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For How Long Do Trans-Saharan Migrants Stop over at an Oasis? Author(s): Daphna Lavee, Uriel N. Safriel and Isaac Meilijson. Source: Ornis Scandinavica ...
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For How Long Do Trans-Saharan Migrants Stop over at an Oasis? Author(s): Daphna Lavee, Uriel N. Safriel and Isaac Meilijson Source: Ornis Scandinavica, Vol. 22, No. 1 (Jan. - Mar., 1991), pp. 33-44 Published by: Wiley on behalf of Nordic Society Oikos Stable URL: http://www.jstor.org/stable/3676619 . Accessed: 07/11/2014 02:04 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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ORNIS SCANDINAVICA 22: 33-44.Copenhagen 1991

Forhowlongdo trans-Saharan migrants stopoverat an oasis? Daphna Lavee, Uriel N. Safrieland Isaac Meilijson Lavee, D., Safriel,U. N. and Meilijson,I. 1991.For howlongdo trans-Saharan migrants stopoverat an oasis?- OrnisScand.22: 33-44. Insectivorous weretrapped autumn andspring inan0.02 passerines during migration km2Sinaidesertoasis 300 kmsouthand 2000kmnorthof thenorthern and the southern route.Meannumber ofrecaptures andmean edgesofthebirds'cross-desert number ofdaysbetween first andlastcaptures wereusedforestimating thelengths of commonspecies'stopover periodsandthesize oftheirstopping-over populations, a constant of staying an additionalday and a constant assuming probability daily ofcapture.Ca 80% ofthebirdswerecaptured probability onlyonce,andprobably andestimated stayedoneday.Species'meanobserved stopovers rangedfrom1 to5 d and 1.5 to 13.6d, respectively. Morebirdsstopped-over, andstopovers wereon the thaninspring, averagelonger,(a) inautumn (b) inearlythaninlateautumn, (c) in latethaninearlyspring, (d) inspeciesandseasonswithlargestopping-over populathaninmales(intwospecieswithsexualdimorphism) inspring, tions,(e) infemales and(f) inspeciesencountering theoasisearlyon theirautumn routethaninspecies itlate.We proposethatnumbers andstopover reaching alighting lengths dependon whenandwherean oasisis encountered. Birdstendto overfly oases or to stopfor whentheoasisisclosetothepointofmigration orwhen initiation onlyonedayeither it is advantageous to reachbreeding territories fast. D. Lavee, Dept of Zoology, The Hebrew Univ.of Jerusalem, Jerusalem91904,Israel (presentaddress) Nature ReservesAuthority,78 YirmeyahuSt., Jerusalem94467, Israel. U. N. Safriel,Dept of Zoology, The Hebrew Univ. of Jerusalem,Jerusalem 91904, Israel and The MitraniCenterfor Desert Ecology, The BlausteinInstitute for DesertResearch,Sede Boqer Campus ofBen GurionUniversity oftheNegev,Israel. I. The Sackler Exact Tel-Aviv Meilijson,Dept of Statistics, Sciences, Facultyof Univ., Tel-Aviv,Israel.

ofstayofa sizeableportion ofthebirdsalighting length at a stopover ofthe site,andalsotoassessthereliability The lengthof timea nocturnalmigrantstaysat a stop- estimate. Thissiteis a tinyoasissurrounded bya harsh over siteand themanagementof itsfuelreservesduring desert(Fig. 1), so thatmostbirdsalighting in it are arecritical ofitsmigration tactics confined withinits boundaries.An intensive stopover components trapping concentrated within sucha smallarearesulted in (e.g. Bairlein1985,Biebachet al. 1986).Butitis diffi- effort cultto ascertain boththedayof arrivaland thedayof the captureof a largeproportion of alighting birds. ofa largesampleofindividual and Furthermore, becausethebirdsdidnotforageorrestin departure migrants, therefore as thetimediffer- areasoutsidetheoasis,markedbirdsfailingto be restopover periodscalculated ence betweenfirstand lastcapture(e.g. Blake 1950, trappedin a givenmorningcould be consideredas Rabol andPetersen1973)maybe underestimates. eitherhavingdepartedduringthepreceding night,or Here we reportthe resultsof a studycarriedout havingstayedin theoasiswithout beingrecaptured. undercircumstances thatenabledus to estimatethe betweenEurope Manypalaearctic passerines migrate

Introduction

Received29 March1989 Revised7 September 1990 1990 Accepted20 September (

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33

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Fig. 1. St. Cathrine's andtheadjacent monastery garden.

