Sexing Laughing Gulls Using External Measurements and Discriminant Analysis

J. Field Ornithol., 56(2):158-164

SEXING LAUGHING GULLS USING EXTERNAL MEASUREMENTS AND DISCRIMINANT ANALYSIS

BY LISE A. HANNERS AND STEPHEN R. PATTON

Discriminantanalysis has been usedfor determiningthe sex of gull speciesnot readilyseparable on the basisof a singlemensural character. Application of a mathematicalfunction speedsidentification of sex in the field without necessitatinglaparotomy. Discriminant analyses have proven usefulfor sexingRing-billed Gulls (Larusdelawarensis; Shugart 1977, Ryder 1978), Herring Gulls (L. argentatusargentatus; Harris and HopeJones 1969, and L. a. smithsonianus;Shugart 1977, Ryder 1978), andSilver and Red-billed gulls (L. novaehollandiaenovaehollandiae; Wooller and Dunlop 1981, and L. n. scopulinus;Mills 1971). In this paper we use discriminantanalyses to derive a classification function that permits accurate sex identification of a population of LaughingGulls (L. atricilla).We describeother usefulinformation that canbe garneredfrom discriminantscores and coefficientsand comment on potential samplingbias that we have observedin the field and encountered in the literature. Terminology associatedwith discriminantanalysis has been usedin- consistentlyin the ornithologicalliterature. We defineour termsusing the approachsuggested by Pimentel(1979). "Discriminantanalysis" is a generalterm for a statisticalprocedure used to distinguishbetween two or more groups.In this paper, we are discriminatingbetween two sexes,and we usethe standardizedmodel for canonicalanalysis of dis- criminance to derive the standardized discriminant function. The standardized discriminantfunction computesa variable which is a linear function of the discriminatingvariables. This function is of the form: Di = dilZ1 + di2Z2 + ... + dipZp where Di is the score on the discriminant function i, the di's are stan- dardizedcoefficients, and the Z's are the standardizedvalues of the p discriminatingvariables used in the analysis(Klecka 1975). A classification function is derived from the standardized function and uses raw data rather than cumbersome standardized data. The classification function takes the form:

Ci = CilV1 + ci2V2 + . . . + cipVp + ciO where Ci is the classification score, the ci's are the classification coef- ficientswith CiO being the constant,and the V's are the raw scoreson the discriminatingvariables (Klecka 1975).

158 Vol.56, No. 2 SexingLaughing Gulls [ 159

STUDY POPULATION AND METHODS We restrictedour sampleof gullsto full adults,that is, birds in defin- itive plumage(Humphrey and Parkes1959). Mostof the gulls(n = 136) camefrom the BaywayLaughing Gull colonyin BocaCiega Bay, Pinellas County,Florida (describedby Dinsmoreand Schreiber1974). From 1981-1983, 77 gullsfound sickor deadin the colonywere collected, measured,and dissectedto determine sex. During the 1982 breeding seasonwe captured42 adultsin the studycolony using walk-in nest traps (Weaverand Kadlec 1970). These gullswere measured,sexed by uni- lateral laparotomy,and released.An additional17 adultswere trapped, measured,and releasedwithout laparotomy.Subsequent observation of copulationsand pre-copulatorybehavior allowed us to determine the sexof theseindividuals. The SuncoastSeabird Sanctuary, located near- by, providedus with 30 dead gullsin 1982 which were measuredand dissected. All gullsused in this studywere collectedand/or capturedand mea- suredbetween April and October in an effort to eliminate geographic variation as a factor in our analyses.We excludedbirds collectedfrom November through March to avoid incorporatingmigrant Laughing Gullsfrom regionsnorth of Floridathat mayreach Florida by November (Southern1980). Most LaughingGulls from northern latitudespresent in Floridaduring summerare immaturesand subadults(Southern 1980) and were not includedin our sample. The variablesused in the analyseswere linear measurementsas describedby Baldwinet al. (1931). These includedheight of bill at angle of gonys(gonys depth hereafter),length of exposedculmen, length of tarsus,length of closedwing (standardwing length),and length of tail. Additionally,we measuredtotal headlength from the tip of the bill to the cerebellarprominence on the backof the head.The headand tarsus measurementswere taken with dial calipersto the nearest0.1 mm. The wing and tail were measuredwith a ruler to the nearest 1 mm. Gulls capturedin walk-in nesttraps or killed by predatorsbut not consumed were weighedwith a 500-g pesolaspring balance to the nearest5 g. The samplesize for weight data wasconsiderably smaller than thoseof other measurements and therefore we excluded those data from our analyses.All measurementswere taken by the authors;prior to data collectionwe standardizedour techniqueto insurereplicability. All measurementswere subjectedto stepwisediscriminant analysis usingRao's V as programmedin the StatisticalPackage for the Social Sciences(SPSS; Klecka 1975). A standardizeddiscriminant function was derivedusing all of the linear measurementsdescribed above. We then selectivelyremoved characters from the analysisto identify the combination of characters that best discriminated between the sexes. We used 122 gulls to derive our discriminant function, and tested its ac- curacyusing the V1 validationprocedure described by Frank et al. (1965) and discussedby Fox et al. (1981). To perform this testwe used 160] L. A. Hannersand S. R. Patton J.Field Ornithol. Spring 1985 an independentsample of 43 gulls.The differencein accuracyof the original function from that of the test sampleprovides a measureof samplingbias in the groupof birdsused to derive the originalfunction. Havingestablished that the biasin our samplewas minimal, we combined the groupsof 122 and 43 gullsand calculateda new function basedon this increasedsample size. This function was then transformed to a classificationfunction (i.e., unstandardizedform) whichis more practical to use, and the one we will emphasizein our discussion.

