Predatorprey relationships] arctic foxes and lemmings · 2010-04-23 · Predatorprey relationships]...

$: Predatorprey relationships] arctic foxes and lemmings · 2010-04-23 · Predatorprey relationships] arctic foxes and lemmings ANDERS ANGERBJO RN˜\ MAGNUS TANNERFELDT˜ and SAM ERLINGE$
Journal of AnimalEcology 0888\57\ 23Ð38

Þ 0888 BritishEcological Society

23

PredatorÐprey relationships] arctic foxes and lemmings

ANDERS ANGERBJOÝRN�\ MAGNUS TANNERFELDT� andSAM ERLINGE�Department of Zoology\ Stockholm University\ SÐ095 80 Stockholm\ Sweden^ and Department of Ecology\Lund University\ SÐ112 51 Lund\ Sweden

Summary

0[ The number of breeding dens and litter sizes of arctic foxes Alopex lagopus wererecorded and the diet of the foxes was analysed during a ship!based expedition to 06sites along the Siberian north coast[ At the same time the cyclic dynamics of co!existing lemming species were examined[1[ The diet of arctic foxes was dominated by the Siberian lemming Lemmus sibiricus"on one site the Norwegian lemming L[ lemmus#\ followed by the collared lemmingDicrostonyx torquatus[2[ The examined Lemmus sibiricus populations were in di}erent phases of the lemmingcycle as determined by age pro_les and population densities[3[ The numerical response of arctic foxes to varying densities of Lemmus had a timelag of 0 year\ producing a pattern of limit cycles in lemmingÐarctic fox interactions[Arctic fox litter sizes showed no time lag\ but a linear relation to Lemmus densities[We found no evidence for a numerical response to population density changes inDicrostonyx[4[ The functional or dietary response of arctic foxes followed a type II curve forLemmus\ but a type III response curve for Dicrostonyx[5[ Arctic foxes act as resident specialist for Lemmus and may increase the amplitudeand period of their population cycles[ For Dicrostonyx\ on the other hand\ arcticfoxes act as generalists which suggests a capacity to dampen oscillations[

Key!words] Arctic\ cycles\ functional response\ numerical response\ tundra[

Journal of Animal Ecology "0888# 57\ 23Ð38

Introduction

The Arctic tundra communities may appear simpledue to low diversity and relatively uncomplicated foodwebs[ Nevertheless\ the population dynamics of manytundra species and interactions between their deter!minants are intriguingly complex[ One of the majorfeatures of these systems are drastic ~uctuations ofsome herbivore populations\ which in turn in~uencea majority of the mammalian and avian species inthe community[ In boreal forests in North America\snowshoe hares Lepus americanus Erxleben are thepivot of these ~uctuations\ with a period of roughly09 years "Elton + Nicholson 0831^ Sinclair et al[ 0882^Boutin et al[ 0884#[ In Eurasia\ the pattern is governedby 2Ð4 years ~uctuations of lemmings "Lemmus andDicrostonyx spp[# and voles "Clethrionomys and Mic!

Correspondence] A[ Angerbjo�rn\ Department of Zoology\Stockholm University\ S!095 80 Stockholm\ Sweden[ Fax]¦35!7!05 66 04[ E!mail] tannerÝzoologi[su[se

rotus spp[# "Collett 0800Ð01^ Hansson + Henttonen0874^ Stenseth + Ims 0882#[ The ~uctuations arereferred to as cycles\ although they may\ in fact\ bechaotic with a strong periodic element "Oksanen +Oksanen 0881^ Hanski et al[ 0882#[ The cause of thesehare and lemming cycles are not yet fully understood\but a number of recent studies have suggested thatpredators play a critical role "e[g[ Erlinge et al[ 0872\0873^ Erlinge 0876^ Tostel et al[ 0876^ Korpima�ki +Norrdahl 0878^ Korpima�ki\ Norrdahl + Rinta!Jas!kari 0880^ Hanski et al[ 0882^ Hanski + Henttonen0883^ Hanski + Korpima�ki 0884^ Krebs et al[ 0884#[Small mustelids are suggested as the most in~uentialpredators {in the north| "Hanski et al[ 0882#[ In modelsof this predatorÐprey complex\ the least weasel "Mus!tela nivalis L[# and Microtus voles are the presumedkey species "Korpima�ki et al[ 0880^ Hanski + Kor!pima�ki 0884#[ Most of these studies have concentratedon the boreal taiga zone[ On the Arctic tundra\however\ the dominant rodents are lemmings and ithas not been shown that small mustelids here play the

24

A[ Angerbjo�rn\M[ Tannerfeld +S[ Erlinge

Þ 0888 BritishEcological SocietyJournal of AnimalEcology\ 57\ 23Ð38

suggested key role[ In some areas\ as on the WrangelIsland\ where lemming numbers ~uctuate in a pro!nounced cyclic pattern "Chernyavskii + Tkachev0871^ Ovsyanikov 0882#\ small mustelids are absent"Dorogoi 0876#[ If the suggested predator!generated~uctuations are valid also for lemming cycles\ theremay be other predators on the tundra that assume arole similar to that of weasels[

Nomadic avian lemming predators can be abundanton the tundra\ especially during summers with rodentpeaks "Potapov 0886^ Wiklund\ Kjelle�n + Isaksson0886#[ The most important of these are long!tailed\pomarine and arctic skuas "Stercorarius longicaudusVieillot\ S[ pomarinus Temminck\ S[ parasiticus L[#\snowy owls Nyctea scandiaca "L[# and rough!leggedbuzzards Buteo lagopus Pontoppidan[ However\ thesespecies lack a number of traits which have beenassumed for the dominant predator in the modelsmentioned above[ First\ avian predators are not pre!sent during the winter season\ which means that rod!ents have a complete refuge from these predators forthree!quarters of the year[ Secondly\ they usually giveup breeding and move elsewhere during rodent lows\and hence do not deepen and prolong rodent popu!lation crashes in the way mustelids are suggested todo "Hanski + Korpima�ki 0884^ Potapov 0886#[ Thir!dly\ the numerical response of avian lemming pred!ators shows no time lag "Potapov 0886^ Wiklund et al[0886#[ This is because many have a generalist diet ormigrate when food abundance decreases[

