bird moving laterally to the left. Six digitized anatomical features are presented in this panel: left wingtip (red), right wingtip (blue), left shoulder (green), right shoulder (orange), head (magenta), and tail (cyan). (D) The frame of reference was transformed by aligning every frame to the head, and every wing stroke to the midpoints between the stroke transitions. The travel angle Ψ is the angle between the wingtip path dividing line and the orientation of the feeder, which is aligned with the x-axis. Ψ is positive when the bird is facing the direction of motion and negative when it is facing away. The bill % is the percentage of the exposed culmen inserted into the feeder.62900-90900-90900-9015090righthoverleftrightrightleftlefthoverhover30-1030-1030-10Representative Wingbeat Traces Average Wingbeat Tracesθ GR (°) ϕ GR (°)α (°)25 milliseconds 1 wingbeat cycleleft wing right wing1509015090303030down upF?⌤?? ⼭⸭ T?☝ ?․?? ? „ ???⌊ᬡ ⌟?? ?? ??? ᤚᬙ? ??ḙ? ??⌴ ᤊ? ?Ḟ???? ??? ?? ???⌊? ?⠢ᬙ ?‡ ᬡ?  ᬡ⌟? „ ᬙᤛ?? ????? ⌊?‡ ᤚ?? ??? ?ᬙ? ?ᬟ ḟ?⌴᤭  Re㘌esentative traces fro? one individual in each of three treat?ents (right lateral flight, hovering, and left lateral flight) are 㘌esented on the left. The 㘅sition angle ϕ, deviation angle ?, and geo?etric angle of attac㜇? are 㘌esented for each treat?ent. The scale bar of 25 ?s is valid for all re㘌esentative traces. The average ?ingbeat  traces, calculated across all individuals, are 㘌esented t?ice in succession on the left side of the figure. Lines re㘌esent average values and trans㘄rent bands indicate the standard errors of the ?ean calculated across birds. The ti?ing for all average traces is nor?ali?ed by do?n㼇and u㘿stro㜊, ?ith each re㘌esenting 50指of the ?ingbeat. Do?nstro㜊s are re㘌esented in gray and u㘓tro㜊 are re㘌esented in ?hite. The left ?ing is indicated in red and the right ?ing is indicated  in blue.63641cmLeft Hover RightFigure 3.3. The average wingbeat kinematics from three perspectives indicate strong difference in wing elevation and kinematic angle of attack between controlled lateral flight and hovering. Left controlled lateral flight is given in the left column with rows 1-3 depicting the front, side, and top views, respectively. The fourth row depicts the kinematic angle of attack. These same perspectives for hovering and right controlled lateral flight are given in the middle and right columns, respectively. The right wingtip path is given in blue and the right shoulder is given in orange. The left wingtip paths is given in red and the left shoulder is given in green. The scale bar of 1 cm is valid for all panels. Black arrows represent direction of flight. Stroke direction is indicated by small blue and red arrows for columns 1-3. The downstroke is shaded in gray for row 4. 6530-301 wingbeat cycleleft wingright wing30-30   030LeftLeftω (°/ms)HoverHoverRight30-30Right   030   030 α (°/ms)Figure 3.4. The leading wing rotates slower during the mid-downstroke and faster during the mid-upstroke relative to the trailing wing during controlled lateral fight. The wing rotation velocity α is calculated as the derivative of the geometric angle of attack, and is presented in the top three traces for the three treatments. The wingtip angular velocity ω is calculated with the spherical law of cosines for the wing position and deviation angles, and is presented in the bottom three traces. The average traces across all birds are presented twice to allow for visualization of the transitions between strokes. Other features of the plots are the same as in figure 2.66788 ms795 ms799 ms804 msFigure 3.5.  A dorsal perspective on controlled lateral flight illustrates that the leading wing is elevated, rotates slower during the downstroke, and faster during the upstroke. A time lapse of images from the same wingbeat during controlled lateral flight to the left are spread out for clarity. The downstroke begins at 788 ms (white text) and the mid-downstroke occurs at 795 ms. The upstroke begins at 799 ms and the mid-upstroke occurs at 804 ms. The distance between each pair of images is equivalent to the distance the bird and feeder would move over 20 wingbeats. The feeder was moving at 15 cm/second. The entire movie from which this sequence is obtained is available in the online supplementary materials (Movie 1).67right lateral flighthovering flightleft lateral flightdirection specific WBA DS (°) 057.5-2.52.5BD EF162 ms173 ms497 ms508 mswingbeat #0 5 10 15bill insertion % 02550Abill insertion %0 25 50CF?⌤?? ⼭㈭ T?? ???⌊?ᬡ ? ᬡ⌟? ?? ??ᬞḝ?ᤝ? ?✊ᤴ? ?㜙??ᤊᤠ ????? ᤴ? ???? ?? ?????? ?? ??ᤠ  ᤴ? ḝ??? ??  (A) The bill insertion 㘊rcentages are 㘆otted for all trials. Hovering trials are indicated in green, and controlled lateral flight to the left and right are indicated in red and blue, res㘊ctively. (B) The direction s㘊cific ?ing ban㜇angle ( WBADS) is 㘆otted across all trials. By this convention a 㘅sitive value signifies the leading ?ing is elevated and the trailing ?ing is de㘌essed. In the hovering trials a 㘅sitive value signifies the left ?ing is higher than the right ?ing Hovering trial averages are calculated as left 㼇right. The leading ?ing is consistently higher than the trailing ?ing across all trials ?ith a ?oving feeder. (C) The ?ing ban㜇angle ?as not related to bill insertion. The 䌳指confidence intervals for the slo㘊 included a slo㘊 of 0 in all cases. In this 㘄nels, each 㘅int re㘌esents the ?ean of the entire trial and the error bars re㘌esent standard error of the ?ean along both a㬊s. Hovering trial averages are calculated as left㼌ight and are not included in the ?odel fit. (D) A fra?e shot fro? the ca?era fil?ing fro? the to㘇is 㘌esented for bird 䄲 ?oving to the left. For this ?ingbeat, the bird has a lo? travel angle (1䍟), 51指of its bill inserted in the feeder, and a difference bet?een the average elevation angles of the leading and trailing ?ings of 䕟. (E) An e㴬ivalent fra?e shot is 㘌esented for bird 䄛, also ?oving to the left. In this ?ingbeat, the bird had a high travel angle (䉂弰, 2指of its bill inserted in the feeder, and a difference bet?een the average elevation angles of the leading and trailing ?ings of 䑟. (F) Fra?e shots fro? a video of a bird ?oving at 30 c??second to the left ?hile feeding fro? a feeder ?ith a large ?indo? designed so that the bird cannot be dragged along. The i?ages are ta㜊n at t?o ?id?do?nstro㜊s (162 ?s, 䉃䐇?s) and the subse㴬ent ?id?u㘓tro㜊s (䉃䐇?s, 50䔇?s). In each of the four i?ages the ?ings are ban㜊d o㘶osite to the  direction of travel.6?69Left lateral Hover Right laterallateral forcevertical forceforward force1 wingbeat cycleupforwardbackwardleftrightinstantaneous force (fraction of body weight)110201110Figure 3.7. The quasi-steady aerodynamic analysis reveals that wing translation generates net lateral forces opposite to the direction of travel during lateral flight.The instantaneous vertical (upper panels), forward (middle panels), and lateral (lower panels) forces were calculated using a blade-element analysis. The columns depict the forces based on the average wingbeat kinematics (Fig. 3) during left lateral, hovering, and right lateral flight. Instantaneous forces generated by the left (red) and right (blue) wings, and the net force (black) are expressed relative to body weight.  The net force over the whole wingbeat and along each axes is depicted by the solid yellow line. The downstroke is depicted in gray and the upstroke is depicted in white.70A BC D89 ms288 msFigure 3.8. Flow visualization during controlled lateral fight illustrates that each wing produces jets that are orthogonal to the stroke plane. Bird #7 was filmed from the dorsal perspective during controlled lateral flight to the left in the presence of a CO2 plume created by the sublimation of dry ice. The complete movie is available in the online supplementary materials (Movie 2). The frame at 89 ms provides a view of the jet generated by the left (leading) wing immediately after mid-downstroke. This frame is provided twice, once as an unmanipulated image (A) and again with the outline of the bird (white) and the jet (red) included (B). The frame at 288 ms from the same video provides a view of the jet generated by the right (trailing) wing immediately after mid-downstroke. Unmanipulated (C) and outlined (D) images are provided. The feeder was moving at 30 cm/second.710.06 0.02 0.03 0.10 0.24 0.03 0.08 0.04 0.32 0.16 0.04 0.00 0.03 0.02 0.06 0.09 0.30 0.06 0.05 0.04 0.32 0.16 0.04 0.000.10 0.02 0.05 0.11 0.19 0.01 0.21 0.21 0.04 0.24 0.01 0.14 0.13 0.02 0.15 0.04 0.28 0.05 0.20 0.21 0.04 0.24 0.01 0.140.08 0.02 0.11 0.05 0.34 0.03 0.01 0.01 0.16 0.18 0.04 0.00 0.07 0.02 0.12 0.01 0.13 0.04 0.06 0.01 0.16 0.18 0.04 0.000.13 0.02 0.02 0.06 0.38 0.01 0.09 0.02 0.11 0.13 0.01 0.03 0.15 0.02 0.01 0.06 0.41 0.06 0.15 0.02 0.11 0.13 0.01 0.030.17 0.03 0.05 0.04 0.26 0.02 0.02 0.13 0.10 0.25 0.10 0.02 0.10 0.03 0.09 0.05 0.28 0.03 0.10 0.13 0.10 0.25 0.10 0.020.08 0.00 0.02 0.10 0.19 0.04 0.12 0.02 0.13 0.20 0.02 0.16 0.00 0.03 0.04 0.32 0.03 0.04 0.02 0.13 0.20 0.020.10 0.00 0.04 0.02 0.19 0.02 0.20 0.06 0.14 0.03 0.02 0.11 0.00 0.02 0.01 0.31 0.01 0.15 0.06 0.14 0.03 0.020.07 0.00 0.06 0.04 0.19 0.00 0.03 0.03 0.07 0.03 0.07 0.07 0.00 0.06 0.02 0.19 0.04 0.06 0.03 0.07 0.03 0.070.08 0.00 0.01 0.08 0.26 0.02 0.11 0.28 0.05 0.30 0.00 0.08 0.00 0.02 0.03 0.30 0.03 0.13 0.28 0.05 0.30 0.000.14 0.00 0.04 0.03 0.20 0.04 0.01 0.20 0.06 0.21 0.09 0.21 0.00 0.01 0.03 0.31 0.04 0.06 0.20 0.06 0.21 0.090.01 0.00 0.00 0.00 0.25 0.00 0.06 0.33 0.00 0.38 0.01 0.00 0.00 0.00 0.20 0.01 0.20 0.33 0.00 0.380.00 0.00 0.01 0.00 0.26 0.01 0.01 0.25 0.12 0.35 0.01 0.00 0.01 0.00 0.24 0.01 0.01 0.25 0.12 0.350.01 0.00 0.00 0.00 0.32 0.00 0.05 0.20 0.06 0.40 0.01 0.00 0.00 0.00 0.21 0.01 0.04 0.20 0.06 0.400.01 0.00 0.00 0.00 0.23 0.00 0.03 0.14 0.12 0.27 0.00 0.00 0.00 0.00 0.23 0.00 0.07 0.14 0.12 0.270.01 0.00 0.01 0.00 0.29 0.00 0.05 0.22 0.03 0.34 0.00 0.00 0.01 0.00 0.26 0.00 0.10 0.22 0.03 0.340.29 0.42 0.33 0.31 0.33 0.25 0.14 0.13 0.24 0.37 0.42 0.33 0.33 0.19 0.30 0.19 0.13 0.240.27 0.43 0.23 0.28 0.19 0.28 0.12 0.04 0.14 0.33 0.41 0.24 0.38 0.12 0.29 0.22 0.04 0.140.25 0.41 0.21 0.22 0.16 0.13 0.19 0.00 0.15 0.36 0.40 0.39 0.24 0.11 0.30 0.22 0.00 0.150.30 0.42 0.20 0.23 0.09 0.17 0.33 0.03 0.20 0.26 0.42 0.31 0.25 0.23 0.12 0.19 0.03 0.200.38 0.40 0.22 0.39 0.21 0.31 0.19 0.26 0.24 0.32 0.40 0.27 0.38 0.29 0.35 0.27 0.26 0.240.18 0.02 0.02 0.10 0.25 0.02 0.12 0.06 0.12 0.02 0.03 0.06 0.19 0.07 0.18 0.060.14 0.03 0.25 0.15 0.16 0.10 0.00 0.08 0.07 0.03 0.24 0.04 0.12 0.10 0.06 0.080.07 0.04 0.03 0.06 0.13 0.01 0.07 0.11 0.20 0.04 0.06 0.07 0.19 0.13 0.29 0.110.07 0.03 0.20 0.07 0.21 0.10 0.00 0.12 0.18 0.03 0.16 0.07 0.16 0.09 0.00 0.120.18 0.03 0.03 0.13 0.15 0.03 0.07 0.08 0.04 0.03 0.01 0.07 0.26 0.14 0.21 0.080.19 0.24 0.15 0.31 0.22 0.28 0.12 0.22 0.32 0.18 0.34 0.28 0.15 0.300.33 0.20 0.27 0.14 0.13 0.15 0.09 0.29 0.23 0.23 0.38 0.17 0.31 0.140.26 0.24 0.16 0.30 0.19 0.15 0.13 0.23 0.27 0.16 0.14 0.25 0.21 0.310.22 0.19 0.27 0.15 0.17 0.01 0.25 0.26 0.18 0.05 0.28 0.18 0.27 0.190.26 0.22 0.21 0.27 0.13 0.17 0.08 0.22 0.21 0.27 0.13 0.22 0.17 0.190.11 0.00 0.07 0.03 0.23 0.02 0.04 0.02 0.10 0.11 0.21 0.110.04 0.00 0.02 0.10 0.26 0.03 0.12 0.04 0.04 0.06 0.25 0.100.02 0.00 0.05 0.02 0.17 0.06 0.04 0.01 0.03 0.12 0.25 0.070.07 0.00 0.03 0.08 0.15 0.01 0.08 0.01 0.02 0.12 0.22 0.050.02 0.00 0.02 0.04 0.17 0.08 0.10 0.02 0.04 0.09 0.12 0.070.01 0.00 0.01 0.00 0.27 0.00 0.00 0.05 0.00 0.170.02 0.00 0.00 0.00 0.32 0.01 0.00 0.00 0.01 0.210.01 0.00 0.00 0.00 0.22 0.00 0.00 0.02 0.00 0.260.03 0.00 0.01 0.00 0.25 0.00 0.00 0.03 0.00 0.370.03 0.00 0.00 0.00 0.32 0.01 0.00 0.01 0.01 0.260.39 0.33 0.28 0.36 0.26 0.28 0.21 0.320.32 0.38 0.34 0.29 0.33 0.30 0.21 0.240.25 0.37 0.04 0.28 0.24 0.29 0.05 0.280.34 0.36 0.07 0.26 0.13 0.35 0.06 0.250.32 0.39 0.29 0.30 0.36 0.41 0.20 0.340.01 0.00 0.00 0.00 0.00 0.000.01 0.00 0.00 0.01 0.00 0.010.00 0.00 0.00 0.00 0.00 0.030.00 0.00 0.01 0.00 0.00 0.000.02 0.00 0.00 0.00 0.00 0.010.01 0.00 0.01 0.000.00 0.00 0.00 0.000.01 0.00 0.03 0.000.01 0.00 0.01 0.000.01 0.00 0.01 0.000.00 0.000.00 0.000.00 0.000.00 0.000.00 0.00-10½1-½Θsp Φsplag αend β χ GR,YZχ GR,XZθGRαmid ΨUtip T WBA WBAΘsp Φspαend β χ GR,YZχ GR,XZθGRαmid ΨUtip T-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½-10½1-½lagWBARWBATΨχ GR,XZχ GR,YZβθGRΦspΘspUtipαmidleft wing right wingF?⌤?? ⼭䠭 A ☛ᤚ?㜊„ ?ᬢ?? ?? ? ???? ? ?‚???ᬙ?‡ ? ᬦ‡⌊??? ?☛? ?? ⠛??ᬗ? ?? ????? ? ?‡ᤚ?? ??? ?ᬙ??? ? ḟ?⌴? ??? ?
???? ? ⴊ Values sho?s are analytical P㼒alues based on the ?edian nu?ber of ti?es that observed cross㼫orrelations ?ere significant relative to rando?i?ed data (see Altshuler et al., 2012 for additional details). The lags of 1 and 㼲 re㘌esent the 㘌eceding and subse㴬ent ?hole ?ingbeats ?hile the lags of 㼲?2 and 1?2 re㘌esent ?ingstro㜊s. P㼒alues are shaded for ease of co?㘄rison. Cells shaded red are significant at alpha ? 0.01䐎 the  al㘪a level ad?usted for a 㘅sitive false discovery rate of 5指(see Methods). The blue shading re㘌esents the strength of P㼒alues that ?ere not significant. Cross㼫orrelations a?ong 㜑ne?atic  variables on the left side of the hu??ingbirds are sho?n in the left colu?n and cross㼫orrelations a?ong 㜑ne?atics on the right side are sho?n in the right colu?ns. A full list of variables and their abbreviations is 㘌ovided in Table 3.1 and Table 3.2.䐗T???? ⼭Ⱝ M?㜝? ☠??? ANOVA 㴦☛㸊„ ???⌊? ?? ?☛ᤢ ??: ?ᤚ??? ????? ??⌟? 㵉㸻 ᬨ??ᬣ? ?? ?⠛ᤢ‡ ᬡ⌟? ? ? GR 㸻 ?ᤚ??? ᬦ???ᤤ ? ? ?? SP㸻 ?? ?⠛ᤢ‡ ᬦ???ᤤ ? ? 㵋 SP 㸻 ᬨ??ᬣ? ???⌙?? ????? ? U??? 㸻 ᬡ? ᬡ⌟? „ ᬙᤛ?? ᬙ ☢?㌘ᤚ?? ? ? ? ??? 㸊ᬡ? ???㌘ ᤚ?? ? ? ? ?℩ 㸊Ḡ? ?’? ?‫?? ᤚ?? ? ? DS㸊ᬡ ? ???ᤚ?? ? ? US㸊? ✊? ?? ⌊ḟ?⌴ ᤊ☠? ? 㴟?ᬩ?? ? ???⌻ ?
???? ? ???⌻ ᤚᬢ ??? ⌊? ?? ⌾ⴊ Bird ?as included as a rando? effect ?ithin the ?odel. The degrees of freedo? for each ANOVA are 2, 10. For ?odels ?ith significant ANOVAs three 㘅st㼪oc co?㘄risons ?ere ?ade? leading vs hovering (L㼥), trailing vs hovering (T?H), and leading vs trailing ?ings (L?T). The ?eans are 㘌esented along ?ith the P values for the ANOVA and the three 㘅st?hoc co??arisons.  The P values for ? DS and ? US are not 㘌esented because the distribution of these variables is bi?odal due to the fra?e of reference chosen and thus violate the assu?㘔ions of the ANOVA.☝ᬡ P ⠛?? ?L?ᬩ??? H
????? T?ᬢ???? ☦? L㌁ T?H L㌖? DS (? ) 1䈉2 10.0 5.6 ? ? ? ?? US (? ) 12.5 䐉2 㼘.5 ? ? ? ?? GR,DS (? ) 13.0 䌉1 5.2 ?0.001 ?0.001 ?0.001 ?0.001? GR,US (? ) 䌉5 5.6 1.2 ?0.001 ?0.001 ?0.001 ?0.001? SP,DS (? ) 1䈛.2 150.? 136.3 0.020 0.51? 0.002 0.05?? SP,US (? ) 1䈛.? 151.2 135.? 0.012 0.5䈘 ?0.001 0.026? SP,DS (? ) 6.2 䔉? 1䈉6 ?0.001 ?0.001 ?0.001 ?0.001? SP,US (? ) 䌉? 15.? 22.? ?0.001 ?0.001 ?0.001 ?0.001Uti㘎DS (??s) 11.0 11.2 10.? 0.13? ? ? ?Uti㘎US (??s) 10.2 10.? 䌉? 0.00? 0.1䑄 ?0.001 0.050? DS,?id (?) 30.3 3䈉1 3䌉1 0.003 0.103 0.01? ?0.001? DS,end (?) 䑂.? 䔘.? 䌙.? 0.01? 0.500 0.0䉃 0.001? US,?id (?) 116.? 12䐉1 130.? 0.002 ?0.001 0.36? ?0.001? US,end (?) 䑂.5 䔲.? 䔘.1 0.32? ? ? ?䐙T???? ⼭⸭ M?㜝? ☠??? ANOVA 㴦☛㸊„ ??‟? ?
✊??? ?☛ᤢ??: ???? ?????? ᤛ⌝ ?????ᤝ? ?? ḝ??? ? 㴇??? 䔾㬊??? ?? ᤚ?? ? ??? ?
 ? T㸻 ᤚᬨ? ? ᬡ⌟? 㵍㸻 ?ᬙ? ?ᬟ ?
✊ᬡ⌟? 㵎 GR??? 㸻 Ḛ??ᤛ? ?
✊ᬡ⌟? 㵎 GR?Y? 㸻 ???⌊?ᬡ ? ᬡ⌟? ? WBA 㸻 ᬡ? ???ᬙ ?⠝ ???⌊? ᬡ ? ??⌟? ? RWBA 㸊? ✊☛? ?? ⠝? 㴟?ḙ ?ᬙ??ᬟ ḟ?⌴᤻ ?
