The Auk 110(3):492-502, 1993

A GENERALIZED DISCRIMINANT FOR SEXING FULMARINE FROM EXTERNAL MEASUREMENTS

J. A. VAN FRANEKER•,2 AND C. J. F. TER BRAAK•,3 •Institutefor Forestryand Nature Research(IBN-DLO), P.O. Box167, NL-1790 AD Den Burg(Texel), The Netherlands; 2Institutefor TaxonomicZoology, University of Amsterdam,The Netherlands; and •AgriculturalMathematics Group (GLW-DLO), Wageningen, The Netherlands

AnSTg•cr.--Discriminant analysiscan use morphometric differencesbetween known male and female to predict the sex of unknown individuals in field studies.Geographic variation in size and shapeoften limits the predictive value of a discriminant function to the populationfrom which it was derived. Specificdiscriminant functions for populationsof five speciesof fulmarine petrels(Northern ,Fulmarus glacialis; , F. glacial- oides;Antarctic , Thalassoicaantarctica; , Daption capense;and , Pagodromanivea) assigned 81 to 98%of birdsin the samplesto the correctsex, but the validity of eachdiscriminant applied to alternativepopulations remained questionable. Our approach to overcomethis limitation is to combinedata from the different speciesinto a single dis- criminant. Adequate performanceof this generalized discriminant in samplesof different speciesshows its validity for use in other populationsof any of thesespecies. The generalized function calculatesthe discriminant scoresfor individual fulmarine petrels as: Y = HL + 2.38BD+ 0.41TL- 0.21CL,where HL is head length, BD is bill depth, TL is tarsuslength and CL is bill length (measurementsin millimeters). The cut point to split sexesis different in each sample and may be calculateddirectly from discriminant scores,without reference to sexedbirds, by using a maximum-likelihoodmethod. Depending on ,the gener- alized method resultsin 84 to 97%correct classifications and can be applied to other popu- lations of fulmarine petrels without requiring samplesof birds of known sex. Received19 November1991, accepted20 November1992.

FULMARINE PETRELS,like most , lack terrestrial birds (e.g. Anderson 1975, Green charactersby which sexesmay be rec- 1982).Various approaches are possible.The most ognized. Small differences in mensural char- usual for discrimination between sexes is to acters, however, may reveal sufficient dimor- constructa single formula that calculatesa dis- phism to distinguish sexes. From known criminant score for each individual on the basis correlations between sex and measurements in of its measurements.The cut point to partition a sampleof sexedbirds, a discriminantanalysis scoresinto male and female groups is usually (Sokal and Rohlf 1981) can weight characters taken as the midpoint of the interval between for their power to distinguishgroups (sexes) of the group means of sexedmales and females. unknown individuals. Unfortunately, there are somedrawbacks that Many statistical packages supply computer prevent general usageof publishedsex discrim- programs for discriminant analysis. Comput- inants. Many speciesshow considerable erized data processinghas promotedthe useof variation in size over their geographicalrange. discriminant analysis. The method has been As a consequence,the cut point calculatedfor successfullyapplied to a wide variety of one population may not be appropriatefor an- speciesfrom different groups, including pen- other. Also, geographicvariation may involve guins (Scolaroet al. 1983, Gales 1988, Williams shape,which couldaffect the weighting of char- 1990, Williams and Croxall 1991), divers (Okill actersin the discriminantformula. For example, et al. 1989), tube-nosed birds (Dunnet and An- Northern (Fulmarus glacialis) from derson 1961, Brooke 1978, Copestakeand Crox- Spitsbergenare not only considerablysmaller all 1985,Sagar 1986, Johnstone and Niven 1989), in overall size, but also have relatively shorter (Shugart 1977,Ryder 1978,Fox et al. 1981, bills than Northern Fulmars from Britain: rel- Nugent 1982, Coulson et al. 1983, Hanners and ative to head length, bill length is about 4% Patton 1985, Schnell et al. 1985), (Hamer shorter in the Spitsbergenbirds (van Franeker and Furness 1991) and also to freshwater and and Wattel 1982, unpubl. data). Wynne-Ed- 492 July1993] SexingFulmarine Petrels 493

T^BLE1. Samplesof birdsused for discriminantfunction analysis. Total numbers,with numbersof sexed males and females in parentheses.

Sex determined by Species Locality Dissection Observation Netherlands 247 (117, 130) -- Northern Fulmar 32 (12, 20) -- Southern Fulmar Ardery Island 27 (13, 14) 103 (51, 52) AntarcticPetrel Ardery Island 11 (6, 5) 66 (30, 36) CapePetrel Ardery Island 30 (19, 11) 32 (16, 16) Snow Petrel CaseyStation -- 32 (15, 17)

