Correlated cycles of snowshoe hares and Dall’ssheep lambs

J.F. Wilmshurst, R. Greer, and J.D. Henry

Abstract: We tested the hypothesis that the number of surviving lambs counted in mid-summer from a Dall’s sheep (Ovisdalli Nelson, 1884) population on Sheep Mountain, Yukon, Canada, is correlated to the density of snowshoe hares (Lepusamericanus Erxleben, 1777) in the surrounding boreal forest. We examined correlations between the number of lambsand the number of snowshoe hares at different phases in the 10-year snowshoe hare cycle. There were significant cross-correlations between the ratio of lambs to nursery sheep and hare densities with 1- and 2-year time lags. Lamb numbersalso showed clockwise rotation with respect to hare densities when points were joined chronologically. Simple popula-tion models suggest several relationships: when hare densities are high, lamb population growth rates are inversely re-lated to hare densities; during the low phase of the hare population cycle, lamb population growth rates show density-independent fluctuations. In the absence of compelling evidence for direct interactions between Dall’s sheep and hares,we hypothesize that the inverse relationship between lamb population growth and hare density is mediated indirectlyby shared predators.

Resume : Nous evaluons l’hypothese selon laquelle le nombre d’agneaux survivants recenses en mi-ete dans une popula-tion de mouflons de Dall (Ovis dalli Nelson, 1884) sur Sheep Mountain, Yukon, Canada, est en correlation avec la densitedes lievres d’Amerique (Lepus americanus Erxleben, 1777) dans la foret boreale avoisinante. Nous examinons les correla-tions entre les nombres d’agneaux et de lievres dans les differentes phases du cycle de 10 ans du lievre d’Amerique. Il y ades correlations croisees significatives entre le rapport numerique des agneaux sur les moutons de nursery, d’une part, etles densites de lievres, d’autre part, mais avec des decalages temporels de 1 et 2 ans. Les nombres d’agneaux subissentaussi une rotation dans le sens des aiguilles d’une montre par rapport aux densites de lievres lorsque les points sont reunischronologiquement. Des modeles demographiques simples indiquent plusieurs relations possibles: lorsque les densites delievres sont elevees, les taux de croissance des populations d’agneaux sont inversement proportionnels aux densites de lie-vres. Dans la phase minimale du cycle demographique des lievres, les taux de croissance des populations d’agneaux subis-sent des fluctuations independantes de la densite. En l’absence de preuves incontestables d’interactions directes entre lesmouflons de Dall et les lievres, nous avancons l’hypothese selon laquelle la relation inverse qui existe entre la croissancede la population d’agneaux et la densite des lievres s’etablit indirectement par l’intermediaire de predateurs communs.

[Traduit par la Redaction]

IntroductionPopulation cycles in natural communities have long been

of both theoretical and empirical interest for ecologists(Elton 1924; Chitty 1960; Kendall et al. 1999; Berryman2002). Clear temporal patterns that are the hallmark of pop-ulation cycles can help identify interactions among popula-tions and their ecosystems (Krebs et al. 2001b). Incommunities containing one or more cycling populations, di-rect links either between predators and prey (Norrdahl andKorpimaki 1996; Korpimaki and Norrdahl 1998) or betweensympatric consumers sharing food resources (Boutin et al.1995; Schmidt and Ostfeld 2003) have often been observed.Indirect links between allopatric species sharing either com-mon predators or resources are less common (Bety et al.2002; Blomqvist et al. 2002). Yet, theory and controlled ex-periments suggest that such indirect links between spatiallydistinct populations should be possible either where sharedpredators range widely (Ostman and Ives 2003) or where ex-

ternal, large-scale, and periodic control is exerted on foodresources (Martin et al. 2001).