Instead\ the arctic fox Alopex lagopus "L[# is a strongcandidate for being a most in~uential lemming pred!ator[ Due to its habit of food caching and a slightlyless specialized diet\ adult mortality is not so stronglyin~uenced by rodent crashes as in mustelids "Hiruki +Stirling 0878^ Tannerfeldt + Angerbjo�rn 0885#[ Also\arctic foxes have the capacity to migrate over vastdistances[ Arctic fox breeding success and populationdynamics are nonetheless strongly in~uenced by lem!ming populations in areas where the species co!exist"Macpherson 0858^ Ovsyanikov 0882^ Angerbjo�rnet al[ 0884^ Kaikusalo + Angerbjo�rn 0884^ Tan!nerfeldt + Angerbjo�rn 0887#[ Furthermore\ arcticfoxes are present on the tundra also in winter and theyoften stay in an area once they have established aterritory "Tannerfeldt + Angerbjo�rn 0885#[ All thesefeatures are characteristic of the modelled predators[Further investigations of the role of arctic foxes inlemming dynamics are thus warranted[ The inter!action has so far only been examined from the view!point that lemmings govern fox populations[

The role of predation in intraguild relationshipsbetween prey species is little known\ but has gainedrecent attention "Boutin 0884^ Schmitz 0884^ Abrams+ Matsuda 0885^ Hanski + Henttonen 0885#[ In mostof the Arctic\ lemmings of the genus Lemmus co!existwith Dicrostonyx[ These di}er in habitat preferenceand in diet[ Lemmus occur preferably in wet grasslandsand feed mainly on sedges\ grasses and moss "Batzli

0882#[ Dicrostonyx prefer dry sandy areas and feedprimarily on dicotelydones\ such as Salix spp[ andDryas spp[ "Batzli 0882#[ Co!existing microtines areexposed to similar variations in predation pressureand their dynamics seem to be linked "Henttonen et al[0876^ but see Pitelka + Batzli 0882#[

Arctic fox predation patterns are also interestingin themselves[ The foxes show a large intraspeci_cvariation in diet and with this follow striking di}er!ences in life history traits and population dynamics"Hersteinsson 0889^ Tannerfeldt + Angerbjo�rn 0887#[Furthermore\ the arctic fox is a species of signi_canteconomic value to the human inhabitants of theArctic[ If we are to evaluate the role of the arctic foxin the tundra community\ we must understand itspredation patterns[ In this study\ we examine thepredatory relationship\ in terms of functional andnumerical response\ of arctic foxes in relation to chan!ges in lemming densities on the Siberian tundra[

Materials and methods

The study was performed during a ship!basedexpedition along the north coast of Siberia in thesummer of 0883 where we visited 06 sites\ from theKola Peninsula in the west to Wrangel Island in theeast "Fig[ 0#[ The sites were not situated in coastalhabitat[ At each site\ Erlinge and co!workers censusedlemming populations\ focusing on the Siberian lem!ming Lemmus sibiricus "Kerr# "Erlinge et al[ 0884#\whereas Angerbjo�rn and Tannerfeldt surveyed arcticfox dens and collected scats for diet analysis "Anger!bjo�rn + Tannerfeldt 0884#[ Some of the western siteswere visited twice "sites 0Ð4 and 7Ð09#[ For arcticfoxes\ data collected during the second visit have beenpooled with data from the _rst visit "Table 0#[ Duringthe 2!month expedition\ we covered 0353 km1 andinspected 031 arctic fox dens[ Normally\ the predatoryresponse to prey population ~uctuations are discussedfor one population along a time scale[ We insteaduse each population as a data point and constructresponse curves along a gradient of prey densities[

CENSUSING ARCTIC FOXES

Arctic fox dens are usually situated in characteristiclandforms and have lush vegetation\ making themrelatively easy to locate "e[g[ Smits et al[ 0878^ Prestrud0881a^ Smith et al[ 0881#[ A single visit at a den wassu.cient to detect if it was occupied with a litteror not[ We are convinced that we found a similarproportion of dens in all inventoried areas and thatthis was a majority of all breeding dens in the area[ Alonger stay was needed at each den to observe thenumber of adult foxes and to estimate litter size[ Littersize estimates were made between June 14 and August15\ i[e[ when the cubs were between 2 and 01 weeksold[ These estimates must be regarded as minimumnumbers "Garrott\ Eberhardt + Hanson 0873^


Fig[ 0[ Map of northern Siberia with study site numbers as in Table 0[

Table 0[ Summary of arctic fox inventories[ Site numbers and names follow Hedberg "0884#[ Asterisk "�# denotes data thatwere excluded from calculations^ at site 2 due to absence of rodents\ at other sites due to small sample sizes[ The summation{Total| is only of scats included in the analyses

Site Site name Inv[ area Fox dens Breeding foxes Fox litter size No[ fresh No[ oldno[ "km1# per 099 km1 per 099 km1 means 2 SD fox scats fox scats

0 Kola Peninsula 098 1=49 2=56 37 1�1 Kanin Peninsula 68 0=56 1=42 1� 392 Kolguyev Island 69 3=33 4=60 08� 11�3 Pechora Bay 73 2=22 6=03 1=49 2 9=60 51 194 W Yamal Peninsula 82 2=52 09=64 1=49 2 1=01 055 295 N Yamal Peninsula 28 1=45 4=02 0=99 2 9=99 49 97 NW Taymyr Peninsula 68 5=56 09=02 1=49 2 9=60 24 148 Chelyuskin Peninsula 54 3=99 5=04 14 14

09 NE Taymyr Peninsula 093 09=99 8=51 24 0400 Olene�kskiy Bay 89 0=00 1=11 29 1901 Yana Delta 56 02=32 15=76 3=69 2 1=45 49 1902a N[S[I[ Faadeyevskiy 099 03=99 17=99 2=01 2 0=44 64 1902b N[S[I[ Kotel|nyy 24 03=18 17=46 39 2903 Indigirka:Lopatka 029 01=20 13=51 2=08 2 0=41 49 0904 Kolyma Delta 009 1=62 4=34 09 905 Ayon Island 49 3=99 7=99 1=99 2 9=99 29 2906 Wrangel Island 059 5=14 01=49 3=99 2 1=13 34 24Total 0353 4=99 00=48 2=43 2 1=90 640 219

N[S[I[ � New Siberian Islands[

Tannerfeldt + Angerbjo�rn 0887#[ It should also benoted that the long time span make litter size com!parisons between populations uncertain[ We have

assumed that each breeding den was occupied by twoadult foxes[ In a total of 74 breeding dens\ there wasonly one observation of three adults at the same den[

