784
ShortCommunications
whereas residents must engage in other activities.
One could test this hypothesisby comparingeither
fat levels or body massper unit size of challengers
and residentsduring takeover attempts.
B. Beuf, G. Barnett, A. Barnett, A. Kukuchka, J. For-
[Auk,Vol. 107
tion of geneticpaternity in tropical House Wrens.
Am.
Nat.
130: 948-954.
1987b. The long term pair bond of tropical
House Wrens: advantageor constraint?Am. Nat.
130: 507-525.
P., & G. A. PARKER.1982. The asymrest, and K. Noddings gave permissionto work on HAMMERSTEIN,
metric war of attrition. J. Theor. Biol. 96: 647the ranchesand provided much logisticalassistance.
M. Eastman, D. Albrecht, N. McCutcheon, M. Merkle,
H. Peterson,A. Vogel, and A. Wallace provided assistancein the field. Financial assistanceto Johnson
wasprovided by a M. M. Nice Award from the Wilson
OrnithologicalSociety,F. M. ChapmanMemorialFund
Awards of the AmericanMuseum of Natural History,
an E. A. Bergstrom Award from the Associationof
Field Ornithologists,a J. Van Tyne Award from the
American Ornithologists' Union, a Grant-in-Aid of
Research from Sigma Xi, and an operating grant
(A9690) to M. R. Lein from the Natural Sciences and
Engineering ResearchCouncil of Canada. Financial
assistanceto Kermott was provided by summer faculty researchgrantsfrom St. Olaf College.Additional
funds were provided by the Bradford Brinton Memorial, Mrs. D. Duncan, and the Bighorn Audubon
Society.K. J.Cash,L. D. Harder, R. Barclay,R. Walton,
682.
JAKOBSSON,
S. 1988. TerritoryfidelityofWillowWarbier (Phylloscopus
trochilus)malesand successin
competition over territories. Behav. Ecol. Sociobiol.
22: 79-84.
JOHNSON,L. $., & L. H. KERMOTT. 1990. The structure
and contextof female songin a north-temperate
populationof HouseWrens.J.Field Ornithol. (in
press).
KREBS,J. R. 1982. Territorial defence in the Great
Tit (Parusmajor):do residentsalwayswin?Behav.
Ecol. Sociobiol.
11: 185-194.
LEIMAR,O., & M. ENQUIST. 1984. Effects of asymmetries in owner-intruder conflicts.J. Theor. Biol.
ii1:
475-491.
M^¾N^RDSMITH,J. 1974. The theory of gamesand
the evolution of animal conflicts. J. Theor. Biol.
K. Ueda, M. R. Lein, and the members of the Behav-
47: 209-221.
ioural EcologyLiterary Critique Hour improvedthe
manuscriptwith comments.To all we are grateful.
metric
ß & G. A. PARKER.1976. The logic of asymcontests. Anim.
Behav.
24: 159-175.
LITERATURE CITED
PARKER,
G. g. 1974. Assessmentstrategyand the
evolution of fighting behaviour. J. Theor. Biol.
ARCESE,
P. 1989. Territory acquisitionand lossin
male Song Sparrows.Anim. Behav. 37: 45-55.
UED^,K. 1986. A polygamoussocialsystemof the
Fan-tailedWarbler Cisticola
juncidis.Ethology73:
47: 223-243.
ECKERT,C. G., & P. J. WEATHERHEAD.1987. Ownersß
floatersand competitiveasymmetriesamongterritorial Red-wingedBlackbirds.Anim. Behav.35:
1317-1323.
FREED,
L. A. 1986. Territory takeoverand sexually
selectedinfanticide in tropicalHouse Wrens.Behav. Ecol. Sociobiol.
19: 197-206.
43-55.
WALTON,R., & V. NOL^NJR. 1986. Imperfect information and the persistenceof pretenders:male
Prairie Warblers contestingfor a territory. Am.
Nat.
128: 427-432.
ReceivedI September
1989, accepted29 April 1990.
1987a. Prospectiveinfanticide and protec-
Measuresof Wing Area and Wing Spanfrom Wing FormulaData
DUNCAN STUART EVERED•
Department
ofBiological
Sciences,
University
ofCincinnati,
Cincinnatiß
Ohio45221USA
The modification of wing shape is an important Fitzpatrick 1985). An accurate and convenient defeature of many avian adaptive radiations, whether scriptionof wing-shapevariation is relevant to many
the differencesare amongmajortaxa(Saville 1957)or systematicand comparativestudiesof birds.
Wing shapeis often describedby meansof tracing
within a groupof closelyrelatedspecies(Gaston1974ß
or photographingthe outline of the extendedwing.