???? ⌻ ??⌴ᤊ?ᬙ??? ? ḟ?⌴᤾? Bird ?as included as a rando? effect ?ithin the ?odel. The degrees of freedo? for the Bill 指ANOVA is 2, 5, and for the other 㘄ra?eters is 2, 䔉 For ?odels ?ith significant ANOVAs three 㘅st㼪oc co?㘄risons ?ere ?ade?  left vs hovering (L?H), right vs hovering (R㼥), and left vs right (L㼟). The ?eans are 㘌esented along ?ith the P values for the ANOVA and the three 㘅st?hoc co?㘄risons. The P values for ? are not re㘅rted because travel angle is not a ?eaningful ?easure?ent during hovering.☝ᬡ P ⠛?? ?L?ḙ H
????? R?⌴? ☦? L㌁ R㌁ L㌈Bill ? 2䈉? 1䌉? 2䐉? 0.6䔙 ? ? ?TDS (?s) 11.? 12.3 11.? 0.02? 0.005 0.02? 0.䍃2TUS (?s) 12.? 13.3 12.? 0.0䉃 0.02? 0.02? 0.䍂??  (?) 21.? ? 㼲0.3 ? ? ? ?? GR,?Z,DS  (?) 5䌉1 66.? 56.5 0.06? ? ? ?? GR,?Z,US  (?) 5䐉6 65.? 5䈉5 0.0䉄 0.052 0.015 0.䑂2? GR,YZ,DS (?) 3.5 0.2 㼲.? 0.00? 0.00? 0.33? ?0.001? GR,YZ,US (?) 2.6 0.2 㼲.3 0.0䈲 0.06? 0.55? 0.00?WBADS 䈉0 0.0 㼗.6 ?0.001 ?0.001 ?0.001 ?0.001WBAUS 䐉? 㼘.6 㽄.? ?0.001 ?0.001 ?0.001 ?0.001RWBADS 䐉5 0.1 䈉? 0.001 ?0.001 0.006 0.111RWBAUS 10.5 㼘.? 䔉? ?0.001 ?0.001 ?0.001 0.5䌳䑂〭 B??᠙ ??᠜? ? ????‚ ? ᬡ?? ????? ? ?᠊? ?? ᠥ???㬊ᬜ ? ?? ? ? ?? ? ‡㬊ᬡ? ????? ?⌊?? ? ? ?? ? ᬡ? ? ?? ????? ?⌗?? ??〭ⰊIℙ??⤤? ??‡The ability of an ani?al to ?aneuver can deter?ine its success at avoiding 㘌edators, obtaining food, and 㘊rfor?ing other funda?ental behaviors that define the ?argin bet?een life and death (Hedenstro? and Rosen, 2001? ?al㜊r et al., 2005? ?ebb, 1䍄6) . Most bio?echanical research on birds has focused on either brief (e.g. ta㜊 off) or steady㼓tate ?ove?ents (e.g. for?ard flight) that can be studied ?ost readily in the laboratory. Maneuverability is therefore one of the ?ost i?㘅rtant but least understood as㘊cts of ani?al loco?otion. ?arric㜇and co?or㜊rs (?arric? and Dial, 1䍃䔺 ?arric㜇et al., 1䍃䔰  㘌o㘅sed that there are both intrinsic and facultative influences on ?aneuvering 㘊rfor?ance. For ani?als that 㘊rfor? 㘅?ered flight, intrinsic ?aneuverability is defined by the 㘪ysical li?itations i?㘅sed by ?ing si?e and sha㘊 (e.g., Norberg and Rayner, 1䍅䐰 , but ?uscle 㘅?er reserves should allo? the? to facultatively overco?e the costs of subo㘔i?al ?or㘪ology, achieving higher levels of 㘊rfor?ance by sacrificing efficiency. Although co??elling, this hy㘅thesis has never been tested e㬶licitly.?ing ?or㘪ology is defined using ?easures of si?e (e.g. area or length) and non㼭i?ensional ?easures of sha㘊 (e.g., as㘊ct ratio). ?ing area and as㘊ct ratio have significant and ?ell 㜐o?n effects on the aerodyna?ics of flight in ani?als (Pennycuic㜎 1䍄5) , and should affect ?aneuvering 㘊rfor?ance. ?ing ?or㘪ology influences flight efficiency 䐳(Feinsinger and Cha㘆in, 1䍄5) , and is correlated ?ith ecological roles (Feinsinger, 1䍄6? Feinsinger and Col?ell, 1䍄䔺 Feinsinger et al., 1䍄䌺 ?arric㜎 1䍃䔰  and co?㘊titive ability (Altshuler, 2006? Feinsinger and Cha㘆in, 1䍄5? Feinsinger and Col?ell, 1䍄䔺 Feinsinger et al., 1䍄䌰 . Because these 㘌evious studies concerned s㘊cies and gender co?㘄risons, less is 㜐o?n about ho? individual variation in ?ing ?or㘪ology influences 㘊rfor?ance, es㘊cially ?ith res㘊ct to ?aneuverability. One co??lication is that different ?ing si?es and sha㘊s can be favored de㘊nding on the s㘊cific ?aneuver 㘊rfor?ed, e.g., ya? versus ban㜊d turns. Given the  diversity of flight behaviors, it is unclear if the re㴬ire?ents for ?aneuvering e㬊rt strong selection on ?ing ?or㘪ology. Muscle 㘅?er reserves in flying ani?als are defined as the difference bet?een the ?ini?u? aerodyna?ic 㘅?er re㴬ired to fly and the ?a㬑?u? aerodyna?ic 㘅?er generated during burst 㘊rfor?ance (Chai and Dudley, 1䍃䌰 . Po?er reserves indicate ho? ?uch additional  force is available for other flight behaviors, such as accelerating ?hile ?aintaining or increasing altitude, or directing force laterally to 㘊rfor? a level turn. Po?er reserves could also be used to co??ensate for subo㘔i?al ?ing 㘅sitions and angles used during body rotations or ?hen ?ing ?ove?ents are anato?ically or s㘄tially constrained (?arric㜎 1䍃䔰 . Altshuler and co?or㜊rs (Altshuler, 2006? Altshuler et al., 200䈄)  de?onstrated that variations in ecological role across s㘊cies are ?ore strongly associated ?ith burst ?uscle ca?acity than ?or㘪ological 㘄ra?eters such as ?ing loading. Burst ?uscle ca㘄city is also associated ?ith s㘊cies? and gender?s㘊cific co??etitive ability at different elevations. Altshuler (2006) suggested that the relationshi㘇bet?een burst ?uscle ca㘄city and co?㘊titive ability ?ay be ?ediated through ?aneuvering 㘊rfor?ance. Voluntary ?aneuvers are difficult to constrain e㬶eri?entally and are not e㬶ected to be 䐛as stereoty㘊d as si?㘆er flight behaviors, as de?onstrated by studies on esca㘊 reactions (Clar㜎  2011b? Mui?res et al., 201䈰  and obstacle avoidance (Iriarte㼝?a? and S?art?, 200䔺 ?illia?s and  Bie?ener, 2015) . Even ?hen ?aneuvering can be constrained ?ithin a laboratory setu㘎 such as ?hen hu??ingbirds trac㜇a revolving feeder, there is considerable variation ?ithin and a?ong individuals in ?ingbeat 㜑ne?atics (Altshuler et al., 2012). Unconstrained and voluntary ?aneuvers have been recorded fro? hoverflies (Geurten et al., 2010), blo?flies (Braun et al., 2010), and cliff s?allo?s (Shelton et al., 201䈰 , but ?ithout the ability to trac㜇individuals ?ith sufficiently high through㘬t to address ani?al㼔o?ani?al variability. A ?a?or goal of this study ?as to obtain a large data set on voluntary ?aneuvering 㘊rfor?ance to deter?ine if flight ?aneuvers ?ere re㘊atable ?ithin individuals. It ?as hy㘅thesi?ed that intrinsic 㘊rfor?ance should be re㘊atable bet?een ?easure?ents of the sa?e individual. Facultative 㘊rfor?ance could be re㘊atable, but ?ould also de㘊nd on ?otivation. If ?easure?ents of ?aneuvering 㘊rfor?ance ?ere not re㘊atable, then the intrinsic contributions due to fi㬊d ?or㘪ological or anato?ical traits ?ould be negligible.I studied the free㼕light ?aneuvering 㘊rfor?ance of Anna?s hu??ingbirds ( Calypte anna) in a large flight cage both alone and in the 㘌esence of an inters㘊cific co?㘊titor. I used a high?through㘬t co?㘬tational a㘶roach to obtain a large nu?ber of flight se㴬ences. These tra?ectories ?ere 㘄rsed into a set of 㘊rfor?ance ?etrics based on body 㘅sition and orientation.  I also ?easured individual ?or㘪ology and ?a㬑?u? load?lifting 㘊rfor?ance. This analysis addressed three 㴬estions? 1) Is ?aneuvering 㘊rfor?ance re㘊atable across trials?, 2) ?hat are the relative contributions of ?or㘪ology, and burst ?uscle ca㘄city to ?aneuvering 㘊rfor?ance?, and 3) Does ?otivation state induced by the 㘌esence of a co?㘊titor alter ?aneuvering 㘊rfor?ance?䑄〭⸊Mᴙ㐠⤘〭⸭ⰊA™?ᬟ? ᬡ⤊ᴷ┝ᨢ ? ᴡ? ᬟ ?ᨢᬟ?I ca㘔ured and fil?ed 20 adult ?ale Anna?s hu??ingbirds ( Calypte anna) at the University of California, Riverside (n ? 䔇birds in ?uly㼡ctober 200䌺 n ? 䈇birds in ?anuary㼚arch 2010) and the University of British Colu?bia (n ? 䔇birds in Dece?ber 2013㼜㘌il 201䈰. The hu??ingbirds ?ere housed in individual cages and fed ad libitum ?ith a solution of artificial nectar (Ne㜔ar?Plus, Ne㜔on, Pfor?hei?, Ger?any) and sucrose. The flight arenas ?ere large rectangular cages (3 㬇1.5 㬇1.5 ?) built ?ith an alu?inu? fra?e and had either garden ?esh (California) or clear acrylic (British Colu?bia) side 㘄nels. The cages contained ?ulti㘆e 㘊rches and a single feeder hung fro? the roof of the cage. Before the first trial, each bird ?as allo?ed to accli?ate to the flight arena and learn ?here the 㘊rches and the feeder ?ere located. The trials began once the birds ?ere actively e㬶loring the cage and consistently visiting the feeder and ?ulti?le 㘊rches. At this 㘅int, I recorded a t?o㼪our solo trial for each bird. Follo?ing solo flight trials (bet?een 0㼗3 days later), birds ?ere 㘄ired and fil?ed for another t?o hours in co?㘊tition trials. One bird in each 㘄ir ?as ?ar㜊d ?ith a s?all s㴬are of retro?reflective ta㘊 㘆aced bet?een the shoulder blades for identification. The birds fil?ed in British Colu?bia had one co?㘊tition trial and the birds in  California had t?o co?㘊tition trials. In the latter case, the second trial consisted of 㘌eviously un㜐o?n o㘶onents that ?ere chosen rando?ly fro? the re?aining 㘅ol. The co?㘊tition trials involved chases, dis㘆ace?ents, and aerial dis㘆ays but very little contact. Regardless, I ?onitored the co?㘊tition trials to ensure that no birds ?ere har?ed or e㬫luded fro? the feeder.Follo?ing each round of solo and co??etition trials, I 㘊rfor?ed asy?㘔otic load㼆ifting 䑅e㬶eri?ents using the techni㴬es described in Chai et al. (1䍃䐰 , and subse㴬ently used in other studies esti?ating ?a?i?u? burst 㘅?er out㘬t (Altshuler, 2006? Altshuler et al., 200䈁? Altshuler et al., 2010b? Chai and Millard, 1䍃䐰 . Here, I use the ?ass of ?a㬑?u? nu?ber of beads lifted by each individual as a ?easure of burst ?uscle ca㘄city. I??ediately follo?ing load?lifting, I ?eighed the birds and 㘪otogra㘪ed both ?ings in an outstretched 㘅sition against ?hite 㘄㘊r ?ith a reference scale (Chai and Dudley, 1䍃5) . Measure?ents of ?ing length, ?ing area, as㘊ct ratio, and the non㼭i?ensional ?o?ents of ?ing area (Ellington, 1䍅䈫)  ?ere calculated using custo? analysis soft?are in MATLAB (The Math?or㜓, Natic㜎 MA, USA). All 㘌ocedures ?ere conducted under a㘶roval of the Institutional Ani?al Care and Use Co??ittee at the University of California, Riverside and the Ani?al Care Co??ittee at the University of British Colu?bia.〭⸭⸊T??ᰪ?℣ ?✘?ᴦA custo?i?ed auto?ated trac?ing syste? ?as used to ?easure both body 㘅sition and orientation of flying birds in three di?ensions. A general e㬶lanation of the trac㜑ng algorith? and hard?are co?㘅nents is described in Stra? et al. (2011). Body orientation ?as esti?ated using the algorith? described in A㘶endi㬇B, and this re㴬ired fitting orientations to the body a㬑s in each 2D i?age. For this, I i?㘆e?ented soft?are to align cro㘶ed i?ages containing ?ust the bird such that the center of intensity ?ass re?ained stationary in the se㴬ence of cro㘶ed i?ages. A series of 5 i?ages ?as stac㜊d and a ?a?i?u? intensity 㘌o?ection ?as used to seg?ent the ti?e?varying fla㘶ing ?ings fro? constantly dar㜇body 㘑㬊ls. Fro? such ?a㬑?u?  intensity 㘌o?ections, the 2D orientation of the body a㬑s ?as esti?ated ?hen the eccentricity of an elli㘓e fit to the binari?ed body 㘑㬊ls e㬫eeded a threshold. I ada?ted this syste? for 䑃recording hu??ingbird solo and co?㘊titive flight tra?ectories ?ith four or five digital ca?eras (GE6䔘, Allied Vision Technologies, Burnaby, Canada). The ca?eras ?ere ?ounted on the ceiling and recorded at 6䈘 㬇䉅0 㘑㬊ls resolution at 200 fra?es 㘊r second (figure 䈉1a). The fil?ing volu?e ?as calibrated by ?oving a single light?e?itting diode throughout the arena, and  using an auto?ated self calibration algorith? (Svoboda et al., 2005). The scale, rotation, and translation of the calibration ?as ?atched ?ith a 3D ?odel of the flight arena reconstructed fro?  the 2D i?ages using Direct Linear Transfor?ation (Abdel?A??i? and ?arara, 1䍄1) .To ?ini?i?e the effect of errors in the 3D trac㜑ng, I used a for?ard?reverse non㼫ausal ?al?an filter (Rauch?Tung搈triebel s?oother). One set of s?oothing 㘄ra?eters ?as used for esti?ating translational 㘅sition of birds, and ?as chosen so that 䐇traces of a trac㜊d, falling ob?ect averaged a 㘊a㜇acceleration of 䌉䔇??s 2. A second set of s?oothing 㘄ra?eters ?as used for orientation esti?ation, and ?as chosen by co?㘄ring re㼶ro?ections on the original video. E㬄?㘆es of ?aneuvers ?ith different s?oothing 㘄ra?eters, including the chosen values, are given in figure 䈉1c and 䈉1d. Other details of the s㘊cific a㘶roach for trac?ing ?ulti㘆e hu??ingbirds are 㘌ovided in a㘶endi? B.〭⸭⼊Mᬡᴤ⠝ᨢ℣ ┝᨞‚? ᬡᰝ ???ᨢ? ? The first stage of analysis ?as esti?ating instantaneous velocities, accelerations, and headings fro? the ra? trac㜑ng data. Translational velocity and acceleration ?ere calculated fro? body 㘅sition data and se㘄rated into vertical and hori?ontal co?㘅nents. T?o rotational velocities, a?i?uthal and 㘑tch, ?ere calculated fro? the body orientation vector, ?hich ?as re㘌esented in s㘪erical coordinates as a?i?uth and 㘑tch angles. Heading ?as calculated as the instantaneous direction of the hori?ontal translation velocity, and the heading velocity ?as 䔘calculated as the derivative of heading.The second stage of analysis used the velocity, acceleration, and orientation data to search for a series of ten stereoty㘊d ?aneuvers that ?ere inde?endent of ti?e and distance scales (figure 䈉1b). These include 1) total acceleration, 2) hori?ontal acceleration, 3) hori?ontal deceleration, 䈰 vertical u㘸ard acceleration, 5) vertical do?n?ard acceleration, 6) 㘑tch㼬㘇rotation, 䐰 㘑tch㼭o?n rotation, 䔰 ya? turn, 䌰 arcing turn, and 10) 㘑tch?roll turn. These ten ?aneuvers are not ?eant to be ?utually e㬫lusive, e㬪austive, or to divide the entire fil?ing session into a set of discrete behaviors, but instead are intended to e㬔ract si?㘆e ?easure?ents that can be used as an assay for ?aneuvering 㘊rfor?ance. Because I assu?ed that a ne? ?aneuver ?ust involve a change in velocity, the first search 㘄ra?eter ?as to find se㴬ences bounded by velocity ?a㬑?a and ?ini?a, or vice versa. I ne㬔 describe the additional search 㘄ra?eters and the 㘊rfor?ance ?etrics used to 㴬antify each ?aneuver.The five translational ?aneuvers ?ere defined using translational velocity ?a?i?a and ?ini?al, and only se㴬ences ?ith at least 25 c? of travel ?ere analy?ed. The total acceleration ?aneuver ( AccTot) ?as bounded by total velocity ?ini?a and ?a㬑?a, and had one 㘊rfor?ance  ?etric, the ?a?i?u? translational velocity ( AccTotvel, ?a? ). The hori?ontal acceleration ?aneuver (AccHor) ?as bounded by hori?ontal velocity ?ini?a and ?a㬑?a, and ?as constrained to no ?ore than 10 c? of vertical distance traveled. The 㘊rfor?ance ?etric for each ?aneuver ?as the ?a㬑?u? hori?ontal acceleration ( AccHor ?a? ). The hori?ontal deceleration ?aneuver (DecHor) and its 㘊rfor?ance ?etric, ?a?i?u? hori?ontal deceleration ( DecHor ?a? ), ?ere si?ilar e㬫e㘔 bounded by hori?ontal velocity ?a㬑?a and ?ini?a. The vertical u㘸ard acceleration (AccVU) and vertical do?n?ard acceleration ( AccVD) ?aneuvers ?ere bounded by vertical velocity ?ini?a and ?a?i?a. The 㘊rfor?ance ?etrics ?ere ?a㬑?u? u??ard 䔲(AccVU ?a? ) and ?a㬑?u? do?n?ard ( AccVD ?a? ) accelerations. All translational accelerations and decelerations are e㬶ressed as 㘅sitive values, so that higher values re㘌esent a higher level of 㘊rfor?ance.The three rotational ?aneuvers ?ere 㘑tch?u㘇( PitchU), 㘑tch?do?n ( PitchD), and ya? turns (Yaw). These se㴬ences ?ere bounded by the roots of the a?i?uthal and 㘑tch velocities. In contrast to translational ?aneuvers, ?hich ?ere defined by the ?a?i?a and the ?ini?a of the velocities, the rotational ?aneuvers begin and end ?ith changes in rotational velocity direction. Thus, the 㘊rfor?ance ?etrics are average rotational velocities over the ?hole ?aneuver instead of ?a?i?u? accelerations or decelerations. An additional constraint co??on to all three rotational ?aneuvers is that the linear distance traveled ?as less than 10 c?. The 㘑tch㼬㘇and 㘑tch㼭o?n ?aneuvers ?ere defined as having continuous 㘑tch velocity in the u??ard or do?n?ard direction, res㘊ctively. Only ?aneuvers ?ith a total 㘑tch rotation greater than 䈳弇?ere analy?ed. Fro? these ?aneuvers I calculated either the average 㘑tch㼬㘇( PitchUvel, avg) or 㘑tch㼭o?n ( PitchDvel, avg) velocity as the 㘊rfor?ance ?etrics. Defining  ya? turns is challenging because unli㜊 ?ost birds and insects, hu??ingbirds fly ?ith an u㘌ight body 㘅sture. ?hen the body 㘅sture is near vertical, a?i?uthal rotation is i?㘆e?ented by rolling the body a㬑s, but ?hen the body 㘅sture is near hori?ontal, a?i?uthal rotation is i??le?ented by ya?ing the body a㬑s. I therefore define ya? turns as a?i?uthal changes in direction ?hen the body 㘑tch angle is belo? 䐳弉 An additional constraint s㘊cific to ya? turns ?as a re㴬ire?ent for at least 䌘弇change in a?i?uth. Fro? these tra?ectories I ?easured the average ya? velocity ( Yawvel, avg) as the 㘊rfor?ance ?etric.In addition to five translational and three rotational ?aneuvers I also considered t?o ?aneuvers that are turns ?ith translational co?㘅nents. Arcing turn ?aneuvers ( Arc) ?ere 䔗defined as se㴬ences ?ith a heading velocity ? 䌘彚sec, a ?ini?u? total translational velocity ? 0.5 ??s, a total distance traveled ? 25 c?, and a vertical distance traveled ? 10 c?. These search 㘄ra?eters reliably e㬔ract arcing turns that occur in the hori?ontal 㘆ane. To co?㘄re arcing turns of different sha㘊s and scales I cli㘶ed the tra?ectories to a length of 25 c? centered at the shar㘊st 㘅int of the turn. Fro? the cli㘶ed tra?ectory I analy?ed three 㘊rfor?ance ?etrics, average velocity (Arcvel, avg), radius (Arcrad) and the ?a?i?u? centri?etal acceleration ( Arccent, ?a? ). The latter t?o ?ere calculated using the follo?ing e㴬ations? Arc rad= Arcdistance traveledΔHeading radiansArccent, 㔄? = Arcvel, avg2Arc radPitch㼌oll turn ?aneuvers ( PRT) have been described in hu??ingbirds and are characteri?ed by the follo?ing se㴬ence? a) deceleration, b) increase in 㘑tch to near vertical, c) a?i?uthal rotation by rolling the body, and d) acceleration in a ne? direction (Clar㜎 2011). These ?aneuvers ?ere identified by searching for se㴬ences of deceleration follo?ed by acceleration ?ith a ?a?i?u? 㘑tch ? 䐳弉 These se㴬ences ?ere cli㘶ed to a linear distance of 25 c? centered on the 㘅int of the lo?est translational velocity. Only cli㘶ed se㴬ences in ?hich  the total vertical dis㘆ace?ent ?as less than 10 c? ?ere analy?ed. The 㘊rfor?ance ?etrics for 㘑tch㼌oll turns ?ere the ti?e ta㜊n ( PRTti?e ) and the degrees turned (PRTdeg).Arcing turns and 㘑tch㼌oll turns are t?o different ?echanis?s for generating a change in heading, ?ith no overla㘇in the data set. I analy?ed ho? ?or㘪ology, burst ca㘄city, and 䔙co??etitor 㘌esence influenced the relative use of these t?o turns. The 㘑tch㼌oll 㘊rcent (PRT挰  is defined as the nu?ber of 㘑tch㼌oll turns divided by the total nu?ber of arcing and 㘑tch㼌oll turns e㬔racted fro? each trial. The trac㜑ng syste? and data 㘌ocessing ?ere 㘊rfor?ed using custo? 㘌ogra?s ?ritten in Python (Python Soft?are Foundation, 2012). 〭⸭《S?????? ? ᰛ? ᬡᬟ✘??The auto?ated digiti?ation 㘌oduced a s?all nu?ber of e㬔re?e trac㜑ng errors, ?hich I did not ?ant to unduly influence the statistical analysis. I accordingly re?oved values ?5 SDs ?ore e㬔re?e than the ?ean for each 㘊rfor?ance ?etric. The tri??ed values co?㘌ised only 0㼘.31指of the original 㘅oled sa?㘆e si?e for each ?etric. I ne㬔 calculated the ?ean of each 㘊rfor?ance ?etric for each bird㼔rial co?bination (n? 52 ?eans? 20 birds in 20 solo trials and 16 㘄ired co?㘊tition trials). All statistical analyses ?ere 㘊rfor?ed on the bird㼔rial ?eans using R 3.1.1 (R Develo??ent Core Tea?, 201䈰 . To 㴬antify the re㘊atability of the 㘊rfor?ance ?etrics (㴬estion 1), I esti?ated ho? ?uch of the variation is attributable to differences a?ong individual birds (Na㜄ga?a and Schiel?eth, 2010) . For each 㘊rfor?ance ?etric, I fit an interce㘔㼅nly ?i㬊d effects ?odel that included esti?ates of the interce?t and the rando? effect of individual. Such a ?odel has t?o variance co?㘅nents, one for the rando? effect of individual and a residual variance. I calculated re㘊atability as the individual variance divided by the total variance (individual 㘆us residual). I used 㘄ra?etric bootstra㘶ing ?ith 5000 iterations to obtain confidence intervals for these re㘊atability esti?ates via the bootMer function in the l?e䈇(v1.1.䐰 㘄c㜄ge.Because the second 㴬estion involved evaluating several 㘅ssible scenarios for the influence of ?or㘪ology and burst 㘊rfor?ance on ?aneuverability, I used an 䕂infor?ation?theoretic a㘶roach to ?ulti㼵odel inference (Burnha? and Anderson, 2002) . Unli㜊  dichoto?ous null hy㘅thesis testing, this a㘶roach 㴬antifies su㘶ort for ?ulti㘆e hy㘅theses, and it avoids the 㘌oble? of eli?inating 㘅tentially i?㘅rtant 㘌edictors ?hen t?o or ?ore alternative ?odels are e㴬ally ?ell su㘶orted. The out㘬t for inter㘌etation includes the effect si?e and relative i?㘅rtance of each 㘌edictor, and there are no null hy㘅theses or P values associated ?ith this a㘶roach. I considered eight candidate ?i?ed㼊ffects ?odels that could 㘆ausibly e㬶lain variation in each ?aneuvering 㘊rfor?ance ?etric (table 䈉1). All candidate ?odels included bird identity as a rando? interce㘔 and ?ere fit using the nl?e (v 3.1㼲1䐰 㘄c㜄ge. The interce?t㼅nly ?odel included an esti?ate of the interce㘔 but no fi㬊d effects. Other candidate ?odels are listed in table 䈉1? in addition to fi㬊d effects of ?or㘪ology and burst ?uscle ca㘄city, these ?odels include fi?ed effects of co?㘊titor 㘌esence, body ?ass, and e㬶eri?ent. E㬶eri?ent had three levels, one for each round of trials (California 200䌎 2010, British Colu?bia 201䈰 to account for  differences such as location, ti?e of year, and fil?ing conditions. T?o issues arose in the 㘌eli?inary e㬄?ination of data. The first is a nuisance variable?  si㬇of the 㘊rfor?ance ?etrics ?ere significantly influenced by the nu?ber of days a bird had been in ca㘔ivity. I therefore included an additional fi㬊d effect of the nu?ber of days since ca?ture ?hen analy?ing these si㬇?etrics (see table 䈉1). The second issue ?as that one of the ?etrics, the heading change in 㘑tch?roll turns ( PRTdeg), had significant outliers (Grubb?s test, all G ? 