26



The number of occupied dens multiplied by two wasused as an index of density of breeding arctic foxes"Angerbjo�rn et al[ 0884#[ The area inventoried at eachsite varied from 24 to 059 km1 "Table 0#\ mostly depen!dent on the number of hours spent at each site[

EXAMINING LEMMING POPULATIONS

We follow Jarrell + Fredga "0882# and regard collaredlemmings from all visited sites as one species\ Dicro!stonyx torquatus "Pallas#[ The Siberian lemmingLemmus sibiricus is the only Lemmus at all sites exceptno[ 0\ the Kola Peninsula\ where it is replaced bythe Norwegian lemming L[ lemmus "L[#[ The brownlemming L[ trimucronatus Davis has been reportedfrom site 05\ Ayon Island\ but is now considered asynonym to L[ sibiricus "Corbett + Hill 0880^ Wilson+ Reeder 0882#[ When discussing the genera separ!ately\ we use the terms {Lemmus| and {Dicrostonyx|\respectively\ while the term {lemmings| refers to bothgenera combined[

The population densities of lemmings were esti!mated by trapping[ We concentrated our trappinge}ort on the Siberian lemming[ Relative density esti!mates of Siberian lemmings were obtained accordingto a standardized grid snap!trapping program\ the{small quadrate method| "Myllima�ki et al[ 0860#[ Oneach locality generally 19 quadrates "04 × 04 m# wereset out\ each with 01 traps "three in each corner of thequadrate#[ The site of a trap was carefully chosen andif possible the traps were set at the entrance of a nestor across a lemming runway[ We placed the quadratesabout 49 m apart on representative and suitable habi!tat for the Siberian lemming "wet grasslands#[ Thetraps were checked every 7 h and trapping was carriedout for 13 h on each locality[ Site 05 was an exceptionwith only 49 trap!nights "Table 1#[ In this trappingprogramme\ the number of captured Lemmus per 099trap!nights was used as an index of their populationdensity[ To obtain further information on thedemography of Siberian lemming populations weplaced additional traps at selected places where therewere signs of recent lemming activity[

Body weight and sex of captured Siberian lemmingswere determined[ We removed eye!lenses to be usedfor age determination according to Hagen et al["0879#[ The weight of eye!lenses made it possible toseparate _ve cohorts] juveniles and sub!adults "lessthan 1 and 3 months old\ respectively#\ and threecategories of adults\ adult 0 "3Ð7 months and born inpreceding winter#\ adult 1 "8Ð03 months and born inprevious summer#\ and adult 2 "more than 03 monthsold#[ The detailed data on age determination will bepublished separately "Sam Erlinge et al[ unpublisheddata#[ The data on Siberian lemmings permitted us todetermine in which phase the examined populationwas[ In doing so\ we used information on present andprevious densities together with information on theage pro_le of the population[ Estimates on previous

densities were based on the amount and frequency ofold lemming faeces and earlier used runways in typicalSiberian lemming habitats[ A population in theincrease phase is expected to have medium presentdensity and indications of low past density^ typically\the age pro_le should be dominated by younger agecategories[ A population in the peak phase\ on theother hand\ is expected to have a high density\ bothin the preceding and present season[ Furthermore\ thepopulation should have a relatively high frequency ofolder individuals[ A population in the decline phaseshould have a moderate present density and high pastdensity\ and an age pro_le dominated by oldercohorts[ The low phase is characterized by very lowpresent density and indications of higher previousdensity[

As discussed earlier\ Lemmus and Dicrostonyx havedi}erent habitat preferences "Rodgers + Lewis 0875^Batzli 0882#[ The grids were set to trap Lemmus\ butDicrostonyx were also trapped to some extent[However\ we do not consider this trapping e.cientfor estimates on Dicrostonyx density[ Other scientistson the expedition trapped lemmings\ especially Dicro!stonyx\ for genetic and taxonomic analyses "Fredgaet al[ 0884#[ They used a constant number of 199 Sher!man live traps and 49 snap!traps\ set selectively atactive Dicrostonyx holes at each site "Vadim Fedorov\personal communication#[ We have used the numberof Dicrostonyx trapped by Fredga and co!workersdivided by the time the 149 traps were active\ i[e[number of trapped animals per 13 h "per 149 traps#[We call this estimate {Dicrostonyx index| "Table 1#[ Itis important to note that this index has a di}erentscale than the number of Lemmus per 099 trap!nights[For an estimate on both species together\ we havetherefore calculated a {total lemming index|[ It isderived in the same way as the Dicrostonyx index\ butalso includes total captures of Lemmus by selectiveand grid trapping\ again per 13 h "Table 1#[ We haveused the most reliable index type for each category oflemmings and the indices cannot be compareddirectly[ However\ testing for Lemmus\ the two typesof trapping indices were highly correlated "r � 9=74\P � 9=9990\ n � 04#[

ANALYSIS OF ARCTIC FOX SCATS

We collected arctic fox scats at occupied dens[ Freshscats\ from the summer of 0883\ were separated fromolder scats by appearance[ Older scats are dry andweathered or overgrown by recent vegetation[ Freshand old scats contained similar proportion of migrat!ing birds\ indicating that scats on the dens were fromsummers only\ making age separation easier[ Weignored scats that were 1 years or older\ as determinedby extensive weathering\ generally being white andbrittle\ or overgrowth of vegetation from previousseasons[ Scats were dried at 89>C and prey remains

27

Arctic foxes andlemmings

Þ 0888 BritishEcological SocietyJournal of AnimalEcology\ 57\ 23Ð38 T

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were identi_ed using reference material[ In the analysisof scats we identi_ed rodent species\ reindeer Rangifertarandus "L[#\ mountain hare Lepus timidus L[\ birdgroups "ducks and geese\ ptarmigan and grouse\waders\ passerines#\ insects and plant material\ as faras possible[ At site 2\ Kolguyev Island\ we found rod!ent remains in one of the arctic fox scats "n � 30#[This is the _rst report of rodents from the island\ butthe remains were only 19) by volume in the singlescat and we were unable to determine the species[Since the amount was negligible\ we excluded datafrom this site from all analyses of predatory responseto rodents[ The remains of Lemmus in the scats fol!lowed known distributions\ with the Norwegian lem!ming Lemmus lemmus only on site 0\ the Kola Penin!sula\ and the Siberian lemming L[ sibiricus on all othersites[ The collared lemming Dicrostonyx torquatus isnot known for sites 0 and 02a "Faadeyevskiy Island#[We found remains of Dicrostonyx in _ve out of 39arctic fox scats from site 02b "Kotel|nyy Island#\ wherethe species previously was unknown[