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and Africaby crossingboth the Mediterraneanand the ca 2000 km of the Sahara Desert. Othersmigratealong the easternend of the palaearcticmigrationfront(Fig. 2), movingthroughLebanon, theMediterraneanregion of Israel, and then cross the Negev and Sinai deserts priorto crossingthe Sahara. The objectiveof thispaper is to provide basic informationon the lengthof stopovers in a small oasis withinthiseasterntrans-Saharan route of migratinginsectivorouspasserines.

museum comparisonsand data pertainingto the rest were used forthe calculationof observedand estimated stopoverperiods. To utilize data fromall studyyears forobtainingan estimate of the total size of a species' stopping-over population,we reconstructedmissingdata for the few non-replicatedsectionswithineach season usinga common extrapolationmethodforcontingency tables based 30 . 3

3,4

6 . 38

Materialsand methods Studysite and fieldmethods The oasis is the garden of St. Catherine's Monastery (28033'37"N, 33059'25"E), in southernSinai, 300 km southof the desert'snorthernedge (Fig. 2), and about 2000 km northof the southernedge of the Sahara. It and comprises0.02 km2 of vegetablebeds, horticultural ornamentaltrees and shrubsaround two small springs (Fig. 1). A fullaccountof theweatheris givenin Safriel and Lavee (1988). Mist nets (108-318 m, weightedmean of 290 m per nettingday) were pitchedin a layoutthatconvertedall siteswithintheoasis intotraps.Many of the bird-visited netswere repositionedor theirlayoutchangedto avoid the effectof learning.Captured birds were identified (using Svensson 1970), banded and released usually withinhalfan hourof capture.Althogetherwe had 206 trappingdays that covered most of 1971 and 1972 autumns,1972 spring,and partsof 1970 and 1971 springs. Data on 2,535 captured individualswere used for the calculationof mean numbersof individualsand species per nettingday. A fewof these birdswere secured for

--

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34

Fig. 2. Regionoftheeastern endofthepalaearctic withthe front, migration positionofSt. Catherine's oasis(blacktriangle). Northern ofthe fringe desertis markedbythe 100mmisohyte. ORNIS SCANDINAVICA 22:1 (1991)

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a 9 10111214161820242835 1 2 3 4 5 6 7 DAYS ofobservedstopover distributions periods. Fig.3. Frequency ofindividuals. on topofthebarsgivenumbers Numbers Stopingroupsof2-4 overslongerthan13daysarelumpedtogether days.Filledbars:autumn;openbars:spring. on the replicatedperiods'between-yearsratios.We definedn,,jas the numberof individualstrapped during seasonal section j of autumn i. Then if for example withinnl,1,..., n,7, and n2,, ..., n2,7,missingdata are n1,4,n1,5and n2,2,thenthe estimateof n2,2is givenby 2.2 = n,2((n2,1+n2,3+n2,62,7)/(n,l+nl,3+n1,6+nl,7))

There are more elaborate methodsusingthe EM algorithmforincompletedata, but we opted forthesimpler one because under the independence assumptionof contingencytables (same migrationpatternin parallel seasons) there is very little differencebetween the methodswhen only a fewcells are missing. In order to determinethe full lengthof a stopover period,one shouldbe certainthata failureto recapture an alreadybanded birdis not due to thisbirdmovingto the adjacent desert or to a nearby oasis. Hence, the birds included in this studyshould be only those that stayed in the oasis throughoutthe whole period betweenalightingand resumingmigration;i.e., birdsthat did not readily move between the tiny oases in the region. Color banding, trappingand observationsin othertinyoases in the regionrevealed thatonly a few granivorousmigrantsbut none of the insectivorousspecies did move between the oases (Safriel and Lavee 1988). This paper concentrateson 43 insectivorous night migrantspecies, excludingthose that also winteredin the oasis.