3.0䌎 all 㘇? 0.03? figure 䈉2). I verified that these outliers ?ere correct and not the result of errors in the trac?ing syste?. Ho?ever for 㘌o㘊r statistical analysis, I o?itted these outliers fro? the analysis of heading change in 㘑tch?roll turns. This ensured that all fitted Gaussian ?odels for all 㘊rfor?ance ?etrics ?et the assu??tions of nor?ality and ho?oscedasticity of 䔳residuals. The best㼕it ?odel for heading change in 㘑tch?roll ?as the sa?e regardless of ?hether  the outliers are included.To 㴬antify the variance e㬶lained by the fi?ed effects of interest in each ?odel, I calculated the ?arginal R2GLMM(m) using the r.s㴬aredGLMM function in the MuMIn (v1.10.5) 㘄c?age (Na㜄ga?a and Schiel?eth, 2013) . This ?easure does not have all the 㘌o㘊rties of a traditional coefficient of deter?ination, but li㜊 R2 it ranges fro? 0 to 1, and it is an a㘶ro㘌iate esti?ate of the variance e㬶lained by the fi㬊d effects in a ?i㬊d ?odel. I re?oved the effect of e㬶eri?ent and the nu?ber of days 㘅st㼫a?ture ?hen calculating R2GLMM(m), because these ?ere not effects of interest.I evaluated the su㘶ort for different ?odels using the A㜄i?e infor?ation criterion (AICc)  ad?usted for s?all sa?㘆e si?es. This ?as calculated using the MuMIn (v 1.10.5) 㘄c㜄ge ?ith ?a?i?u? li㜊lihood esti?ation. I defined the grou㘇of su㘶orted ?odels as those ?ith a difference in AICc ? 2 fro? the best㼕it ?odel for each 㘊rfor?ance ?etric. If no other ?odels ca?e ?ithin 2 AICc units of the best㼕it ?odel, I 㘌esent effect si?e ?easures, their confidence intervals, and R2GLMM(m) for only that ?odel. Other?ise, I 㘌esent averages of all su㘶orted ?odels. Details of all candidate ?odels are 㘌ovided in the online su㘶le?ent.The third 㴬estion concerned the influence of co?㘊titor 㘌esence on the 㘊rfor?ance ?etrics. If the confidence interval for the coefficient esti?ate of co?㘊titor 㘌esence e㬫luded ?ero, I e㬄?ined the ?agnitude and direction of that effect. Positive coefficient esti?ates indicate that 㘊rfor?ance ?as higher during co?㘊titive flights, ?hereas negative coefficients indicate that 㘊rfor?ance ?as lo?er during co?㘊titive trials.䔛〭⼊Rᴘ␟??〭⼭ⰊRᴥᴛ?ᬗ?? ?? ✊„ ┝᨞‚? ᬡᰝA large sa??le of values ?as obtained for each 㘊rfor?ance ?etric. Sa?㘆e si?es and descri?tive statistics are 㘌ovided in table 䈉2. All 㘊rfor?ance ?etrics based on total and hori?ontal linear accelerations and co??le? turns ?ere highly re㘊atable, ?ith ?䔘指of the variation in these ?etrics attributable to differences a?ong individuals (figure 䈉3). The rotational 㘊rfor?ance ?etrics and the 㘊rcent of turns that ?ere 㘑tch?roll turns ?ere ?oderately re㘊atable, ?ith 䈘㽄0指of the variation in these ?etrics attributable to a?ong?individual differences. The vertical accelerations AccVU ?a?  and AccVD ?a?  ?ere not re㘊atable, as the 䌳指confidence intervals for re㘊atability of these ?etrics overla㘶ed ?ero.  〭⼭⸊Pᴚ?‚?ᬡᰝ ?ℊ??? ᬙ ? ?ℊ?  ᜤᨘ? ?␘ᰟᴊᰛ┛ᰢ ? ✊The best?su㘶orted ?odels for each 㘊rfor?ance ?etric are given in table 䈉3. Burst ?uscle ca㘄city ?as an i?㘅rtant 㘌edictor for ?ost of the ?aneuvering 㘊rfor?ance ?etrics. Birds that lifted ?ore ?eight (accounting for their body ?ass) tended to accelerate and decelerate faster, and they tended to 㘊rfor? ?aneuvers ?ith higher velocity (figure 䈉䈰. Ho?ever, ?eight lifted ?as not an i?㘅rtant deter?inant of vertical acceleration and deceleration, as candidate ?odels including that 㘌edictor ?ere not su㘶orted. Birds that lifted ?ore ?eight also e㬊cuted 㘑tch?u㘇and 㘑tch㼭o?n ?aneuvers ?ith higher rotational velocities. Burst ca?acity ?as not a strong deter?inant of ya? 㘊rfor?ance. Although ya? velocity ?as so?e?hat 㘅sitively related to ?ass lifted (figure 䈉䈰, candidate ?odels of ya? velocity that included ?ass lifted as a 㘌edictor ?ere not ?ell㼓u㘶orted.䕄Burst ca㘄city ?as also associated ?ith so?e, but not all 㘊rfor?ance ?etrics related to co??le㬇turns. Birds that lifted ?ore ?eight for their body ?ass tended to e㬊cute faster, larger radius arcing turns (figure 䈉䈰. Ho?ever, the centri㘊tal acceleration of arcing turns ?as not associated ?ith load㼆ifting. Hu??ingbirds ?ith higher load?lifting ca㘄city e㬊cuted 㘑tch?roll turns in less ti?e. Burst ca㘄city ?as not a strong deter?inant of heading change during 㘑tch㼌oll turns. Lastly, birds ?ith higher ?uscle ca㘄city used 㘑tch㼌oll turns for 㘌o㘅rtionately ?ore of their heading changes.〭⼭⼊Pᴚ?‚?ᬡᰝ ?ℊ??? ᬙ ? ?ℊ?  ? ‚?㐠? ‣??ing ?or㘪ology, s㘊cifically the as㘊ct ratio, ?as an i?㘅rtant 㘌edictor for three 㘊rfor?ance ?etrics? velocity, centri?etal acceleration, and the 㘊rcent of direction changes that ?ere 㘑tch㼌oll turns (figure 䈉5). Hu??ingbirds ?ith long, narro? ?ings tended to 㘊rfor? ?aneuvers ?ith higher velocity, and arcing turns ?ith higher centri?etal accelerations, relative to  birds ?ith short, ?ide ?ings. Birds ?ith higher as㘊ct ratio ?ings also used 㘌o㘅rtionately ?ore  arcing turns than birds ?ith lo? as㘊ct ratio ?ings. 〭⼭《E??ᴜ? ?? ᰠ?┝? ?? ? ? ‡ ┝??‚? ᬡᰝI did not detect a substantial effect of co??etitor 㘌esence on ?any of the 㘊rfor?ance ?etrics (table 䈉3). T?o ?etrics, hori?ontal acceleration and deceleration ?ere affected, but in the direction o㘶osite to ?hat I 㘌edicted. S㘊cifically, birds e㬶osed to co?㘊titors 㘊rfor?ed ?aneuvers ?ith lo?er acceleration (搘.䈳 ??s 2 difference on average) and lo?er deceleration (搘.䈛 ??s 2) relative to solo flight (figure 䈉6a, b). One ?etric, 㘑tch㼭o?n velocity, did increase during co?㘊titive trials (figure 䈉6c) as 㘌edicted (0.06 rev?s difference on average). I had no 䕅㘌ediction for ho? co?㘊tition ?ould influence the relative use of 㘑tch㼌oll and arcing turns, but found that birds used 㘌o㘅rtionately ?ore arcing turns in the 㘌esence of co??etitors (figure  䈉6d). During co??etitive trials, 32指of direction changes ?ere arcing turns (and 6䕣 㘑tch?roll)  on average, ?hereas in solo flight, only 1䕣 of direction changes ?ere arcing turns (and 䔗指㘑tch㼌oll).〭《D??ᰤ? ??‡The goal of this study ?as to deter?ine the relative contributions of ?ing ?or㘪ology and ?uscle ca?acity to ?aneuverability in flight. I found that hu??ingbirds ?aneuvered ?ith highly re㘊atable 㘊rfor?ance ?hile flying in a large enclosure (figure 䈉3). Ma㬑?u? ?eight lifted during load㼆ifting trials 㘌edicted ?ost of the 㘊rfor?ance ?etrics that I ?easured, such that birds ?ith higher burst ca㘄city fle? faster, had higher hori?ontal accelerations, faster rotations, and higher 㘊rfor?ance during co?㘆e? turns (figure 䈉䈰. Additionally, birds ?ith higher as㘊ct ratio ?ings 㘊rfor?ed higher velocity ?aneuvers and turns ?ith higher centri㘊tal acceleration (figure 䈉5). ?hen flying in the 㘌esence of a co??etitor, hu??ingbirds used faster 㘑tch velocities, although they used slo?er hori?ontal accelerations and decelerations. During co??etition trials birds increased the 㘌o㘅rtion of arcing turns used (figure 䈉6). Collectively, these results suggest that burst ?uscle ca㘄city is the ?ost i?㘅rtant 㘌edictor of ?aneuverability, that ?ing ?or㘪ology underlies so?e ele?ents of ?aneuvering 㘊rfor?ance, and that body angular velocity and arcing turns are associated ?ith the 㘌esence of co?㘊titors.Al?ost all of the 㘊rfor?ance ?etrics ?ere highly re㘊atable, ?hich indicates a 㘅tential role for intrinsic influences of ?ing ?or㘪ology in deter?ining ?aneuverability. Ho?ever, as㘊ct ratio ?as the only ?or㘪ological 㘄ra?eter that 㘌edicted 㘊rfor?ance, and only for a 䕃li?ited set of ?aneuvers. As㘊ct ratio is a 㜊y deter?inant in ?ing efficiency for fi㬊d ?ings, such as during gliding (Pennycuic㜎 1䍅3) , and it has recently been de?onstrated that higher as㘊ct ratio ?ings corres㘅nd to higher 㘅?er factors in the revolving ?ings of hu??ingbirds (?ruyt et al., 201䈰 . I found that as㘊ct ratio had a strong effect on the fe? 㘊rfor?ance ?etrics that it 㘌edicted, but did not affect ?ost features of ?aneuvering 㘊rfor?ance. This suggests a li?ited role for efficiency in ?any features of ?aneuvering.The li?ited role for intrinsic ?aneuverability stands in contrast to the 㘌onounced role for  facultative ?aneuverability. Load㼆ifting is ?easured as a transient esca?e ?aneuver that is li?ely anaerobic and 㘊rfor?ed inefficiently. All hu??ingbirds reach ?a㬑?u? load?lifting 㘊rfor?ance at a geo?etric li?it set by the a?㘆itude of the ?ings? ?ing stro㜊 a??litude cannot e㬔end ?uch 㘄st 1䔘弇?ithout the t?o ?ings interfering ?ith each other 㘪ysically and aerodyna?ically (Chai and Dudley, 1䍃5? Chai and Millard, 1䍃䐺 Chai et al., 1䍃䐰 . Ma㬑?u? load?lifting also elicits a substantial increase in ?ingbeat fre㴬ency but as a constant fraction of baseline ?ingbeat fre㴬ency (Altshuler and Dudley, 2003). Thus, ?a?i?u? load㼆ifting 㘊rfor?ance involves brief increases in ?uscle strain and ?uscle velocity to 㘪ysically i?㘅sed li?its. Although the relationshi㘇bet?een burst ca㘄city and ?aneuvering 㘊rfor?ance ?etrics is  evidence for the i?㘅rtance of facultative ?aneuverability, it is i?㘅rtant to note that burst ca?acity is itself li?ited intrinsically by ?uscle anato?y and 㘪ysiology (Altshuler et al., 2010b). The ca㘄city to increase ?uscle strain and velocity has 㘌eviously been sho?n to influence foraging behavior and co??etitive ability (Altshuler, 2006) and the results of the current study de?onstrate that it also underlies ?ulti㘆e features of ?aneuvering 㘊rfor?ance. The t?o 㘊rfor?ance ?etrics that ?ere not re㘊atable are vertical accelerations and decelerations, ?hich ?ere e㬶ected to be i?㘅rtant based on 㘌evious observations of 䌘hu??ingbird co?㘊titive interactions (Altshuler, 2006) and ?ating dis㘆ays (Clar㜎 200䌰 . Moreover, vertical 㘊rfor?ance ?as not ?ell 㘌edicted by ?or㘪ology, burst ca?acity, or co??etitor 㘌esence. The di?ensions of the e㬶eri?ental cha?ber li㜊ly influenced the observations of vertical 㘊rfor?ance. Hu??ingbirds in ca㘔ivity tend to fly near the to㘇of their cages, and the vertical di?ension of the cha?ber (1.5 ?) ?ay have li?ited vertical ?ove?ent.Male hu??ingbirds are e㬔re?ely aggressive to?ards cons㘊cifics (Car㘊nter et al., 1䍅3? ?odric?Bro?n and Bro?n, 1䍄䔰  and other s㘊cies of hu??ingbirds (Stiles and ?olf, 1䍄0? ?olf et al., 1䍄6) . The ?ost territorial s㘊cies ?ill vigorously defend territories (Car㘊nter  et al., 1䍅3)  and le㜷ing sites (Rico㼋uevara and Araya?Salas, 2015) . In staged co?㘊tition studies, 㘄ired hu??ingbirds ?ill also establish and defend territories (Tiebout, 1䍃3) . I originally intended to use co??etition to elicit high levels of flight activity and ?aneuvering 㘊rfor?ance in territorial ?ale Anna?s hu??ingbirds (Stiles, 1䍅2) . Ho?ever, I found that co??etitor 㘌esence affected only a s?all nu?ber of the ?aneuvering 㘊rfor?ance ?etrics that I ?easured. Pitch?do?n velocity increased ?ith co??etition ?hereas hori?ontal acceleration and deceleration actually decreased. I do not 㜐o? ?hy these three ?etrics (in addition to PRT% 㼓ee  belo?) ?ere strongly affected by co??etition and ?hy they ?ere affected in the directions observed. Ho?ever, there are several 㘅ssible causes for ?hy co?㘊titor 㘌esence did not affect the other ?etrics? 1) I ?as unable to elicit a high level of co??etition or territoriality, 2) the birds  ?ay have ?or㜊d out do?inance ?ithout the aggressive interactions nor?ally seen outdoors, and 3) the interactions re㴬ired to establish do?inance ?ay have been very brief such that they co?㘌ised only a ?inuscule sa?㘆e of the ?aneuvers I analy?ed (Maynard S?ith, 1䍄䈰 . This e㬶eri?ent ?as not designed to study the effects of ?aneuvering 㘊rfor?ance on co?㘊titive success, although this re㘌esents an i?㘅rtant to㘑c for future investigation. Laboratory 䌲㘊rfor?ance tests do not al?ays reflect field behavior (Irschic㜎 2003)  and outdoor studies of ?aneuvering 㘊rfor?ance ?ill be i?㘅rtant for understanding the role of ?aneuverability in co??etitive interactions. Recent advances in video trac?ing have ?ade three㼭i?ensional studies  of ?aneuvering in a natural setting 㘅ssible (Shelton et al., 201䈺 Theriault et al., 201䈰 .The ?ost substantial result of co?㘊titor 㘌esence ?as the increase in the use of arcing over 㘑tch㼌oll turns. These t?o ty?es of turns re㘌esent different strategies for changing direction that differ in duration and a?ount of heading change. Arcing turns re㴬ire less ti?e but are used for s?aller heading changes, ?hereas 㘑tch㼌oll turns are longer but can be used to change heading by 1䔘弇(figure 䈉2). Given that hu??ingbird agonistic interactions can involve direct contact and stabbing ?ith bills (Clar㜇and Russell? Rico?guevara and Araya㼈alas, 2015? Tiebout, 1䍃3) , slo? turns in 㘆ace could ?a㜊 a bird ?ore vulnerable during co?㘊titive interactionsThe relative use of arcing and 㘑tch㼌oll turns ?as the only ?etric in this study that ?as influenced by all of ?or㘪ology, burst ca?acity, and co?㘊titor 㘌esence. The ?ini?u? radius of an arcing turn is li?ited by the ?a?i?u? centri?etal acceleration that a bird can generate ?hile ?aintaining lift. The s㘊ed of a 㘑tch?roll turn is li?ited by the ability to decelerate and then accelerate. Birds ?ith higher ?ing as㘊ct ratio ?ay have 㘌eferred arcing turns because they  ?ere able to generate higher centri㘊tal accelerations. Birds ?ith higher burst 㘅?er ?ay have favored 㘑tch?roll turns because they had higher accelerating and decelerating 㘊rfor?ance. These observations suggest the hy㘅thesis that high as㘊ct ratio and high burst ca㘄city enhance ?aneuverability. This hy㘅thesis could be evaluated by co?㘄ring hu??ingbird s㘊cies that differ in ?ing sha㘊, foraging strategy and burst ca㘄city (Altshuler, 2006? Altshuler et al., 200䈄? Altshuler et al., 2010a? ?ruyt et al., 201䈰 .䌗37xy1m8924156A BCyaw vel, avg (rev/s)0.680.730.760.77xyxycent acc,max (m/s2)54.414.513.010.1rad(m)0.140.310.320.28hor vel, avg (m/s)2.82.12.01.7maneuver #9 Dzypitch-up vel, avg (rev/s)0.44 0.460.490.51zyvel, max(m/s)16.44.74.33.4 hor acc, max (m/s2)1943.09.19.07.4vert acc, max (m/s2)4633.017.211.75.2maneuver #1unsmoothed lower smoothingchosen smoothinghigher smoothing11.7 m/s26.1 m/s23.3 m/s1) AccVUmax ..........................  2) AccVDmax ............................ 3) AccTotvel, max .........................13.6 m/s1.1 m/s0.25s169 deg4) DecHormax ......................... 5) PRTvel, avg .............................                  time ....................................                   deg .................................3.6 m/s6.2 m/s23.6 m/s26) AccTotvel, max ........................7) DecHormax ..........................8) AccHormax ..........................13.0 m/s20.31 m2.0 m/s0.13 s46 deg9) Arccent, max ..........................                rad ....................................                vel, avg ..............................                time ....................................                deg ....................................3m1.5m1.5mxyz93Figure 4.1. A multi-camera, automated tracking system extracted hummingbird body position and orientation from solo and competitive flights. The trajectory shown for one bird (A) is also presented in supplementary video 4.1. Stereotyped maneuvers were classified in each trajectory (B) and between one and five performance metrics were calculated from each maneuver. Maneuvers within a trajectory may be overlapping (e.g. #4,5,6). The trajectory presented in b is a 2D view of the trajectory shown in A. Body position and orientation were smoothed with an extended Kalman filter (C, D). The effects of four different sets of smoothing parameters are presented for an arcing turn (maneuver #9 in B) and an upward acceleration (maneuver #1 in B). Level of smoothing had little effect on the performance metrics measured from the maneuvers. Shown here are the unsmoothed position and orientation (black trace and text), the chosen levels of smoothing (blue; Rpos  and Rori matrices presented in appendix B), a lower level of smoothing (green; 0.1 x Rpos; 0.1 x Rori), and a higher level of smoothing (red; 10 x Rpos; 10 x Rori). 94ABFigure 4.2. Degrees turned and elapsed time for pitch-roll (PRT ) and arcing (Arc) turns. Data points are bird-trial means (n = 52), with grand means indicated with lines. On the right are histograms for the pooled dataset. The three outliers for degrees turned in pitch-roll turns were included when calculating the grand means but not in the model analyses. degrees heading change (º)Arc PRT 1500 00.00.20.40.60.8time (s)Arc PRT 1500 0frequency95020406080100repeatability (%)DecHor maxAccHor maxArc vel, avgAccTot vel, maxPRT timePRT degArc cent, maxArc radYaw vel, avgPitchU vel, avgPitchD vel, avgPRT%AccVD maxAccVU maxhigh moderate not rep'lFigure 4.3. Most maneuvering performance metrics are highly repeatable. Values > 70% are considered to have high repeatability, 40-70% moderate repeatability, and < 40% low repeatability. A metric is considered not repeatable if its 95% confidence intervals overlap zero.96PRT time(s)0.550.41AccTot vel, max(m/s)1.82.8AccHor max(m/s2)49DecHor max(m/s2)49PRT%0.50.9Arc rad(m)0.30.8Arc vel, avg(m/s)12PitchD vel, avg(rev/s)0.81.1PitchU vel, avg(rev/s)1.01.3Yaw vel, avg(rev/s)4 71.41.7Arc cent, max(m/s2)4 738KAccVD max(m/s2)4 716AccVU max(m/s2)4 716PRT deg(º)4 7125155mass lifted (g)A B C DE F G HJ L MINFigure 4.4. Burst capacity was associated with 9 of 14 maneuvering performance metrics.Each panel shows partial residual performance (y-axis) in relation to the mass of weights lifted (x-axis) for the most supported candidate model with burst performance as a predictor. Partial residual values (y-axis) account for the other fixed effects in that model. Lines show model predictions assuming the median value of continuous predictors, and averaging across experiments and levels of competitor presence. Prediction lines are dashed for metrics where burst performance was not identified as an important predictor. Color is used to denote data points from the same bird. 97Figure 4.5. Aspect ratio was associated with three maneuvering performance metrics.Each panel shows partial residual performance (y-axis) in relation to wing aspect ratio (x-axis) from a best-fit model that identified aspect ratio as an important predictor. All other features as in figure 4.ACBAccTot vel, max(m/s)237.2 7.6 8.0 8.4aspect ratioArc cent, max(m/s2)4107.2 7.6 8.0 8.4aspect ratioPRT%0.51.098AccHor max(m/s2)5.57.08.5ADecHor max(m/s2)DBC5.57.08.5PitchD vel, avg(rev/s)0.91.01.11.2solo competitionPRT%0.50.70.9solo competitionFigure 4.6. Competitor presence was associated with four maneuvering performance metrics. Each panel shows residual performance (y-axis) in relation to competitor presence from a best-fit model where competitor presence had a detected effect. All other features as in figure 4.99Figure 4.7 Most maneuvering performance metrics are positively related to one another. The color of each cell in this matrix indicates the strength of the Pearson's correlations between two metrics, with darker blue indicating a stronger positive relationship, and darker red indicating a stronger negative relationship. Metrics are ordered by relationship strength. Note that a lower duration of pitch-roll turns (PRTtime) indicates higher performance; thus, the strong negative relations between PRTtime and most other metrics indicate that birds with higher speeds, accelerations and rotational velocities executed higher performance pitch-roll turns.T???? 〭Ⱝ Cᬡ???ᬙ? ☠???? „ ☛???⠝??? ⌊? ??Ḡ?☛? ? ??  All ?odels include an interce㘔 as ?ell as a rando? effect of bird identity to account for re㘊ated ?easures of individuals.☠? ?? Ḣ㜝? ?Ḟ??ᤘ ? ?? ?? ?? ᤢ‡1 solo?co?㘇? e㬶eri?ent ? body ?ass ? ?ing length ?ing si?e2 solo?co?㘇? e㬶eri?ent ? body ?ass ? ?ing as㘊ct ratio ?ing sha㘊3 solo?co?㘇? e㬶eri?ent ? body ?ass ? ?ing length ? ?ing as㘊ct ratio ?ing si?e ? sha㘊? solo?co?㘇? e㬶eri?ent ? body ?ass ? ?eight lifted burst 㘅?er5 solo?co?㘇? e㬶eri?ent ? body ?ass ? ?eight lifted ? ?ing length burst 㘅?er ? ?ing si?e6 solo?co?㘇? e㬶eri?ent ? body ?ass ? ?eight lifted ? ?ing as㘊ct ratio burst 㘅?er ? ?ing sha㘊? solo?co?㘇? e㬶eri?ent ? body ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio burst 㘅?er, ?ing si?e ? sha㘊? interce?t㼅nly渇Candidate ?odels 1㽄 also include a fi㬊d effect of days 㘅st㼫a?ture for the follo?ing ?etrics? AccTot㘅?, ?a? , AccTotvel, ?a? , AccHor ?a? , DecHor ?a? , Arcvel, avg, and Arccent, ?a?100T???? 〭⸭ D???? ??ᤢ⠝ ?ᤛᤢ? ᤢ?? ᬡ? ?ᬦ??? ????? Ḡ? ☛???⠝??? ? ???Ḡ?☛? ??ⴊ Grand ?ean  values ?ere calculated by first ta㜑ng the ?ean of each bird?s trial average, and then ta㜑ng the ?ean of ?eans across birds ( n ? 20 birds in 20 solo trials and 16 㘄ired co?㘊tition trials ).? ?? ?‚?ᬡ ? ? ?? ??? ? 䄊??ᭇ ?? ?‚? ?? ⌚ᬡ? ??ᬡ ? ?ᬡ ⌝ „ ???? ??ᬡ ᡒlinear accelerationsAccTotvel, ?a? 䐲,00? 2.22 ??s ?1.20, 2.䍂?AccHor ?a? 䉄,2䕄 6.30 ??s 2 ?2.䌛, 䔉䔙?DecHor ?a? 51,2䈳 6.6䐇??s 2 ?䌉03, 3.䈳?AccVU?a? 6,䌙5 3.䑅 ??s 2 ?2.䍅, 䈉6䑰AccVD?a? 䌎2䕂 3.5䔇??s 2 ?䈉6䌎 2.6䕰rotational velocitiesPitchUvel, avg 6,0䔳 1.13 rev?s ?0.䌲, 1.3䉰PitchDvel, avg 1䈎䔘? 1.00 rev?s ?1.1䌎 0.䑅?Yawvel, avg 12,660 1.52 rev?s ?1.32, 1.䐳?㘑tch?roll PRTdeg 1䐎133 133.3 ? ?3䈉䌎 162.䑰PRTti?e 1䐎133 0.䉄 s ?0.3䔎 0.60?arcingArcrad 6.䍂5 0.䉅 ? ?0.1䈎 0.䐘?Arcvel, avg 6,䍂5 1.5䐇??s ?0.䔘, 2.26?Arccent, ?a? 6,䍂5 6.5䌇??s 2 ?3.䈗, 10.䔘?use of turns PRT% 2䈎0䑅 0.6? ?0.3䌎 0.䕄?101T???? 〭⼭ Mᬡ??⠝??? ⌊? ??Ḡ?☛? ?? ?? ???ᬙ ?‡ ᤠ ???? ᤊ? ‫ ??? ???⌊☠?? ? ‟‣?? ᬡ? ?…??ᤢᤠ ? ???? ?? ?? 㴡 ? ⹔ ????? ?? ⹔ ?‟ ᤚ?? ?? ??? ⰲ ?ᬢ??? ?…??ᤢ? ?‡ ᤚ?ᬟ? 㸭  Standardi?ed beta coefficients and R2GLMM(?)  are re㘅rted for either the best?fit ?odel, or, if there ?as su㘶ort for ?ore than one ?odel, the average of su㘶orted ?odels. The standardi?ed beta coefficient is a ?easure of effect si?e that can be co??ared a?ong 㘌edictors in the sa?e ?odel. Relative i?㘅rtance is a ?easure of the ?eight of evidence in favor of a 㘌edictor sub?ect to ?odel selection,on a scale fro? 0㼲, and is re㘅rted for burst ca㘄city and ?ing ?or㘪ology variables as these alone ?ere sub?ect to ?odel selection. Marginal R2GLMM(?)  㘌ovides a ?easure of the co?bined e㬶lanatory 㘅?er of fi㬊d effects of interest (co?㘊titor 㘌esence, burst ca?acity, and ?ing ?or㘪ology effects co?bined). Detail of all candidate ?odels are 㘌ovided in  A㘶endi? C.?