We used a modi_ed frequency of occurrence mea!sure to estimate the amount of each prey category[When there were remains from more than one speciesin a single scat\ we took into account the proportionof each prey species by dry volume[ For example\ onescat with 39) Lemmus and 59) Dicrostonyx plusanother scat with 59) Lemmus and 39) Dicrostonyx\were considered to be equivalent to one scat with099) Lemmus and one with 099) Dicrostonyx[ Wecall this semi!quantitative measure {percentage wholescat equivalents| ") WSE#[ Sample sizes remain thesame as for frequency of occurrence[ The advantageof this measure is that the relative amount of eachprey category in the faeces is taken into account[ Thisis especially important for prey items such as insects\which occur in small quantities in each scat[ With astrict frequency of occurrence measure\ these will beover!estimated[ Very small or broken scats were joinedwith others from the same sample to form a scat ofnormal size[

We could not classify all prey items to species level[In some cases\ lemming remains could be identi_ed\but not as species "03) WSE in fresh\ 8) in oldscats#[ That class of remains was for each site dividedinto the Lemmus and Dicrostonyx classes\ respectively\in the same proportion as the remains identi_ed tospecies level[ We have no reason to believe that therewas a bias towards one species in the unidenti_edlemming class[ In the same way we divided the classof unidenti_ed rodents "11) WSE in fresh and 02)in old scats# among all rodents species found at eachsite[ Beside Lemmus and Dicrostonyx\ these were Mic!rotus spp[ and Clethrionomys spp[ We did not identifythese voles to species level\ but trapped species wereM[ oeconomus "Pallas# "sites 0\ 1\ 3#\ M[ gregalis"Pallas# "sites 4\ 04#\ Clethrionomys rufocanus "Sun!devall# "site 0# and C[ rutilus "Pallas# "site 4# "Fredgaet al[ 0884#[

Results

ARCTIC FOX DIET

We collected a total of 640 fresh and 219 old arcticfox scats at dens\ excluding those at site 2 due toabsence of rodents\ and at a few other sites due tovery low sample sizes "Table 0#[ In the following\ per!centage WSE will be given for fresh scats "with old inparentheses#[ The diet of arctic foxes in Siberia\ asrevealed from analyses of scats\ was dominated byLemmus "on most sites the Siberian lemming L[ sibi!ricus# 48) "43)#\ followed by the collared lemmingDicrostonyx torquatus 13) "10)# "Fig[ 1#[ Alto!gether\ both species of lemmings constituted 72)"63)# and together with Microtus\ Clethrionomys andunidenti_ed rodents\ arctic foxes included 76) "65)#of small rodents in their diet[ In addition\ birds wereimportant\ forming 7) "05)# of the diet[ A similardistribution of prey items appeared in fresh and oldscats "Fig[ 1#[ The proportion of migrating birds "all

Fig[ 1[ Diet of arctic foxes as measured from "a# fresh and "b#old scats[ Shown is the percentage of whole scat equivalents"WSE# for all sites combined[ The measure WSE is a modi_edfrequency of occurrence measure that takes into account theproportion of each prey species by dry volume[

39



bird species except ptarmigan and grouse# was rela!tively high in both old "03)# and fresh scats "6)#[

LEMMING DENSITIES AND THE PHASE OF THE

CYCLE

The number of Siberian lemmings obtained in the gridtrapping "small quadrate method#\ varied from 9 to18 captured animals per 099 trap!nights[ Informationon densities and age pro_les showed that the popu!lations were in di}erent phases of the lemming cycle"Table 1#[ On the islands in the east "sites 02a\ 02b and06#\ densities were very high and the age pro_le had adominance of older individuals[ Frequent old lem!ming faeces and runways indicated that densities hadbeen high also during previous winter[ These datastrongly suggest that the populations were in the peakphase[ We did not catch any Lemmus in the grid trap!ping at site 00\ but there were indications of a recentcrash[ The density had been high during the past win!ter^ at suitable wintering sites the ground was coveredby lemming faeces[ Also at site 0\ no Lemmus werecaught in the grid trapping\ but here there were fewsigns of past activity[ The population at site 8 crashedduring the summer[ In June\ the density was inter!mediate and the age pro_le was dominated by olderindividuals[ Upon our return in August\ no Lemmuswere caught[ The population at site 03 showed strongindications to be in the decline phase[ The age pro_lehad a predominance of older individuals and presentdensity was rather low[ Frequent old lemming faecesand runways also suggested that past density had beenhigh[ The Lemmus populations on sites 4\ 7\ 09 and04 had medium densities and age pro_les dominatedby young individuals[ On the later visit in August\densities at sites 7 and 09 were similar to thoseobtained in June[ Signs "faeces and runways# fromprevious season indicated a considerable lemmingpresence[ At site 04\ on the other hand\ the few signsof lemming activity indicated low previous density[Altogether\ these observations suggest that theLemmus population at site 04 was in an early increasephase\ whereas the populations at sites 4\ 7 and 09were in the late increase or peak phase[ Eye!lenses ofthe individuals at site 01 were lost during transport\but body weight could be used to separate youngerage categories "juveniles and sub!adults# from adults[The majority of captured Siberian lemmings on thislocality belonged to the younger age category "06 outof 20\ i[e[ 44)#[ The age pro_le dominated by youngerindividuals\ medium present density and signs sug!gesting low previous density\ point at a population inthe increase phase "Table 1#[

Also collared lemming populations densitiesdi}ered between sites\ with an index ranging from 9to 38 "Fig[ 2#[ From the population density estimates\there was no evident synchrony between Lemmus andDicrostonyx populations "Table 1\ Fig[ 2#[ At a fewsites there were signs of correlated densities[ Sites 1\ 5

Fig[ 2[ The relation between Dicrostonyx and Lemmus trapindices at each study site^ note that the scales of the twoindices are not the same[ Study site numbers as in Table 0[

and 00 had low densities of both species[ The Dicro!stonyx population density was highest at site 8\ whereLemmus reached an intermediate peak during thesummer[ At site 06\ with the highest Lemmus density\there was also a high Dicrostonyx density "Fig[ 2#[ Welack data on population phases for Dicrostonyx andcan therefore not analyse the relation of populationdynamics between lemming species in detail[