The snowshoe hare (Lepus americanus Erxleben, 1777)cycle has been extensively studied (Krebs et al. 2001a,2001b). Henry (2002) reviewed the biology of the snowshoehare and some of the research conducted on this cycle. Re-peating approximately every 8–11 years, the cycle consistsof a gradual increase in the hare population followed by asudden decline and then 3–4 years of low hare densities.The main predators of snowshoe hares have a similar cyclewith a 1- to 2-year time lag behind the hares.

A striking characteristic of the snowshoe hare cycle is thedegree of synchrony that occurs in this cycle across the bor-eal forest of North America (Krebs et al. 2001a; Henry2002). A recently completed long-term experiment in theKluane region of the southwest Yukon Territory, Canada,demonstrated that predation is the proximal cause of the de-cline of the hare population in each cycle (Krebs et al.

Received 16 June 2005. Accepted 10 March 2006. Published on the NRC Research Press Web site at http://cjz.nrc.ca on 7 June 2006.

J.F. Wilmshurst.1 Parks Canada, 145 McDermot Avenue, Winnipeg, MB R3B 0R1, Canada.R. Greer and J.D. Henry. Kluane National Park and Reserve, P.O. Box 5495, Haines Junction, YT Y0B 1L0, Canada.

1Corresponding author (e-mail: John.Wilmshurst@pc.gc.ca).

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2001b). However, the factors (likely food and predation)that contribute to the 10-year timing of the cycle (Ruesinket al. 2002), the exact causes of the sustained low phaseafter the crash (Boonstra et al. 1998; Hodges et al. 1999),and the phenomena that synchronize the cycle across theboreal forest region of North America (Sinclair and Gosline1997) have yet to be conclusively determined. It is clear thatthe hare cycle itself is an important driver of biotic interac-tions in the boreal forest (Krebs et al. 2001b). From thelagged cycling of their terrestrial predators, such as the lynx(Lynx canadensis Kerr, 1792) and coyote (Canis latransSay, 1823) (Elton and Nicholson 1942; O’Donoghue et al.1997), to the effects of hare browsing intensity on the phe-nol concentration of adventitious shoots in boreal foresttrees (Bryant 1981; Henry 2002), the ebb and flow of thehare population influences many species in the boreal forestcommunity (Krebs et al. 2001b).

Indirect effects of the snowshoe hare cycle have not beenextensively studied. In Stenseth et al.’s (1997) illustration ofthe links to snowshoe hares in the boreal food web (Boutinet al. 1995; Krebs et al. 1995), the golden eagle (Aquilachrysaetos L., 1758), American kestrel (Falco sparveriusL., 1758), moose (Alces alces L., 1758), spruce grouse(Canachites canadensis L., 1758), and willow ptarmigan(Lagopus lagopus L., 1758) were the only animal speciesidentified with indirect links. Boutin et al. (1995) found thatonly the population changes of spruce grouse and willowptarmigan correlated with changes in snowshoe hare den-sities. Golden eagles are known to predate snowshoe haresin parts of their range (Scotton 1997; Arthur 2003; Prugh2005), so their interaction with snowshoe hares in theKluane region may also be direct.

Dall’s sheep (Ovis dalli Nelson, 1884) have not been pre-viously considered as a species interacting with snowshoehares in the Kluane ecosystem. However, 30 years of moni-toring data of the Dall’s sheep population on Sheep Moun-tain, Yukon Territory, adjacent to the snowshoe hare studyarea, suggest that low counts on the nursery range (whereewes, lambs, and non-breeding yearlings aggregate afterlambing season) consistently follow peak densities of snow-shoe hares (Greer 2004). Here, we use time-series analysisto verify the consistency of this observation and, using sur-vey data, we test three hypotheses that could account for thisobservation. First, we test the hypothesis that there is directcompetition between these two populations. This hypothesispredicts that there should be evidence for shared use of alimiting resource (e.g., food, mineral licks), little or no timelag between the population dynamics of hares and sheep,and a negative relationship between hare densities and lambcounts. Second, we test the hypothesis that the populationsare responding to a common external cue, such as weather(Ranta et al. 1999) or a celestial event (Sinclair and Gosline1997), that may be synchronizing the population patterns ofnursery sheep and hares without there being any interactionbetween these two populations. This hypothesis predicts thatthe population responses will be simultaneous and that theirhighs and lows will correspond. Lastly, we test the hypothe-sis that there is an indirect interaction between the popula-tions, such as a common predator. This hypothesis predictsthat there should be a time lag between the dynamics ofone population and those of the other as the predator