? ? ?? ? ?? ?? ‚ ? ?‚ ? ?㜝? ??? ?? ? ? ??? ??? ᬊ?”? ?䠱䔊CI? ???ᬙ ??? ??? ?? ? ᬡ? ? R? GLMM???AccTotvel, ?a? ?ing sha㘊 ?burst co?㘊titor 㘌esence?ass?eight lifted?ing length?ing as?ect ratioe㬶eri?ent (CA1)e㬶eri?ent (CA2)days 㘅st?ca㘔ure搘.0䈇?搘.1䔎 0.11?  0.0䌇?搘.03, 0.20?   0.12 ?搘.002, 0.2䉰搘.0䔇?搘.21, 0.06?  0.1䔇?搘.02, 0.3䕰  0.䌘 ?0.3䔎 1.䈲?  0.䑃 ?0.30, 1.2䕰搘.003 ?搘.01, 0.002?????1.000.250.䑄??? ?? ?0.66AccHor ?a? burst ?co?㘊titionco?㘊titor 㘌esence?ass?eight lifted?ing as?ect ratioe㬶eri?ent(CA1)e㬶eri?ent(CA2)days 㘅st?ca㘔ure搘.䈳 ?搘.䔳, 搘.06?  0.15 ?搘.3䈎 0.66?  0.䈗 ?搘.0䌎 0.䌙?  0.䉅 ?搘.35, 1.30?  3.䔛 ?2.06, 5.6䑰  3.䔘 ?2.0䈎 5.55?搘.01 ?搘.03, 0.01?????1.000.3?????? ?0.3䐇DecHor ?a? burst ?co?㘊titionco?㘊titor 㘌esence?ass?eight lifted?ing as?ect ratioe㬶eri?ent(CA1)e㬶eri?ent(CA2)days 㘅st?ca㘔ure搘.䈛 ?搘.䔘, 搘.12?0.2䐇?搘.1䐎 0.䐗?0.䉄 ?0.02, 0.䌙?  0.3䔇?搘.3䐎 1.1䉰3.6䐇?2.06, 5.2䍰3.䌙 ?2.䈙, 5.䈗?搘.01 ?搘.02, 0.01?????1.000.30????? ?0.䈘 AccVU ?a? interce㘔?only NA NA NA 0 (NA)AccVD ?a? interce㘔?only NA NA NA 0 (NA)PitchUvel, avg burst co?㘊titor 㘌esence?ass?eight liftede㬶eri?ent(CA1)e㬶eri?ent(CA2)0.02 ?搘.02, 0.06?0.0001 ?搘.0䈎 0.0䉰0.0䈇?搘.01, 0.0䕰0.13 ?0.0䈎 0.22?0.1䐇?0.06, 0.2䍰??? ?1.00????0.06 PitchDvel, avg co?㘊tition? burstco?㘊titor 㘌esence?ass?eight lifted?ing lengthe㬶eri?ent(CA1)e㬶eri?ent(CA2)0.06 ?0.01, 0.10?0.01 ?搘.0䈎 0.05?0.05 ?搘.01, 0.10?0.0䈇?搘.03, 0.11?0.15 ?0.01, 0.3?0.25 ?0.11, 0.3䕰??? ?1.000.33????0.12Yawvel, avg interce㘔?only NA NA NA 0 (NA)102?
? ? ?? ? ?? ?? ‚ ? ?‚ ? ?㜝? ??? ?? ? ? ??? ??? ᬊ?”? ?䠱䔊CI? ???ᬙ ??? ??? ?? ? ᬡ? ? R? GLMM???PRTdeg interce㘔?only NA NA NA 0 (NA)PRTti?e burst co?㘊titor 㘌esence?ass?eight lifted?ing lengthe㬶eri?ent(CA1)e㬶eri?ent(CA2)搘.001 ?搘.01, 0.01?搘.01 ?搘.03, 0.003?搘.02 ?搘.0䈎 搘.00䉰搘.01 ?搘.03, 0.01?搘.0䐇?搘.11, 搘.03?搘.12 ?搘.1䐎 搘.0䕰???1.000.2????0.16 Arcrad burst co?㘊titor 㘌esence?ass?eight liftede㬶eri?ent(CA1)e㬶eri?ent(CA2)搘.02 ?搘.0䐎 0.02?0.01 ?搘.03, 0.06?0.0䔇?0.03, 0.13?0.20 ?0.10, 0.30?0.31 ?0.1䌎 0.䉂???? ?1.00???0.11Arcvel, avg burst co?㘊titor 㘌esence?ass?eight lifted?ing as?ect ratioe㬶eri?ent(CA1)e㬶eri?ent(CA2)days 㘅st?ca㘔ure搘.01 ?搘.10, 0.0䍰0.03 ?搘.06, 0.13?0.1䈇?0.0䈎 0.2䉰0.13 ?搘.02, 0.2䍰0.䑄 ?0.3䌎 1.15?0.䐗 ?0.31, 1.15?搘.001 ?搘.005, 0.002???1.000.5????? ?0.3?Acccent, ?a? ?ing sha?e co?㘊titor 㘌esence?ass?ing as?ect ratioe㬶eri?ent(CA1)e㬶eri?ent(CA2)days 㘅st?ca㘔ure0.2䌇?搘.3䐎 0.䍂?搘.20 ?搘.䑂, 0.3䉰1.0䌇?0.1䌎 1.䍃?5.䌙 ?䈉02, 䐉䕂?0.䔳 ?搲.5䌎 3.2䕰搘.0䈇?搘.06, 搘.02???? ?1.00????? ?0.䈘PRT% co?㘊tition ? ?ing sha㘊 ?burst ? ?ing si?eco?㘊titor 㘌esence?ass?eight lifted?ing length?ing as?ect ratioe㬶eri?ent(CA1)e㬶eri?ent(CA2)搘.1䈇?搘.1䌎 搘.0䍰搘.001 ?搘.0䈎 0.05?0.06 ?0.002, 0.12?搘.06 ?搘.13, 0.01?搘.11 ?搘.20, 搘.01?0.10 ?搘.11, 0.31?0.3䌇?0.1䈎 0.65?????1.000.611.00????0.31103ㄭ M???ᬡ??ᬟ ?‡??? ᬢ ??᠊‡ ????? ?‫?? ??᠝?⠝ ᠊?? ? ??ᬘ? ?ᬡ??⠝ ?? ?? ????‚? ᬡ? ? ?? ????? ?⌗? ? ??ㄭⰊIℙ??⤤? ??‡Ani?als flying at high elevation face the dual challenges of reduced o㬂gen availability, ?hich constrains ?etabolic in㘬t, and decreased air density, ?hich constrains ?echanical 㘅?er out㘬t. Hu??ingbirds have one of the ?ost e㬶ensive for?s of flight but are nonetheless co??on in high elevation habitats throughout the ?estern he?is㘪ere (Bro?n and ?odric?Bro?n, 1䍄䌺 Car㘊nter et al., 1䍅3? Feinsinger et al., 1䍄䌺 Stiles, 1䍅0) . Research ?ith hu??ingbirds has de?onstrated that the ?etabolic and ?echanical costs of hovering increase at higher elevations (Altshuler and Dudley, 2003? Chai and Dudley, 1䍃6? ?elch, and Suare?, 200䔰 . Additionally, e㬶eri?ents ?ith variable gas ?i㬔ures have revealed that reduction in o㬂gen availability leads to decreases in ?ingbeat fre㴬ency, ?hile reduction in air density leads  to increases in ?ingbeat a?㘆itude (Altshuler and Dudley, 2003? Chai and Dudley, 1䍃5) . It is e㬶ected that other features of flight 㘊rfor?ance should also be influenced by environ?ental changes along elevational gradients (Altshuler and Dudley, 2006? Altshuler et al., 200䈁) . In 㘄rticular, hu??ingbirds rely on their high level of ?aneuverability to 㘊rfor? co?㘆e? ?ating dis㘆ays (Clar㜎 200䌺 Clar㜇et al., 2012? Felton et al., 200䔺 Feo and Clar㜎 2010) , ca㘔ure insects (Stiles, 1䍃5? Yanega and Rubega, 200䈰 , and aggressively defend territories (Altshuler, 2006? Car㘊nter et al., 1䍅3) . Ho?ever, ho? ?aneuvering 㘊rfor?ance is affected by the reduced o㬂gen and decreased air density found at high elevations re?ains largely un㜐o?n. Maneuvering flight re㴬ires the ability to generate and reorient e㬫ess aerodyna?ic force 10?(Dudley, 2002). The ca㘄city for hu??ingbirds to generate additional force for brief 㘊riods of ti?e can be ?easured using the techni㴬e of asy?㘔otic load㼆ifting, and is often referred to as the burst 㘅?er reserves (Chai and Millard, 1䍃䐺 Chai et al., 1䍃䐰 . I recently tested the hy㘅thesis that 㘊rfor?ance during voluntary ?aneuvers ?as associated ?ith an individual hu??ingbird?s 㘅?er reserves (Cha㘔er 䈰 . Hu??ingbirds ?ith higher 㘅?er reserves accelerated, decelerated and turned faster than birds ?ith lo?er 㘅?er reserves. Moreover, the ?agnitude of the 㘅?er reserves ?as the ?ost co??on 㘌edictor of different features of ?aneuvering 㘊rfor?ance, ?uch ?ore than ?ing ?or㘪ology or even the 㘌esence of a co??etitor. At high elevations, hu??ingbird 㘅?er reserves are reduced. Hu??ingbirds caught at high elevation sites de?onstrated significantly lo?er 㘅?er reserves co?㘄red to individuals of the sa?e s㘊cies caught at lo?er elevation sites (Altshuler, 2006). Because load?lifting e㬶eri?ents have not been co?bined ?ith gas ?i㬔ure trials, it is un㜐o?n ho? ?uscle ca?acity at high elevation is influenced by o㬂gen availability and air density.  If 㘅?er reserves directly affect ?aneuvering 㘊rfor?ance, then birds flying at high elevation should also e㬶erience a decrease in ?aneuverability. Given the association bet?een 㘅?er reserves and ?aneuvering 㘊rfor?ance (Segre et al.), I sought to deter?ine if hu??ingbird ?aneuvering 㘊rfor?ance declines at higher elevation  (figure 5.1c? H1). I ?easured ?aneuvering behavior of Anna?s hu??ingbirds (Calypte anna) using a high㼓㘊ed video trac㜑ng syste?. The sa?e birds ?ere tested during solitary and co??etitive flights in a large flight cha?ber at both a lo? elevation (326?) and at a high elevation (3䔘0?) site. The high elevation site ?as chosen because it is slightly higher than their natural range and high enough to i?㘅se a challenge to 㘅?er reserves ?ithout detri?entally 105restricting flight ca㘄bilities (Altshuler and Dudley, 2003). This e㬶eri?ent revealed significant declines in all of the ?aneuvering 㘊rfor?ance ?etrics that I considered. I designed an additional e㬶eri?ent to deter?ine if the declines in ?aneuvering 㘊rfor?ance ?ere caused by changes in o㬂gen availability (figure 5.1c? H2) or air density (figure 5.1c? H3). This e㬶eri?ent tested the ?aneuvering 㘊rfor?ance of hu??ingbirds in an airtight flight cha?ber infused ?ith either nitrogen, to lo?er o㬂gen availability, or helio㬎 to lo?er air density (Altshuler and Dudley, 2003? Chai and Dudley, 1䍃6) . Collectively, these e㬶eri?ents address the 㴬estion? ?hat are the challenges to hu??ingbird ?aneuvering 㘊rfor?ance i?㘅sed by high elevations?ㄭ⸊Mᬙᴚ?? ?? ᬡ⤊?ᴙ㐠⤘I ca㘔ured and fil?ed 16 adult ?ale Anna?s hu??ingbirds near the University of California, Riverside (n ? 䔇birds in ?une?October 200䌰 for the translocation e㬶eri?ent and near the University of British Colu?bia (n ? 䔇birds in Dece?ber 2013㼜㘌il 201䈰 for the gas substitution e㬶eri?ent. The hu??ingbirds ?ere ca㘔ured ?ith dro㘿door tra㘓, housed in individual cages, and fed ad libidum ?ith a solution of artificial nectar (Ne㜔ar?Plus, Ne㜔on, Pfor?hei?, Ger?any) and sucrose. All of the 㘌ocedures ?ere conducted under a㘶roval of the Institutional Ani?al Care and Use Co??ittee at the University of California, Riverside and the Ani?al Care co??ittee at the University of British Colu?bia. Birds ?ere fil?ed during free㼕light to describe their ?aneuvering 㘊rfor?ance. The ?aneuverability trials ?ere conducted in a large flight cage (3 㬇1.5 㬇1.5 ?eters), built ?ith a ?etal fra?e and garden ?esh (translocation) or 㘆e?iglass (gas substitution) side 㘄nels, and containing several 㘊rches and a feeder. The birds ?ere allo?ed ti?e to accli?ate to the cage and  ?ere then fil?ed flying individually for t?o hours. Each bird ?as also fil?ed flying in the 106㘌esence of a rando?i?ed and 㘌eviously un㜐o?n co?㘊titor for a se㘄rate t?o㼪our trial. During the co?㘊tition trials one bird ?as ?ar㜊d ?ith a 㘑ece of retro㼌eflective ta?e. After data  㘌ocessing ?as co?㘆ete the digiti?ed ?aneuvers ?ere re㼶ro?ected onto the videos, and a tea? of digiti?ers attributed each ?aneuver to the ?ar?ed or un?ar?ed individual. To deter?ine the burst 㘅?er ca㘄city of each bird, body ?ass ?as recorded and load㼆ifting trials ?ere conducted  using the sa?e ?ethods described in 㘌evious studies (Altshuler, 2006? Chai et al., 1䍃䐰 .ㄭ⸭ⰊT??ᰪ?℣ ?✘?ᴦDuring the ?aneuverability trials the birds ?ere fil?ed using a ?ulti?ca?era trac?ing syste? that auto?atically ?easures body 㘅sition and orientation. A detailed descri㘔ion of the trac㜑ng syste? and 㘊rfor?ance ?etrics is available in Cha㘔er 䈉 Briefly, I e㬔racted a series of  stereoty㘊d ?aneuvers? total accelerations, hori?ontal accelerations, hori?ontal decelerations, arcing turns, hovering 㘑tch?u㘇rotations, hovering 㘑tch㼭o?n rotations, and hovering ya? turns.  For each ty㘊 of ?aneuver I calculated one or t?o 㘊rfor?ance ?etrics. I focused on 㘊rfor?ance ?etrics that are  re㘊atable and reliably surveyed by this e㬶eri?ental setu㘇(Cha㘔er 䈰 . For total accelerations ?aneuvers I ?easured the ?a㬑?u? velocity ( AccTotvel, ?a? ). For hori?ontal accelerations and decelerations I ?easured the ?a?i?u? accelerations (AccHor ?a? ) and decelerations (DecHor ?a? ) res㘊ctively. Fro? the arcing turns I ?easured the ?a?i?u? centri㘊tal acceleration ( Arccent, ?a? ). Fro? the hovering 㘑tch㼬㘎 㘑tch㼭o?n, and ya? ?aneuvers I ?easured average rotational velocity ( PitchUvel, avg , PitchDvel, avg , Yawvel, avg). ㄭ⸭⸊T?ᬡ??“ᬙ ? ‡ ᴷ┝ᨢ? ᴡ?Hu??ingbirds ?ere ca㘔ured at lo? elevations and trans㘅rted to a high elevation site at 10??hite Mountain Research Center?s Barcroft Laboratory (elevation 3䔘0 ?, 䰇? 0.䑃 㜋?? 3, o㬂gen 㘄rtial 㘌essure ? 102 ?? Hg) in t?o grou㘓. The first ca㘔ure grou㘇included three birds that ?ere given four ?ee㜓 to accli?ate to the high altitude site, and the second ca?ture grou㘇includ ed five birds that ?ere given t?o ?ee㜓 to accli?ate. Once the fil?ing ?as co??leted the birds ?ere trans㘅rted bac㜇to the lo? elevation site at the University of California Riverside (elevation 326 ?, 䰇? 1.1䔇㜋?? 3, o㬂gen 㘄rtial 㘌essure ? 153 ?? Hg) and allo?ed to accli?ate for four ?ee㜓 before being fil?ed. Birds ?ere 㜊㘔 in cloth bags during trans㘅rt and ?ere ?onitored for signs of stress and hand?fed every thirty ?inutes. All trials ?ere conducted at 22?C, and every bird ?as fil?ed once in solo flight and t?ice in co??etitive flight. ㄭ⸭⼊Gᬘ ?␗???? ␙ ? ‡ ᴷ┝ᨢ? ᴡ?Hu??ingbirds ?ere fil?ed at the University of British Colu?bia (elevation 䌲 ?, 䰇? 1.13 㜋?? 3, o㬂gen 㘄rtial 㘌essure ? 15䌇?? Hg, average lab te??erature ? 1䔉5?C) in three gas treat?ents designed to ?atch the air density and o㬂gen concentrations in the translocation study. The first treat?ent ?a s in air, the second treat?ent added nitrogen to create nor?odense and hy㘅㬑c conditions, and the third treat?ent added heliu? and o㬂gen (helio㬰 to create hy㘅dense and nor?o㬑c conditions. The o㬂gen content and air density ?ithin the sealed acrylic flight cha?ber ?ere controlled ?ith a gas ?i㬊r (MFC㽂, Sable Syste?s, Las Vegas NV, USA) that regulated ?ass flo? valves (MC㼗0 ? MCP㼲00, Alicat Scientific, Tuscon AZ, USA).  During gas ?i㬑ng, a relief 㘅rt in the side of the cha?ber ?as left o㘊n to allo? o㬂gen to esca㘊 and a s?all electric fan circulated the contents of the cha?ber. O㬂gen concentrations and air density ?ere ?onitored continuously during gas ?i?ing and every thirty ?inutes during 10?fil?ing. O㬂gen ?as ?easured ?ith an o㬂gen analy?er (OM㼲1, Model 2䈗B, Bec㜵an Instru?ents, Pasadena CA, USA) and air density ?as calculated si?ilar to 㘌evious studies (Altshuler and Dudley, 2003? Chai and Dudley, 1䍃6)  ?here the fre㴬ency of a Galton ?histle inside the flight cha?ber ?as recorded (Raven Lite 1.0, Cornell Lab of Ornithology, Ithaca NY, USA) and calculated ?ith a custo? Matlab scri㘔 (Matlab, Math?or㜓, Natic? MA, USA). This fre㴬ency, as ?ell as the cha?ber?s te?㘊rature, hu?idity, and baro?etric 㘌essure ?as used to calculate the initial air density ?ithin the cha?ber and subse㴬ent changes in ?histle fre㴬ency ?ith the addition of helio㬇?ere used to deter?ine changes in air density. Additional nitrogen or helio㬇?as added to the flight cha?ber as needed to ?aintain the air density and o㬂gen concentration of hy㘅dense treat?ents (average air density ? 0.䑃 㜋?? 3, average o㬂gen 㘄rtial 㘌essure ?  15䐇?? Hg) and hy㘅㬑c treat?ents (average air density ? 1.10 㜋?? 3, average o㬂gen 㘄rtial 㘌essure ? 101 ?? Hg) as closely as 㘅ssible to those at the ?hite Mountain Research Center (elevation 3䔘0 ?, air density ? 0.䑃 㜋?? 3, o㬂gen 㘄rtial 㘌essure ? 102 ?? Hg). For each gas ?i㬔ure treat?ent, every bird ?as fil?ed once in solitary flight and once in co??etition against a 㘌eviously un㜐o?n o㘶onent. ㄭ⸭《S?????? ? ᰛ? ᬡᬟ✘??The data sets fro? California and British Colu?bia ?ere analy?ed se㘄rately because they resulted fro? t?o different e㬶eri?ents. Ho?ever, it is i?㘅rtant to note that the data sets also differed in ti?e of year, air te??erature, and visual environ?ent of the flight cha?ber bet?een California and British Colu?bia e㬶eri?ents.Quality chec㜑ng of the video trac?ing revealed fe? errors, but the syste? occasionally 㘌oduced unrealistic changes in 㘅sition and orientation. Because I did not ?ant trac㜑ng errors 10?to have a dis㘌o㘅rtionate effect on the analysis, for each 㘊rfor?ance ?etric I re?oved values that ?ere ?ore e㬔re?e than five standard deviations fro? the 㘅oled ?ean. The total nu?ber of e㬔re?e values re?oved ?as 䑄 out of 2䈗,0䑂 data 㘅ints for the trans㘆ant e㬶eri?ent, and 䉅 out of 2䑅,1䌲 for the gas substitution e㬶eri?ent, or ? 0.0䈇指of both datasets. ?ith the re?aining data, I calculated a ?ean value for each bird㼔rial co?bination (elevation? n ? 䉅? 䔇birds in 16 solo trials and 16 co?㘊tition trials? gas substitution? n ? 䉅? 䔇birds in 2䈇solo trials and 12 co?㘊tition trials). The calculated ?eans ?ere used in the subse㴬ent statistical analyses.The trans㘆ant e㬶eri?ent ?as designed to test the effects of elevation on ?aneuvering 㘊rfor?ance ?etrics. I fit a se㘄rate linear ?i㬊d effects ?odel for each 㘊rfor?ance ?etric that included fi?ed effects of elevation, co??etitor 㘌esence, body ?ass, ?ass lifted during load?lifting, and ca?ture?grou㘎 as ?ell as a rando? effect of bird identity to account for re㘊ated  ?easures of individuals. I used ?ald?s test to evaluate the effect of elevation.The gas ?i?ture e㬶eri?ents ?ere designed to test ho? reduction in o㬂gen availability and in air density affected ?aneuvering 㘊rfor?ance ?etrics. I follo?ed a si?ilar 㘌ocedure, fitting a se㘄rate ?odel ?ith fi㬊d effects of gas treat?ent (nitrogen, helio㬎 nor?al air), co??etitor 㘌esence, body ?ass, ?ass lifted, nu?ber of days since ca㘔ure, and a rando? effect of bird identity for each 㘊rfor?ance ?etric. I used Dunnett?s tests to evaluate the inde㘊ndent effects of air density (helio? ?i㬔ure vs. air) and hy㘅㬑a (nitrogen ?i?ture vs. air) in the gas substitution e㬶eri?ent. I accounted for ?ulti㘆e testing of the seven 㘊rfor?ance ?etrics using the Ben?a?ini搥ochberg 㘌ocedure. I used a false discovery rate of 㴇? 0.05 ?ithin each of the follo?ing co?㘄rison sets? (i) high vs. lo? elevation, (ii) nitrogen vs. air, and (iii) helio㬇vs. air. 110ㄭ⼊Rᴘ␟??Mor㘪ology and flight 㘊rfor?ance of individual Anna?s hu??ingbirds are given in table  5.1. The birds fro? California and British Colu?bia that ?ere used in the elevation and gas ?i?ture e㬶eri?ent, res㘊ctively, differed in ?ing ?or㘪ology, and so?e features of hovering and load㼆ifting 㘊rfor?ance values. The hu??ingbirds studied in the translocation e㬶eri?ent 㘌oduced a si?ilar nu?ber of ?aneuvers at both sites. Sa?㘆e si?es for ?ost ?aneuvers ?ere lo?er at high elevation ?ith the only e㬫e㘔ions being total accelerations, ?hich ?ere essentially identical bet?een sites, and arcing turns, ?hich ?ere ?ore ?ore fre㴬ent at high elevation (table 5.2). In every 㘊rfor?ance ?etric, the birds at higher elevation e㬶erienced a significant decrease in ?aneuverability (all P ?  001). I did observe individual differences in the 㘊rfor?ance ?etrics at both sites and in the strength of the declines bet?een sites (figure 5.2a).The hu??ingbird studied in the gas ?i?ture e㬶eri?ents 㘌oduced a large nu?ber of tra?ectories. Sa?