Determinationof stopoverlength The observed stopover period is the numberof days betweenfirstand last captureof an individualbird,the days of firstand last captureincluded.Thus, birdscapturedonlyonce had an observedstopoverperiodof one

day. For birdscapturedmore than once (excludingrecapturesin the same day), on average2.1 + 2.2 d (SD), (n= 526) elapsed between two successive captures, hence the firstand thelast day of captureof a birdwere not necessarilythefirstand thelast day ofitsstayin the oasis. We found (Appendix 1) that the frequenciesof the observed stopover periods were distributedin a way thatfitsreasonablywell model D of Jolly(1982) which is a special case of the Jolly-Sebermodel (Jolly1965, Seber 1973). This model is based on the followingassumptions:(a) the stopoverlengthand capturepattern of differentindividualsof the same species using the oasis are independentand identicallydistributed;(b) theprobabilityof a birdstayingan additionalday,given the lengthof its stopoverso far,is independentof that length;and (c) captureon a givenday duringthe stopover period is independentof the positionof thatday withinthe stopoverperiod,of the lengthof thisperiod, and of the individual'spreviouscapturehistory. This model utilizesthe individualobserved stopover periods and the numberof captures withinan individual's observedstopoverperiod, and generatesan estimatedspecies mean actual stopoverlengthas well as an estimatedspecies alightingpopulationsize (1/(1-o) and N, respectively,Appendix 1, where parameterestimation is performedthrough closed-formsolutions to Model D, based on samplingduringthe entiremigrationseason). Estimateswere calculatedforspecies with observed population size n ? 15. Many species were representedin at least one season by a smallernumber of alightingbirds, and for these, estimated stopover periods could not be calculated. We thereforebased some tests for seasonal differenceson observed stopoverperiods(whichare at least as long as the estimated ones).

Results Observedstopover periods Lengthsof observedstopovers The frequencydistributionof lengthsof periods between firstand last capture is skewed (Fig. 3), since 79% of the captured birds were captured only once. Althougha few birdsstayedeven more than 10 d, the median was only 1.14 d. In autumnthe longestperiod was 35 d (one WillowWarblerPhylloscopustrochilus), in springthe longest period was 15 d (one Redstart Phoenicurusphoenicurus). Such extremelylong stopover periods, however, may be due to injuries: two OrpheanWarblersSylviahortensisand one Red-backed ShrikeLanius colluriothathad lostsome flightfeathers had observedstopoversof 20 d each. Mean observed autumn stopover (x= 1.96 d, n= 1715) was slightlybut significantly longer (Z=2.25, P=0.02, Mann-WhitneyU-test) than the springone 35

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of meanobserved Table 1. Numberof speciesin categories Data fromAppendix2 andAppendix3. stopover lengths.

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(d) Stopoverlength*

Spring Autumn

0

1

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12 5

18 13

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* Zero = no stopovers. of variationfor (x = 1.75 d, n = 748), and thecoefficient autumnwas largertoo (1.63 for autumnand 1.01 for spring). The overall species mean observed stopoverperiod ranged from 1 to 5 d, with 30% of autumn species havinga mean stopoverperiodof one day and 36% of 2 d, whereasin spring54% had a mean observedstopover period of one day, but only 11% one of 2 d (X2= 4.15, df= 1, P < 0.05). The 25 species withan observedstopover periodof 1 d in anyone season (Appendix2), were then rare (n5 6). Among the 28 species with mean observedstopoverperiod >1 day (Appendix 3), mean observedstopoversrangedfrom1.1 to 4.5 d. Assuming thatall speciesrecordedin St. Catherine'suse thisroute in both seasons, there were relativelymore species whichtotallyskipped the oasis or stayedfor only one day in spring (29 vs 13) than in autumn (17 vs 25,

Seasonal trendsin relationto observedpopulationsizes The sectionalmean numberof species, individualsand observed stopovers were greater in autumn than in spring (Table 2). The differencesin mean observed stopover period between differentseasonal sections were non-significant (autumn X2= 6.39, df= 12, n.s., springX2 = 6.67, df= 7, n.s., Kruskal-Wallistest), but there was a significantpositive correlationin spring betweenmean observedstopoverlengthsand numbers (Table 2), such that numbers and stopover lengths peaked simultaneously (Fig. 4). Thus, morebirdsalight Table2. Observedstopoverperiodsand numberof birdsby seasonalsections. Speciesper netting day

Individuals pernetting day

Autumn : 2.0?0.9 (13) 5.5?1.8 (14) 13.6?5.8 (14) r -0.12(12) 0.13(12) R 1.8?0.3 ( 8) 3.9?1.9 (11) 9.8?7.3 (11) Spring r 0.88(7)*** 0.93(7)***