NUMERICAL RESPONSE

The density of breeding arctic foxes varied betweensites from 1 to 18 per 099 km1\ a ratio of over 0]03"Table 0#[ When plotting the numerical response ofarctic foxes preying on Lemmus "Fig[ 3a#\ there wasone group of sites with low density of both Lemmusand arctic foxes "sites 0\ 1\ 5\ 00\ 05#[ Another grouphad medium density of Lemmus\ but low to mediumdensity of foxes "sites 4\ 7\ 8\ 09\ 04#[ A third grouphad a high density of Lemmus and medium or highdensity of foxes "sites 02a\ 02b\ 06#[ Sites 01 and 03had low to medium Lemmus density\ but high foxdensity[ The numerical response of arctic foxes pre!ying on Dicrostonyx showed a di}erent pattern"Fig[ 3b#[ No site had high density of both arctic foxesand Dicrostonyx[ When we combined all lemmings inthe analysis\ the pattern resembled that for Lemmus"Fig[ 3c#[

We have also compared how the proportion ")WSE# of lemmings\ in fresh and old scats\ respectively\could predict the number of breeding arctic foxes[ In alinear regression\ there was no signi_cant relationshipbetween the estimated number of breeding foxes andDicrostonyx\ neither for fresh "P � 9=57\ t00 � −9=32#nor old scats "P � 9=19^ t00 � −0=24#[ The same wastrue for all lemmings combined "fresh] P � 9=07\t02 � 0=31^ old] P � 9=01\ t00 � 0=56#[ However\ theproportion of Lemmus in fresh scats tended to bepositively correlated with the number of breedingfoxes "P � 9=950\ b � 9=085\ t02 � 1=94# and for one!year!old scats the relationship was signi_cant"P � 9=900\ b � 9=089\ t00 � 2=92^ Fig[ 4#[

30



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Total lemming index (per 24 h)

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arc

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oxes p

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Dicrostonyx index (per 24 h)

0 10 20 30 40

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11

Bre

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tic f

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Lemmus index (per 100 trapnights)

0 5 10 15 20 25

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Bre

ed

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111

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105

1412 13a13b

8

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13b 1214

10 8

156

2

517

9

2

9

13a13b

1412

1

8

11

6

5

10

15

17

Fig[ 3[ Numerical response of arctic foxes to di}erent population densities of "a# Lemmus\ "b# Dicrostonyx and "c# all lemmingscombined[ Fox density is measured as number of breeding adults per 099 km1[ Lemming trap indices are explained in the text[Study site numbers as in Table 0[

In total\ we counted 080 cubs in 43 dens at eightsites "mean � 2=43\ SD � 1=90\ Table 0#[ Mean littersize at each site was not related to total lemmingdensity "Spearman rs � 9=41\ P � 9=08\ t5 � 0=36# norto Dicrostonyx density "rs � 9=34\ P � 9=20\ t4 � 0=02#\but there was a positive correlation with Lemmus den!sity "rs � 9=60\ P � 9=937\ t5 � 1=37^ Fig[ 5#[ No timelag could be detected for this parameter[ Thus\ arcticfoxes responded to high Lemmus abundance withlarge litter sizes the same season[

FUNCTIONAL RESPONSE

Information on fox diet and lemming density atdi}erent sites made it possible to analyse how arctic

foxes utilized prey in relation to prey abundance\ i[e[the functional response[ In the following\ we only usedata from fresh scats[ When we plotted the proportionof Lemmus in fresh scats against the relative densitiesof Lemmus\ a Holling|s type II curve could be _ttedwhen capture values of zero were excluded "y � 52=2x:"x ¦ 9=26#^ R1 � 9=90\ P � 9=60^ Fig[ 6a#[ This curve_t was not signi_cant^ neither was a type III functionalresponse curve _t "y � 50=8 × 1:"x1 ¦ 9=63#^R1 � 9=91\ P � 9=57#[ However\ at densities so lowthat we were unable to trap Lemmus\ they constituted15Ð78) of the arctic foxes| diet[ This indicates thatarctic foxes showed a functional response to Lemmuswhich corresponds to a Holling|s type II curve[ Thefunctional response of foxes to di}erent densities of

31



0

25

20

30

Percent Lemmus in old fox scats (WSE)

Bre

ed

ing

arc

tic f

ox

es p

er

10

0 k

m2

0 40 60 80 100

11

20

15

10

5

4

29

16

175

10

8

14

12

13b

13a

Fig[ 4[ The relationship between the density of breeding arctic foxes and the percentage of whole scat equivalents "WSE# ofLemmus in 0!year!old scats "only L[ sibiricus is present at these sites#[ The line _t was signi_cant "P � 9=900\ b � 9=089\t00 � 2=92# indicating that the numerical response of arctic foxes to changes in L[ sibiricus population density had a time lagof approximately one year[ Study site numbers as in Table 0[

Arc

tic f

ox lit

ter

siz

e m

ean

s (

±SD

)

05

8


0

1

2

3

4

5

6

7

10 15 20 25 30

Fig[ 5[ Arctic fox litter size means "2 SD# against Lemmus trap index for eight sites[ There was a correlation between littersize means and Lemmus density "rs � 9=60\ P � 9=937\ t5 � 1=37#[ Litter size estimates are minimum numbers for cubs at 2Ð01weeks of age[

Dicrostonyx could be _t to a type III response curve"y � 69=5 × 1:"x1 ¦ 054=4^ R1 � 9=34\ P � 9=913^Fig[ 6b#[ There was no signi_cant _t to a type II func!tional response curve for the Dicrostonyx data"y � 86=0x:"x ¦ 11=7#^ R1 � 9=07\ P � 9=08#[However\ the coe.cient of determination for the typeIII function was not signi_cantly higher than for thetype II "P � 9=12#[ For both Lemmus and Dicrostonyxthere was a considerable variance in the foxes|response at all prey densities[ This variance dis!appeared when we analysed the functional responseto total lemming densities "Fig[ 6c#[ Here\ data couldbe signi_cantly explained both by a type II "y � 83=8x:"x ¦ 9=46#^ R1 � 9=31\ P � 9=901# and a type III func!tional response curve "y � 82=1 × 1:"x1 ¦ 9=57#^ R1 �9=44\ P � 9=992#[ Pech et al[ "0881# described a linetest to discriminate between type II and III functions[In this test a linear regression is _tted and successively

the data points with the highest x!values are deleteduntil n � 4[ In short\ if the slope of the new _tted linegets steeper and the intercept is positive andapproaches zero when n decreases\ a type II functioncan be inferred[ If the slope approaches zero and theintercept goes from positive to negative values as ndecreases\ a type III function is suggested[ In this testfor all lemmings the slope increased while the interceptdecreased\ indicating a type II function "Fig[ 6c#[ Arc!tic foxes responded very quickly to an increase inlemming abundance and used these species close to099) already at moderate lemming densities[Although data was scarce for low lemming densities\we therefore conclude that the response to all lem!mings combined was of type II[