㘆e si?es ?ere si?ilar bet?een air and lo? o㬂gen availability trails, but lo? air density trials had generally fe?er sa?㘆es. Hu??ingbirds flying in a hy㘅㬑c gas ?i㬔ure ?ith o㬂gen levels e㴬ivalent to 3䌗5 ? did not e㬶erience a decrease in any of the ?aneuvering 㘊rfor?ance ?etrics I ?easured (all P ? 0.2? table 5.2? figure 5.2b). Ho?ever, flying in a hy㘅dense ?i㬔ure ?ith a density e㴬ivalent to 3䔘0 ? significantly decreased hori?ontal acceleration (P ? 0.02䈰, hori?ontal deceleration ( P ? 0.006), 㘑tch?u㘇velocity ( P ? 0.003), and ya? velocity ( P ? 0.00䔺 figure 5.1c, table 5.3). Notably, I found that lo? air density decreased 㘊rfor?ance on both translational and rotational ?aneuvers. 111ㄭ《D??ᰤ? ??‡The goal of this study ?as to deter?ine if the ?aneuvering 㘊rfor?ance of flying birds is affected by high elevation, and if so, ?hether this is due to decreases in o㬂gen availability or lo?er air density (figure 5.1). Using a ?ulti?ca?era trac?ing syste?, I de?onstrated that all of the ?etrics I used to 㴬antify ?aneuvering 㘊rfor?ance in hu??ingbirds ?ere lo?er at high elevation (table 5.2, figure 5.2). E㬶eri?ental decreases in o㬂gen availability via nitrogen infusion did not lead to any ?easurable changes in ?aneuvering 㘊rfor?ance (table 5.3). In contrast, e㬶eri?ental decreases in air density via helio㬇infusion decreased hori?ontal accelerations and decelerations, ya? velocities, and 㘑tch㼬㘇velocities. Collectively, these e㬶eri?ents de?onstrate a strong influence of elevation on the ?aneuvering 㘊rfor?ance of hu??ingbirds, ?hich is driven ?ore by changes in air density than o㬂gen availability.  Hu??ingbirds translocated to higher elevation e㬶erienced a significant reduction in ?aneuverability. Perfor?ance of translational velocities and accelerations, and rotational velocities decreased co?㘄red to 㘊rfor?ance at lo? elevation. Decreased ?aneuverability ?ay re㘌esent a cost of 㘊r?anently (Altshuler et al., 200䈁? Feinsinger et al., 1䍄䌰  or te?㘅rarily (Altshuler, 2006? Car㘊nter et al., 1䍅3)  living at higher elevations. Hu??ingbirds rely on their high level of ?aneuverability to 㘊rfor? a range of i?㘅rtant behaviors. Co?㘆e㬇dis㘆ays re㴬ire high accelerations (Clar㜎 200䌺 Hurly et al., 2001) , rotations (Felton et al., 200䔰 , and load carrying ca㘄bilities (Zusi and Gill, 200䌰  to obtain ?ates and to inti?idate co?㘊titors. Additionally, ?any hu??ingbird s㘊cies de㘊nd on aerial insectivory to su㘶le?ent their nectar  based diet (Stiles, 1䍃5? Yanega and Rubega, 200䈰 . Finally, there is evidence that ?aneuvering 㘊rfor?ance affects the outco?es of territorial contests. Altshuler et al. (Altshuler, 2006) suggested that ra㘑d vertical ascents ?ay 㘆ay a role in establishing do?inance. Vertical 112accelerations and decelerations ?ere not re㘊atably surveyed using the e㬶eri?ental setu㘎 㘅ssibly because of the li?ited height of the cage (Segre et al.). The influence of ?aneuvering 㘊rfor?ance on the outco?es of behaviors such as courtshi? dis㘆ays, 㘌edatory chases, and territorial co?㘊titions has not been tested and re?ains an area ?ith 㘅tential for future ?or㜉 I did not find an influence of lo? o㬂gen on hu??ingbird ?aneuvering 㘊rfor?ance. Previous studies ?ith hy㘅㬑c nor?odense gas ?i㬔ures sho?ed that as o㬂gen concentration is reduced, hovering hu??ingbirds slightly decrease their ?ingbeat fre㴬ency (Altshuler, 2006? Altshuler and Dudley, 2003). This is li㜊ly the effect of fatigue, since the ?echanical cost of hovering does not change. Because burst 㘊rfor?ance is transient and li?ely anaerobic (Altshuler and Dudley, 2003), the effects of hy㘅㬑a on ?a㬑?u? force generation ?ay be li?ited, although this re?ains to be tested. Therefore, it is 㘅ssible that ?aneuvering 㘊rfor?ance does not change because 㘅?er reserves (the difference bet?een the ?ini?u? 㘅?er re㴬ired to fly and ?a㬑?u? 㘅?er generated during burst 㘊rfor?ance) are unaffected by hy㘅㬑a. It is 㘌obable that hu??ingbirds e㬶erienced increased fatigue ?hile flying in hy㘅㬑a, ho?ever I did not test this.Hu??ingbirds flying in lo? air density e㬪ibited decreased 㘊rfor?ance in several translational and rotational ?etrics. I found reductions in hori?ontal accelerations and decelerations, as ?ell as 㘑tch?u㘇and ya? velocities. Interestingly, I did not find any effect on translational velocity, centri㘊tal acceleration, or 㘑tch?do?n velocity. It is 㘅ssible that the co?bined effect of a ?etabolic challenge and a ?echanical challenge ?ould decrease 㘊rfor?ance ?ore than either one se㘄rately, and this could e㬶lain ?hy I found a dra?atic decrease in 㘊rfor?ance during the translocation e㬶eri?ent but only a ?odest decrease during the gas substitution e㬶eri?ent.  Ho?ever, this re?ains to be tested in future studies, as ?y t?o 113e㬶eri?ents cannot be directly co??ared because of the differences in setu㘇and source 㘅㘬lations.   A large body of ?or㜇on hu??ingbirds has sho?n that the 㜑ne?atic changes to hovering  flight that occur in res㘅nse to elevation are being driven by decreased air density, not reduced o㬂gen availability (revie?ed in Altshuler and Dudley, 2006) . Ho?ever, lo? o㬂gen availability can e㬄cerbate the challenges caused by lo? density. This study e㬔ends these observations to the  ?ore co?㘆icated ?aneuvering flight of hu??ingbirds. At high elevation ?here 㘅?er reserves are lo?, 㘊rfor?ance of co??le㬇?aneuvers decreases. Further?ore, the ?echanical challenge i?㘅sed by lo? air density has a greater effect on ?aneuvering 㘊rfor?ance than the ?etabolic challenge of flying in hy㘅㬑a.11?B3m1.5m1.5mxyzCair density (mm Hg)low(0.79)high(1.10-1.18)low(101-102)high(153-159)oxygen (kg/m3)GasGasElev.Elev.Gashigh elevationlow elevationhypodensehypoxicH1H2H3B. GollerAFigure 5.1. Methods to measure hummingbird maneuvering performance across elevations and in physically variable gas mixtures. (A) Experiments were conducted with males Anna's hummingbirds (Calypte anna). (B) A multi camera tracking system measured maneuvering performance in solitary and paired flight trials. Blue circles indicate the body position for a single trajectory and red lines denote body orientation. (C) A translocation experiment was performed to measure the effects of elevation on maneuvering performance (H1). A gas substitution experiment was performed to measure the independent effects of low oxygen (H2) and low density (H3) on maneuvering performance.  115116elevation translocation321-12-7-2127212721.81.20.6-1.8-1.2-0.61.81.20.6 low   high  low   high  low   high  low   high  low   high  low   high  low   highAccTotvel, max(m/s)AccHormax(m/s2)DecHormax(m/s2) (rev/s)PitchUvel, avg(rev/s)PitchDvel, avg(rev/s)Yawvel, avgArccent, max(m/s2)* * * * * * *density challenge321-12-7-2127212721.81.20.6-1.8-1.2-0.61.81.20.6 air hypodense  air hypodense  air hypodense  air hypodense  air hypodense  air hypodense  air hypodense* * *** denotes significanceoxygen challenge air  hypoxic  air  hypoxic  air  hypoxic air  hypoxic  air  hypoxic  air  hypoxic321-12-7-2127212721.81.20.6-1.8-1.2-0.61.81.20.6  air  hypoxicABCFigure 5.2. At high elevation where power reserves are low, hummingbird maneuvering performance decreases. We measured seven maneuvering performance metrics: velocity (AccTotvel, max), horizontal acceleration (AccHormax)  and deceleration (DecHormax), arcing turn centripetal acceleration (Arccent, max), hovering pitch-up , pitch-down, and yaw velocities (PitchUvel, avg , PitchDvel, avg , Yawvel, avg). (A) The mean for each bird at low (326 m) and high (3800 m) elevations. At high elevation there was a significant decrease in every performance metric analyzed. (B) When challenged to fly in a normodense hypoxic gas mixture (oxygen equivalent: 3925 m), there was no decrease in maneuvering performance compared to flying in normal air. (C) When challenged to fly in a hypodense normoxic gas mixture there was a significant decrease in horizontal deceleration, pitch-up velocity, and yaw velocity, relative to flying in normal air.  T???? ㄭⰭ I???⠢?? ᬟ ☠???‟‣✊ᬡ ? ?‛?㌟?ḙ?? ? ?ᬚᬦ?? ???  (?ass m (gra?s), ?ing length L (??), ?ing area S (?? 2), as㘊ct ratio AR, and hovering (hov) and load㼆ifting (ll) 㘊rfor?ance  (lifted ?ass load (g), ?ingbeat fre㴬ency f (H?) and ?ing stro㜊 a??litude ? (?)  during hovering and load㼆ifting). Differences bet?een e㬶eri?ents ?ere assessed using t㼠ests ?ith significance indicated by 渇( P ?.01) and 湮 ( P ?.0001).Bird id m L** S** AR? fhov ? hov? load fll? ? llelev 1 䈉䈘 䉃.0 12䐲 䐉6 䈘.3 162.? 6.05 䉄.6 1䔲.2elev 2 䈉䉅 䉃.? 1306 䐉6 3䔉? 152.3 5.66 䉄.6 1䐛.5elev 3 䈉0? 䈳.? 1051 䔉0 3䔉? 152.5 6.䉂 䉄.6 1䕂.6elev ? 䈉䔗 51.? 13䑅 䐉? 3䔉5 1䉂.? 䐉2? 䉅.5 1䌗.3elev 5 5.5? 䉃.1 1236 䐉? 䈲.? 166.? 5.66 50.5 1䕂.1elev 6 䈉5? 䉃.? 12䈳 䔉0 3䌉6 1䉃.5 6.䐳 䉅.? 1䔘.?elev ? 䈉5? 䉄.? 1200 䐉6 3䌉? 1䉃.1 6.3 䈛.5 1䕃.6elev ? 5.61 䈛.? 1131 䐉? 䈗.0 15䈉? 6 䉃.1 1䔗.?gas 1 䈉50 51.6 1䉃6 䐉1 䈳.? 1䈲.? 䐉22 50.2 1䍄.5gas 2 䈉3? 52.? 1䈗? 䐉? 36.5 1䉄.6 䈉䕅 䉅.5 1䑄.?gas 3 䈉62 55.? 1620 䐉6 䈲.1 130.? 5.66 50.2 1䑃.2gas ? 䈉63 5䈉2 1653 䐉1 䈙.6 131.5 5.66 52.? 1䕂.0gas 5 䈉23 52.5 151? 䐉3 3䔉? 156.? 6.䉂 50.? 1䕄.5gas 6 䈉䐳 53.6 1525 䐉6 䈘.? 153.6 5.2? 䉄.? 1䔛.?gas ? 䈉䉂 52.1 1䉅? 䐉3 䈲.? 13䌉? 6.䉂 51.6 1䕄.5gas ? 䈉6? 53.5 155? 䐉? 䈲.3 1䈙.? 6.䉂 䉅.1 1䔳.311?T???? ㄭ⸭  Mᬡ??⠝??? ⌊? ??Ḡ?☛? ? ? ᬙ ??⌴ ᬡ? ?‫ ???⠛ᤢ‡ ? ⴊ The 㘊rfor?ance ?etrics are velocity (AccTotvel, ?a? ), hori?ontal acceleration ( AccHor ?a? )  and deceleration (DecHor ?a? ), arcing turn centri㘊tal acceleration ( Arccent, ?a? ), hovering 㘑tch㼬㘇, 㘑tch㼭o?n, and ya? velocities (PitchUvel, avg , PitchDvel, avg , Yawvel, avg). The ?odel included fi㬊d effects of elevation, co??etitor 㘌esence , body ?ass, load㼆ifting 㘊rfor?ance,  and ca㘔ure㼋rou㘎 as ?ell as a rando? effect of bird identity. The nu?ber of tra?ectories ?easured, the ?ean and standard errors, and the treat?ent effects are 㘌esented for each ?etric. ?? ?⠛?? ‡ ??ᬡ ᠟ “ᬙ? ‡䄊??ᭇ ?? ?‚? ?? ⌚ᬡ? ??ᬡ ? SE ???ᬙ? ?? ? ?? ?? ?? ??? ? ?‫?? ‫ ???? ? ? ???? ? ‫ ???? ? ? ???? ?”? ? ?䠱? CI? ? ??⠛? ? ?AccTotvel, max 2䔙3? 2䔛5? 2.6 ? 0.1 2.2 ? 0.1 ?0.䈘 ??0.55, ?0.2䉰 ?䈉䌳 噔ⵔ听?AccHormax 1䔗䕅 1䉃55 䐉6 ? 0.? 5.䔇? 0.5 ?1.䔛 ??2.32, ?1.䈘? ?䐉䌳 噔ⵔ听?DecHormax 200䈛 15012 ?䔉1 ? 0.3 ?6.0 ? 0.5 2.0䔇?1.63, 2.53? 䔉䍅 噔ⵔ听?Arccent, max 2䍃3 3351 䔉3 ? 0.6 6.䈇? 0.5 ?1.䍃 ??2.6䐎 ?1.31? ?5.䐙 噔ⵔ听?PitchUvel, avg 1䌙5 1026 1.2 ? 0.0 1.1 ? 0.0 ?0.15 ??0.20, ?0.10? ?5.䌳 噔ⵔ听?PitchDvel, avg 60䈛 3䈘3 ?1.1 ? 0.0 ?1.0 ? 0.0 0.11 ?0.06, 0.15? 䈉䑂 噔ⵔ听?Yawvel, avg 䈗02 2䐘0 1.6 ? 0.0 1.5 ? 0.0 ?0.10 ??0.16, ?0.0䉰 ?3.䈙 吭呔ⱗ渇denotes significance11?T???? ㄭ⼭  Mᬡ??⠝??? ⌊? ??Ḡ?☛? ? ? ?? ?‚☠??? ? ? ???‷?? ⌛? ??? ?‚☛? ᬢ? ⴊ The 㘊rfor?ance ?etrics are velocity ( AccTotvel, ?a? ), hori?ontal acceleration ( AccHor ?a? )  and deceleration (DecHor ?a? ), arcing turn centri㘊tal acceleration ( Arccent, ?a? ), hovering 㘑tch?u㘇, 㘑tch㼭o?n, and ya? velocities ( PitchUvel, avg , PitchDvel, avg , Yawvel, avg). The ?odel included fi㬊d effects of gas ?i㬔ure, co?㘊titor 㘌esence , body ?ass, load㼆ifting 㘊rfor?ance, and days since ca?ture , as ?ell as a rando? effect of bird identity. The nu?ber of tra?ectories ?easured, the ?ean and standard errors, and the treat?ent effects are 㘌esented for each ?etric. ‷✣?? ??ᬟ? ?? ⌝䄊??ᭇ ?? ?‚? ?? ⌚ᬡ? ??ᬡ ? SE ???ᬙ? ?? ? ?? ?? ?? ??✥ ‷? ? ? ᬢ??ᬢ ? ?✥ ‷? ? ᬢ ? ?✥ ‷? ? ?”? ? ?䠱? CI? ? ??⠛? ? ?AccTotvel, max 230䉄 23䈗2 1.6 ? 0.1 1.䐇? 0.1 0.0䐇??0.0䈎 0.1䕰 1.2? 0.32?AccHormax 163䑅 16305 䈉2 ? 0.? 䈉1 ? 0.2 ?0.12 ??0.5䈎 0.31? ?0.5? 0.䔘?DecHormax 1䐙10 1䐙01 ?䈉5 ? 0.? ?䈉5 ? 0.3 0.10 ??0.31, 0.51? 0.䉅 0.䕂?Arccent, max 1䑅? 2䉂6 䈉3 ? 0.3 䈉6 ? 0.? ?0.03 ??0.0䔎 0.02? ?1.16 0.3䍃PitchUvel, avg 310? 2231 1.0 ? 0.0 1.0 ? 0.0 0.03 ??0.02, 0.0䑰 1.23 0.360PitchDvel, avg 5䉃? 䉅䌳 ?0.䌇? 0.0 ?0.䌇? 0.0 ?0.0䈇??0.10, 0.01? ?1.䉅 0.23?Yawvel, avg 6530 52䑅 1.5 ? 0.1 1.䈇? 0.0 0.23 ??0.30, 0.䐳? 0.䕂 0.60?渇denotes significance11?T???? ㄭ《Mᬡ??⠝??? ⌊? ??Ḡ?☛? ?? ☝ᤚ? ?? ?? ???
?? ? ? ?‚☠㜢? ⌛? ᬡ? ?‚☛ ? ᬢ?? The 㘊rfor?ance ?etrics are velocity ( AccTotvel, ?a? ), hori?ontal acceleration ( AccHor ?a? )  and deceleration (DecHor ?a? ), arcing turn centri㘊tal acceleration ( Arccent, ?a? ), hovering 㘑tch?u㘇, 㘑tch㼭o?n, and ya? velocities ( PitchUvel, avg , PitchDvel, avg , Yawvel, avg). The ?odel included fi㬊d effects of gas ?i㬔ure, co?㘊titor 㘌esence, body ?ass, load㼆ifting 㘊rfor?ance, and days since ca?ture, as ?ell as a rando? effect of bird identity. The nu?ber of tra?ectories ?easured, the ?ean and standard errors, and the treat?ent effects are 㘌esented for each ?etric. ? ?? ᠢ ?✊?? ᬟ? ?? ⌝䄊??ᭇ ?? ?‚? ?? ⌚ᬡ? ??ᬡ ? SE ???ᬙ ??? ? ??? ??? ???? 
 ?? ᠝ ? ??? ?ᬢ ? ? ?? 
 ?? ᠝ ᬢ ? ?✥ 
 ??᠝ ?”? ? ?䠱? CI? ? ??⠛? ? ?AccTotvel, max 230䉄 1䔗51 1.6 ? 0.1 1.6 ? 0.1 ?0.05 ??0.16, 0.06? ?0.䌘 0.5䐘AccHormax 163䑅 13䉅? 䈉2 ? 0.? 3.䐇? 0.3 ?0.5䈇??0.䌛, ?0.11? ?2.䉃 吭吮しDecHormax 1䐙10 13䍄0 ?䈉5 ? 0.? ?3.䌇? 0.3 0.62 ?0.21, 1.03? 2.䍄  吭呔㉗Arccent, max 1䑅? 1005 䈉3 ? 0.3 䈉0 ? 0.3 ?0.3䈇??0.䕄, 0.1䕰 ?1.2? 0.336PitchUvel, avg 310? 1䕅0 1.0 ? 0.0 1.0 ? 0.0 ?0.0䔇??0.13, ?0.03? ?3.13  吭呔⽗PitchDvel, avg 5䉃? 3䌲? ?0.䌇? 0.0 ?0.䌇? 0.0 0.03 ??0.01, 0.0䑰 1.䉄 0.2䉂Yawvel, avg 6530 5䕅? 1.5 ? 0.1 1.䈇? 0.0 ?0.0䔇??0.1䈎 ?0.03? ?2.䔳  吭呔㙗渇denotes significance120㈭ C‡???ᠢ ‡?Hu??ingbirds are a highly successful and diverse avian fa?ily found throughout North and South A?erica. They rely on their ?ell?docu?ented agility to 㘊rfor? a ?ide range of co??le㬇behaviors such as territorial co?㘊titions, aerial insect ca㘔ures, and highly coordinated  ?ating dis㘆ays. The ?otivation behind the research 㘌esented in this dissertation ?as to further understand the aerodyna?ic, 㜑ne?atic, and ?or㘪ological under㘑nnings that give hu??ingbirds their s㘊ctacular ?aneuvering ability.  ㈭ⰊB????ᴚᬟ ?ᬪᴊ??ᨤᰙ? ????ith the 㘌oliferation of high s㘊ed video and high resolution 㘄rticle i?aging techni㴬es, our understanding of the ?a㜊 structures created by flying ani?als has greatly increased in recent years. The general 㘄ttern described for birds is that the ?a㜊 㘌oduced by the ?ings is connected over the body, generating a single vorte? loo㘇at slo? s㘊eds (?o㜓hays㜂, 1䍄䌺 S㘊dding, 1䍅䐁) . As the s㘊ed increases the loo㘓 beco?e increasingly ?erged to for? a ladder?li?e ?a㜊 structure (S㘊dding et al., 2003) . In contrast, bats generate bilateral vorte? rings, ?ith each ?ing 㘌oducing inde㘊ndent vorte? loo㘓 (Mui?res et al., 200䔰 . In insects, both single vorte㬇rings (Bo?㘪rey et al., 2005)  and bilateral vorte㬇rings (Bo?㘪rey et al., 200䌰  have been observed. Ho?ever, recent studies have revealed that ?ore co??le㬇flo? structures are also found in flying ani?al ?a㜊s, and that the 㘌esence of these structures ?ay vary ?ith different ta㬄 and flight ?odes (?ohansson and Hedenstr圵, 200䌺 Mui?res et al., 200䔰 .121Hu??ingbirds are uni㴬e a?ong birds in their high ?ingbeat fre㴬ency, their ability to hover, (Greene?alt, 1䌛0)  and their aerodyna?ically active u㘓tro㜊 that 㘌ovides 帙5指of body?eight su㘶ort (?olf et al., 2013) . These features li㜊ly have an i?㘅rtant influence on the ?a㜊 structure that hu??ingbirds generate. In the second cha?ter of this dissertation, I used flo?  visuali?ation to test the hy㘅thesis that hovering hu??ingbirds create bilateral vorte? ?ets. Previously, t?o vorte㬇flo? 㘄tterns had been 㘌o㘅sed for the ?a㜊 of hovering hu??ingbirds?  1) the t?o ?ings for? a single, ?erged vorte? ring during each stro㜊 (Ellington, 1䍅䈄? Rayner,  1䍄䌺 Rayner and Gordon, 1䍃䔰 ? and 2) the t?o ?ings for? bilateral vorte㬇loo㘓 during each stro㜊 (Altshuler et al., 200䌰 . My study resulted in three i?㘅rtant contributions. First, I 㘌esent a novel ?ethod of lo?㼔ech flo? visuali?ation for use in birds or ani?als that ?ay be sensitive to  the s?o㜊 or che?icals co??only used in engineering trials. This techni㴬e uses 㘆u?es of carbon dio㬑de created fro? dry ice that can be fil?ed to identify vorte㬇structures. Secondly, I found t?o structural features that su㘶ort the hy㘅thesis that hu??ingbirds use bilateral vorte㬇?ets ?hile hovering? 1) the airflo? under the ?ings for?s t?o distinct ?ets, and 2) vorte? loo㘓 around each ?et are shed during each u?stro㜊 and do?nstro㜊. I then used the 3D 㜑ne?atic 㘄tterns of hovering ?ings to create a detailed ?odel of the vorte㬇㘄ttern shed by hovering hu??ingbirds. Since this study has been 㘬blished another research grou㘇has inde㘊ndently confir?ed ?y results and the validity of ?y 㘌o㘅sed bilateral vorte㬇?odel (?olf et al., 2013) . The aerodyna?ic i?㘆ications of using a single vorte? ring versus bilateral vorte㬇rings are not ?ell understood. It has been hy㘅thesi?ed that a single vorte? loo㘇?ay be ?ore efficient (Mui?res et al., 2012? Norberg et al., 1䍃3) , ?hile bilateral vorte? loo㘓 ?ay enhance the ability for the ?ings to 㘌oduce left?right asy??etries and ?ay i?㘌ove ?aneuvering 㘊rfor?ance (Bo?㘪rey  122et al., 200䌺 Henningsson et al., 2011) , but this re?ains to be tested. ㈭⸊C‡??ᨛ?ℝ? ?