Howeverßwing formulae, long recognizedas useful
• Present address: Cincinnati
Museum
of Natural
descriptorsof wing shape (Johnson1963, Svensson
Historyß1720GilbertAvenue,Cincinnati,Ohio 45202 1975), have several important advantages.For exUSA.
ample, measuring the distance between successive
October
1990]
Short
Communications
785
primary tips on the closedwing is inherently more
precisethan obtainingthe outlineof an outstretched
wing, becausethe precisionwith which wing outlines
can be defined depends critically on the subjective
control of the extension and flatness of the wing.
Further,datageneratedfrom wing formulaeare better suited to familiar statistical techniques than are
dataderived from the outlinesof wings (but seeBookstein et al. 1985). Finally, wing outlines can be ob-
43
8
ß• 80
tainedonly from materialthat allowsthe wing to be
extended.In contrast,wing formulaecanalsobe taken
from study skins, which are relatively numerousin
museum collections
and often include
rare or extinct
x
species.
Wing spanandwing areaare fundamentaldescriptors of wing shape. Both are important variables in
systematicand comparativestudies of wing-shape
variation (e.g. Fitzpatrick 1985) that draw on aerodynamictheory (Brown 1963,Rayner 1988).Despite
considerableeffortsto obtain wing areasand wing
spansdirectly from spreadwings, the limited availability of the necessaryliving, alcohol-preserved,
or
freshly killed specimenshasseverelyrestrictedsample size within speciesand the scopeof taxonomic
coveragein manystudies.Thesesamplingconstraints
couldbe alleviatedif adequatemeasuresof wing span
and wing area can be derived from wing formulae
taken from study skins in museumcollections.
I evaluated the adequacyof using wing formulae
to characterizethe interspecificvariation in wing area
andwing spanof 27 speciesof North Americanwoodwarbler (Parulinae). I used linear regressiontechniquesto assess
how much variation canbe modeled
from wing-formula data, and to what extent unex-
plained variation is due to samplingbias and the
existenceof different linear relationshipsin the different genera(phylogeneticallometry).
Wing spanand wing area can be defined graphically (Fig. la). When wing area and wing span are
measuredfrom a single wing, their definitions are
not identical with those used in flight mechanics,
which includesboth wings and the body betweenthe
wing roots.However, these"singlewing" definitions
of wing area and wing spanyield variablesproportional to thoseusedin flight mechanics,given that a
bird'swingsare the samesize,and bodysizeis proportional to wing size.
From 1982-1988 I recorded wing formulae from
wood-warblers mist-netted in Massachusetts, Michi-
gan, Ohio, and Ontario. Most (85%) were examined
during early autumn migration to ensuremost individualshad fresh,fully grown primaries.Individuals
with signsof primary molt, or with worn or broken
primary tips, were excludedfrom the analysis.I measuredthe distancesbetween successive
primary tips
on the naturally closedwing with Mitutoyo dial calipers to the nearest0.1 mm, and wing length (wing
flattenedand straightened)with a rule to the nearest
0.5 mm (Svensson 1975). From these data, I calculated
9
8
7
6
5
4
3
2
1
1
PRIM•,RIES
2
3
4
5
6
SECONd)ARIES
Fig. 1. Representations
of the wing of the YellowbreastedChat (Icteriavirens).(a) A singlewing tracing
to define the conventionsusedto measurewing span
and closethe wing outline (dashedline) for areameasurement.(b) Averageremexlengthscalculatedfrom
wing formulae. The index of area was obtainedby
summingthese remex lengths.
the distancefrom carpaljoint to primary tip on the
foldedwing for eachof the nine primaries(hereafter
primary length). An index of areawas found by summing the primary lengths and six secondarylengths
(Fig. lb). The secondarieswere not measured,but
they were on averagethe samelength as the innermost primary.
Wing tracingsand wing length (natural, unflattened chord to the nearest 1 mm) were obtained from
fresh, window-killed
wood-warblers
collected from
1978-1985in Chicago,Illinois. I measuredwing span
(to the nearest1 mm) from thesewing tracingswith
calipers.Wing outlineswere completedby extending
a curve that followed the inner edge of the seventh
secondary(first tertial) to the proximal leading edge
of the wing (Fig. la). The seventhsecondarywaschosen because its outline
was more consistent than the
sixthsecondaryin thisparticularsetof wing tracings.
The outline of eachwing wasdigitized on a 30 cm x
30 cm Summagrafics
digitizing tablet, and the wing
area computedby trapezoidalintegration in a BASIC
program.I used the mean of two replicatesto representthe areaof eachwing tracing.Computedareas
were highly repeatable,r = 0.996,with a mean replicate difference(+SD) = 0.22 + 0.16 cm2. Sample
sizesfor the 27 speciesin nine genera commonto
thesemeasuresvaried widely (Table 1).
