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Sexing Laughing Gulls Using External Measurements and Discriminant Analysis

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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 en- countered 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 stan- dardized 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 classifi- cation function is derived from the standardized function and uses raw data rather than cumbersome standardized data. The classification func- tion 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 de- scribedby 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 com- bination 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, coef- ficientsof 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 func- tion (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
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