switches from one food source to another (Pech and Hood1998) and that this interaction should be negative; i.e., a de-cline in the first prey population should correspond to a pop-ulation high in the second prey population.

Materials and methods

Animal surveys have been conducted in the greaterKluane ecosystem in the Yukon Territory, Canada, since1974. In most years, aerial Dall’s sheep surveys were con-ducted on Sheep Mountain (61803’N, 139835’W) in theKluane National Park and Reserve of Canada (KNPR) dur-ing mid-summer, when dependent lambs are discernablefrom the air. Because the Sheep Mountain population ap-pears to occupy a discrete and well-defined range, each sur-vey was conducted on a single day using a ‘‘total count’’methodology from a helicopter (Caughley 1977). In thesesurveys, the number of individuals in each of three sex/ageclasses (rams, young-of-year, and nursery groups) was re-corded. Nursery groups consist of females and immaturemales that are closely associated and are indistinguishablefrom the air. Throughout this study we refer to sheep fromthis group as nursery sheep (NS).

Since 1977, snowshoe hare surveys have been conductedin the white spruce (Picea glauca (Moench) Voss) domi-nated forests in the valley bottoms and on the lower moun-tain slopes adjacent to KNPR. Snowshoe hares weresurveyed using livetrapping techniques on the experimentaland control plots that made up the Kluane Boreal ForestEcosystem Project 1986–1996 (Krebs et al. 2001b). Live-trapping of hares was conducted on eight grids, each 60 hain size, located within the study area. Between 1977 and2004, trapping has been conducted twice annually (springand fall) and the density estimate calculated as the mean ofthe two annual trapping events (Krebs et al. 2001c). Haredensities were calculated from the livetrapping data usingJolly–Seber mark–recapture analysis (Krebs 1989).

Our mensurative data do not permit a direct test of the hy-pothesis that the lamb and hare population cycles are linked;however, we tested the plausibility of the hypothesis throughcorrelative and graphical analyses, and we examined thepredictions of the hypothesis using population models. Allanalyses were conducted on hare densities (number/ha) andthe number of lambs counted during the Sheep Mountainaerial surveys. Lamb counts were log-transformed for analy-ses, but we found no significant relationship between lamband NS counts (P = 0.954), meaning that we did not haveto adjust lamb counts for variation in the NS population.

First, to determine whether hare densities and lamb num-bers were positively or negatively related, we comparedhare densities and lamb numbers for each year using sim-ple correlation procedures in SYSTAT1 11 (Systat Soft-ware Inc. 2004); Bonferroni probabilities and Bartlett’s w2

statistic were used to estimate significance. Data were log-transformed to meet normality and homogeneity of var-iance assumptions. We tested for both significant linearand significant quadratic trends in the direct relationshipbetween hare densities and lamb numbers. This test al-lowed us to distinguish the first and third hypotheses,which predict a negative relationship between lamb and

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hare populations, from the second hypothesis, which pre-dicts a positive relationship.

Second, we measured the synchrony of the two popula-tions using time-series analysis. Using the SERIES proce-dure in SYSTAT1 11, we calculated cross-correlations ofsnowshoe hare densities and lamb numbers at time lagsfrom 0 to 10 years for three 10-year snowshoe hare popula-tion cycles. We tested first for temporal trends in the databefore proceeding with time-series analysis. This test al-lowed us to distinguish the third hypothesis (indirect compe-tition), which predicts a time lag, from the second (externalcontrol) and first (direct competition) hypotheses, which pre-dict little or no time lag between population responses.