ᬡᴤ⠝ᨘAlthough, ?uch of the se?inal ?or㜇on ani?al flight aerodyna?ics and 㜑ne?atics has focused on the 㘊rfor?ance of steady state behaviors, attention has recently turned to investigating the initiation and ?aintenance of ?aneuvers. It has long been debated ?hether aerial ?aneuvers are 㘊rfor?ed by tilting the body to orient the forces (?agner, 1䍅6c)  or by tilting the ?ings ?ithout ad?usting the body 㘅sture (Blondeau, 1䍅1? Nachtigall, 1䍄䌰 . To address this 㴬estion, I fil?ed hu??ingbirds as they 㘊rfor?ed controlled lateral flight ?hile trac㜑ng a ?oving feeder to deter?ine ?hich ?echanis? ?as e?㘆oyed. I designed a fra?e?or?  to ?odel, describe, and co?㘄re the 3D 㜑ne?atics of the ?ings, e㬔racted fro? the synchroni?ed videos. ?ine?atic ?easure?ents revealed that hu??ingbirds ban㜊d their stro㜊 㘆ane ?hile ?aintaining an u㘌ight body 㘅sture. Ho?ever, the stro㜊 㘆ane ?as ban㜊d against the direction of travel and therefore o㘶osite to ?hat ?as 㘌edicted. This sur㘌ising result led to the 㴬estion? ho? is the lateral force 㘌oduced? A 㴬asi?steady aerodyna?ic analysis suggests that the net lateral force ?ay result fro? unsteady aerodyna?ic ?echanis?s o㘊rating during stro㜊 reversal (Dic㜑nson et al., 1䍃䌰 , although this re?ains to be tested.There is ?ounting evidence that ?any flying ani?als have the ability to 㘊rfor? ?aneuvers that are initiated by force vectoring as ?ell as ?aneuvers that are initiated ?ith co??le㬇?ing asy??etries. In addition to the ?or㜇㘌esented in this dissertation, I have collaborated on a series of studies that use the 㜑ne?atic fra?e?or㜇that I develo㘊d in cha?ter three to study hu??ingbirds 㘊rfor?ing ya? turns (Altshuler et al., 2012) and ban㜑ng turns (Read, 2015). Collectively, these three studies have sho?n that hu??ingbirds use 123body㼑nde?endent asy??etrical ?ing 㜑ne?atics to 㘊rfor? both ya? turns and controlled lateral flight, but they use force vectoring to 㘊rfor? fast, ban㜊d turns. Si?ilar results have been  de?onstrated in other ta㬄. Fruit bats 㘊rfor?ed slo? turns ?ith a translating ya? and fast turns by ban㜑ng (Iriarte?D?a? and S?art?, 200䔰 . Li㜊?ise, slo? ?oving 㘑geons relied on ?ingbeat 㜑ne?atics to turn (Ros et al., 2015), but faster ?oving 㘑geons 㘊rfor?ed ban㜑ng turns (Ros et al., 2011). In fruit flies, saccades are used for voluntary e㬶loratory turns (Fry et al., 2003), ?hile  ra㘑d esca㘊s are initiated by force vectoring (Mui?res et al., 201䈰 . These studies suggest that the ability to 㘊rfor? both force vectoring and ?ingstro㜊 driven ?aneuvers ?ay be ?ore co??on than 㘌eviously thought.㈭⼊F??ᴳ?? ?⌴? ?ᬡᴤ⠝ᨢ℣ ┝᨞‚?ᬡᰝTo understand the effects of ?aneuvering 㘊rfor?ance on behavior, ecology, and evolution, it is i?㘅rtant to ?easure the breadth of an ani?al?s ?aneuvering ca㘄bilities in a natural or se?i㼐atural setting. Recently, co?㘬tational a㘶roaches have been used to categori?e and co?㘄re si?ilar ?aneuvering tra?ectories (Braun et al., 2010? Geurten et al., 2010? Shelton et al., 201䈰 , although the full 㘅tential of this technology is only starting to beco?e a㘶arent. In this dissertation I develo㘊d a fra?e?or? to ?easure and co?㘄re free?flight ?aneuvering 㘊rfor?ance in hu??ingbirds. This a㘶roach uses a high㼔hrough㘬t analysis to co?㘄re body 㘅sition and orientation data e㬔racted fro? synchroni?ed videos. In cha㘔ers four and five, I use this ?ethod to investigate the ?or㘪ological and 㘪ysiological deter?inants of individual ?aneuvering 㘊rfor?ance. It has been 㘌o㘅sed that ?aneuverability is deter?ined by both intrinsic constraints, such as body ?ass, ?ing si?e and sha㘊, and by facultative ca㘄city, such as ?uscle 㘅?er 12?out㘬t (?arric㜇and Dial, 1䍃䔺 ?arric? et al., 1䍃䔰 . Ho?ever, there have been no studies that have correlated individual characteristics ?ith ?aneuvering 㘊rfor?ance. To address this 㴬estion I studied the free?flight of ?ale hu??ingbirds to deter?ine the e㬔ent to ?hich ?aneuvering 㘊rfor?ance is 1) re㘊atable across trials, 2) deter?ined by body and ?ing ?or㘪ology or burst ?uscle ca㘄city, and 3) influenced by 㘌esence of a co??etitor. Using a ?ulti?ca?era trac?ing syste?, I analy?ed 㘊rfor?ance ?etrics of velocity and acceleration based  on body 㘅sition and orientation. Most of these ?easures ?ere highly re㘊atable. Burst 㘅?er ?as associated ?ith the ?a?ority of the 㘊rfor?ance ?etrics, ?hereas ?ing sha㘊 and si?e ?ere only associated ?ith a fe? of the 㘊rfor?ance ?etrics ?easured. Acceleration, deceleration, and ?echanical 㘅?er had lo?er ?agnitude ?hen hu??ingbirds fle? in the 㘌esence of a co??etitor. Ho?ever, body angular velocity during slo? flight, es㘊cially 㘑tch㼭o?n velocity, ?as higher for co?㘊titive flights as ?as the relative use of arcing versus 㘑tch?roll turns. These results indicate that burst 㘅?er ca㘄city is a 㜊y 㘌edictor of ?aneuverability, and that body angular velocity and arcing turns are associated ?ith co?㘊tition in flight. Hu??ingbirds rely on their high level of ?aneuverability to 㘊rfor? co??le㬇?ating dis㘆ays (Clar㜎 200䌺 Clar㜇et  al., 2012? Felton et al., 200䔺 Feo and Clar㜎 2010) , ca?ture insects (Stiles, 1䍃5? Yanega and Rubega, 200䈰 , and aggressively defend territories (Altshuler, 2006? Car㘊nter et al., 1䍅3) . Ho?ever, the e㬔ent to ?hich ?aneuvering 㘊rfor?ance deter?ines success in these behaviors has not been tested.Hu??ingbirds have one of the ?ore e㬶ensive for?s of flight but are nonetheless co??on in high elevation habitats (Bro?n and ?odric?Bro?n, 1䍄䌺 Car㘊nter et al., 1䍅3? Feinsinger and Col?ell, 1䍄䔺 Stiles, 1䍅0) . Ani?als flying at high elevation face the dual challenges of reduced o㬂gen availability, ?hich constrains ?etabolic in㘬t, and decreased air 125density, ?hich constrains ?echanical 㘅?er out㘬t. Ho?ever, ho? ?aneuvering 㘊rfor?ance is affected by the reduced o㬂gen and decreased air density found at high elevations ?as not 㜐o?n. I tested the effects of altering 㘅?er reserves on individual ?aneuvering 㘊rfor?ance using natural and si?ulated elevation gradients. ?ith the ?ulti?ca?era trac?ing syste? and co?㘬tational fra?e?or㜇develo㘊d in the fourth cha㘔er, I ?easured the ?aneuvering 㘊rfor?ance of hu??ingbirds at lo? and high elevations. I as㜊d the 㴬estion? ho? does individual ?aneuvering 㘊rfor?ance change ?ith increased elevation ?here 㘅?er reserves are lo?? In a follo?㼬㘇e㬶eri?ent I as㜊d the 㴬estion? ho? do ?etabolic restrictions i?㘅sed by lo? o㬂gen availability and ?echanical restrictions i?㘅sed by lo? air density inde㘊ndently affect ?aneuvering 㘊rfor?ance? To address this 㴬estion I co?㘄red the ?aneuvering 㘊rfor?ance of individual Anna?s hu??ingbirds flying in nor?al air, in a hy㘅㬑c nor?odense ?i?ture of nitrogen and air designed to i?㘅se a ?echanical challenge to 㘅?er reserves, and in a nor?o㬑c hy㘅dense ?i㬔ure of heliu?. At high elevation ?here 㘅?er reserves are lo?, 㘊rfor?ance of co?㘆e? ?aneuvers decreases. Further?ore, the ?echanical challenge i?㘅sed by lo? air density has a greater effect on ?aneuvering 㘊rfor?ance than the ?etabolic challenge of flying in hy㘅㬑a. A large body of ?or㜇on hu??ingbirds has sho?n that the 㜑ne?atic changes to hovering flight that occur in res㘅nse to elevation are being driven by decreased air density, not reduced o㬂gen availability (Altshuler and Dudley, 2006). Ho?ever, lo? o㬂gen availability can e㬄cerbate the challenges caused by lo? density. This study e㬔ends these observations to the ?ore co??licated ?aneuvering flight of hu??ingbirds. The study of self?selected ?aneuvering 㘊rfor?ance is a relatively ne? field ?ith the 㘅tential to unite the study of loco?otion ?ith 㴬estions of behavior, ecology, and evolution, in a  ?ay that ?as not 㘌eviously 㘅ssible. In hu??ingbirds, v oluntary ?aneuvers at lo? elevation 126are 㘌i?arily influenced by facultative ca㘄city, s㘊cifically burst 㘅?er, and to a lesser e㬔ent by intrinsic li?its, s㘊cifically ?ing as㘊ct ratio. At higher elevations, ?aneuvering 㘊rfor?ance  declines due to decreases in air density. This research de?onstrates that the re?ar㜄ble ?aneuverability of hu??ingbirds derives fro? their ability to control their ?ings inde㘊ndently and fro? high ?uscle 㘅?er reserves for generating aerodyna?ic force. ㈭《F␙␚? ⤢??ᰙ ?‡?In the last fe? years several research grou㘓 have begun to investigate the ?aneuvering 㘊rfor?ance of a㴬atic, terrestrial, and flying ani?als, and ?y ?or㜇adds significantly to this gro?ing body of literature. Many of these studies have focused on laboratory?based 㘊rfor?ance, but the ne㬔 ste㘇?ill undoubtedly involve 㴬estions dealing ?ith behavior in ?ore  natural settings. One of the goals of ?y dissertation ?as to develo㘇㘅rtable techni㴬es that can be a㘶lied to field?based 㴬estions. The flo? visuali?ation ?ethod that I used in the second cha?ter can be 㘊rfor?ed al?ost any?here ?ith ?ini?al e㴬i㘵ent. Although it cannot be used to 㴬antify flo? 㘌o㘊rties, this ?ethod allo?s researchers to vie? the ?a㜊 structures of free?flying ani?als at a high level of s㘄tial and te?㘅ral resolution. Historically, the intricate laboratory e㴬i㘵ent re㴬ired to study ?a㜊 to㘅logy has li?ited the a?ount of s㘊cies that have been studied. A techni㴬e si?ilar to the one described could be used to conduct a large?scale, field based co?㘄rative study of si?㘆e ?a㜊 structures. The 㘅rtability of high s㘊ed ca?eras cou㘆ed ?ith the ability to calibrate large three di?ensional s㘄ces have ?ade natural studies of ?aneuvering 㘊rfor?ance 㘅ssible. The 㜑ne?atic fra?e?or㜇that I develo㘊d to ?easure and co??are hu??ingbird ?ingbeat 㜑ne?atics is currently being used to ?easure a variety of ?aneuvers both in the lab (e.g. drifting  12?and studies of ?ingbeat re㘊atability by t?o current graduate students, D. A. S㜄ndalis and B. Goller) and in the field (e.g. elaborate shuttle dis㘆ays by C. ?. Clar㜇fro? the University of California, Riverside). Once a sufficient re㘊rtoire of ?aneuvers is e㬄?ined, it ?ay e?erge that  hu??ingbirds use co?binations of ?ingbeat 㜑ne?atic features such as ?ing elevation angles, elevation a?㘆itudes, and angles of attac? that are consistently associated. At the ?o?ent, ?ingbeats ?easured fro? hovering (Pourna?eri et al., 2012) , ya? turns (Altshuler et al., 2012), ban㜊d turns (Read, 2015), and lateral flight suggest that this ?ay be a 㘅ssibility. It re?ains to be seen if these 㘄tterns hold for other flight behaviors, and if they are driven by aerodyna?ic or anato?ical constraints. Very little is 㜐o?n about variation in the 㘊rfor?ance of constrained ?aneuvers. To focus on re㘊ated ?ingbeat 㘄tterns ?ost studies have not loo㜊d at variation across ?ingbeats, trials and individuals (a notable e㬫e?tion being Iriarte㼝ia? et al., 2012) . Variation in individual ?ingbeats ?ay 㘌ove i?㘅rtant for stability and control, variation bet?een trials ?ay reflect influences of ?otivation, and differences bet?een individuals could be deter?ined by ?or㘪ological, 㘪ysiological, or aerodyna?ic constraints on ?aneuvering 㘊rfor?ance. Additionally, it re?ains to be seen if any universal 㘄tterns e?erge for the control of s㘊cific ?aneuvers across s㘊cies. Evidence is ?ounting that behaviors that rely on ra㘑d accelerations and changes in direction are li?ely 㘊rfor?ed by force vectoring ?hereas dis㘆ays that involve stability, control, and 㘌ecision ?ay rely on ?ingbeat 㜑ne?atics. Ho?ever, given the novelty of the field, to date this 㘄ttern has only been docu?ented in a fe? s㘊cies.Finally, the auto?ated trac㜑ng syste? designed and built for the fourth and fifth cha?ters  is a 㘅?erful tool that ?ill be indis㘊nsable for ans?ering 㴬estions that re㴬ire large a?ounts of data to ans?er. It has already been used to trac? hovering res㘅nses to o㘔ic flo? (Goller and 12?Altshuler, 201䈰  and is being used to ?easure a variety of behavioral res㘅nses to other ty㘊s of visual sti?uli. In addition, it is currently being used to study for?ard flight control in res㘅nse to  different visual sti?uli (R. L. Da㜑n, un㘬blished data). The trac㜑ng syste? is also currently being used to investigate the relative contributions of ecological role, ?ing ?or㘪ology, and ?uscle 㘅?er reserves to ?aneuvering 㘊rfor?ance across a ?ide range of tro㘑cal hu??ingbird s㘊cies.One of the ?ost e㬫iting develo??ents in the field of bio?echanics is the increasingly 㘅rtable technology that ?a㜊s it 㘅ssible to conduct rigorous studies in the field. Ine㬶ensive, rugged syste?s 㘌ovide the o㘶ortunity to ta㜊 basic bio?echanics studies and lin㜇the? to their  relevant environ?ental conte㬔s. This is the ne?est frontier in the study of flight ?aneuvering 㘊rfor?ance and ensures that it ?ill re?ain an e㬫iting research field for years to co?e. 12?B????‣?ᬥ??A????㌋????? Y? Iⴊ??? ?ᬚᬚᬻ HⴊM?  (1䍄1). Direct linear transfor?ation fro? co?㘄rator coordinates into ob?ect s㘄ce coordinates in close㼌ange 㘪otogra??etry. In Proceedings of the Symposium on Close-range Photogrammetry, 㘶. 1搲䔉A?????⌝? H?  (1䍅6). Manoeuvrability and ecological segregation in the little bro?n ( Myotis lucifugus) and Yu?a ( M . yumanensis) bats (Chiro㘔era? Ves㘊rtilionidae). Can. J. Zool. ㈰ , 1䕄䕤1䕅2.A?ᤘ??? ??? DⴊL?  (2006). Flight 㘊rfor?ance and co?㘊titive dis㘆ace?ent of hu??ingbirds across elevational gradients. Am. Nat. ⰲ? , 216搗䌉A?ᤘ??? ??? DⴊLⴊᬡ? D?????? R?  (2003). ?ine?atics of hovering hu??ingbird flight along si?ulated and natural elevational gradients. J. Exp. Biol. ⹔? , 313䍤31䉄.A?ᤘ??? ??? DⴊLⴊᬡ? D?????? R?  (2006). The 㘪ysiology and bio?echanics of avian flight at high altitude. Integr. Comp. Biol. 〲 , 62摄1.A?ᤘ??? ??? DⴊLⴻ Sᤢ???㬊F? Gⴊᬡ? D?????? R?  (200䈄). Of hu??ingbirds and helico㘔ers? hovering costs, co??etitive ability, and foraging strategies. Am. Nat. ⰲ? , 16搗5.A?ᤘ??? ??? DⴊLⴻ D???? ?? Rⴊ??? M?G????㬊堭 A?  (200䈁). Resolution of a 㘄rado?? hu??ingbird flight at high elevation does not co?e ?ithout a cost. PNAS ⱔ? , 1䑄31搛.A?ᤘ??? ??? DⴊLⴻ D??????㬊?? Bⴻ V????? 堭 T?? R‗??ᤘ㬊SⴊP? ᬡ? D?????? ?? 㬊M? H?  (2005). Short㼄?㘆itude high㼕re㴬ency ?ing stro㜊s deter?ine the aerodyna?ics of honeybee flight. PNAS ⱔ? , 1䔗13摅.A?ᤘ??? ??? DⴊLⴻ P???? ?⠛?㬊Mⴻ Pᬡ㬊Hⴊᬡ? L‸ᬡ※ 堭  (200䌰. ?a㜊 㘄tterns of the ?ings and tail of hovering hu??ingbirds. Exp. Fluids 〲 , 䔙5摅䈛.A?ᤘ??? ??? DⴊLⴻ D???? ?? Rⴻ H?????ᬻ SⴊM? ??? M?G????㬊堭 A?  (2010a). Allo?etry of hu??ingbird lifting 㘊rfor?ance. J. Exp. Biol. ⸬? , 䐗5搙䈉A?ᤘ??? ??? DⴊLⴻ ?????? ?ⴊCⴻ C?※ BⴊHⴻ ??? ??㬊DⴊBⴻ L??㬊AⴊF?㬊D????‡㬊?? Bⴊ??? D?????? ?? 㬊M? H?  (2010b). Neuro?uscular control of ?ingbeat 㜑ne?atics in Anna?s hu??ingbirds ( Calypte anna). J. Exp. Biol. ⸬? , 250䑤1䈉A?ᤘ??? ??? DⴊLⴻ ????ᬸ夡 ?R???※ EⴊMⴻ S?⌚?? P? Sⴊᬡ? M?????ᤠ? ? ?ⴊM?  (2012). ?ingbeat  㜑ne?atics and ?otor control of ya? turns in Anna?s hu??ingbirds ( Calypte anna). J. Exp. Biol. ⸬? , 䈘䐘摅䈉130A?????‡㬊堭 D?  (1䍃1). Fundamentals of aerodynamics. 2nd ed. Ne? Yor㜹 McGra? Hill.B᬴?☛?㬊堭 ??? S?ᬚᤸ? SⴊMⴻ R?????㬊Dⴊ?ⴊᬡ? B?????? ?? S?  (2013a). Glide 㘊rfor?ance and aerodyna?ics of non㼊㴬ilibriu? glides in northern flying s㴬irrels (Glauco?ys sabrinus). J. R. Soc. Interface ⱔ , 20120䑃䈉B᬴?☛?㬊堭 ??? S?ᬚᤸ? SⴊMⴊᬡ? B???? ?? ?ⴊS?  (2013b). Design and characteri?ation of a ?ulti㼄rticulated robotic bat ?ing. Bioinspir. Biomim. ? , 01600䌉B??⌻ A? Mⴊᬡ? B???????? AⴊA?  (200䔰. ?ine?atics and 㘅?er re㴬ire?ents of ascending and descending flight in the 㘑geon (Colu?ba livia). J. Exp. Biol. ⸬? , 1120搙0.B?????? ?? Aⴊᬡ? B??????ᤙ?? R?  (1䍃5). In vivo ?uscle force and elastic energy storage during steady㼓㘊ed ho㘶ing of ta??ar ?allabies (Macro㘬s eugenii). J. Exp. Biol. ⱈ? , 1䔗䍤1䕂1.B?????? ?? AⴊAⴻ T?…??‡㬊堭㬊G†????? 㬊A? ??? Lᬡ✠?㬊LⴊE?  (1䍅3). Bone stress in the horse foreli?b during loco?otion at different gaits? a co?㘄rison of t?o e㬶eri?ental ?ethods. J. Biomech. ⰲ , 565搳䐛.B????? 堭 M?  (2003). The influence of ?ing㼸a㜊 interactions on the 㘌oduction of aerodyna?ic forces in fla㘶ing flight. J. Exp. Biol. ⹔? , 225䑤22䐗.B????? 堭 Mⴊᬡ? D?????? ‡ 㬊MⴊH?  (2001). S㘄n?ise flo? and the attach?ent of the leading?edge vorte㬇on insect ?ings. Nature 〬? , 䐗䍤䐙3.B????? 堭 Mⴊᬡ? D?????? ‡ 㬊MⴊH?  (2003). The influence of ?ing㼸a㜊 interactions on the 㘌oduction of aerodyna?ic forces in fla㘶ing flight. J. Exp. Biol. ⹔? , 225䑤22䐗.B?‡??ᬤ㬊堭  (1䍅1). Aerodyna?ic ca㘄bilities of flies, as revealed by a ne? techni㴬e. J. Exp. Biol. 155搲6䈉B…?????? Rⴊ堭㬊Lᬫ?‡㬊Nⴊ堭㬊Hᬚ???⌻ Nⴊ堭㬊T???‚? G? ?ⴊᬡ? T?…ᬘ㬊A? LⴊR?  (2005). The aerodyna?ics of Manduca sexta ? digital 㘄rticle i?age veloci?etry analysis of the leading?edge vorte㬉 J. Exp. Biol. ⹔? , 10䑃搲0䍂.B…?????? Rⴊ堭㬊Lᬫ?‡㬊Nⴊ堭㬊T???‚? G? ?ⴊᬡ? T?…ᬘ㬊A? LⴊR?  (2006). A㘶lication of digital 㘄rticle i?age veloci?etry to insect aerodyna?ics? Measure?ent of the leading?edge vorte㬇and near ?a㜊 of a ha?㜵oth. Exp. Fluids ご , 5䈛搳5䈉B…?????? Rⴊ堭㬊T???‚? Gⴊ?ⴊᬡ? T?…ᬘ㬊AⴊLⴊR?  (200䌰. S?o㜊 visuali?ation of free㼕lying bu?blebees indicates inde㘊ndent leading㼊dge vortices on each ?ing 㘄ir. Exp. Fluids 〲 , 䔲1摅21.B?ᬤ?㬊Eⴻ G???ᤝ?? Bⴊ??? E⌝??ᬛḻ M?  (2010). Identifying 㘌ototy?ical co?㘅nents in behaviour using clustering algorith?s. PLoS One ? , e䌙61.131B????㬊堭 Hⴊᬡ? ?