wards (1952) described further variation in bill METHODS shapesand in levels of sexual dimorphism in populations of the Northern Fulmar. Age-de- Samples of sexed fulmarine petrels are character- pendent variation in size or shape can be a fur- ized in Table 1. Northern Fulmars, beached in the Netherlands between 1980 and 1988, were dissected ther complicatingfactor (e.g. Coulson et al. 1983, for morphological and pollution-related studies (van Scolaro et al. 1983). The uncertainties induced Franeker 1983, 1985). Several other North Atlantic by these types of variation urged authors to fulmar populations were studied, but an adequate caution against the unchecked application of sample of sexed birds was available only from Jan their sexdiscriminant to other populations(e.g. Mayen (van Franeker et al. 1986). Southern Fulmars, Fox et al. 1981, Nugent 1982, Witt et al. 1984, Antarctic Petrels,Cape Petrelsand Snow Petrelswere Gales 1988, Hamer and Furness 1991). studied in 1984-1985 and 1986-1987 at the Australian Since 1980 the first author has worked on baseCasey (66øS, 110øE) and the nearby Ardery Island, several projects involving five species of ful- Wilkes Land, (van Franeker et al. 1990). marine petrels: Northern Fulmar, Southern Ful- For Antarctic species,two groups of sexedbirds were mar (F. glacialoides), (Thalassoica available: birds sexed by dissection;and birds sexed by observing characteristic behaviors or external antarctica),Cape Petrel (Daption capense),and anatomy. Data on the latter group involved cloacal Snow Petrel (Pagodromanivea). All studies re- evidence (Serventy 1956, Boersmaand Davies 1987), quired knowledge of the sex of birds handled copulation position, laying, incubation shifts in the field. In some field projects,birds sexed (Pinder 1966), known sex of partner and, for Snow by dissectionor by field observationsallowed Petrel, voice level (Bretagnolle1990). Although gen- the construction of a discriminant function that erally reliable, a small risk for incidental misinter- could be applied to other birds within the pop- pretation of such observationsmay occur. Therefore, ulation. However, in other study populations, our calculationsin this paper have often been made it was not possible to sex an adequate sample separatelyfor dissectedbirds, and for all sexed birds of birds. In spite of a good general impression (dissection + observation). Skins of dissectedspeci- mens from known breeding localities have been de- of sexual dimorphism in fulmarine petrels, we posited in the care of the Zoological Museum of the were unable to give a reliable prediction of sex- Institute ot Taxonomic Zoology, University of Am- es of birds in those populations where sexed sterdam. individuals were missing. The same problem Measurements.--Measurementsof the following will alsobe encounteredin future projects.Thus, characterswere taken from fresh corpsesor live spec- we decided to reconsider all our data in an at- imens(Fig. 1;Cramp and Simmons1977): bill length tempt to construct a reproducible method to (CL), from edge of implantation of feathers to most discriminate sexes in populations of the ful- distant part of curve of hook (accuracy_+ 0.1 mm); bill marine petrelswithout requiring birds of known depth (BD), from angle of gonysto dorsalsurface of sex. The method calculates(1) a single gener- hook(ñ 0.1 ram);head length (HL), from supraoccip- alized discriminant from data on sexed birds of ital to front edge of bill (_+1ram); tarsus length (TL), from middle of midtarsal joint to distal end of tar- a number of different populations, and (2) pop- sometatarsus(+0.5 mm); wing length (WL), maxi- ulation-specificcut points without referenceto mum flattened chord, from carpal joint to tip of lon- sexedbirds. The predictive power of the meth- gest primary (ñ 1 ram); tail length (TA), central tail od is demonstratedfor populationsof five spe- feathersfrom point where emerging from skin to tip cies of fulmarine petrels. (_+1 ram). Lengths of wing and tail were not always 494 vANFRAIqEKER AND TER BP,•A•< [Auk,Vol. 110