To investigate a possible preference for Lemmusrelative to Dicrostonyx\ we plotted the proportion ofLemmus to all lemmings eaten by arctic foxes "from

32



0 80

20

Perc

en

t le

mm

ing

s in

fo

x d

iet

(WS

E)

10 20 30 40 50 60 70

40

60

80

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8

0 50

20

Dicrostonyx index (per 24 h)

Pe

rce

nt

Dic

rosto

ny

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n f

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SE

)

10 20 30 40

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10121411

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13b 1513a 17 9

95

15

13b

10

14 812

611

255 15

13b

13a

17

10

6

11 14

16

15 8

95

1

Fig[ 6[ Functional response of arctic foxes to di}erent population densities of "a# Lemmus\ "b# Dicrostonyx and "c# all lemmingscombined[ Fitted are curves of type II for "a# and "c# and type III for "b# The diet of arctic foxes is measured as the percentageof whole scat equivalents "WSE# for each site[ Lemming trap indices are explained in the text[ Study site numbers as in Table 0[

fresh scats# at each site against the relative abundanceof Lemmus available "proportion of Lemmus to alllemmings in captures# "Fig[ 7#[ The slope of the _ttedline "y � 9=17 ¦ 9=38x# was not signi_cantly di}erentfrom 0\ i[e[ y � x "P � 9=948\ t8 � −1=05#[ At site 5\no Lemmus were caught although they constituted70) of the foxes| diet and fresh carcasses were plen!tiful[ The reason might be that the trapping was car!ried out in untypical habitat[ Because site 5 was anextreme outlier we excluded it from this analysis[ Inall other analyses this site has been included[

Discussion

LEMMING CYCLICITY IN SIBERIA

A pronounced between!year cyclic pattern charac!terizes the dynamics of lemmings on the Siberian tun!dra as shown by long!term studies on several sites weinvestigated\ e[g[ the Kola peninsula "Koshkina 0879#\Yamal "Dunaeva 0837^ Kalyakin 0879\ 0874^ Danilov0884#\ Taymyr "Sdobnikov 0848^ Kuksov 0863#\Kolyma "Chernyavskii et al[ 0870#\ and the WrangelIsland "Chernyavskii + Tkachev 0871^ Dorogoi 0876#[

33



Fig[ 7[ Proportion of Lemmus in diet "measured as WSE in scats# against proportion in captures "trapping index#[ There wasa tendency that at low relative abundance\ Dicrostonyx constituted a higher proportion of the diet than expected "t8 � −1=05\P � 9=948#[ Study site numbers as in Table 0[ Site 5 was an extreme outlier and as such excluded from the analysis[

Generally\ peak numbers have occurred with an inter!val of 2 or 3 years\ but on the Wrangel Island thecyclic period has been 4 years "Chernyavskii + Tka!chev 0871#[ In most cases "in 00 recorded cases out of04 in studies we have reviewed\ references above# peaknumbers of co!existing Siberian and collared lem!mings have coincided[ In details\ however\ thedynamic pattern of the two species di}er[ Generally\the increase and the decline of the Siberian lemmingpopulations have been more dramatic than for thecollared lemming "Chernyavskii + Tkachev 0871^Dorogoi 0876#[ The cyclic pattern is not synchronousover the entire Siberian tundra region\ but ~uctuationscan be synchronous over extensive areas[ For exam!ple\ peak numbers have generally occurred the sameyears on the Yamal and Taymyr peninsulas "Table 1and references above#[

How accurate is our phase determination< We havecompared our suggestions with available data fromrecent Russian studies and reported observations atvarious sites in the Wader Study Group Bulletin"Tomkovich 0883a\b\ 0885#[ On the Wrangel Island"site 06#\ the lemming populations were studied indetail during 0878Ð85 "Menyushina 0886#[ Both theSiberian and the collared lemming reached peak num!bers in 0883 and declined in 0884 to low densities in0885[ This is in accordance with our phase deter!mination "Table 1#[ On the Yamal and Taymyr pen!insulas "sites 4Ð09#\ large or average number of lem!mings "species not stated# were reported during 0883and in some areas "two areas out of six in Yamaland _ve out of 01 in Taymyr# a declining trend wasobserved over the summer "Tomkovich 0885#[ Thereports suggest peak or early decline phase in theseareas[ Decreasing or low numbers of lemmings werereported from these areas in summer 0881 and lowor increasing densities in 0882 "Tomkovich 0883a\b#[Altogether\ available information indicates that on

Yamal and Taymyr the lemming populations in 0883were in various stages close to the peak phase "cf[Table 1#[ Furthermore\ in 0883 Russian observersreported a declining lemming population in the Indi!girka:Lopatka area "site 03#\ and an increasing popu!lation at Kolyma "site 04# "Tomkovich 0885#[ Thesereports are in agreement with our phase determination"Table 1#[ We have also compared our phase deter!minations with information from dend!rochronological analyses performed during the sameexpedition "Danell et al[ 0884#[ By this method\ yearsof peak microtine populations are identi_ed from theintensity of scars on willow stems\ resulting from bark!ing by rodents during winter food shortages[ At Yanaand Kolyma "sites 01 and 04#\ the last winter withhigh intensity of scarred willow stems had occurred in0889:80 and Danell estimated that these populationswere in the increase phase in 0883 "Kjell Danell\unpublished data#[ This is in accordance with ourphase determination "Table 1#[ On Yamal and onWrangel Island "sites 4\ 5 and 06#\ high barking inten!sity had occurred over winter 0882:83 indicating highdensities and populations in the peak or decline phasein summer 0883 "cf[ Table 1#[ No data for dendro!chronological analysis was obtained on Taymyr[ AtOlene�kskiy "site 00# we found clear indications of arecent crash from local high density during previouswinter[ The dendrochronological analysis from thissite suggests a peak in 0878:89\ but low densities sincethen[ Obviously\ the local high density in winter0882:83 at this site was missed in the dendro!chronological analysis[ The sample size for this analy!sis\ however\ is limited from site 00 and the peakdensity might have been very local[ In short\ the accu!racy of our phase determination is supported by datafrom independent Russian studies and informationfrom dendrochronological analyses[