????B????㬊A?  (1䍄䌰. Convergence, co?㘊tition, and ?i?icry in a te?㘊rate co??unity of hu??ingbird?㘅llinated flo?ers. Ecology ㉔ , 1022搲035.B???☛??㬊??? C?ᬨ??㬊堭 Aⴻ D???? ?? Rⴻ M?G????㬊堭 Aⴻ S☢ᤴ㬊T? Bⴊᬡ? A?ᤘ?????? DⴊL?  (2011). Pro?ected changes in elevational distribution and flight 㘊rfor?ance of ?ontane Neotro㘑cal hu??ingbirds in res㘅nse to cli?ate change. Glob. Chang. Biol. ⰵ , 16䐲搲6䔘.B????ᬦ㬊?ⴊP? ᬡ? A?????‡㬊DⴊR?  (2002). Model selection and multimodel inference: a practical information-theoretic approach.Cᬚ???ᤝ?? F? Lⴻ Pᬙ‡㬊DⴊCⴊᬡ? H?㜠?㬊MⴊA?  (1䍅3). ?eight gain and ad?ust?ent of feeding  territory si?e in ?igrant hu??ingbirds. PNAS 㙔 , 䐗5䍤䐗63.C?ᬢ㬊P? ᬡ? D???? ?? R?  (1䍃5). Li?its to vertebrate loco?otor energetics suggested by hu??ingbirds hovering in helio㬉 Nature ⼵? , 䐗2摄25.C?ᬢ㬊P? ᬡ? D???? ?? R?  (1䍃6). Li?its to flight energetics of hu??ingbirds hovering in hy㘅dense and hy㘅㬑c gas ?i㬔ures. J. Exp. Biol. ⱈ? , 22䔳摃5.C?ᬢ㬊P? ᬡ? D???? ?? R?  (1䍃䌰. Ma㬑?u? flight 㘊rfor?ance of hu??ingbirds? ca?acities, constraints, and trade offs. ‐ Am. Nat. ⰱ? , 3䍅摂11.C?ᬢ㬊P? ᬡ? M???ᬚ?㬊D?  (1䍃䐰. Flight and si?e constraints? hovering 㘊rfor?ance of large hu??ingbirds under ?a㬑?al loading. J. Exp. Biol. ⹔? , 2䐳䑤2䐛3.C?ᬢ㬊P?㬊C???㬊堭 Sⴊ??? D???? ?? R?  (1䍃䐰. Transient hovering 㘊rfor?ance of hu??ingbirds under conditions of ?a㬑?al loading. J. Exp. Biol. ⹔? , 䌗1摃2䌉C?ᬚ?㬊Cⴊ堭  (200䌰. Courtshi㘇dives of Anna?s hu??ingbird offer insights into flight 㘊rfor?ance li?its. Proc. R. Soc. B ⸵? , 30䉄搳2.C?ᬚ?㬊Cⴊ堭  (2011a). ?ing, tail, and vocal contributions to the co?㘆e? acoustic signals of courting Callio?e hu??ingbirds. Curr. Zool. ㄵ , 1䕄搲䌛.C?ᬚ?㬊Cⴊ堭  (2011b). Effects of tail length on an esca?e ?aneuver of the Red㼁illed strea?ertail.  J. Ornithol. ⰱ? , 3䍄摂0䔉C?ᬚ?㬊Cⴊ堭 ᬡ? R????? ?㬊SⴊM?  Anna?s hu??ingbird ( Calypte anna). Birds N. Am. Online.C?ᬚ?㬊Cⴊ堭㬊F?※ T? 堭 ᬡ? B?✛?㬊?ⴊB?  (2012). Courtshi? dis㘆ays and sonations of a hybrid ?ale broad㼔ailed? blac㜿chinned hu??ingbird. Condor ??? , 32䍤3䈘.C?ᬚ?㬊Cⴊ堭㬊F?※ T? 堭 ᬡ? ⠛? D‡⌝?㬊?? F? D?  (2013). Sounds and courtshi㘇dis㘆ays of the Peruvian sheartail, Chilean ?oodstar, oasis hu??ingbird, and a hybrid ?ale Peruvian sheartail? Chilean ?oodstar. Condor ??? , 55䕤5䐳.132C‟??ᤙ? T? Sⴊᬡ? Lᬡ?㬊M? F?  (1䍄5). Visual control of flight behaviour in the hoverfly Syritta pipiens l. J. Comp. Physiol. 䡈 , 1搛6.C???ᬡ㌌⠝??ᤙ? D?  (2000). Multi?le co?㘄risons? 㘪iloso㘪ies and illustrations. Am. J. Physiol. ⸵? , R1搟䔉Dᬨ??㬊CⴊT?  (1䍄䔰. The relationshi? bet?een body angle and flight s㘊ed in free?flying Drosophila. Physiol. Entomol. ? , 1䌲搲䌳.D?ᬟ? ?ⴊP?  (1䍃2). Activity 㘄tterns of the ?ing ?uscles of the 㘑geon ( Columba livia) during different ?odes of flight. J. Exp. Zool. ⸲? , 35䑤3䐙.D?????? ‡ 㬊MⴊHⴻ L??☛??㬊F? O? ??? Sᬡ?㬊SⴊP?  (1䍃䌰. ?ing rotation and the aerodyna?ic basis of insect flight. Science ⸶? , 1䌳䉤1䌛0.D…?????? P? ᬡ? B?ᬪ?㬊Rⴊ??  (1䍃䐰. The 㜑ne?atics and 㘊rfor?ance of fish fast?start s?i??ing. J. Exp. Biol. ⹔? , 1165搲1䑅.D?????? R?  (1䍃5). E㬔raordinary flight 㘊rfor?ance of orchid bees (A㘑dae? Euglossini) hovering in helio? (䔘指He?20指O2). J. Exp. Biol. ⱈ? , 1065摄0.D?????? R?  (2002). Mechanis?s and i?㘆ications of ani?al flight ?aneuverability. Integr. Comp. Biol. 〮 , 135摂0.E????⌙‡㬊CⴊP?  (1䍅䈄). The aerodyna?ics of hovering insect flight. VI. lift and 㘅?er re㴬ire?ents. Philos. Trans. R. Soc. B ⽔? , 1䈳搲䔲.E????⌙‡㬊CⴊP?  (1䍅䈁). The aerodyna?ics of hovering insect flight. I. the 㴬asi?steady analysis. Philos. Trans. R. Soc. B ⽔? , 1搲5.E????⌙‡㬊CⴊP?  (1䍅䈫). The aerodyna?ics of hovering insect flight. II. ?or㘪ological 㘄ra?eters. Philos. Trans. R. Soc. B ⽔? , 1䑤䈘.E????⌙‡㬊CⴊP?  (1䍅䈭). The aerodyna?ics of hovering insect flight. V. a vorte? theory. Philos. Trans. R. Soc. B ⽔? , 115搲䉂.E????⌙‡㬊CⴊP?  (1䍃䌰. The novel aerodyna?ics of insect flight? a㘶lications to ?icro㼄ir vehicles. J. Exp. Biol. ⹔? , 3䈙䍤3䉂䔉E?ᤢ?⌻ Rⴊ堭 ᬡ? Cᬘ??? T? M?  (1䍄3). Po?er out㘬t and ?ing disc loading in hovering hu??ingbirds. Am. Nat. ⱔ? , 䐛1.F??????⌝?? P?  (1䍄6). Organi?ation of a tro㘑cal guild of nectarivorous birds. Ecol. Monogr. 25䑤2䌲.133F??????⌝?? P? ??? C?ᬥ???? SⴊB?  (1䍄5). On the relationshi㘇bet?een ?ing disc loading and foraging strategy in hu??ingbirds. Am. Nat. ⱔ? , 21䐉F??????⌝?? P? ??? C‟????? Rⴊ??  (1䍄䔰. Co??unity organi?ation a?ong neotro?ical nectar?feeding birds. Integr. Comp. Biol. ⰶ , 䑄䍤䑃5.F??????⌝?? P?? C‟??? ?㬊Rⴊ?ⴻ T???‚⌴㬊堭 ᬡ? C?ᬥ???㬊SⴊB?  (1䍄䌰. Elevation and the ?or㘪ology, flight energetics, and foraging ecology of tro?ical hu??ingbirds. Am. Nat. ??? , 䉅1.F??ᤠ?㬊Aⴻ F??ᤠ?? A? Mⴊᬡ? L?????☛✝ ?? DⴊB?  (200䔰. The dis㘆ay of a Reddish her?it (Phaethornis ruber) in a lo?land rainforest, Bolivia. Wilson J. Ornithol. Ⱞ? , 201搗0䈉F?※ T? 堭 ??? C?ᬚ?㬊Cⴊ堭  (2010). The dis㘆ays and sonations of the blac㜿chinned hu??ingbird (Trochilidae? Archilochus alexandri). Auk Ⱞ? , 䑅䑤䑃6.F??? SⴊNⴻ Sᬧᬦᬡ㬊Rⴊᬡ? D?????? ‡ 㬊MⴊH?  (2003). The aerodyna?ics of free?flight ?aneuvers in Drosophila. Science ⽔? , 䉃5摂䍅.F??? SⴊNⴻ Sᬧᬦᬡ㬊Rⴊᬡ? D?????? ‡ 㬊MⴊH?  (2005). The aerodyna?ics of hovering flight in Drosophila. J. Exp. Biol. ⹔? , 2303搲䔉G???? ??㬊BⴊRⴊHⴻ ????㬊Rⴻ B?ᬤ?㬊Eⴊᬡ? E⌝??ᬛḻ M?  (2010). A synta㬇of hoverfly flight 㘌ototy㘊s. J. Exp. Biol. ⸬? , 2䈛1摄5.G‟???? Bⴊᬡ? A?ᤘ?????? DⴊL?  (201䈰. Hu??ingbirds control hovering flight by stabili?ing visual ?otion. PNAS ??? , 1䔙䐳摅0.G娙?? ??  (1䌛䔰. Flight control in Drosophila by visual 㘊rce㘔ion of ?otion. Kybernetik ? , 1䍃搗0䔉G????㬊S?  (1䍃5). Fluid vortices: fluid mechanics and its applications. S㘌inger Science ? Business Media.G?????? ᬟ᤻ CⴊH?  (1䌛0). Hummingbirds. Courier Cor㘅ration.H?????ᤚ?☻ Aⴊᬡ? R????㬊M?  (2001). Predator versus 㘌ey? on aerial hunting and esca?e strategies in birds. Behav. Ecol. Ⱞ , 150搲56.H?????ᤚ娦? Aⴻ 堠?ᬡ?? ‡ 㬊LⴊCⴻ ???ḻ Mⴻ ⠠? B????? Rⴻ ???ᤝ ?? Y? ??? S?????? ⌻ GⴊR?  (200䐰. Bat flight generates co??le? aerodyna?ic trac㜓. Science ⼬? , 䕃䉤䕃䐉H?????ᤚ娦? Aⴻ M??䜚??㬊F? T?㬊V?? B????? Rⴻ 堠?ᬡ?? ‡ 㬊LⴊCⴻ ???ᤝ ?? Y? ᬡ? S?????? ⌻ GⴊR?  (200䌰. High㼓㘊ed stereo DPIV ?easure?ent of ?a㜊s of t?o bat s㘊cies flying freely in a ?ind tunnel. Exp. Fluids 〲 , 361搙䐘.13?H??????㬊T? L?  (200䔰. Soft?are techni㴬es for t?o㼇and three?di?ensional 㜑ne?atic ?easure?ents of biological and bio?i?etic syste?s. Bioinspir. Biomim. ? , 03䈘01.H??????㬊T? Lⴊᬡ? B???????? AⴊA?  (200䐰. Lo? s㘊ed ?aneuvering flight of the rose㼁reasted coc㜄too ( Eolophus roseicapillus). I. ?ine?atic and neuro?uscular control of turning. J. Exp.  Biol. ⸬? , 1䕃䑤䌲1.H??????㬊T? Lⴻ T??ᬟ???? Bⴊ?? ᬡ? B?????? ?? A? ?  (2002). Esti?ates of circulation and gait change based on a three?di?ensional 㜑ne?atic analysis of flight in coc㜄tiels (Ny?㘪icus hollandicus) and ringed turtle㼭oves (Stre㘔o㘊lia risoria). J. Exp. Biol. ⹔? , 13䕃搲䈘䌉H??????㬊T? Lⴻ U?????†? 㬊堭 Rⴊ??? B?????? ?? AⴊA?  (200䐰. Lo? s㘊ed ?aneuvering flight of the rose㼁reasted coc㜄too ( Eolophus roseicapillus). II. Inertial and aerodyna?ic reorientation. J. Exp. Biol. ⸬? , 1䌲2搲䌗䈉H??????㬊T? Lⴻ C???⌻ Bⴊᬡ? D??⌻ ??  (200䌰. ?ingbeat ti?e and the scaling of 㘄ssive rotational da?㘑ng in fla㘶ing flight. Science ⼮? , 252搗55.H?????⌘ ? ‡ 㬊P? ᬡ? H?????ᤚ娦? A?  (2011). Aerodyna?ics of gliding flight in co??on s?ifts.  J. Exp. Biol. ⸬? , 3䔗摃3.H?????⌘ ? ‡ 㬊P?? M??䜚??㬊F? T? ᬡ? H?????ᤚ娦㬊A?  (2011). Ti?e?resolved vorte? ?a㜊 of a co??on s?ift flying over a range of flight s㘊eds. J. R. Soc. Interface ? , 䔘䑤䔲6.H’?‚?㬊T?㬊B??ᤸ? F? ᬡ? ???ᤞ? ??㬊P?  (200䔰. Si?ultaneous inference in general 㘄ra?etric ?odels. Biometrical J. ㅔ , 3䈛搙63.H‫?ᬡ?㬊HⴊC?  (1䍄䈰. O㘔i?al strategies for 㘌edator avoidance? the relative i?㘅rtance of s㘊ed and ?anoeuvrability. J. Theor. Biol. 〵 , 333搙50.H????? T? Y?? H???ᤠ?? NⴊIⴻ S?ᬚᤸ? SⴊMⴊᬡ? B???? ?? ?ⴊS?  (2010a). Ti?e㼌esolved ?a㜊 structure and 㜑ne?atics of bat flight. Anim. Locomot. 3䐲搙䔲.H????? T? Y?? R?????㬊Dⴊ?ⴻ S?ᬚᤸ㬊SⴊMⴊᬡ? B?????? ?? S?  (2010b). ?a?e structure and ?ing 㜑ne?atics? the flight of the lesser dog㼕aced fruit bat, Cynopterus brachyotis . J. Exp. Biol. ⸬? , 3䈗䑤3䉂0.H????? T? Y?? H???ᤠ?? NⴊIⴻ S?ᬚᤸ? SⴊMⴊᬡ? B???? ?? ?ⴊS?  (2012). Changes in 㜑ne?atics and aerodyna?ics over a range of s㘊eds in Tadarida brasiliensis, the Bra?ilian free?tailed bat. J. R. Soc. Interface ? , 1120搲130.H???? RⴊBⴊ??? H????㬊P? E?  (1䍅䈰. Effects of body si?e and slo㘊 on acceleration of a li?ard (Stellio stellio). J. Exp. Biol. ??? , 113搲23.H????? T? Aⴻ S?’᤻ RⴊDⴊᬡ? H?ᬟ?? SⴊD?  (2001). The function of dis㘆ays of ?ale rufous hu??ingbirds. Condor ⱔ? , 6䉄搛51.135I??ᬚ? ?㌉ ?ᬸ㬊堭㬊R?????㬊Dⴊ?ⴻ B?????? ?? Sⴊᬡ? S?ᬚᤸ? SⴊM?  (2012). ?ine?atic 㘆asticity during flight in fruit bats? individual variability in res㘅nse to loading. PLoS One ? , e36665.I??ᬚ? ?㌉ ?ᬸ㬊堭 ᬡ? S?ᬚᤸ? SⴊM?  (200䔰. ?ine?atics of slo? turn ?aneuvering in the fruit bat Cynopterus brachyotis. J. Exp. Biol. ⸬? , 3䉄䕤3䉅䌉I??????? 㬊Dⴊ堭  (2003). Measuring 㘊rfor?ance in nature? i?㘆ications for studies of fitness ?ithin 㘅㘬lations. Integr. Comp. Biol. 〯 , 3䌛摂0䐉I????? ?? ᬡ? T?‚??㬊Sⴊ?ⴊS?  (2003). Gait 㘄ra?eters in vertical cli?bing of ca?tive, rehabilitant and ?ild Su?atran orang㼬tans (Pongo 㘂g?aeus abelii). J. Exp. Biol. ⹔? , 䈘䔲摂0䌛.堛?? ? ‡ 㬊BⴊEⴊ??? D?ᬟ? ?ⴊP?  (2011). Scaling of ?echanical 㘅?er out㘬t during burst esca㘊 flight in the Corvidae. J. Exp. Biol. ⸬? , 䈳2搛1.堠? ᬡ? ? ‡ 㬊LⴊCⴊ??? H?????ᤚ娦㬊A?  (200䌰. The vorte㬇?a㜊 of blac㜫a㘓 (Sylvia atricapilla  L.) ?easured using high㼓㘊ed digital 㘄rticle i?age veloci?etry (DPIV). J. Exp. Biol. ⸬? , 3365搙3䐛.?
 ?? ?㌇??? ? 㬊A? ??? B????㬊堭 H?  (1䍄䔰. Influence of econo?ics, inters㘊cific co?㘊tition, and se㬬al di?or㘪is? on territoriality of ?igrant rufous hu??ingbirds. Ecology ㅈ , 2䔳搗䌛.?‪ ? ? ᬧ? ? ?? NⴊV?  (1䍄䌰. Tracing the ?a㜊 of a flying bird. Nature ⸵? , 1䈛搲䉅.??? ✙? 堭 ??㬊?? ? ?ᬸ夡 ㌈ ?? ?※ EⴊMⴻ H??䜘᤻ G? F? V??㬊A?ᤘ?????? DⴊLⴊᬡ? L??ᤢ??㬊D?  (201䈰. Hu??ingbird ?ing efficacy de㘊nds on as㘊ct ratio and co?㘄res ?ith helico㘔er rotors. J. R. Soc. Interface ?? , 201䈘5䔳.Lᬤ???? G? V?  (2000). Function of the caudal fin during loco?otion in fishes? 㜑ne?atics, flo? visuali?ation, and evolutionary 㘄tterns. Integr. Comp. Biol. ご , 101搲22.L??㬊Hⴻ E????⌙‡㬊CⴊP?㬊?ᬫᬜ? ?? ?ⴻ ⠛? ??? B??⌻ Cⴊ??? ????☠ᤙ? A? P?  (1䍃䔰. A co?㘬tational fluid dyna?ic study of ha?㜵oth hovering. J. Exp. Biol. ⹔? , 䈛1摂䑄.M᬴ᬟ??⌛☻ Sⴊᬡ? ????? ? ?ⴊC?  (2013). Neuro?uscular control of hovering ?ingbeat 㜑ne?atics in res㘅nse to distinct flight challenges in the ruby㼔hroated hu??ingbird, Archilochus colubris. J. Exp. Biol. ⸬? , 䈲61摄1.Mᬚ???? 堭 H?  (1䍅䐰. Ma㬑?u? lift 㘌oduction during ta㜊off in flying ani?als. J. Exp. Biol. Ⱟ? , 235搗3䔉Mᬧ?ᬚ? S☢ᤴ㬊堭  (1䍄䈰. The theory of ga?es and the evolution of ani?al conflict. J. Theor. Biol. 〵 , 20䍤221.136M?G????? 堭 Aⴻ ??ᤙ? CⴊCⴻ R?????㬊堭 V?㬊D?????? Rⴊᬡ? A?ᤘ???? ?? DⴊL?  (200䔰. A higher?level ta㬅no?y for hu??ingbirds. J. Ornithol. ⰱ? , 155搲65.M??䜚??? F? T?? 堠???? ? ?? 㬊LⴊCⴻ BᬚḢ???㬊Rⴻ ???ḻ Mⴻ S?????? ⌻ GⴊRⴊ??? H?????ᤚ娦㬊A?  (200䔰. Leading㼊dge vorte? i?㘌oves lift in slo?㼕lying bats. Science ⼬? , 1250搲253.M??䜚??? F? T?? 堠???? ? ?? 㬊LⴊCⴻ ???ᤝ?? Y? ᬡ? H?????ᤚ娦㬊A?  (2011). Co?㘄rative aerodyna?ic 㘊rfor?ance of fla㘶ing flight in t?o bat s㘊cies using ti?e㼌esolved ?a㜊 visuali?ation. J. R. Soc. Interface ? , 1䈲䕤1䈗䔉M??䜚??? F? T?? B?????㬊MⴊSⴻ 堠???? ? ?? 㬊LⴊCⴊᬡ? H?????ᤚ?☻ A?  (2012). Vorte㬇?a㜊, do?n?ash distribution, aerodyna?ic 㘊rfor?ance and ?ingbeat 㜑ne?atics in slo?㼕lying 㘑ed flycatchers. J. R. Soc. Interface ? , 2䌗搙03.M??䜚??? F? T?? E????⌛㬊M? 堭㬊M????? 堭 Mⴊᬡ? D?????? ‡ 㬊MⴊH?  (201䈰. Flies evade loo?ing targets by e㬊cuting ra㘑d visually directed ban㜊d turns. Science ⼰? , 1䐗搲䑄.Nᬜ?ᤢ⌛??? ??  (1䍄䌰. Schiebeflug bei der Sch?eissflieg Calliphora erytheocephala (Di㘔era? Calli㘪oridae). Ent. gen. ? , 255搗65.Nᬪᬣ??ᬻ Sⴊᬡ? S???? ???ᤴ ? H?  (2010). Re㘊atability for Gaussian and non㼧aussian data? A 㘌actical guide for biologists. Biol. Rev. 㘱 , 䌙5摃56.Nᬪᬣ??ᬻ Sⴊᬡ? S???? ???ᤴ ? H?  (2013). A general and si?㘆e ?ethod for obtaining R2 fro? generali?ed linear ?i㬊d?effects ?odels. Methods Ecol. Evol. ? , 133搲䈗.N‚???⌻ UⴊMⴊᬡ? Rᬧ???? 堭 MⴊV?  (1䍅䐰. Ecological Mor㘪ology and Flight in Bats (Mammalia; Chiroptera)? ?ing Ada?tations, Flight Perfor?ance, Foraging Strategy and Echolocation. Philos. Trans. R. Soc. B ⼬? , 335摂2䐉N‚???⌻ UⴊMⴻ ????㬊T? Hⴻ SᤝḞ??? ?? 㬊堭 F?? ???ᤝ ?? Y? ᬡ? ⠠? H??⠝???? 㬊O?  (1䍃3). The cost of hovering and for?ard flight in a nectar?feeding bat, Glossophaga soricina, esti?ated fro? aerodyna?ic theory. J. Exp. Biol. ⰶ? , 20䑤22䐉O???⌛㍘?☝? ??? V? Mⴊᬡ? D?????? R?  (2012). Flying in the rain? hovering 㘊rfor?ance of Anna?s hu??ingbirds under varied 㘌eci㘑tation. Proc. R. Soc. B ⸵? , 3䍃6摂002.P???✜???? ? Cⴊ堭  (1䌛䔰. Po?er re㴬ire?ents for hori?ontal flight in the 㘑geon Colu?bia Livia. J. Exp. Biol. え , 52䑤555.P???✜???? ? Cⴊ堭  (1䍄5). Mechanics of flight. In Avian Biology (ed. Farner, D. S., ?ing, ?. R., and Par㜊s, ?. C.), 㘶. 1摄5. London? Acade?ic Press.P???✜???? ? Cⴊ堭  (1䍅3). Ther?al soaring co?㘄red in three dissi?ilar tro?ical bird s㘊cies, Fregata Magnificens, Pelecanus Occidentals and Coragy㘓 Atratus. J. Exp. Biol. ⱔ? , 30䑤325.13?P???✜???? ? Cⴊ堭  (1䍅䔰. On the reconstruction of 㘔erosaurs and their ?anner of flight, ?ith notes on vorte? ?a㜊s. Biol. Rev. ㈯ , 2䍃搙31.P․??ᬸ? ??㬊Sⴻ S?⌚?? P? Sⴻ P?????⠛ ?㬊Mⴊᬡ? A?ᤘ???? ?? DⴊL?  (2012). Hu??ingbirds generate bilateral vorte? loo㘓 during hovering? evidence fro? flo? visuali?ation. Exp. Fluids ㄰ , 1䈙䌉R D?⠝?‥☝?ᤊC‚? T?ᬦ  (201䈰. R? A Language and Environ?ent for Statistical Co?㘬ting. R Foundation for Statistical Computing Vienna Austria ? , ?ISBN? 3摃00051搘䑤0.Rᬧ???? 堭 MⴊV?  (1䍄䌰. A vorte㬇theory of ani?al flight. Part 1. The vorte? ?a㜊 of a hovering ani?al. J. Fluid Mech. 䠬 , 6䍄.Rᬧ???? 堭 MⴊV ᬡ? G‚?‡㬊R?  (1䍃䔰. Vi?uali?ation and ?odelling of the ?a㜊s of flying birds. Biona Rep Ⱟ , 156搲䐙.R?ᬩ㬊T? 堭 G?  (2015). Hu??ingbirds use ban㜑ng to achieve faster turns and asy??etrical ?ingstro?es to achieve tighter turns.R??″???⠛?ᬻ A? ᬡ? A?ᬧᬳSᬟᬘ㬊M?  (2015). Bills as daggers ? A test for se㬬ally di?or㘪ic  ?ea㘅ns in a le㜷ing hu??ingbird. Anim. Behav. ⸲ , 21搗䌉R?????㬊Dⴊ?ⴻ B᬴?☛?㬊堭 ??㬊H????? T? Y?? Rᬙ???Ḟ?? 堭 Mⴻ ????㬊T? Hⴊᬡ? S?ᬚᤸ? SⴊM?  (200䌰. Bats go head?under?heels? the bio?echanics of landing on a ceiling. J. Exp. Biol. ⸬? , 䍂5摃53.R??ᤚ???㬊Lⴻ B??☛?㬊Gⴊ堭㬊B??⌠?㬊Aⴊ堭㬊??? ⌻ 倭 堭 ᬡ? C‴??㬊I?  (200䌰. Auto?ated hull reconstruction ?otion trac㜑ng (HRMT) a㘶lied to side?ays ?aneuvers of free?flying insects.  J. Exp. Biol. ⸬? , 132䉤35.R‘㬊IⴊGⴻ B???☛?㬊LⴊCⴻ Bᬩ⌝?? MⴊAⴻ P??????㬊AⴊNⴊᬡ? B???????? AⴊA?  (2011). Pigeons steer li?e helico㘔ers and generate do?n㼇and u㘓tro㜊 lift during lo? s㘊ed turns. PNAS ⱔ? , 1䍃䌘搳.R‘㬊IⴊGⴻ B??⌝?? MⴊAⴻ P????‡㬊A? Nⴻ Bᬘ?☛?㬊LⴊCⴊᬡ? B???????? AⴊA?  (2015). Pigeons 㘌oduce aerodyna?ic tor㴬es through changes in ?ing tra?ectory during lo? s㘊ed aerial turns. J. Exp. Biol. ⸬? , 䉅0摂䌘.R??????? SⴊMⴊᬡ? R????? ?㬊RⴊO?  (2001). The North American banders’ manual for banding hummingbirds. North A?erican Banding Council.Sᬡ?㬊SⴊP?  (2006). Induced airflo? in flying insects I. A theoretical ?odel of the induced flo?. J.  Exp. Biol. ⹔? , 32摂2.Sᬥ??? Nⴊᬡ? D?????? R?  (2012). Bac㜸ard flight in hu??ingbirds e?㘆oys uni㴬e 㜑ne?atic ad?ust?ents and entails lo? ?etabolic cost. J. Exp. Biol. ⸬? , 3603搲1.13?S?⌚?? P? Sⴻ Dᬪ??㬊Rⴻ Sᤚᬫ? AⴊDⴻ 倠????㬊V? Bⴻ D?????? ‡ 㬊MⴊHⴊᬡ? A?ᤘ???? ?? DⴊL?  Burst 㘊rfor?ance underlies ?ulti㘆e features of ?aneuverability in hu??ingbirds. in review.S???ᤠ?㬊RⴊMⴻ 堛????? 㬊BⴊEⴊᬡ? H???? ??㬊T? L?  (201䈰. The ?echanics and behavior of cliff s?allo?s during tande? flights. J. Exp. Biol.S??????⌻ GⴊR?  (1䍅䐄). The ?a㜊 of a 㜊stral (Falco tinnunculus) in fla㘶ing flight. J. Exp. Biol. 㔶 , 5䍤䑅.S??????⌻ GⴊR?  (1䍅䐁). The ?a㜊 of a 㜊strel (Falco tinnunculus) in fla㘶ing flight. J. Exp. Biol. Ⱞ? , 5䍤䑅.S??????⌻ GⴊRⴻ Rᬧ???? 堭 MⴊV ᬡ? P???✜???? 㬊Cⴊ堭  (1䍅䈰. Mo?entu? and energy in the ?a㜊 of a 㘑geon (Columba livia) in slo? flight. J Exp Biol ??? , 䔲搲02.S??????⌻ GⴊRⴻ R‘??㬊Mⴊᬡ? H?????ᤚ娦㬊A?  (2003). A fa?ily of vorte㬇?a㜊s generated by a thrush nightingale in free flight in a ?ind tunnel over its entire natural range of flight s㘊eds. J. Exp. Biol. ⹔? , 2313搗3䉂.S??ᬧ???? ?? 堭 DⴊHⴊᬡ? Dᬡ???? T? L?  (200䐰. Flo?er trac㜑ng in ha?㜵oths? behavior and energetics. J. Exp. Biol. ⸬? , 3䑤䈳.Sᤢ???? F? G?  (1䍅0). The annual cycle in a tro㘑cal ?et forest hu??ingbird co??unity. Ibis Ⱞ? , 322搙䈙.Sᤢ???? F? G?  (1䍅2). Aggressive and courtshi㘇dis㘆ays of the ?ale Anna?s hu??ingbird. Condor 㘰 , 20䔉Sᤢ???? F?  (1䍃5). Behavioral, ecological and ?or㘪ological correlates of foraging for arthro㘅ds by the hu??ingbirds of a tro㘑cal ?et forest. Condor 䠵 , 䔳3摅䑅.Sᤢ???? F? Gⴊᬡ? ???ḻ LⴊL?  (1䍄0). Hu??ingbird territoriality at a tro㘑cal flo?ering tree. Auk 㘵 , 䈛䑤䉃1.Sᤠ???㬊M? ??? 倢☦? ?? ??  (1䌙䌰. Der sch?irrflug des 㜅libri i? ?eitlu㘊nfil?. J. fur Ornithol. 㘵 , 136搲55.Sᤠ???? 堭 D?  (2002). A direct a㘶roach to false discovery rates. J. R. Stat. Soc. B. ㈰ , 䉄䍤䉃䔉Sᤚᬫ? AⴊDⴻ B?ᬡ???㬊?ⴻ N??☛??㬊T? Rⴊᬡ? D?????? ?? 㬊M? H?  (2011). Multi?ca?era real?ti?e three?di?ensional trac㜑ng of ?ulti?le flying ani?als. J. R. Soc. Interface ? , 3䌳摂0䌉S⠠?