HL fulmarine petrels (Appendix), the sign of the coeffi- cients was chosen in such a way that a score of an unsexed bird above the cut point indicates a male, and values below indicate a female. Discriminant analyseswere carried out with both the original measurementsand their logarithms.Log- arithmic transformation did not improve results and is not discussedfurther. Multiple-regressionanalysis in Genstat supplies information on outliers, such as birds with malelike measurements but sexed as fe- males.Outliers were checkedfor errorsin data entry, but were not omitted from analyses. Reliability of sexassignment by discriminantfunc- tions was testedby various methods.First, a self test was used in which performanceof the discriminant function is tested on the material from which the function was calculated.As self testsignore bias due to sample size, two other testsbased on the principles of the V• validation procedure (Frank et al. 1965) were also applied. The cross test (Stone 1974) randomly attributes all birds in a sample to one of four groups. Fig. 1. Four measurementstaken on fulmarine In each possible combination of these groups, the petrels:head length (HL); bill depth (BD);bill length performance of a discriminant function calculated (CL); and tarsuslength (TL). from three groupsis testedon the remaining group. Thus, all birds are tested in a discriminant function derived from other birds. We also applied the jack- knife test (Lachenbruch 1975, Dixon 1985), which is taken because of extreme wear or molt. Measurements similar to the cross test, but calculates a discriminant of birds sexed by dissection are summarized in the function for all but one of the birds in the sample, Appendix. Body mass was not used in the analysis evaluatesthat bird, and repeatsthe procedure for all becauseof strong seasonaland short-term variability birds in the sample. We consider the jackknife test (cf. Johnstone and Niven 1989). the best indicator of performance becausediscrimi- Discriminantanalysis.--We developed a discrimi- nants based on all individuals except from one will nant-function formula for calculatingindividual dis- suffer least from small sample sizes.In small samples, criminant scoresand a cutpoint to partition scores self tests will tend to overestimate and cross tests will into male and female groups(Lachenbruch 1975). For- tend to underestimatethe performanceof a function. mulasfor separatepopulations were calculatedby use Nevertheless, we have also listed results of these tests, of stepwise multiple-regressionanalysis (Genstat 5; as they are used in literature on sex discriminants in Payne et al. 1987). Stepwisemultiple regressionranks birds. characters according to their discriminative power Multisamplediscriminant analysis.--If samples of sexed and supplies estimatesfor a constantand a regression birds in different populationsare small, but different coefficientb, (i.e. the character'sweight) for each of populations have a similar morphology (i.e. shape), the characters (i = 1,..., n) from which discriminant it may be advantageousto estimatea generalizeddis- scores of birds can be calculated. To facilitate com- criminant from the combined samples(cf. Rayensand parison between formulas for discriminant functions, Greene 1991). The generalized discriminant calcu- we have omitted the constant and divided the coef- lates a single set of weights of charactersfor use in ficients by that of the first-ranked character.The dis- all populations. The cut point of course has to be criminant score (DS) of birds is then calculatedby: population-specific.A generalized discriminant can be calculated for a group of different populations DS = m• + w2m2 + ... + w,m,, (1) within a species,or, as in our case, for a group of where m, is the measurementof the bird for character different species.Details of the methodare asfollows. i, and w, is b,/b• the adjustedcoefficient. The adjusted In a population-specificdiscriminant for population coefficient for the first character is, thus, always re- p, the weights (equation 1) depend on the mean dif- calculated to value 1. Scores of birds of known sex ferencevector (b,) betweenthe sexesand the pooled can be usedto calculatethe cut point to split the male within-group covariancematrix (Sp).In the formula, and female componentsof the frequencydistribution thevector of weightscan be expressedas S, •bp(Lach- of discriminant scores.The cut point was calculated enbruch 1975). An analogous generalized discrimi- as the midpoint between the mean scoresfor males nant canbe obtainedby S lb, where the within-group and females. As males are larger than females in all covariance matrix S and the mean difference July1993] SexingFulmarine Petrels 495 vector b are pooled acrosspopulations. This idea is cut-point calculationsare available from the first au- not new; it is an option in the BMDP package(Dixon thor. 1985:530-531and 679-681). The method of pooling needs some further consideration. If the true within- RESULTS AND DISCUSSION groups covariancematrices are identical, an efficient methodof pooling is to assigneach individual equal Population-specificsexdiscriminants.--Stepwise weight in the calculationof b and S. However, when multiple regression of the measurementsof the true within-groups covariancematrices differ, such Northern Fulmars from the Netherlands indi- a way of pooling may be misleading:the populations cated the following sequence of charactersin that are overrepresentedin the sample will unduly influence the generalized discriminant. To avoid this, of decreasingimportance to a sexdiscrim- eachpopulation can be given equal weight (i.e. b and inant: head length, bill depth, tarsuslength and S are averagedover the population-specificb, and bill length. Also, when repeating the analysis S,). The latter methodwas chosenfor our data so as with wing length and/or tail length (smaller to not overemphasizesex differences in the largesam- sample sizes becauseof missing data), head ples of Northern Fulmars. length proved to be the most discriminating Performance of multisample discriminant func- character. Discriminant functions with from one tions(MDF) wasevaluated by calculatingspecies-spe- to six characters,starting with head length and cific cut points for MDF scoresand checkingthe per- eachtime adding the next mostimportant char- formance for birds of known sexin each species.This procedure looks similar to the self test, but differs acter,are shown in Table 2. Functionsnot using from it by the fact that the discriminantfunction was head length do not perform as well. A discrim- derived from a much larger (multispecies)sample of inant function using only bill length and bill sexedbirds than the (single species)sample that was depth (CL + 2.519BD;cut point = 81.44)resulted tested. The crosstest and jacknife test could not be in 93.1% correct classifications.In appearance applied becauseof species-specificcut points. and performance,this function is very similar Cut-pointcalculation without reference to sexedbirds.- to the discriminants based on CL and BD that Becauseof size variation, each population needs a were developedby Dunnet and Anderson(1961) population-specificcut point to partition scoresinto and MacDonald (1977) for Northern Fulmars maleand femalegroups. In the absenceof sexedbirds, breeding in Scotland.Such similarity was to be the cut point has to be derived from the shape of the expected as the majority of Northern Fulmars frequency distribution of discriminantscores. A dis- cussion on different methods for decomposing beachedin the Netherlands are of British origin mixtures of distributions into their componentswas (van Franeker 1979). Head length alone dis- given by Titterington et al. (1985). We have chosen criminates between sexes better than the com- to use the method of maximum likelihood based on bination of bill length and depth mentioned the assumption that the distribution is a mixture of above. Adding charactersto head length im- two univariate normals with possibly unequal vari- proves performance for Northern Fulmars ance. The calculationswere performed with the ex- beached in the Netherlands to about 98% ac- pectation-maximizationalgorithm as detailed in ex- cording to all tests. More variables also en- ample 4.3.2 of Titterington et al. (1985:84-87). This hanced bimodality in the frequency distribu- algorithm yields estimatesof the means (#•, #2) and variances (0.•, 0.2)of the normals. From these, the cut tions of discriminant scores,which improves point is derived by solving for the point where the classificationreliability for individual birds. two normal densities intersect. In formula, the cut In discriminant function NL4 (Table 2) for point is: Dutch beached Northern Fulmars, bill length Xg= (0'22-- 0.12)1{,11.10.22 -- ,11.20.12 is weighted negatively,whereas male bills av- •- 0.10.2[(•1-- •2)2 eragesignificantly larger than female bills. The correlation structure of the variables (as well as •- (0.12-- 0.22)1n0.12/0.22)]ø.5}. (2) the sample size) indicates that the additional discriminative power of bill length in the for- In the petrel speciesunder considerationhere, males mula lies not within its absolute value, but in are larger than females in overall size and in all in- its value relative to other characters,especially dividual characters (van Franeker and Wattel 1982; seeAppendix). After calculationof the cut point, this head length. Apparently,at a given head length, knowledgesuffices to assignsexes to birdsin the sam- a male is likely to have a relatively smallerbill ple. Information on VAX Genstarand personal com- than a female having the same head length. puter programsfor calculationsof a generalized dis- Negative weights of other characterscan be in- criminant functionfrom different samplesand for the terpreted in a similar way. Okill et al. (1989) 496 vta• FP,A•EICER • •a• BRAAIC [Auk,Vol. 110