The adequacyof the wing formula derived variables was evaluatedby two linear regressions,wing
areavs.index of area,andwing spanvs.wing length.
I assessed
the influence of the general size of each
specieson these regressionsby repeating each re-
786
ShortCommunications
[Auk,Vol. 107
T^BLE1. Sample sizes for 27 speciesof Parulinae
usedin the wing tracingand wing formula datasets.
•
Y=O.O909X-38.8,
r•=0.94
•,•,•
Sample size
5o
Wing
Species
•r
Vermivorachrysoptera
V. peregrina
40
0/m
$0
25
ß
i
i
750
800
i
i
850
INDEX
900
OF
ß Vermivora
b=
AREA
i
i
950
1000
(ram)
/X Setophaga
ß Oporornis
ß Dendroica ß Seiurus
• Wilsonia
E] Mniotilta
•
0 Geothlypis
Icteria
lOO
Y=1.32X-4.80,
E
r•=0.93
90
55
60
WING
6
70
LENGTH
(ram)
7
4
62
1
1!
7
30
3
1
11
3
13
29
111
23
D. caerulescens
D. coronata
D. virens
2
4
4
15
58
26
D. fusca
D. palmarum
2
1
6
16
D. castanea
4
D. striata
Mniotilta varia
1
5
26
65
47
6
10
59
5
2
27
19
3
10
1
41
6
17
6
Dendroicapetechia
D. pensylvanica
D. magnolia
D. tigrina
Geothlypis
trichas
Oporornis
formosus
O. philadelphia
O. agilis
ß
1
8
V. ruficapilla
S. noveboracensis
Q- 80
Wing formula
V. celata
Setophaga
ruticilla
Seiurusaurocapillus
v
tracing
Wilsonia citrina
!
8
W. pusilla
4
21
W. canadensis
Icteria virens
9
2
23
22
Mean
+ SD
4.8 + 4.5
30.4 + 24.5
Fig. 2. Regressions
of (a) wing area vs. index of
area,and (b) wing spanvs. wing length; samplemeans
used for each species.There was no significant dif-
ferencebetweendifferentgenerain the form of either
of these linear relationships.
sizessubstantiallyimproved the fit (Table 2). The excellentfit of datato the regressionmodelsis especially
noteworthy, becauseweighting by sample size can
gressionwith wing variablesmade independentof only incompletely accountfor age/sex bias and does
size. The size-independent wing variables usedwere
not accountfor the likely geographicsourcesof variresidualsfrom separatelinear regressionsof each ation between samples.
original variable against the geometric mean of 54
Size variation among speciesdid not appreciably
linear skeletalmeasurements
(n = 20 for eachspecies, inflate the strength of these relationships.The profrom Ostroff 1985).I assessed
the effectof sampling portion of variation explained in the regressionswas
biason the fit of the regressionmodelsby weighting only slightly decreasedwhen each variable was replaced by its size-independent analogue. After
each speciesby either the tracing samplesize, wing
formulasamplesize,or productof thesesamplesizes. weighting by the product of sample sizes,r2 = 0.92
Allometric effectsdue to phylogeny were investigat- in both regressions.
I found no significant effects (ANCOVA) due to
ed by testing for the significanteffect of genus. I
performedthe general linear model of the analysis genus for either the wing-area or wing-span relaof variance (ANOVA) and covariance (ANCOVA) on
tionships.However, significancemay be difficult to
SYSTAT (Wilkinson 1988).
Strong relationshipsexist between index of area
and actualwing area, and between wing length and
wing span (Fig. 2). Furthermore, a substantialproportion of the scatteraround these regressionlines
was attributable to sample heterogeneity. For both
ret•ressions,
weighting by the productof the sample
demonstrate as speciesnumbers were low in most
genera (Table 1). To effectively increasesamplesize,
I consideredindividuals in the relationshipbetween
wing spanand wing length. The regressionrelationship between the wing length and wing span of individuals was similar to that obtained using species'
means,
October1990]
ShortCommunications
TAnLE2. The effect of weighting the wing area and
wing span regressionsby samplesize (n).
TAnLE3. A partial decompositionof the sums of
squares(SS)for the specieseffectin the wing span
vs. wing length ANCOVA, R• = 0.97.
Proportion of variance
explained
Area
Weightingvariable
Span
regression regression
None
0.94
0.93
Wing formula, n•
Wing tracing, n2
0.96
0.98
0.96
0.97
n• x n2
0.99
0.98
WING
SPAN = 4.16 + 1.21 x WING
LENGTH,
r 2 = 0.93.