ᬻ T?㬊Mᬚ?????㬊Dⴊᬡ? Pᭇ??ᬻ T?  (2005). A convenient ?ultica?era self?calibration for  virtual environ?ents. Presence ⰰ , 䈘䑤䈗2.13?T????ᬤ?᤻ DⴊHⴻ F???? ?? Nⴊ??? 堛??? ‡ 㬊BⴊEⴻ B???☻ Eⴻ E⠛?⌝??? ᤛ㬊Dⴻ ??㬊倭㬊B?ᤪ?? Mⴊᬡ? H??????㬊T? L?  (201䈰. A 㘌otocol and calibration ?ethod for accurate ?ulti?ca?era field videogra㘪y. J. Exp. Biol. 1䕂3搲䕂䔉T???․᤻ H? M?  (1䍃3). Mechanis?s of co??etition in tro㘑cal hu??ingbirds? ?etabolic costs for losers and ?inners. Ecology 㔰 , 䈘5摂1䔉T??ᬟ???㬊Bⴊ??  (2000). Bio?echanics and 㘪ysiology of gait selection in flying birds. Physiol. Biochem. Zool. 㔯 , 䐙6摄50.T??ᬟ???㬊Bⴊ?? ᬡ? D?ᬟ? ?ⴊP?  (2000). Effects of body si?e on ta㜊㼅ff flight 㘊rfor?ance in the Phasianidae (Aves). J. Exp. Biol. ⹔? , 331䍤3332.T??ᬟ???㬊Bⴊ??? A?ᤘ???? ?? DⴊLⴊᬡ? P‫???? DⴊR?  (200䈰. Ta㜊㼅ff ?echanics in hu??ingbirds (Trochilidae). J. Exp. Biol. ⹔? , 13䈳搲352.T??ᬟ???㬊Bⴊ??? ????? ?? 㬊DⴊRⴻ C?ᬚ?㬊Cⴊ堭㬊P‫???㬊DⴊRⴻ H??????㬊T? Lⴻ H✩??? GⴊAⴊᬡ? B?????? ?? AⴊA?  (200䐰. Three?di?ensional 㜑ne?atics of hu??ingbird flight. J. Exp. Biol. ⸬? , 236䕤䔗.U?????†? 㬊堭 Rⴻ H???? ??㬊T? Lⴊ??? B?????? ?? Aⴊ?  (2003). The aerodyna?ics of avian ta㜊?off fro? direct 㘌essure ?easure?ents in Canada geese (Branta canadensis). J. Exp. Biol. ⹔? , 䈘51摂056.V?? B???⌝?㬊F? ??? D?????? ‡ 㬊MⴊH?  (201䈰. Plu?e?trac?ing behavior of flying Drosophila e?erges fro? a set of distinct sensory㼵otor refle㬊s. Curr. Biol. ⸰ , 2䑂摅6.V????㬊堭 T?㬊A?ᤘ?????? DⴊLⴻ D??????㬊?? Bⴻ D?????? ‡ 㬊MⴊHⴊᬡ? R????ᤘ㬊SⴊP?  (201䈰. Hovering flight in the honey bee A?is ?ellifera? 㜑ne?atic ?echanis?s for varying aerodyna?ic forces. Physiol. Biochem. Zool. 㘵 , 䕄0摅䔲.V????? S?  (1䌛6). Flight in Drosophila ? I. flight 㘊rfor?ance of tethered flies. J. Exp. Biol. 〰 , 56䑤5䑅.??⌡ ? ?? H?  (1䍅6a). Flight 㘊rfor?ance and visual control of flight of the free㼕lying housefly (Musca domestica l.) II. Pursuit of targets. Philos. Trans. R. Soc. B ⼬? , 553搳䑃.??⌡ ? ?? H?  (1䍅6b). Flight 㘊rfor?ance and visual control of flight of the free㼕lying housefly (Musca domestica l.) I. Organi?ation of the flight ?otor. Philos. Trans. R. Soc. B ⼬? , 52䑤551.??⌡ ? ?? H?  (1䍅6c). Flight 㘊rfor?ance and visual control of flight of the free㼕lying housefly (Musca domestica l.) III. Interactions bet?een angular ?ove?ent induced by ?ide㼇and s?allfield sti?uli. Philos. Trans. R. Soc. B ⼬? , 5䔲搳䌳.1䈘???? ? ?? 堭 Aⴻ G?ᬟᬦ?? ?? Cⴊ?ⴻ G????᤻ O? Lⴻ M?????? ?? Dⴊ??? R??????㬊DⴊN?  (2005). Do faster starts increase the 㘌obability of evading 㘌edators? Funct. Ecol. ⱈ , 䔘䕤䔲5.??? ⌻ ?ⴊ?ⴊ?? ? ??㬊倭 N?  (2010). Stro㜊?averaged lift forces due to vorte? rings and their ?utual interactions for a fla㘶ing flight ?odel. J. Fluid Mech. ㈱? , 䈳3摂䐗.??? ???? 㬊DⴊR?  (1䍃䔰. The turning? and linear??aneuvering 㘊rfor?ance of birds? the cost of efficiency for coursing insectivores. Can. J. Zool. 㔲 , 1063搲0䑃.??? ???? 㬊DⴊRⴊᬡ? D?ᬟ? ?ⴊP?  (1䍃䔰. ?ine?atic, aerodyna?ic and anato?ical ?echanis?s in the slo?, ?aneuvering flight of 㘑geons. J. Exp. Biol. ⹔Ⰺ㴎ᤊⰮ , 655摄2.??? ???? 㬊Dⴻ D?ᬟ㬊?? ᬡ? B?????? ?? A?  (1䍃䔰. Asy??etrical force 㘌oduction in the ?aneuvering flight of 㘑geons. Auk ??? , 䌲6摃2䔉??? ???? 㬊DⴊRⴻ T??ᬟ???㬊Bⴊ?? ᬡ? P‫???㬊DⴊR?  (2005). Aerodyna?ics of the hovering hu??ingbird. Nature 〯? , 10䍂搲0䍄.??? ???? 㬊DⴊRⴻ T??ᬟ???㬊Bⴊ?? ᬡ? P‫???㬊DⴊR?  (200䌰. Lift 㘌oduction in the hovering hu??ingbird. Proc. R. Soc. B ⸵? , 3䑂䑤3䐳2.??? ? 㬊P? ??  (1䍄6). The effect of si?e on the fast㼓tart 㘊rfor?ance of rainbo? trout Sal?o cairdneri, and a consideration of 㘑scivorous 㘌edator?㘌ey interactions. J. Exp. Biol. ㈱ , 15䑤1䑄.???? ?F‣?㬊T?  (1䍄2). Energetics of hovering flight in hu??ingbirds and in Drosophila. J. Exp. Biol. ㄲ , 䑃 搲0䈉???? ?F‣?㬊T?  (1䍄3). Quic㜇esti?ates of flight fitness in hovering ani?als, including novel ?echanis?s for lift 㘌oduction. J. Exp. Biol. ㅈ , 16䍤230.??? ?? 㬊?? Cⴊᬡ? S?ᬚ??? Rⴊ??  (200䔰. Altitude and te?㘊rature effects on the energetic cost of hover?feeding in ?igratory rufous hu??ingbirds, Selasphorus rufus. Can. J. Zool. 㘲 , 161搲6䌉??? ??ᬦ? 㬊CⴊDⴊᬡ? B?????? ?? A? A?  (2015). Pigeons trade efficiency for stability in res㘅nse to  level of challenge during confined flight. PNAS ??? , 33䌗搛.??? ?☠ᤙ㬊AⴊP? ᬡ? E????⌙‡ 㬊CⴊP?  (1䍃䐰. The ?echanics of flight in the ha?㜵oth Manduca se㬔a. II. aerodyna?ic conse㴬ences of 㜑ne?atic and ?or㘪ological variation. J. Exp. Biol. ⹔? , 2䐗3搗䑂5.??ᤴ ??? 㬊P? C?  (1䍅1). An aerodyna?ic analysis of bird ?ings as fi㬊d aerofoils. J. Exp. Biol. 䡔 , 1䈙搲62.1䈲???ḻ LⴊLⴻ Sᤢ???㬊F? Gⴊᬡ? H?????‚ᤴ 㬊F? R?  (1䍄6). Ecological Organi?ation of a Tro㘑cal, Highland Hu??ingbird Co??unity. J. Anim. Ecol. 〱 , 3䉃搙䑃.???ḻ Mⴻ O???⌛㍘?☝? ??? V? Mⴊᬡ? D?????? R?  (2013). Structure of the vorte㬇?a㜊 in hovering Anna?s hu??ingbirds (Calypte anna). Proc. R. Soc. B ⸶? , 201323䌲.Y???⌛? GⴊMⴊᬡ? R???⌛㬊MⴊA?  (200䈰. Feeding ?echanis?s? hu??ingbird ?a? bends to aid  insect ca㘔ure. Nature 〮? , 615.倴 ᬡ ⌻ Y? Lⴊᬡ? S??㬊M?  (2011). Control for s?all?s㘊ed lateral flight in a ?odel insect. Bioinspir. Biomim. ? , 036003.値 ? ?㬊Rⴊ??? G???? F?  (200䌰. The ?arvelous tail of Loddigesia ?irabilis (Trochilidae). 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The feeder ?as ?oving at 15 c??second and the video is slo?ed do?n 䈘㬉 V??? ⼭⸊ A ?ovie of a bird 㘊rfor?ing controlled lateral flight to the left through a 㘆u?e of CO2. The 㘆u?e ?as created by subli?ation of dry ice. The feeder ?as ?oving at 30 c??second and the video is slo?ed do?n 䈘㬉V??? 〭Ⱝ  The ?ulti?ca?era, auto?ated trac㜑ng syste? fil?ing t?o hu??ingbirds in the flight arena at 200 fra?es 㘊r second . Continuously trac㜊d se㴬ences are assigned an ob?ect nu?ber (fro? 0 to 䈇over this se㴬ence). Body 㘅sition and orientation are calculated and re㘌o?ected onto the video of four ca?eras. The videos are saved using a custo? designed co?㘌ession algorith? that only records the sections of the i?age that are ?oving. Thus, birds disa㘶ear fro? the video ?hen they land and sto㘇?oving. The tra?ectory sho?n in figure 䈉1 is ta?en fro? the bird labeled 䄗 and begins at 5.1 seconds and ends at 䔉05 seconds.1䉂A┥ᴡ⤢㜊B: T?ᬜ⨢℣ ?✘?ᴦ ┛ᨛ?ᴙᴚ?The auto?ated trac?ing syste? e㬔racts the 3D coordinates of ?ulti㘆e flying ani?als and  saves each tra?ectory as a se㘄rate ob?ect. An ob?ect begins ?hen the trac?ing syste? 㘑c㜓 u㘇ne? ?ove?ent and ends ?hen either the ob?ect sto?s ?oving, the error in the 3D re㘌o?ection gro?s too large, or ?ulti?le ob?ects co?e ?ithin 2 c? of each other. In ?y e㬶eri?ents trac?ing hu??ingbird flight led to t?o 㘌oble?s in deter?ining distinct ob?ects. The first is that very stable hovering can be ?isidentified as 㘊rching. For e㬄??le, as a bird goes into an e㬔ended hovering bout, such as at a feeder, the trac㜑ng syste? considers it to have sto㘶ed ?oving and ends the tra?ectory. Conversely, ?hen the bird 㘊rches at the end of a flight or in bet?een t?o flights, es㘊cially if it continues to ?ove its head or fluff its feathers, the trac?ing syste? ?ould consider the bird as ?oving and ?ould continue trac㜑ng. Since ?y study focuses on identifying and analy?ing relatively long, ?oving tra?ectories, these ty㘊s of errors did not cause 㘌oble?s. The second challenge concerns identification of birds during close encounters in co?㘊tition trials. ?hen t?o trac㜊d ob?ects get close enough to each other, even if they do not 㘪ysically touch, the trac㜑ng syste? cannot accurately distinguish the?. I used a conservative solution and ter?inated the tra?ectories ?henever t?o birds ca?e into close 㘌o㬑?ity and the trac㜊d ob?ects ?erged. Birds ?ere later identified ?anually by a tea? of digiti?ers ?ho vie?ed the videos and assigned each ob?ect nu?ber to either the ?ar㜊d or un?ar㜊d bird. S?†?㐢℣ ┛ᨛ?ᴙ ᴚ ?A si?㘆e for?ard?reverse non㼫ausal ?al?an filter ?as used to ?ini?i?e the effect of errors in the 3D trac㜑ng. The s?oothing 㘄ra?eters ?ere chosen so that 䐇traces of a trac㜊d, falling ob?ect averaged a 㘊a㜇acceleration of 䌉䔇??s 2. The 㘌ocess covariance ?atri㬇 I used is?1䈳Q pos=[0.0033 0 0 0.005 0 00 0.0033 0 0 0.005 00 0 0.0033 0 0 0.0050.005 0 0 0.01 0 00 0.005 0 0 0.01 00 0 0.005 0 0 0.01 ]and the observation covariance ?atri? I used is? R pos=[0.0001䉂 0 00 0.0001䉂 00 0 0.0001䉂 ]Figure 䈉1c and 䈉1d sho? e㬄?㘆es of t?o tra?ectories ?ith 㘆ots of the uns?oothed data, the data s?oothed ?ith Q ?os  and R㘅s , and the effects of t?o different s?oothing 㘄ra?eters ( R ?os  㬇10, R ?os  㬇0.1).Follo?ing establish?ent of the 3D tra?ectories, the trac㜑ng syste? assigns 3D body orientation vectors to each bird in each fra?e based on 2D esti?ates of the long a㬑s of the body.  Orientation vector assign?ents ?ere also s?oothed ?ith a ?al?an filter using ?ore restrictive s?oothing 㘄ra?eters than used to s?ooth the body 㘅sition. To deter?ine a㘶ro㘌iate s?oothing 㘄ra?eters I re㘆otted the s?oothed body orientation vectors onto a sa?㘆e of videos,  and visually chose the ones that fit the best. The 㘌ocess covariance ?atri? used for body orientation is?1䈛Qori=[0.0033 0 0 0.005 0 00 0.0033 0 0 0.005 00 0 0.0033 0 0 0.0050.005 0 0 0.01 0 00 0.005 0 0 0.01 00 0 0.005 0 0 0.01 ]and the observation covariance ?atri? used is?R pos=[0.000001䉂 0 00 0.000001䉂 00 0 0.000001?? ]For ?y final 㘊rfor?ance ?etrics I used instantaneous body orientation and orientation velocity, but not orientation acceleration. Because of this, the choice of s?oothing 㘄ra?eters for  body orientation had little effect on the final results. Traces of the body orientation and the calculated average orientation velocities at different levels of s?oothing (uns?oothed, s?oothed,  R ?os  㬇10, R ?os  㬇0.1) for sa?㘆e flight tra?ectories are also sho?n in figure 䈉1c and 䈉1d of the ?ain te?t. Oᨢᴡ????‡ ᬘ??⌡? ᴡ?Once the body orientations ?ere calculated I used a dyna?ic 㘌ogra??ing algorith? to decide ?hich end of the vector ?as the head and ?hich end ?as the tail. The direction of the head ?as chosen based on the direction of the 㘌evious orientation, the direction of travel, and the vertical u㘇direction. For each fra?e ( n), the ?cost? associated ?ith the t?o 㘅ssible orientations (O i, -O irr rr ) ?ere calculated? 1䉄CostOri=Speed ( O⃗rin ⋅ V⃗el 㔅d|O⃗ri n||V⃗el 㔅d |)+(1−Speed )( O⃗rin ⋅U⃗p|O⃗ri n||U⃗p|)+(1−Speed )( O⃗ri n⋅ O⃗rin㼲|O⃗rin||O⃗ri n㼲 |)Cost ?Ori =Speed (−O⃗ri n ⋅ V⃗el ?od|O⃗rin||V⃗el ?od | )+ (1−Speed )(−O⃗rin ⋅U⃗p|O⃗ri n||U⃗p| )+ (1−Speed )(−O⃗rin ⋅O⃗ri n?1|O⃗rin||O⃗rin?1 | )?here O irr  is the body vector, V ler ?od  is the ?odified velocity vector ti㘶ed u㘇15 ?  to?ards the vertical direction. Upr is the vertical direction vector, O irr n?1  is the orientation during the 㘌evious fra?e, and if the ?agnitude of the velocity is greater than 0.5??s?Speed=|V⃗el|other?ise?Speed=0.5 This ta㜊s into account the 㘌o㘊nsity of hu??ingbirds to fly for?ards and ?ith an u㘌ight 㘅sture, but allo?s for e㬫e?tions in the case of bac㜸ards flight, inversions, and dives, 㘄rticularly if they occur at lo? s㘊eds.1䉅A┥ᴡ⤢㜊C: Cᬡ⤢⤛?ᴊ?
? ?? „ ?ᬡᴤ⠝ᨢ℣ ┝᨞‚?ᬡᰝ ?ᴙᨢᰘCandidate ?odels of ?aneuvering 㘊rfor?ance ?etrics (n ? 20 birds in 20 solo trials and 16 㘄ired co?㘊tition trials ). Models are ran㜊d by AICc, ?ith su㘶orted ?odels ?ithin 2 AICc units of the best㼕it ?odel highlighted in bold. A㜄i㜊 ?eight is a ?easure of the 㘌obability that a given ?odel is the best㼕it ?odel relative to others in that ?odel set.?
 ?? ᠝? ?ᬡ ? ?? 㜝? ??? ?? ?? ? ? AIC? ????ᬊAIC? A?ᬢ?? ???⌴ ?AccTotpow, max 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊?ᠥ ?? ? ?ᬙ?? 崊?㜥 ??? ? ?? ? 崊?ᬧ??…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊? ?? ⌙? 崊??? ⌊ᬘ? ? ?? ?? ??  崊?㜥 ??? ? ?? ? 崊?ᬧ?co?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?eight lifted ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?ing length ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?ent ? daysno fi㬊d effects1011??10?103232.䔛233.䕄2䈘.3?2䈗.152䈗.312䈙.䍅2䈙.䍅2䐛.䕃01.01䐉53䌉2?䌉䈳11.1211.12䉂.030.60.3?0.010.010.01000AccTotvel, max 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊?ᠥ ?? ? ?ᬙ?? 崊?㜥 ??? ? ?? ? 崊?ᬧ??…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊? ?? ⌙? 崊??? ⌊ᬘ? ? ?? ?? ??  崊?㜥 ??? ? ?? ? 崊?ᬧ??…? ??? ?? ‡ 崊?ᬘ᠊崊?? ? ⌊ᬘ? ??? ?ᬙ? 崊?㜥 ? ?? ??? ? 崊?ᬧ?co?㘊tition ? ?ass ? ?eight lifted ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?ing length ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?ent ? daysno fi㬊d effects1011???101031䐉䑅1䌉211䌉3?1䌉䕅20.3?21.2?21.䐲51.6301.䈙1.5?2.12.5?3.53.䌙33.䔳0.350.1?0.160.120.10.060.050AccHormax 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊?㜥 ??? ? ?? ? 崊?ᬧ??…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊?ᠥ ?? ? ?ᬙ?? 崊?㜥 ??? ? ?? ? 崊?ᬧ?co?㘊tition  ? ?ass ? ?ing length ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?ent ? daysno fi㬊d effects?10?10?111031䈘.䈙1䈲.䐛1䈙.31䈙.31䈙.?1䉂.?1䈛.251䐗.3101.332.䕄2.䕄2.䍄䈉365.䔗31.䕅0.䈗0.220.10.10.10.050.0201䉃?
 ?? ᠝? ?ᬡ ? ?? 㜝? ??? ?? ?? ? ? AIC? ????ᬊAIC? A?ᬢ?? ???⌴ ?DecHormax 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊?㜥 ??? ? ?? ? 崊?ᬧ??…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊?ᠥ ?? ? ?ᬙ?? 崊?㜥 ??? ? ?? ? 崊?ᬧ?co?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?ing length ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?ent ? daysno fi㬊d effects?101011??10312䐉0?12䔉䔲130.12132.02132.0?132.15135.1?165.6501.䑂3.0?䈉䍂5.025.0?䔉13䔉5?0.530.220.110.0?0.0?0.0?0.010AccVUmax 123?56??? ?? 㜝? ???? ???  co?㘊tition  ? ?ass ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?ent3??????10121.䐗130.13130.䔙131.23132.3?133.01133.䐳135.䈙0䔉䈲䌉11䌉5110.6?11.2?12.0313.䐲0.䌛0.010.010.010000AccVDmax 123?56??? ?? 㜝? ???? ???  co?㘊tition  ? ?ass ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?ent3??????10111.䈗116.5111䔉?11䔉䑄11䌉0511䌉䈙121.33122.105.0?6.䍅䐉35䐉63䔉01䌉䌲10.6?0.䕂0.0?0.030.020.020.020.010PitchUvel, avg 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊?㜥 ??? ? ?? ?no fi㬊d effects  co?㘊tition  ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?ent?3????10??䕃.䌳? 䕄.5??䕄.2??䕄.1?䕄.1?䔛.䍃?䕂.3?䕂.1?02.3?2.662.䕂2.䔳2.䌛5.655.䑄0.䈗0.130.110.10.10.10.020.02150?
 ?? ᠝? ?ᬡ ? ?? 㜝? ??? ?? ?? ? ? AIC? ????ᬊAIC? A?ᬢ?? ???⌴ ?PitchDvel, avg 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊?㜥 ??? ? ?? ??…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊? ?? ⌙? 崊?㜥 ? ?? ??? ?co?㘊tition  ? ?ass ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?entno fi㬊d effects  ??????103?䔗.01?䔘.5??䑃.䔗? 䑃.12?䑃.0??䑄.䔙? 䑄.5?䐗.0201.䉂2.1?2.䕃2.䌙䈉1?䈉51䌉䍃0.?0.1?0.130.0?0.0?0.050.0?0Yawvel, avg 123?56??? ?? 㜝? ???? ???  co?㘊tition  ? ?ass ? ?eight lifted ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?ent3??????10?䐙.䑂?䐘.12?6䌉䕅?6䔉䍃?6䐉䍄?6䐉䈙?66.䌳?65.1303.623.䔛䈉䐳5.䑄6.316.䑃䔉610.650.110.0?0.060.0?0.030.020.01PRTdeg 123?56??? ?? 㜝? ???? ???  co?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition ? ?ass ? ?eight lifted ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?ent3??????10䈘䈉2?䈘6.䌗䈘6.䌳䈘6.䍃䈘䌉䔗䈘䌉䌙䈘䌉䌛䈲2.䍅02.6?2.䐲2.䐳5.5?5.6?5.䐲䔉䑂0.510.130.130.130.030.030.030.01PRTtime 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊?㜥 ??? ? ?? ??…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊? ?? ⌙? 崊?㜥 ? ?? ??? ?co?㘊tition ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition ? ?ass ? ?ing length ? e㬶eri?entco?㘊tition ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?entno fi㬊d effects  ???10???3?206.02?20䈉06?203.1??201.0??200.3??200.1??1䍅.2??1䌘.3101.䍄2.䔙䈉䍂5.6?5.䕃䐉䐳15.䐲0.5?0.20.130.050.030.030.010151?
 ?? ᠝? ?ᬡ ? ?? 㜝? ??? ?? ?? ? ? AIC? ????ᬊAIC? A?ᬢ?? ???⌴ ?Arcrad 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊?㜥 ??? ? ?? ?co?㘊tition  ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?entno fi㬊d effects  ???10???3?䑅.52?䐳.5??䐳.5??䐗.51?䐘.䈙?6䔉䔳?6䐉5??6䈉䍂02.䌙2.䍂6.01䔉0?䌉6?10.䍅13.5?0.650.150.150.030.010.0100Arcvel, avg 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊?ᠥ ?? ? ?ᬙ?? 崊?㜥 ??? ? ?? ? 崊?ᬧ??…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊?㜥 ??? ? ?? ? 崊?ᬧ?co?㘊tition ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?ing length ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?ent ? daysno fi㬊d effects  10?1110??103?15.2??1䈉??12.0??11.6??䐉䕄? 䐉䐛? 䈉?16.1300.5?3.23.6?䐉䈗䐉5210.䉅31.䈲0.䈛0.3?0.0?0.0?0.010.0100Arcacc, max 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊?? ? ⌊ᬘ? ??? ?ᬙ? 崊?㜥 ? ?? ??? ? 崊?ᬧ?co?㘊tition ? ?ass ? ?eight lifted ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?eight lifted ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? ?ing as㘊ct ratio ? e㬶eri?ent ? daysco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?ent ? daysco?㘊tition ? ?ass ? ?ing length ? e㬶eri?ent ? daysno fi㬊d effects  ?1010?1110?31䔛.231䕅.261䕃.031䕃.5?1䌲.261䌗.䉃1䌗.䐲213.䉄02.032.?3.365.036.266.䉅2䐉2?0.510.1?0.130.10.0?0.020.020PRT% 123?56???…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊? ?? ⌙? 崊??? ⌊ᬘ? ? ?? ?? ??  崊?㜥 ??? ? ?? ??…? ??? ?? ‡ 崊?ᬘ᠊崊? ?? ?? ? ???? ?? 崊??? ⌊?ᠥ ?? ? ?ᬙ?? 崊?㜥 ??? ? ?? ?co?㘊tition  ? ?ass ? ?ing as㘊ct ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? ?ing length ? e㬶eri?entco?㘊tition  ? ?ass ? ?eight lifted ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? ?ing as?ect ratio ? e㬶eri?entco?㘊tition  ? ?ass ? ?ing length ? e㬶eri?entno fi㬊d effects  10??????3?䐛.1??䐳.2??䐙.䔗? 䐙.56?䐙.䈲?䐙.䈲?65.63?50.3300.䕄2.322.5?2.䑂2.䑂10.5125.䔲0.360.2?0.110.10.0?0.0?00152

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