TA•3LE2. Discriminant functions for Northern Fulmars from The Netherlands. Function names given as codesindicating locality/speciesand numbers of charactersused. For example, function NL3 for Dutch Fulmarsbased on 247 sexedindividuals uses three charactersof head length, bill depth and tarsuslength to calculate discriminant scoresas HL + 1.057BD + 0.428TL and classifiesbirds with scoreover cut point 136.0as males,and all lower valuesas females.Tests indicate that 97 to 98%of birdsare assignedto correct sex by this function.

Percent correctly classified Estimates for discriminant formula Cut Self Cross Jack- Function n HL BD TL CL WL TA point test test knife NL1 247 1 95.2 95 95 95 NL2 247 1 0.919 110.6 97 97 97 NL3 247 1 1.057 0.428 136.0 97 98 97 NL4 247 1 0.935 0.365 -0.400 114.9 98 98 98 NL5 214 1 1.056 0.436 -0.457 -0.025 110.4 98 98 98 NL6 189 1 1.084 0.371 -0.510 0.015 -0.096 106.9 97 97 97

and Hamer and Furness(1991) also found neg- known, however, is the reliability of thesefunc- ative signsof coefficientsreflecting differences tions when applied to morphologically differ- in shape rather than size. ent subspeciesfrom the High- Atlantic (F. For further analysis, we focus on the char- g. glacialis)or from the Pacific(F. g. rodgersii;van acter combination of head length, bill depth, Franeker and Wattel 1982, Wynne-Edwards tarsuslength and bill length (asin function NL4 1952). Analysesfor Southern Fulmar, Antarctic in Table 2). Wing and tail lengths have been Petrel, Cape Petrel, and Snow Petrel ranked the omitted because their contribution to the dis- characters HL, BD, TL and CL in the same se- criminant is small, and they contain missing quence of importance as in Northern Fulmars, values in all our samples.The other four char- but estimatesfor regression coefficientsfluc- acterswere included becausewhile head length tuated widely between species. is very important for Northern Fulmars from Strong fluctuationsin regressioncoefficients the Netherlands, this is not necessarilythe case were not limited to different species,but also for other populations or species.Also, frequen- occurredwithin a single species.Our discrimi- cy distributions of discriminant scorestended nants derived from the large samplesof birds to show strongerbimodality when more char- sexedby dissectionor observationwere some- acterswere used, which is important when de- times remarkably different from discriminants termining cut points without referenceto sexed derived from dissectedbirds only. The corre- birds. lation structure among variables, as well as the Table 3 shows the results of discriminant sample size, could account for a number of these analysis using the four selectedcharacters for differences. There were, however, no obvious all samples/species.For some Antarctic species, differences in performance. We also tested the two discriminants were calculated: one for birds performancesof formulas derived from the small sexed by dissection,and another for all sexed sampleof dissectedbirds to the large sampleof birds (sex determined by dissection or by ob- all sexedbirds and vice versa. In any particular servations). The functions based only on dis- sample, the two formulas produced almost equal sected birds have the disadvantage of being results, in spite of the differencesin weights of based on small sample size, but the advantage characters. of certainty that the sex determinationsare cor- The observation that, within a species,two rect. The samplesthat combine all sexed birds rather different discriminant formulas operated are larger but may contain missexedindividu- in a very similar manner was reason to do fur- als. Discriminant function JM4 for Northern ther tests to determine the value of our popu- Fulmars from Jan Mayen is not unlike the func- lation-specific discriminant functions. There- tion for Dutch Northern Fulmars. Similarity in fore, we tested the performance of the formula results for the two populations was expected, derived from our largest sample (NL4 of Dutch as both are assignedto the samesubspecies (F. Northern Fulmars) to all other samples. Cut glacialisauduboni; van Franeker et al. 1986). Un- points were calculatedas the midpoint between July1993] SexingFulmarine Petrels 497

TABLE3. Population-specificdiscriminant functions using head length, bill depth, tarsuslength and bill length. Functionsderived from samplesof birds sexedby dissectionare named(e.g. TH4) and, when sexed by dissectionor observation, OBS is added to the designation (e.g. TH4 + OBS).

Percent correctly classified Estimates for discriminant formula Cut Self Cross Jack- Function n HL BD TL CL point test test knife Northern Fulmar (Netherlands) NL4 247 1 0.935 0.365 -0.400 114.9 98 98 98 Northern Fulmar (Jan Mayen) JM4 32 1 1.763 0.503 -0.585 130.5 97 100 97 Southern Fulmar FU4 27 1 4.876 1.748 0.776 306.4 96 96 96 FU4 + OBS 130 1 24.31 1.755 3.174 724.5 90 86 89

Antarctic Petrel TH4 11 1 6.063 10.74 14.63 1,201.0 100 64 82 TH4 + OBS 77 1 4.633 0.712 -0.386 176.4 86 79 82 Cape Petrel DA4 30 1 2.355 0.333 -0.775 95.8 87 77 83 DA4 + OBS 62 1 1.164 0.208 0.819 126.7 86 76 81