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X2=5.81,P tend not to wander outside its boundaries, > passerines in in autumn and 1.5d Estimated are 3d spring. stopovers 2 and> 1.5dinspring. inspiredthe developmentof a statisticalmodel forthe are> 3d inautumn 3 Estimated stopovers estimationof actual stopoverlengths("estimatedstopover") of birdsalightingin oases (Appendix 1). However,in manycases samplesizes are suchthatthemodel Stopping-over patternsand the distancefrom cannot be used, and stopoversare calculated as days breedingranges between firstand last capture of an individual("obUsing Moreau's (1972) distributionmaps, we divided served stopover"). It followsfromour model that,at the species captured in the oasis into three distance low capture probabilities,the deviation of estimated categories (Appendix 3): those with breeding ranges stopoversfromobservedones increaseswithincreasing nearestto the oasis ("short-distance migrants"),species observedstopovers.Captureprobabilitieswere low (Tawithpartof theirbreedingrangesas close to theoasis as ble 6), and indeed, in species forwhichestimatedstopthose of the firstcategorybut also extendingmuch overs were calculated,mean estimatedstopoverswere furthernorth("medium-distancemigrants"),and spe- 1.4 d longerthanmean observedstopoversof one day, cies with distantbreeding ranges ("long-distancemi- but 3.2 d longerthanmean observedstopoversof three grants"). Thirteenof the 25 rare species that had an days (Fig. 5). observedstopoverof onlyone day were short-distance On average, capture probabilityof birds stopping migrants(Appendix 2), and of all 17 short-distance over in springwas twiceas highas thatof autumnones migrantsonlyfourstayedforlongerperiods(Appendix (Table 6). This maybe a resultof moreencounterswith 3). Among species for which differencesbetween au- nets, probablydue to more intenseforaging,in spring tumnand springstopoverscould be evaluated statisti- thanin autumn. cally (n ? 30), the two short-distance species, the Reed Finally, since shortobserved stopoverswere rather WarblerAcrocephalusscirpaceusand S. hortensishad a similarto estimatedones, our fulldata set of observed remarkable autumn preponderance. Among the two stopoversforall species (Fig. 3) exhibitsone-daymodal long-distanceones P. trochilustoo was abundant in stopoversforboth seasons. A prioriwe postulatedthat autumnand did not occur in spring,whereas S. borin the migrating birdsshouldexhibittwo distinctstopover showedno autumnpreponderance(Table 3). Finally,at behaviours:one-daystopovers,probablyused forrestTable6. Captureprobabilities betweenautumnandspring in captureprobabilities'1. (P ? SE) andtestsfordifferences

Anthustrivialis Muscicapastriata Phoenicurus phoenicurus Phylloscopus collybita Sylviaatricapilla Sylviaborin Sylviacurruca Acrocephalus scirpaceus Laniuscollurio Motacilla flava trochilus Phylloscopus Saxicolarubetra Sylviacommunis Sylviahortensis

Autumn

Spring

0.232?0.022 0.064?0.022 0.142?0.054 0.012?0.008 0.043?0.017 0.189?0.213 0.038?0.006 0.302?0.057 0.170?0.031 0.088?0.033 0.008?0.004 0.400?0.133 0.043?0.022 0.092?0.013

0.371?0.097 0.221?0.066 0.311?0.038 0.315?0.054 0.133?0.041 0.365?0.198 0.082?0.060

differences betweenautumnand spring,n.s. 1 Z-valuesfortesting P = 0.257,Z = -3.330, P

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ing, and longerstopovers,apparentlyused forfeeding. However, despite the fact that Fig. 3 displaysa mass pointat one-daystopover,our model does not support this hypothesis.On the contrary,the data are in full agreementwiththe one-class,homogenousmodel. The relativelyhighone-dayfrequencyresultsfromthe low captureprobability.

ACTUAL

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seasonal disparityin numbers,but do not explain the factthatwhen numbersare small stopoverperiods are also short.