Third, we plotted hare density versus lamb numbers as‘‘phase plane’’ diagrams in which consecutive data pointswere connected to show the continuous temporal sequenceof hare density and lamb numbers. Population cycles mayhave distinct increasing, decreasing, high, and low phasesfor which mechanistic explanations are commonly sought(Boonstra et al. 1998). While time-series analysis and gen-eral linear modelling are effective at identifying the strengthof the interaction between study populations, they do nothighlight the simultaneous behaviour of each population.While this does not provide a statistical test of the data, itdoes give important insights into the temporal pattern of thehare and sheep interaction that, by replicating with models,can point to mechanisms, if any, that could be responsiblefor the observed cycles.

Finally, to identify the key variables in the sheep–hare in-teraction, we constructed three simple population models inVisual BASIC1 (Microsoft Corporation 2001). Because ourpurpose was to understand the interactions that are key tothe cyclic behaviour, as opposed to simulating the sheep–hare interaction per se, we chose greatly simplified parame-ter combinations. In the first model we created an oscillatinghare population by setting the finite growth rate (l) to an ar-bitrarily high value (1.2) when the hare population was low(<300) and to a low value (0.8) when the hare populationwas high (‡300). These parameter values accomplished thegoal of having two oscillating (cycling) but stationary (nolong-term increase or decrease) populations. In the secondmodel we modified the hare dynamics by imposing a 5-yearlow phase before a return to higher growth rates at low haredensities. During the low, the hare population fluctuated ran-domly, with a l between 0.96 and 1.01, and we made thelamb population density-dependent by inversely relating itto its own density at low hare densities. In the third modelwe removed all density dependence in the lamb populationand allowed it to vary between 0.8 and 1.27 (mean slightlygreater that 1.0) at the low phase of the hare cycle, simulat-ing density-independent dynamics.

Results and discussionSnowshoe hare densities peaked in the Kluane area in

1980–1981, 1988–1990, and 1997–1998 (Fig. 1). After eachpeak, the hare population declined abruptly and remainedlow for 3–4 years before increasing again (Fig. 1). Lambnumbers showed more erratic dynamics with time but,nevertheless, peaks and valleys appeared. Although peakswere evident in 1978–1979, 1988–1989, and 1996–1997,

the population densities between these peaks were more var-iable than those observed for the snowshoe hares (Fig. 1).

The correlation between concurrent hare densities andlamb numbers was low (Pearson’s coefficient = 0.058)and the significance test of the correlation was negative(Bartlett’s w2 = 0.101, Bonferroni probability = 0.75). Thisresult is consistent with the indirect competition hypothesisbut is not consistent with either the external cue or the di-rect competition hypothesis.

Before testing for cross-correlations between hare den-sities and lamb numbers, we analyzed the data for trends(to see whether either population was increasing or decreas-ing) and temporal autocorrelation. Using linear regression,we determined that neither the lamb (P = 0.674) nor thesheep (P = 0.765) population had an increasing or decreasingtrend over the study period. Analysis of the lamb numbersfor autocorrelation revealed a positive correlation at 9 yearsapproaching the 95% confidence interval threshold for sig-nificance (Fig. 2a). No other period was close to signifi-cance, supporting the approximate 10-year cyclicity of ourlamb data set. A partial autocorrelation plot revealed a sig-nificant positive correlation at 9 years (Fig. 2b), reflectingdirect density dependence in the cycling pattern of thelambs, and a negative correlation at 10 years that ap-proached significance. This reflects a degree of delay inthe density-dependent interaction (Williams et al. 2004).