Snow Petrel PA4 + OBS 32 1 3.096 -1.230 2.471 106.9 94 91 91

the group means of scoresof known males and ally a problem when working in these popu- females.Test resultsfor percentagesof correct lations, but it does create considerable uncer- classifications were: Northern Fulmar Jan Ma- tainty when applying the functions to other yen, 96.9%; Southern Fulmar, 92.6 and 86.9%; populationsthat may be morphologicallydif- Antarctic Petrel, 90.9 and 83.1%; Cape Petrel, ferent. On the other hand, the results indicate 86.7 and 83.9%; and Snow Petrel, 87.5% (when that there may be sufficientsimilarities in mor- two figures given, first refers to dissectedbirds phology betweendifferent speciesof fulmarine and secondto enlargedsample of all birds sexed petrels to constructa generalizeddiscriminant by dissectionor observation).When comparing for all thesespecies. If we are able to construct these results to jackknife test results in Table 3, a reliable generaldiscriminant for different spe- formula NL4 for the Dutch Northern Fulmars cies, such a discriminant likely will perform classifiessexes in other speciesalmost as well adequatelyin unknown populationsof each of as population-specific discriminants. In those speciesbecause morphological variation Southern Fulmar and Snow Petrel the percent- between speciesis larger than variation within age of correct classificationsby formula NL4 species.In our attempt to constructa multispe- was somewhat lower than when using popu- cies discriminant, we are aware that it cannot lation-specific discriminants, but in Antarctic improve on the performanceof proper single- Petrel and Cape Petrel performance was im- speciesdiscriminants based on an adequateva- proved. riety of samples of different populations, or The strong differences in characterweight- maybe even a single population. However, as ings within a population (Table 3) and the sim- in our case,adequate samplesfor such species- ilar performancesof widely different functions specific discriminants often are lacking. Our throw some doubt on the value of the character approachis to provide a testedgeneral discrim- weights in our population-specific discrimi- inant that can be usedas long as testedspecies- nants, at least for the Antarctic species.Appar- specificdiscriminants are missing. ently, our population samplesare inadequate Generalizeddiscriminant for fulmarinepetrels.- to give a consistent and optimal (better than All samples of birds sexed by dissection plus general) description of sexual dimorphism the sample of Snow Petrels sexed by observa- within the populations studied. This is not re- tions (379 birds from six populations of five 498 v• FRANEKERAND TER BP, A•aC [Auk,Vol. 110

TABLE4. Generalized discriminant formulas for fulmarine petrels based on morphology of all species.Per- formance testedin samplesof birds sexedby dissection(1) or in enlarged samplescontaining both dissected birds and birds sexed by observations(2) of: Northern Fulmar, Netherlands (n• = 247); Southern Fulmar (n2 = 27 and n2 = 130); Antarctic Petrel (n, = 11 and n2 = 77); Cape Petrel (n• = 30 and n2 = 62); and Snow Petrel (n2 = 32).

Percent correctlyclassified

Estimates for North- Southern Antarctic Cape discriminant formula ern Fulmar Petrel Petrel Snow Fulmar Petrel Formula HL BD TL CL 1 1 2 1 2 1 2 2

GEN1 1 95 89 86 100 79 80 84 91 GEN2 1 2.29 96 93 89 100 83 84 84 91 GEN3 1 2.61 0.48 96 96 91 100 83 87 86 88 GEN4 1 2.38 0.41 -0.21 97 96 91 100 83 87 87 91

species;Table 1) were used in the calculation mars were classified correctly as to sex. Simi- of a generalized multispeciesdiscriminant for larly, a generalized formula calculatedwithout fulmarine petrels. Table 4 shows the general the use of the Northern Fulmars of Jan Mayen discriminant for the selected combination of four provided 97% correct classificationswhen test- main characters (GEN4), as well as for combi- ed on the independent sample of Jan Mayen nations using only some of these characters. birds. Performance of the generalized discriminants The increase in performance between just was tested on samplesof all species.Cut points measuring head length (GEN1) and the more were calculatedas the midpoint of the interval complicateduse of GEN4 may seemsmall. In- between group means of scoresof known males deed, head length would be sufficientto give a and females in the tested sample. Values for generalimpression of relative numbersof males these cut points are not shown in the table as and females in many samples. However, many they are specific for the sample and not for a studies require accuratesex assignmentsfor as species. many individualsas possible, with the leastpos- Sexdiscrimination by the GEN4 formula,with sible doubt in each individual. Formulas using cut points calculated from sexed birds, equals more charactersmeet both demandsby increas- the performance of population-specificformu- ing performanceand by enhancing bimodality las.Tests of performanceof GEN4 (Table 4) show in frequency distributions (Fig. 2). We recom- results almost equal to those of self tests, and mend the use of formula GEN4. often better than those of jackknife tests for Generalized formulas in Table 4 were con- population-specific discriminants (Table 3). A structed using the samples of birds sexed by theoretical problem with test resultsfrom Table dissection.When using the larger samples in- 4 is that generalizedformulas were derived from cluding birds sexed by observations, the for- the testedsamples. As eachsample is only partly mulaslooked very similar and showedonly mi- responsible for the generalized discriminant, nor differences in test results. the effects are expected to be small. However, Cut pointswithout reference to sexedbirds.--It to validate our approach,independent testswere was our intention to provide a method for dis- done on Northern Fulmars. Because two sam- criminating sexes in samples from unknown ples of Northern Fulmars were available, one populations without reference to sexed birds. of them could be omitted from the calculations Therefore, we calculated cut points in GEN4 of a generalized discriminant without loss of scoresfor all samples by means of the expec- the morphological variability of all five species. tation-maximization-algorithm procedure. The A generalized discriminant for fulmarine pe- resulting cut points differed only slightly from trels was calculatedwithout using the sample those calculated from scores of known males of Dutch Northern Fulmars, so only using five and females. The performance of the combi- samples and specieswith 132 sexed birds. The nation GEN4 formula with the cut point based resulting formula was similar to GEN4 and in on this algorithm is shown in Table 5 and com- a performancetest, 96% of Dutch Northern Ful- pared to that of population-specificdiscrimi- July1993] SexingFulmarine Petrels 499