We have examined data from several locations to

34



reveal patterns between arctic foxes and lemmingsinstead of following populations at a single place[ Toget a sample size similar to this from one site wouldrequire a 06 years study[ Furthermore\ even if lem!ming populations from di}erent parts of Siberia mightbe di}erent in their basic population pattern\ arcticfoxes are truly nomadic and have a capacity to migratemore than 0999 km in one season[ When we measuredpredator response to di}erent lemming densitiesacross areas\ it is therefore likely to be a general arcticfox response[

NUMERICAL RESPONSE

We have found that during one summer\ densities ofboth arctic foxes and lemmings di}ered widelybetween sites along the Siberian north coast[ Lem!mings were the main prey item for arctic foxes\ butthe predatory response to Lemmus spp[ "the Siberianand Norwegian lemmings# was di}erent from theresponse to Dicrostonyx torquatus "the collared lem!ming#[ Our data suggest that arctic foxes respondednumerically with a time lag to changes in Lemmusdensity[ The observed pattern can be described as alimit cycle\ generated by such a time lag "May 0865#[This was supported by phase determination of thelemming populations[ A high density of arctic foxeswas related to a declining Siberian lemming popu!lation at site 03 and the Siberian lemming populationat site 04 in the increase phase was associated with lowarctic fox numbers[ However\ site 01 was an exception\where the lemming population was suggested to be inthe increase phase but fox density was already high"Fig[ 3a#[ This could be due to the di}erent spatialscales of lemming and fox inventories if the lemmingincrease was very local\ as discussed for Lemmus inAlaska "Garrott et al[ 0872#[ Another possibility islocal immigration of arctic foxes[ The lemming popu!lations on the Yamal and Taymyr peninsulas "sites 4\7\ 8 and 09# were estimated to be close to the peakphase while fox numbers were low to moderate"Table 1\ Fig[ 3a#[ The densities of Lemmus were mod!erate on these sites compared with the densities onsites 02a\ 02b and 06[ What seemed like peaks in thesepopulations might be a temporary cessation of growthduring summer\ that could be followed by a furtherincrease\ i[e[ a {second peak|[ Unfortunately\ we haveno information from these areas on Lemmus densitiesin 0884[ The numerical response of arctic foxes relativeto collared lemming densities showed a di}erent pat!tern "Fig[ 3b#[ No site had high densities of both arcticfoxes and collared lemmings[ However\ when we com!bined all lemmings in the analysis\ Lemmus dominatedand we again got a pattern which to some extent _tsthe description of a limit cycle "Figs 3c and 8#[

Lemming cycles in Eurasia have a periodicity of2Ð4 years "Chernyavskii + Tkachev 0871^ Hanski\Hansson + Henttonen 0880#\ which can be describedas limit cycles[ If these cycles consist of four transitions

as illustrated in Fig[ 8a# time lag between lemmingsand arctic foxes of ¼01 months "8Ð04# can be inferred[In our study\ the proportion of migrating birds waseven higher in old scats than in fresh ones\ implyingthat the old scats were from the previous summerand not winter scats[ Macpherson "0858# found thatranked proportions of lemmings in the diet were cor!related with ranked lemming density as measured bytrapping[ We found that the number of breeding arcticfoxes was better predicted by the proportion of Sib!erian lemmings in old scats than in fresh scats[ Thus\regardless of the functional response\ the size of thebreeding population of arctic foxes was determined bytheir consumption of Siberian lemmings the previousyear[ The strongest evidence for a limit cycle was thephase determination of the lemming cycle\ as shownin Fig[ 8[ Arctic foxes on the Siberian tundra thusshowed a numerical response with a time lag of ¼01months to the Siberian lemming\ but we found noevidence for a numerical response to population den!sity changes in the collared lemming[

The time lag in numerical response was probablydue to the di}erent reproductive rates of lemmingsand arctic foxes[ No time lag could be detected forlitter sizes[ However\ whereas lemmings can have sev!eral litters throughout the winter and summer\ arcticfoxes can only produce a single litter each year[ Thearctic fox can respond to high abundance of smallrodents by producing litters of up to 08 cubs\ althoughsuch large litters only result from high food avail!ability during winter and early spring "Angerbjo�rnet al[ 0880^ Ovsyanikov 0882^ Angerbjo�rn et al[ 0884^Tannerfeldt + Angerbjo�rn 0887#[ Our interpretationof the pattern observed in this study\ based also onother studies "Angerbjo�rn et al[ 0884^ Tannerfeldt +Angerbjo�rn 0885\ 0887#\ is that the delay in numericalresponse is due to the fact that arctic foxes reproduceonly once a year[ In the year following a lemmingpeak\ increased recruitment results in large numbersof reproducing arctic foxes[ An alternative would bethat migrating foxes that encounter a lemming peakstay and reproduce the following year[ However\ thiswould imply summer migration\ contrary to knownpatterns "Br%strup 0830^ Elton 0838^ Pulliainen 0854^Chesemore 0857^ Bannikov 0869^ Eberhardt + Han!son 0867#[ Furthermore\ summer migration would notbe advantageous since a peak in lemming numbersis likely to be followed by a crash "Tannerfeldt +Angerbjo�rn 0885#[ Avian predators\ on the otherhand\ migrate over vast areas seasonally and have anumerical response without a time lag "Korpima�ki0883^ Potapov 0886^ Reid\ Krebs + Kenney 0886#[

Arctic fox litter sizes in this study were surprisinglysmall "Tannerfeldt + Angerbjo�rn 0887#[ The reasonmight be that the investigated area was in the north!ernmost part of Siberia\ where the soil mostly consistsof mud and sand with a thawing active layer less than0 m in most soils "Goryachkin 0883#[ The frequentsoil movements caused by permafrost may therefore

35



Fig[ 8[ Arrows added to Fig[ 3"a#\ suggesting how arctic foxes respond numerically with a time lag to changes in lemmingdensity[ The pattern can be explained as a limit cycle\ generated by such a time lag[ This was supported by phase determinationof the Lemmus populations\ except at site 01 "denoted by a cross# which was suggested to be in the increase phase by Lemmusdata and in the decrease phase according to this _gure[

prevent dens from becoming very large "cf[ Chesemore0858#\ and small dens presumably infer larger pre!dation risks[ Arctic foxes sometimes split their litteras a precaution against predation\ using two or moredens "Prestrud 0881b^ Anthony 0885\ personal obser!vation#[ An alternative explanation to the small litterscould be that foxes in these areas migrate seasonallyand are not present during winter "to react to increasesin lemming populations#[ Some authors describe {sea!sonal migrations| in northern Siberia "e[g[ Bannikov0869#\ but there have been no studies with individuallymarked animals to show the exact nature of suchmovements[ An additional problem with these littersize estimates is the long time span of the study[ Theage of cubs varied from ¼2Ð01 weeks and postnatalmortality will have a}ected litters di}erently "Tan!nerfeldt + Angerbjo�rn 0887#[