RESULTS Table 1 presentsthe samplesizes, means, standard deviations, coefficientsof variation,and rangesfor eachmeasured character. Culmen, total head, and tarsuslengths were the least variable measurements (CV = 2.2-4.1%). Gonysdepth, tail andwing lengths were slightly more variable (CV = 3.6-5.1%). As expected,weight was the most variable character (CV = 6.6% for femalesand 7.6% for males). Resultsof Stu- dent'st-tests presented in Table 1 indicatethat maleswere significantly larger than femaleswith respectto all 7 mensuralcharacters (P < 0.05). Total head length (THL) and gonysdepth (GD) measuredin milli- meterswere, in combination,the two mostdiscriminating variables. The classificationfunction using these variables correctly classified the sex of 95.1% of the LaughingGulls used to derive the function. This function (n = 122) was: 46.278 = (0.442 x THL)+ (0.533 x GD). A Laughing Gull is classifiedas male if substitutionof its raw measure- mentsinto the equationyields a valuegreater than 46.278; smallervalues classifythat gull as a female. Using this function, 64 of 67 maleswere correctlyclassified (95.5%), as were 52 of 55 females(94.5%). Usinga testsample of 43 birds this functioncorrectly classified 17 of 19 males and 24 of 24 females,providing an overalltest accuracyof 95.3%. The classificationaccuracies of our original sample(n -- 122, 95.1%) and of our test sample(n = 43, 95.3%) were similar indicatingthat samplingbias was minimal. We combinedthese samples and derivedthe new classification function below: 45.985 = (0.433 x THL) + (0.641 x GD). The classificationaccuracy of this functionwas 95.2%; this is the ap- propriatefunction to usein the field becauseit is derivedfrom a larger samplesize. The relationshipbetween total headlength and gonysdepth is shown in Figure 1. The magnitudeof the coefficientsof the standardizedfunc- tion indicates the relative contribution of each variable to discrimination betweenthe sexes.In this case,the coefficientsfor total head length and gonysdepth are 0.878 and 0.331, respectively,indicating that total head length wasthe most discriminatingvariable. Vol. 56, No. 2 SexingLaughing Gulls [ 161

TABLE 1. Measurements'of maleand femaleLaughing Gulls from Tampa Bay,Florida. All t valuesfor comparisonof sexeswere significant(P < 0.05).

Females Males

• _ SD • _ SD n (range) CV n (range) CV t Gonys 79 10.8 _+0.5 4.5 86 11.6 _+0.5 4.8 10.4 depth (9.8-12.2) (10.5-13.0) Culmen 79 36.9 _ 1.5 3.8 86 40.3 _ 1.5 4.1 14.6 length (33.4-39.8) (36.3-43.5) Total head 79 86.4 _ 2.0 2.2 86 92.5 - 2.1 2.3 19.3 length (80.1-90.2) (87.5-97.4) Tarsus 79 48.9 _ 1.6 3.6 86 52.8 _ 2.0 3.3 14.2 length (45.1-52.7) (47.3-57.1) Tail 74 114 _ 5 4.3 80 121 _ 5 4.0 8.5 length (103-122) (100-133) Wing 68 317 _ 12 5.1 77 328 - 17 3.6 4.3 length (261-345) (271-354) Weight 33 289 -+ 41 6.6 37 327 -+ 25 7.6 4.8 (203-371) (249-366)

All linear measurementsare in millimeters;weights are in grams.