T,•BLE 5. Performance of GEN4 discriminant with Southern Fulrnar population-specificcut points calculated without 2o reference to sexedbirds. Percentagesof correct sex assignmentscompared with those for population- specificdiscriminants with cutpoints derived from m 0 females sexedbirds (Table 3). When two samplesmentioned under same heading, the first refers to birds sexed by dissectionand the secondto all birds sexedby either dissection or observation.

Percent correctly classifiedby Population- specificdis- Species(n) criminanta GEN4b o Northern Fulmar NL (247) 98 93 15 ' lrl•Omin a ore __ Northern Fulmar JM (32) 97 97 B G•-•-•4d•sc Southern Fulmar (27, 130) 96, 89 96, 91 Antarctic Petrel (lt, 77) 82, 82 tOO,84 Cape Petrel (30, 62) 83, 81 90, 87 ß• 10 Snow Petrel (32) 91 88

Jackknife test (Table 3). Cut points calculatedusing expectation-maximizationalgorithm. nants. Calculating cut points without reference to sexed birds sometimes caused a decrease in o III I performanceas compared to population specific 147 153 159 165 functions, especially so in Northern Fulmars discriminant score from the Netherlands. However, performance improved in some other samplesand overall Fig. 2. Improved bimodality in frequency distri- butions of discriminant scores of Southern Fulmars reliability is still between 84 and 97% depend- when number of characters in function was increased: ing on species.The fact that unequal sex ratios (A) GENt useshead length only; (B) GEN4 adds bill (e.g. in the Jan Mayen birds) did not have a depth, tarsuslength and bill length. detrimental effect on cut-point calculationpro- vides support for the use of the expectation- maximization algorithm when it is needed. solved. Morphological variation between spe- Concludingrernarks.--Population-specific dis- ciesis larger than variation within species.The criminant functions for several speciesof ful- fact that a generalized discriminant formula marine petrels showed fluctuations in the performed well in populationsof five different weights given to certain characters.Certainly, species suggests that one would have similar each population or each specieswill have its predictive value for other populationsof these own morphological properties with a specific species.By combining the generalized discrim- weighting of charactersand a specificcut point inant with the procedure involving the expec- that optimally splits males and females.How- tation-maximization algorithm to calculate cut ever, depending on the morphological vari- points, samplesof sexedbirds from such pop- ability of a species,one might need samplesof ulations are no longer essential. sexed birds from several populations to arrive It seems reasonable to assume a more or less at an optimal species-specificdiscriminant func- constantlevel of sexualdimorphism within most tion. Our sampleswere shown to be insufficient species.In the two samplesof Northern Fulmars to developoptimal species-specificfunctions for from the Netherlandsand JanMayen (both sub- fulmarine petrels. A species-specificfunction speciesF. glacialisauduboni) similar levels of sex- that has been derived from, and tested in one ual dimorphism were found. According to population only, may produceuncertain results Wynne-Edwards(1952), Northern Fulmarsfrom in other populations. (F. g. glacialis)and the North Pacific By looking at similarities in morphology be- (F. g. rodgersii)may be less dimorphic, tween different species,this problem could be but still considerablymore sothan the Southern 500 VANFRANEKER AIqD TER BP, AAK [Auk,Vol. 110