Time-series analysis of hares and lambs revealed signifi-cant cross-correlations between the hare densities and lambnumbers that exceeded an absolute Pearson’s coefficient of0.5 with 1- and 2-year lags (Fig. 3). One to two years priorto the hare peak, lamb densities are also increasing, whilelamb densities decline 1–2 years after hare densities beginto decline. Thus, time-series analysis confirmed what theraw data plots suggested; that is, during most years lambnumbers are highest before the hare population peaks (ashare densities are increasing) and lowest in the 2 years di-rectly after the hare population peaks. This supports the ob-

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Fig. 1. Snowshoe hare (Lepus americanus) densities from theKluane Boreal Forest Project study area (solid line) and Dall’ssheep (Ovis dalli) lamb counts from annual Sheep Mountain aerialsurveys (dashed line). Hare data are mean annual counts fromspring and fall livetrapping events and are available from http://www.zoology.ubc.ca/~krebs.

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servation that the dynamics of the two populations are inter-acting but is inconsistent with the hypothesis that an exter-nal cue is synchronizing the two populations, given the lackof synchrony and the negative relationship. The lack of syn-chrony is also inconsistent with the direct competition hy-pothesis. Hence, the only hypothesis of the three that wecannot reject is that of indirect competition.

Plotting lamb numbers against hare densities in phaseplane diagrams revealed clockwise cycling of hare densitiesversus lamb numbers with a periodicity of approximately 9years (Fig. 4). Clockwise cycling of lamb numbers with re-spect to hare densities signifies predominantly negative in-teractions between populations. When hare densities werehigh, lamb numbers consistently declined from one year to

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Fig. 2. Autocorrelation (a) and partial autocorrelation (b) plots of Dall’s sheep lamb counts from 1977 to 2004. Bars represent the ordinaryPearson’s correlation (r) between the number of lambs counted in a year and those counted in another year at the specified annual time lag.Lines above and below the bars are 95% confidence limits that approximate significance.

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the next, and when hare densities were low, lamb countstended to increase, although not as consistently as they de-clined when hare densities were high (Fig. 5). However,from the perspective of the hare population, positive interac-tions are evident. The data also correlate well going theother way. When lamb numbers were high, hares tended toincrease, and when lamb numbers were low, hares tended todecrease. Nevertheless, we assumed that the hares are driv-ing the interaction, given their status as keystone (Sinclair2003) in the ecosystem, and so we pursued the analysisfrom the perspective of the sheep population responding tohare densities.

Our model of potential interactions suggested that clock-wise phase cycling most likely occurs under two conditions:first, increases in lamb numbers are inversely related to haredensity at high hare densities, and second, changes in lambnumbers vary independently of hares at low hare densities.Using simple growth models, we altered two variables: thepattern of hare population cycles and the growth rate of thelamb population at low hare densities. Models that did nothave a lag phase to the hare population cycle did not showany phase plane rotation but rather simple oscillations be-

tween alternate density states (Fig. 6a). Simulating the longlow phase of the hare cycle improved the model’s ability toreplicate cycles in both populations. Additionally, incorpo-rating density dependence within the sheep population(lamb population growth rate dependent upon lamb density)at low hare densities produced rough cycles that approachedthose we observed in our data (Fig. 6b). Indeed, this is likelythe direct and delayed density dependence that the partialautocorrelation data revealed at 9 and 10 years. Only whenwe included three parameters (10-year hare cycles with ex-tended low phases and punctuated population highs, lowlamb population growth rates at high hare densities, and var-iable low or high lamb population growth at low hare den-sities) did the result resemble the symmetrical cycling thatwe observed in the field data (Fig. 6c). These simulationssuggest that for such interspecific cycling to occur consis-tently, there has to be a relaxed phase (a lag) in the dynam-ics of the dominant species (hares in this case) that enablesthe other species to increase before the negative effects ofthe dominant species recur. What is also evident is that thegrowth rate of the lamb population, in this case, should berelatively low during the hare population lag and may evenfluctuate haphazardly, perhaps in a density-independentfashion. Pure density dependence of the lamb populationwhen hares are scarce also did not result in smooth cycling.