FUNCTIONAL RESPONSE

The functional response for Lemmus followed a Hol!ling|s type II curve\ but for Dicrostonyx it was a typeIII curve[ For all lemmings combined the functionalresponse was described by a type II function sinceLemmus was the dominating prey "Fig[ 6#[ Arctic foxesbase their diet on lemmings at densities so low thatwe had di.culties to trap even a single animal[ Thefunctional response curves are therefore unclear atlow densities[ Nevertheless\ there was a markeddi}erence in arctic fox preference between the lem!ming species\ with a steep functional response curvefor Lemmus[ At densities that were low relative toLemmus\ however\ there was still a considerable pro!portion of Dicrostonyx in the diet "Fig[ 7#[ This isexpected if it is important for arctic foxes to sampleprey densities in di}erent types of habitat within theirterritory[ Many of their prey species ~uctuate andthese ~uctuations are not always synchronized "e[g[

Batzli + Lesieutre 0884#[ Several studies have shownthat the arctic fox\ while often being dependent onlemmings for breeding\ is an extremely curious oppor!tunist that will utilize almost any type of food source"e[g[ Fay + Stephenson 0878^ Stickney 0878^ Birks +Penford 0889^ Hersteinsson + Macdonald 0885#[

A functional response curve of type III can becaused by prey switching or a longer handling time atlow prey densities "Taylor 0873#[ It is thus possiblethat arctic foxes search for Lemmus rather than forDicrostonyx at low densities[ The two lemming generaare found in di}erent habitats\ especially at low densit!ies\ with Lemmus in wet areas and Dicrostonyx indry areas "Rodgers + Lewis 0875#[ However\ it isimportant to note that the scale of habitat het!erogeneity is smaller than an arctic fox home rangeand both habitat types are normally available for asingle fox[ The second alternative\ that handling timeis longer for Dicrostonyx at lower densities than athigher densities and than for Lemmus\ is also possible[Because Dicrostonyx dig extensive burrows\ they maybe better protected against predation[ This would bemore pronounced at low population densities whenburrows and food are plentiful[ A similar phenom!enon was suggested by Hanski + Henttonen "0885#for Clethrionomys and Microtus rodents[

The total predatory response "the product of func!tional and numerical responses# determines the e}ectof predation on a prey population "Pech et al[ 0881#[We cannot quantify this total response in our material\but a qualitative comparison following Pech et al["0881# implies that the predation rate for Lemmuswill decrease with increasing prey density\ while it forDicrostonyx will increase at low to medium densitiesbut decrease at higher densities[ This suggests thatpredation by arctic foxes may regulate a populationof Dicrostonyx at low and moderate densities[ Accord!ing to theoretical models\ a time lag in numerical

36



response\ as the one observed for Lemmus\ might gen!erate cyclicity in a predatorÐprey system "Hanski +Korpima�ki 0884#[ Many authors have argued thatcyclic rodent oscillations in the northern boreal zoneare generated by mustelid predation "Hansson +Henttonen 0874^ 0877^ Hanski et al[ 0880\ 0882^ Han!ski + Korpima�ki 0884^ Hanski + Henttonen 0885^Turchin + Hanski 0886#[ Their models are based onthe fact that small mustelids are specialized predatorswith a type II functional response and a time lag innumerical response to rodent population ~uctuations[This system can not be applied to areas where mus!telids are absent\ e[g[ on the Wrangel Island[ However\arctic foxes might play the same role on the tundra asmustelids are suggested to do in boreal areas[ ForLemmus\ they have a time lag of approximately oneyear in their numerical response to prey populationpeaks and a functional response characteristic for aspecialized predator[ We therefore argue that forLemmus as prey\ the arctic fox falls into the generalcategory resident specialists "sensu Andersson +Erlinge 0866#\ where also small mustelids belong[ ForDicrostonyx\ arctic foxes instead act as generalists[The e}ect on these prey species will therefore be verydi}erent[

In conclusion\ arctic foxes seem to have the capacityto deepen and prolong the crash phase of Lemmuscycles and thereby increase both amplitude and periodof cycles "e[g[ Henttonen et al[ 0876^ Hanski + Kor!pima�ki 0884#[ For Dicrostonyx\ their predatory pat!terns instead suggests a capacity to dampen oscil!lations "Andersson + Erlinge 0866^ Turchin + Hanski0886#[ There was only one site with a very high Dicro!stonyx density\ the polar desert at Cape Chelyuskin"site 8# on the northernmost point on the Eurasianmainland[ It is possible that Dicrostonyx have anadvantage over Lemmus in this type of environment"Rodgers + Lewis 0875#[ The relationship between thearctic fox and a lemming species cannot be analysedin detail without taking other co!existing prey speciesinto account "cf[ Boutin 0884^ Pech et al[ 0884^ Sch!mitz 0884#[ For a more thorough understanding ofthe tundra community\ we also need data from areaswhere the lemming species are allopatric[ There alsoseems to be a need for theoretical models of popu!lation ~uctuations that include several prey species forwhich the predatory responses are di}erent "Schmitz0884^ Abrams + Matsuda 0885^ Hanski + Henttonen0885#[

Acknowledgements

V[ Fedorov and K[ Fredga trapped the collared lem!mings and several people\ especially E[ Isaksson andN[ Kjelle�n\ helped us with inventories of fox dens[ Weare immensely indebted to D[ Fucik for his patienceand skill in helping us with analyses of fox scats[ Wethank P[ Frodin\ D[ Hasselquist\ P[ Nilsson\ and M[Svensson for help with lemming trapping and ana!

lysing these data\ K[ Danell for providing unpublisheddata from his dendrochronological analyses\ and L[Baskin for translating Russian papers on lemmingstudies in Siberia[ We are very grateful to the SwedishPolar Secretariat for organizing the Tundra EcologyExpedition 0883[ Financial support was obtainedfrom NFR "BÐBU 2213Ð297# to Erlinge and Fredga\and from the Ymer foundation to Angerbjo�rn[

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Received 06 October 0886^ revision received 01 March 0887

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