Fulmar. For Cape Petrels, Sagar (1986) con- Islands, Wilkes Land, Antarctica), where two structed a sex discriminant for subspeciesD. size morphs are breeding (Cowan 1981,van Fra- capenseaustrale that assigned82% of birds to the neker in prep.). The Snow Petrels around the correct sex, which is similar to our findings for nearbyCasey Station (sample used in this pa- D.c. capensewhen using similar characters.As- per) are all small-morph birds. In the caseof suming that the sampled populations are more Snow Petrels of Ardery Island, field observa- or less representative for levels of sexual di- tions of pair bonds,as well as the shapeof the morphism within each species,the GEN4 for- frequency distribution of discriminant scores mula, combined with the cut-point calculation from the GEN4 formula, clearly indicatedthat using the expectation-maximizationalgorithm, the samplewas not homogeneous.As far aspos- is likely to have a successrate of 85 to 90% for sible, such circumstantial evidence should be correct sex assignments in Antarctic Petrels, checkedbefore applying any sex-discriminant Cape Pigeons and Snow Petrels, as well as over analysis.A situation like the one on Ardery 90% in Southern Fulmars and up to 97% in Island may be consideredhighly exceptional Northern Fulmars. and doesnot invalidate the applicationof the The remaining speciesof fulmarine petrels generalizeddiscriminant formula and cut-point (Macronectesspp.) were not studied, but sexual calculationto unknown populations. dimorphism as described by Bourne and War- The approachof a generalized discriminant ham (1966), Johnstone(1977) and Hunter (1984), might be valuablefor other bird groupsas well. suggestsreliable resultsof generalized discrim- For example, there are several publicationson inants for Giant Petrels as well. Possibly,the population-specificdiscriminant functions for generalized discriminant can be applied to oth- differentspecies of gulls. Most can only be ap- er procellariid species when alternatives are plied to the studypopulations from which they lacking, but this needs further testing. were derived; thoseauthors that explicitly dis- Evidently, our statementthat the generalized cussthe possibleuse of their discriminant in discriminantcan be applied to any population other populations warn that usefulnessof their of fulmarine petrels with a predictablelevel of function has to be tested in each other popu- performance is only true when the sample used lation with a sampleof birds of known sex(Fox is from a homogeneouspopulation. The sample et al. 1981, Nugent 1982).When comparingthe from beachedDutch Northern Fulmarsis large- various functions for gulls, it is remarkable that ly of British (or southern North Atlantic) origin, head length and bill depth are weighted in a but is heterogeneousin the sense that it con- ratio of: about 1:2.6 in the Herring (Larus tains an admixture of birds from High Arctic argentatus;Fox et al. 1981), 1:2.3 in the Black- populationsand of juvenilesdying shortly after backedGull (L. dominicanus;Nugent 1982),and fledging. Both these groups differ in size and 1:1.9 in the Laughing Gull (L. atricilla;Hanners shape.As a result,the GEN4 procedurewas less and Patton 1985). Apart from being similar to accuratethan the population-specificdiscrimi- the HL:BD ratio in fulmarine petrels (function nant (93 vs. 98%correct sex assignments). When GEN2), the concurrence in ratio for different dark-colored individuals, which definitely Larusgulls suggeststhat a generalized formula originate from High Arctic populations (van for this gull would be possible.Inte- Franeker and Wattel 1982),and likely juveniles grated analysisof the data in such casescould (as judged from anatomy and plumage devel- mean that the predictive value of existing dis- opment; van Franeker 1983) are removed from criminant functionscould be extendedto pop- the Dutch sample,the generalizeddiscriminant ulations or speciesfor which specificfunctions did better (96% correctsex assignments).In our are not yet available. analyses,we did not a priori remove specimens Our approach does not replace optimized of this from the Dutch samplebecause sim- functionsfor local populationsor species,but ilar situations may occur when sampling un- is offeredas a practicalsolution for the many known populations.In our opinion, the results cases where sexed birds cannot be obtained and indicate an acceptable level of error in such where testedpopulation- or species-specificdis- cases. criminant functions are not available. Our There may be exceptionalsituations of het- method can be usedto developspecies-specific erogeneouspopulations. We experienced this discriminantsby combiningsamples from dif- with Snow Petrels at Ardery Island (Windmill ferentpopulations. Lack of multiplesamples for July1993] SexingFulmarine Petrels 501 individual speciesof fulmarine petrels forced Fox, G. A., C. R. COOPER,AND J.P. RYoER. 1981. Pre- us to start on a multispecies level. Becausethe dicting the sexof Herring Gulls by using external generalized discriminant has been testedon dif- measurements. J. Field Ornithol. 52:1-19. ferent species,it has predictableperformance FRANK, R. E., W. F. MASSY, AND D. G. MORRISON. 1965. Bias in multiple discriminant analysis. J. Mar- in populationsof thesespecies. When more data keting Res. 2:250-258. becomeavailable for the separatespecies, we GALES,R. 1988. Sexing adult Blue Penguins by ex- aim at developing species-specificdiscrimi- ternal measurements. Notornis 35:71-75. nants for the fulmarine petrels. GREEN,P.T. 1982. Sexing Rooks Corvusfrugilegus by discriminant analysis. Ibis 124:320-324.

ACKNOWLEDGMENTS HAMER,K. C., aNo R. W. FURNESs.1991. Sexing Great SkuasCatharacta by discriminant analysisus- This researchwas supported by the AustralianAnt- ing external measurements.Ringing & Migr. 12: arctic Division, the Australian Antarctic Science Ad- 16-22. visory Committee (ASAC), the Netherlands Marine HANNERS,L. A., AND S. R. PATTON. 1985. Sexing Research Foundation (SOZ-NWO), the Netherlands Laughing Gulls using external measurementsand Foundation for Arctic Biological Research,and the discriminant analysis. J. Field Ornithol. 56:158- Plancius Foundation. Further support was given by 164. many Norwegian and Australian institutes, crews of HUNIT=R,S. 1984. Breeding biology and population polar stations,and volunteers of the Dutch Beached dynamics of giant petrels Macronectesat South Bird Survey (NZG/NSO). The personal help of G. W. Georgia (Aves:). J. Zool. (Lond.) Johnstone,J. Wattel, R. Luttik, C. J. Camphuysen,T. 203:441-460. L. Montague, P. J. Bell, S. Creet, and many others is JOHNSTONE,G.W. 1977. Comparative feeding ecol- gratefullyacknowledged. Valuable suggestions to im- ogy of the giant petrels Macronectesgiganteus prove the manuscriptwere receivedfrom J.P. Ryder, (Gmelin) and M. halli (Mathews). Pages647-668 G. D. Schnell and an anonymousreviewer. in Adaptations within Antarctic ecosystems(G. A. Llano, Ed.). Proceedings of the Third SCAR Symposiumon Antarctic Biology, Houston, Tex- LITERATtIRE CITED as.

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APPENDIX. Measurementsof fulmarine petrels sexed by dissection,except for Snow Petrels, which were sexedbased on observations.Measurements in millimeters for: (CL) bill length; (BD) bill depth; (HL) head length; (TL) tarsuslength; (WL) wing length; (TA) tail length. For each sex, data presented as œ+ SD (n), range, and with t-value indicated for comparisonbetween sexes.*, P < 0.05; **, P < 0.01; ***, P < 0.001.