Demographic data suggest that peaks in this sheep popu-lation coincide with several other attributes: high lambcrops, high recruitment of lambs to yearlings, and high over-winter survival of adults (Hoefs and Bayer 1983). Further-more, peaks seem to be determined by winter range forageproduction (Hoefs and Bayer 1983). Hence, it would appearpossible that sheep population growth is influenced by foodavailability, at least at peak sheep densities. Additionally,there is experimental evidence in relation to the snowshoehare cycle that herb and shrub growth in the Kluane ecosys-tem is under donor (nutrient) control rather than control bygrazing herbivores (Turkington et al. 2001).

Portier et al. (1998) found that density-dependent factorsaffected the survival of bighorn sheep lambs (Ovis canaden-sis Shaw, 1804) in Alberta, and they suggested that springforage availability was the agent of density dependence.The feedback between forage availability and survival mayalso operate in Dall’s sheep because they share several traits

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Fig. 4. Symmetrical phase diagrams of Dall’s sheep lamb counts plotted against snowshoe hare densities. Points are joined in sequence byyear and are divided into three panels, each representing a cycle beginning and ending with low hare density.

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Fig. 5. Schematic illustrating the rotation of the lamb and hare cy-cle. At high hare densities, lamb counts show a downward trend; atlow hare densities, downward pressure is less. However, upwardpressure on lamb numbers is high when lamb densities are low(density dependence). Therefore, when lamb densities are high andhare densities are low, upward pressures are weaker, as indicatedby the dashed line.

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with bighorn sheep, namely physical and behavioural adap-tations for surviving harsh winters and a strong dependencyupon high-quality spring forage to rebuild fat and protein re-serves (Burles and Hoefs 1984).

It seems unlikely that there is a direct interaction (e.g.,food competition, facilitation) between sheep and hares.Dall’s sheep are predominantly grazers with a diet consist-ing largely of grass and sedges (66%) and some forbs andshrubs (17%) (Nichols 1978). Hares are predominantlybrowsers, with shrubs constituting more than 80% of theirwinter diet and more than 50% of their summer diet (forbsconstitute most of the remainder of their summer diet andare usually plentiful) (Wolff 1980; Sinclair et al. 1982). Ad-ditionally, Dall’s sheep occupy steep alpine slopes andmeadows in this region (Burles and Hoefs 1984), whereassnowshoe hares occupy the subalpine and valley-bottom bor-eal forests (Krebs et al. 2001b). However, it is not unheardof for hares to compete for food with ungulates (Hulbert andAndersen 2001), and hares can facilitate food intake bygeese, as found in the Netherlands (van der Wal et al.2000). As well, it is possible that at peak hare densities inthe Kluane region, when high-quality food for hares be-comes scarce in the valley bottoms, hares may expand theirdiet to include non-preferred items that overlap with theDall’s sheep diet. We have not observed this, nor could wefind any published reports of this, but such behaviour coulddrive cycles in Dall’s sheep lambs like the ones we have ob-served. Nevertheless, we think that the hypothesis suggest-ing a direct link between Kluane sheep and the adjacentsnowshoe hare population through food competition or facil-itation is unlikely to be strongly supported because the hab-itats and diets of these two species differ so much.

External cues that synchronize spatially separated popula-tions have been studied for some time (Moran 1953; Bjorn-stad 2000). This ‘‘Moran effect’’ poses that either dispersalor some large-scale external (climatic or celestial) eventsserve as either a cue or a driver for population cycles andexplain their remarkable synchrony across continents (Sin-clair et al. 1993; Sinclair and Gosline 1997; Ranta et al.1999; Post and Forchhammer 2002). Although the Moran ef-fect specifically refers to disjunct populations of the same

species (hence dispersal is a potential driver), it is relevantto our study of interspecific cycles through its reference toclimatic or celestial cues. It seems reasonable that herbi-vores of any species should be affected by the same cyclicvariation in the quality or abundance of herbage, even iftheir diets do not strongly overlap. However, our analysesdo not support this hypothesis, principally due to the timelag between the increases and decreases in the lamb andhare populations. Hence, we conclude that it is unlikely thatthe relationships we have documented are due to an externalcue.