The specieseffectin this regressionmodel was significant and due to two species(Table 3). The TenneseeWarbler (Vermivora
peregrina)
had a disproportionately shortinner wing, and the Black-and-white
Warbler (Mniotiltavaria)a relatively long inner wing.
This impliesthat significantallometriceffectsare demonstrable,but becausethe speciesare in different
genera,there wasa lack of appreciablephylogenetic
allometry.
I suggest that wing length and an index of area
obtained from wing formula data are adequatesurrogatevariablesfor wing spanand wing area,at least
for the purposesof interspecificcomparisons
within
the Parulinae.The regressionequationsobtainedseparately for eachgenuswere not significantlydifferent, despite the overall morphologicaldiversity of
theseparulines.I recommendthat phylogeneticallometry be testedwhenever possible,as its importancemay vary in different taxa.
I measured wing formulae on live birds, but the
utility of the argumentsmade here concernstaking
wing formulae from museumspecimens.In my experience, wing formulae from study skins produce
reliabledescriptions
of wing shape.Caremustbe taken
in the selectionof specimensbecausedamagethat is
due to shot, poor setting of the wings, and yearsof
physicalabusemay distort the specimen.The effects
of more subtlechangesin the relativepositionof the
primary tips, due to uneven wing shrinkage or the
deformationof primariescausedby somepreparation
techniques,canbe minimizedby samplingfrom several independent series.
The index of area I usedreflectedthe flight feather
configurationof wood-warblers(nine primaries and
six secondaries). For taxa with different numbers of
remiges,different indices of area will be more appropriate.The treatmentof the secondaries
as equal
in averagelength to the innermost primary is an assumption that should be qualified, especially in
taxawith more rounded wings.
Specialthanksto J. W. Fitzpatrickand A. T. Peterson of the Field Museum of Natural History for the
loan of the wing tracingstaken from specimenscollectedby Field Museumstaff.Logisticalsupportwas
787
Source
SS
Wing length
Vermivora
peregrina
334.61
100.98
Mniotilta varia
52.06
Other species
96.56
Error
266.05
df
P
I
1
<0.0001
<0.0001
1
0.001
16
0.05
83
provided by the Manomet and Long Point bird observatories, and the Kalamazoo Nature Center. Travel
grants from St. Peter's College and the Department
of Zoology,Universityof Oxford,andseveralsummer
fellowshipsfrom the University of Cincinnati,were
much appreciated.For superb field assistance,I am
indebtedto L. R.Messick,T. R. Leukering,P. W. Sykes
Jr., and C. B. Kepler. K. M. Cruikshank wrote the
BASIC program, D. B. Nash acquiredthe digitizer,
and L. R. Messickdrafted the figures.D.C. Duffy, T.
C. Kane,R. S. Kennedy,L. R. Messick,S. Pelikan, A.
T. Petersonand an anonymousreviewer provided
helpful commentson the draft manuscript.
LITERATURE CITED
BOOKSTEIN,F. L., B. CHERNOFF,R. L. ELDER,J. M.
HUMPHRIES, G. R. SMITH, & R. E. STRAUSS. 1985.
Morphometrics in evolutionary biology. Acad.
Nat. Sci.Philadelphia,Spec.Publ. 15.
BROWN,
R. H.J. 1963. The flight of birds. Biol. Rev.
38: 460-489.
FITZPATRICK,
J. W. 1985. Form, foraging behavior,
and adaptive radiation in the Tyrannidae. Pp.
447-470 in Neotropical ornithology. Ornithol.
Monogr. 36.
GASTON,
A. J. 1974. Adaptationin the genusPhylloscopus.
Ibis 116: 432-450.
JOHNSON,
N.K. 1963. Biosystematics
of sibling species of flycatchersin the Empidonax
hammondiioberholseri-wrightii
complex.Univ. California Publ.
Zool. 66: 79-238.
OSTROFF,
S.J. 1985. A phenetic study of the woodwarblers (Parulidae). Ph.D. dissertation, Toronto,
Univ.
Toronto.
RAYNER,J. M.V.
1988. Form and function in avian
flight. Curt. Ornithol. 5: 1-66.
SAVILLE,
D. B. O. 1957. Adaptive evolution in the
avian wing. Evolution 11: 212-224.
SVENSSON,
L. 1975. Identification guide to European
passetines.Naturhistoriska Riksmuseet,Stockholm.
WILKINSON,
L. 1988. SYSTAT:the systemfor statistics.Evanston,Illinois, SystatInc. (version4).
Received
I December
1989,accepted
12 May 1990.