NorthernFulmars from TheNetherlands.--CL: c3 40.7 AntarcticPetrels from Ardery Island, Wilkes Land, Ant- + 1.67 (117), 36.9-45.1; • 37.4 + 1.36 (130), 33.5-39.9; arctica.--CL: • 37.4 + 0.98 (6), 35.9-38.9; $ 35.4 + 1.38 t = 16.87'**. BD: • 17.6 + 0.75 (117), 15.7-19.4; • 16.0 (5), 33.8-37.0; t = 2.79*. BD: g 13.9 + 0.47 (6), 13.5- + 0.70 (130), 14.5-17.6; t = 18.07'**. HL: • 98.8 + 14.8; $12.9 + 0.53 (5), 12.5-13.8; t = 3.24*. HL: g 96.7 2.33 (117), 91-103; • 91.6 + 2.07 (130), 86-97; t = + 1.86 (6), 95-99; $ 92.8 + 1.64 (5), 90-94; t = 3.61'*. 25.71'**. TL: • 55.8 + 1.85 (117), 50.5-61.0; • 51.7 + TL: g 46.7 + 1.51 (6), 44.5-48.5; $ 45.1 + 1.56 (5), 54.5- 1.72 (130), 43.0-55.5; t = 18.25'**. WL: • 337.3 + 8.46 47.0; t = 1.70. WL: g 334.8 + 7.83 (6), 327-348; $ 328.8 (97), 316-360; • 324.9 + 8.71 (117), 301-347; t = + 5.26 (5), 322-335; t = 1.45 TL: g 121.8 + 4.79 (6), 10.51'**. TL: • 122.1 + 5.40 (90), 109-139; • 118.9 + 116-129; $ 121.0 + 6.48 (5), 114-127; t = 0.24. 5.15 (109), 104-133; t = 4.27***. CapePetrels from Ardery Island, Wilkes Land, Antarc- NorthernFulmars from Jan Mayen.--CL: • 39.6+ 1.68 tica.--CL: c331.7 + 1.05 (19), 30.0-33.4; $ 30.2 + 1.09 (12), 37.0-42.2;• 37.3 + 1.23(20), 34.8-39.5;t = 4.57***. (11), 28.3-31.7; t = 3.59**. BD: g 10.7 + 0.42 (19), 9.7- BD: • 17.8 + 0.57 (12), 16.4-18.3; • 16.0 + 0.50 (20), 11.5; $ 10.0 + 0.42 (11), 9.4-10.8; t = 4.10'**. HL: g 14.9-16.6; t = 9.07***. HL: g 99.3 + 1.87 (12), 95-102; 81.6 + 1.71 (19), 79-84; $ 78.4 + 1.75 (11), 75-81; t = $ 92.4 + 1.79 (20), 89-96; t = 10.34'**. TL: g 56.0 + 4.93***. TL: g 47.1 + 1.50 (19), 44.5-50.5; $ 45.7 + 1.45 2.02 (12), 53.5-59.0; $ 52.5 + 1.20 (20), 50.5-55.5; t = (11), 43.0-48.5; t = 2.58*. WL: g 283.6 + 4.45 (19), 273- 6.25***. WL.' g 337.7 + 9.65 (6), 325-348; $ 329.2 + 292; $ 278.3 + 6.96 (11), 266-288; t = 2.55*. TL: g 107.8 7.91 (15), 317-344; t = 2.09*. TL: g 125.3 + 2.55 (9), + 2.79 (19), 102-112; $ 106.0 + 3.10 (11), 103-111; t 122-129; $ 120.3 + 4.53 (19), 111-128; t = 3.07**. = 1.63. SouthernFulmars from Ardery Island, Wilkes Land, A nt- SnowPetrels from CaseyStation, Wilkes Land, Antarc- arctica.--CL: c345.6 + 1.36 (13), 43.0-47.6; $ 42.8 + tica.--CL: c321.4 + 0.49 (15), 20.4-22.1; $19.7 + 0.83 1.71 (14), 38.9-45.5; t = 4.72***. BD: g 16.4 + 0.59 (17), 18.2-21.2; t = 7.00***. BD: g 9.3 + 0.38 (15), 8.7- (13), 15.1-17.1;e 15.3 + 0.48 (14), 14.4-16.1; t = 5.05***. 10.1; $ 8.6 + 0.39 (17), 7.8-9.5; t = 5.05***. HL: g 72.2 HL: g 104.0 + 1.78 (13), 101-107; $ 100.2 + 1.97 (14), + 1.32(15), 70-76; $ 68.7 + 1.93(17), 64-72; t = 5.89***. 95-103; t = 5.25***. TL.' g 54.3 + 1.55 (13), 52.0-56.5; TL: g 34.4 + 0.83 (15), 33.0-35.5; $ 33.9 + 1.46 (17), $ 51.9 + 1.06 (14), 50.0-53.5; t = 4.91'**. WL: g 354.1 30.5-37.0; t = 1.15. WL: g 273.9 + 6.35 (15), 263-283; + 9.85 (13), 331-365; $ 346.5 + 5.75 (14), 337-357; t $ 264.4 + 7.75 (17), 251-277; t = 3.76***. TL g 116.5 = 2.47*. TL: g 135.2 + 4.88 (13), 125-143; $ 133.4 + + 5.01 (15), 107-123; $ 115.0 + 4.47 (16), 110-125; t 3.27 (14), 127-140; t = 1.13. = 0.88.