DISCUSSION Although male LaughingGulls were significantlylarger than females in all 7 measurements,the overlap in rangeswas too great to permit discriminationof sexby singlecharacters. Schreiber and Schreiber (1979) collectedlinear measurementsof culmen, tarsus,wing, and tail from Tampa BayLaughing Gulls and found no significantdifferences in mea- surementsbetween the sexes.Reanalysis of their data indicatesthat for all of their measurements the sexes were different at P < 0.05 and the Schreibersconcur (pers. comm.). Our analysisindicated that total head length and gonysdepth were the two most useful charactersfor distinguishingbetween the sexesof LaughingGulls. These characters together or in combinationwith other mensuralcharacters have proven useful in discriminatingbetween the sexesof other gull species(Ring-billed Gulls, Fox et al. 1981; Herring Gulls,Shugart 1977, Fox et al. 1981;Silver and Red-billed gulls, Wooller and Dunlop 1981, Mills 1971). For the measurementsof eachLaughing Gull usedin the discriminant analysis,a classificationscore was calculated. These scoresform a nu- mericalcontinuum from smallfemales (smallest = 41.293) to largemales (largest= 49.878). The relativemagnitude of the scoremay providea measureof individual deviationfrom the classificationscore separating malesfrom females(a midpoint of 45.985 in our function). It may be appropriateto excludebirds whosescores fall closeto the midpoint, for studiesin whichpositive determination of sexis critical.Using our data, the rangeof scoresfor incorrectlyclassified birds was 45.034 to 46.005. 162] L. A. Hanners and S. R. Patton J. Field Ornithol. Spring 1985 FEMALE=ø• ß ß

• • ß e. ee ß •._ße•' e oO • '".'•-•Z_._': .. o o oOoOoo.Oo_ ;.=.: -- - o oo -. '-' o oo -o_v--o•go•o'• _ :

J o v v • MALE-'' I I I I I I I I [ I I I I I I [ I I [ I 80 85 90 95

TOTAL HEAD LENGTH (mm) FICt:RE1. Relationshipbetween total head lengthand gonysdepth in male and female LaughingGulls (n = 165). Line S representsthe standardizeddiscriminant function: Di = (0.331 x THL) + (0.878 x GD). Line C representsthe classificationfunction: 45.985 = (0.433 x THL) + (0.641 x GD).

Seventeenof 165 birds correctly classifiedhad scoresthat fell within thisrange. For somepurposes these birds may be too closeto the cutoff to be confident of their sex. A discriminantfunction derived from a samplepopulation maximizes the predictivepower for that particular populationand must be tested for accuracywith an independentsample. The V 1 validationprocedure providesan unbiasedestimate of accuracyby using a sampleof birds unrelatedto the analysissample. In their studieson the Herring Gull, Fox et al. (1981) usedthe V1 validationprocedure but we questionthe compositionof their samples.Fox et al. used "confirmedsex samples" (by gonadalinspection) and "assumedsex samples" (see below) to gen- erate and test their functions.They obtainedthe assumedsex samples by trappingboth membersof a pair, and assigninga male designation to the member of the pair that wasdistinctly larger in the majority of measurements.If both individualswere similar in size, they were ex- cludedfrom the analysis.Their purposein usingan assumedsex sample wasto demonstratethe usefulnessof this samplewhen a confirmed sex sampleis not available.Unfortunately, this techniqueintroduced a new bias.By selectingonly birdsthat were distinctlysize dimorphic, Fox et al. eliminatedthe overlappingtails of the normal curveof sizevariability for malesand females(i.e., large femalesand small males).These ex- treme individuals will still be encountered when someoneattempts to Vol.56, •o. 2 SexingLaughing Gulls [ 163 usetheir function.In our studiesof LaughingGulls we frequentlyhave handled paired birds that were not obviouslysize dimorphic. Indeed evenafter theseindividuals were measuredit wasoften difficult to assign a sex to eachbird without laparotomyor direct observationsof copu- lations.We cautioninvestigators to recognizethe limitationsof discriminant analysis.

SUMMARY Gullsare sexuallydimorphic in sizebut are not distinguishableon the basisof a single mensuralcharacter. Laughing Gull adults (n -- 165) from Tampa Bay, Florida, were measuredto determine gonysdepth, culmenlength, total head length, tarsuslength, tail length,wing length, and weight.Discriminant analysis identified total headlength and gonys depth as the two most discriminatingcharacters for identificationof sex.The derivedclassification function was 95.1% accuratein assigning sexto individualbirds and was95.3% accuratein identifyingthe sexof an independenttest sampleof birds. We pooled the samplesto derive a new function for use in the field. Classificationscores may provide additional information about individual birds.

ACKNOWLEDGMENTS We acknowledgethe assistanceof G. ThomasBancroft, Wayne Hoff- man, Eva B. Jones,Gary D. Schnell,and Glen E. Woolfendenfor com- ments on this paper. Earl D. McCoy provided advice on our use of discriminantanalysis. We thank the SuncoastSeabird Sanctuaryfor donationof specimens.This project wascompleted as part of a larger studyfunded in part during 1982 and 1983 by grantsfrom the Frank M. Chapman Fund to L. Hanners.

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