Numbersand stopoverlengthsrelatedto fuelling

Birdsencountering theoasisinautumn havecompleted 300 km of their cross-desert only journeyand haveto travelca 2000 kmmore.Theymaytherefore use the Possible causes of seasonal disparities oasisforrefuelling themajorpartof priorto resuming Ourfindings thatmostbirdsstopoverforonlyoneday, theircross-desert trip.We foundthatsome species ofBairlein(1985)and whichhadtravelled agreewithautumnobservations onlya shortdistancebeforereachBiebachet al. (1986) in the Sahara.However,as we ingtheoasis(becausetheirbreeding wererelaquarters thisis in agreement withthehypothesis of tivelyclose by) tendednotto alightthereat all, and that mentioned, homogeneity, namelythatthestopoverlengthof dif- thosealighting stoppedoverforrelatively long.It may ferent of thesamespeciesare independent be thatamongthesebirdsmanydid notcompletethe individuals andidentically distributed. Wefoundthatthispattern is pre-desertcrossingfuellingand attemptedto do so in also trueforspring,but fewerbirdsoccurredin spring the oasis. On the other hand, we found that species

thaninautumn, andthestopovers ofthosethatalighted whichtravellong distancesbeforeencountering the intheoasiswereoftenshorter inspring thaninautumn. oasis seemalreadyto havecompleted earlier; fuelling or iftheydid,theystayedfor Many of the birds that stop over in autumnperish theytendednotto alight,

lateron migrationand in wintering quarters.If thiswas the sole cause of the seasonal disparityin numbers,we

a shorttime. Such distance-relatedbehaviourwas proposed forlong-rangemigrantsin NorthAmerica (Cald-

thatstopped over in autumnhad perishedby the time

In spring,however, birds of all distance categories tended not to alight,or stopped-overfora shorttime

wouldhavetoconcludethatmorethan70% ofthebirds wellet al. 1964).

theyshouldhave migratedover the oasis in spring. Birdscan also use different routesin springand in autumn(Moreau1972).Thus,use ofalternative routes and migration mortality mayaccountfortheobserved

only.This is unexpectedbecausein springthe birds encounter theoasisafterhavingtravelled acrossmostof the desert,mostlyalso againsta head wind(Moreau 39

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formorethan 1972).Indeed,thosethatstayedinspring References one daymighthaveforagedmoreactively(and hence F. 1985.Bodyweights andfatdeposition ofPalaearcwerecapturedmorefrequently duringtheirstay)than Bairlein, ticpasserinemigrants thecentralSahara.- Oecologia in in autumn. (Berlin)66: 141-146. somebirdsremainontheir Biebach,H., Friedrich, thatinautumn Wesuggest W. andHeine,G. 1986.Interaction of

bodymass,fat, foragingand stopoverperiodin translongto acquiremostof breedinggroundsforsufficiently Saharamigrating birds.- Oecologia(Berlin)69: passerine the required fuel, but they thereforeleave relatively 370-379. and overlate. These birdsdo not need further fuelling - BirdBanding Blake,C. H. 1950.Lengthofstayofmigrants. 21: 151-152. flythe oasis. Other birdsdo not wait to accumulateall therequiredfuelin Europe, but leave earlyand depend Caldwell,L. D., Odum,E. P. and Marshall,S. G. 1964. offatlevelsinmigrating birdskilledat a cenComparison on stopoversites,at least along the firstsectionof their and a FloridaGulfcoasttelevision tralMichigan tower.route. WilsonBull.75: 428-434. In springmost birdsmay stillbe adequately stocked Haartman, L. von1972.Influence ofterritory uponstructure and dynamics of birdpopulations. and even whenclose to the end of theirdesert-crossing, Populationecologyof - In: WildlifeResearch birds:A symposium. migratory overfly.This is particularlytrue with regard to those of the U.S. 2, Interior, Report Department pp. 101-111. whichreturnto Europe early.These birdsare knownto fromcapture-recapture Jolly,G. M. 1965.Explicitestimates be more successfulbreeders than others (Lack 1968), datawithbothdeathandimmigration-stochastic model.52: 225-247. Biometrika and our findingssuggest that they may also be very modelswithparameters constant in successfulmigrants.Later on, whenthespringstopping- - 1982.Mark-recapture time. Biometrics 38: 301-321. overpopulationpeaked, some of thebirdsdid stopover forbreeding inbirds.Lack,D. 1968.Ecologicaladaptations for relativelylong periods. Some of them could have London. Methuen, been less successfulmigrants,and stayedlong attempt- Moreau,R. E. 1972.The Palaearctic-African birdmigration - AcademicPress,London. systems. ing to feed in the oasis. F. D. 1973.Lengths ofresting timein Rabol,J.andPetersen, variousnight-migrating passerinesat Hessel0, southern Denmark.- OrnisScand.4: 33-46. Kattegat, Numbersand stopoverlengthsas relatedto the Safriel,U. N. and Lavee, D. 1988.Weightchangesof crossdesertmigrants at an oasis- do energetic considerations birds' annual schedule - Oecologia(Beralonedetermine ofstopover? thelength lin)76: 611-619. in spring We propose that migrantsbehave differently G. A. F. 1973.Theestimation ofanimalabundance and Seber, and autumnnot because theyhave different energetic - Griffin, relatedparameters. London. because have but different requirements, they prior- Slagsvold,T. 1985.Habitatphenology and springmigration - Proc.XVIIthInt.Orn.Congr.:638-647. schedules. ities, related to events in the annual cycle. Thus, if guideto Europeanpassereachingbreedingterritory earlygives a strongerselec- Svensson,L. 1970.Identification rines.- Naturhistoriska Stockholm. Riksmuseet, tiveadvantage winter thanreaching early(von Zacks,S. 1971.The theoryof statistical quarters - Wiley, inference. Haartman 1972, Slagsvold 1985), thenbirdsshould fatNewYork. tensufficiently on the wintering groundsso thattheydo not need to make use of small oases en route. Furthermore,ifreaching 1. Estimating breedinggroundsin good condition Appendix stopover periodsandpopulation but late is selectivelydisadvantageousas compared to sizesfrommist-netting recaptures arrivingearly but in an inferiorstate because arriving A statisticalmodel terri- This earlyguaranteesthe possession of a high-quality problemis, in principle,a special case of theJollytory,thenthe skippingof stopoversitesand shortening Seber mark-recapture model. This general model for of stopoverperiods (especially by males of territorial the size of homogeneous(one species) open estimating species) are expected in spring.To conclude, we pro- populationsis based on samplingthe population on a pose thatthe need to acquire a good breedingterritory numberof occasions, and recordingall indibanding has an overridingeffecton springmigrationtactics: viduals captured.All individualspresenton occasion i, whereas in autumn birds minimizeflightenergyconindependentlyof each other,have equal probabilityPi sumption,in springtheyminimizemigrationtime. of beingcapturedon thisoccasion and equal probability - We wishto thanktheauthorities of St. oi of being present(whethercapturedor not) on occaAcknowledgements Catherine's andIsraelDefenseForceforhospitality sion i+1. Under model A (Jolly-Seber),no constraints Monastery andlogistic fieldwork;theIsraeliMeteorolog- are imposedon the Pi, values. Jolly(1965) and Seber support during 0i icalServiceforclimatic data;S. Ashkenazie, R. Ben-Shlomo, determinedclosed formformulasforthe maxi(1973) B. Gal, S. Hayat,T. Kosh,T. Felsenburg and S. Shtokelman forassistance inthefield,andP. J.Jonesfora critical review. mumlikelihoodestimatesof theseparametersand their Thisresearch wassupported bya grantfromFrankA. Chap- standarderrors. manMemorialFund,The American MuseumofNaturalHisUnder models B, C and D (Jolly1982) the o's are tory,N.Y. to U. N. Safriel,and by a grantof theHebrew assumedto correspondto a constantsurvivalrate (with ofJerusalem's CenterfortheStudyand PreservaUniversity tionoftheEnvironment toD. Lavee.Thispaperispublication no constraintson the P's), all P's are assumed equal No. 113oftheMitrani CenterforDesertEcology. (with no constraintson the o's), and the two assump40

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tionstogether, No closedformsolutions respectively. are available,andtheparameters, as wellas theirstandard errorsare derivedby iterativenumericaltechniques(usingpackagesJOLLYandJOLLYAGEdeveloped byJolly). It turnsout thatifthesampling occasionscoverthe entiremigration season,modelD admitssimpleclosed formtreatment, basedon verysimplestatistics. Wewill nowshowthatitis enoughto measurethenumber(n) of birdscaptured,theaveragenumber(k) ofcaptures and theaverageobservedstopover period(t) perbird. LetT be theobserved stopover period,S thestopover andK thenumber ofcaptures. periodafterlastcapture, Thentheprobability thata birdthatis captured willbe capturedon days 1 = tl