Alternatively, indirect interactions between hares andsheep mediated through common predators seem plausible(Comins and Hassel 1976; Bety et al. 2002). The dominantpredator of adult Dall’s sheep in the Kluane area is the coy-ote, whereas coyotes, lynx (Burles and Hoefs 1984; Frid1997), and golden eagles (C.L. McIntyre, personal commu-nication) are the main predators of lambs. Both lynx andcoyotes are effective mammalian predators of snowshoehares (O’Donoghue et al. 1997), and golden eagle nestingsuccess may be linked to snowshoe hare densities in Alaska(Prugh 2005). Frid (1997) reported that predation pressurefrom lynx and coyotes on lambs was low during his study,and he attributed this to low hare densities adjacent to hisstudy area. Coyote densities undergo wide fluctuations in re-sponse to snowshoe hare densities across their geographicdistribution (Todd et al. 1981). Hence, conditions exist forthe population dynamics of lambs, as secondary prey oflynx, coyotes, and eagles, to be affected indirectly by thepopulation density of snowshoe hares via their commonpredators.

That a shared predator of hares and lambs is responsiblefor correlated cycles in these two populations implies by def-inition that the predator is a generalist. However, predator–prey dynamics involving generalist predators should bedirectly density-dependent and should not induce popula-tion cycles (Hanski et al. 1991; Williams et al. 2004).How is it, then, that we observe cyclic dynamics with ageneralist predator in Kluane? The most prominent cyclicpatterns in the Kluane system occur among the snowshoehare, its specialist predators (lynx and great-horned owls

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Fig. 6. Population model output illustrating three feasible interaction scenarios for snowshoe hares and Dall’s sheep. In panel a, sheeppopulation growth is inversely related to hare density and hare population growth is strictly density-dependent. In panel b, sheep populationgrowth at low hare densities has been changed to be self-regulating (density-dependent) and independent of hare densities. In panel c, sheeppopulation growth is density-independent when hare densities are low. In panels b and c, a 4-year duration of the low phase of the harepopulation cycle has been imposed.

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(Bubo virginianus Gmelin, 1788)), and its food supply(Krebs et al. 2001b). Coyote populations also cycle in re-sponse to hare densities (O’Donoghue et al. 1997), but be-cause coyotes are generalist predators, this predatorpopulation affects not only its primary prey, the snowshoehare, but also secondary prey such as Dall’s sheep lambs.Hence, our reasoning does not rely on a generalist predatorcausing cycling in Dall’s sheep lambs, but is based on thelamb population being affected by the cyclic dynamics ofthe snowshoe hare via a common predator.

In conclusion, the dynamics of Dall’s sheep lamb num-bers appear to be dependent upon two factors. The first is adepressing effect on lamb numbers of high hare densitieswith a 1- or 2-year time lag. We hypothesize that this is re-lated to the abundance of predators that are maintained byhares but take lambs either as a secondary prey item (whenhares are abundant) or as a primary prey item (when haresare scarce). To establish this as the mechanism of the cyclesin the Dall’s sheep lamb population (as opposed to alterna-tives such as shared food resources) will require further studyof the functional responses of predators in this ecosystem.The second factor is density-independent fluctuations in lambnumbers (with an increasing tendency) during the relativelylong low phase of the hare population cycle. We contendthat it is more likely a release from predation accompanyingthe hare crash rather than any increase in food availabilitythat permits lamb number increases during this phase.

AcknowledgementsThe authors thank M. Hoefs, D. Hik, C. Krebs, C. McIntyre,

L. Prugh, T. Skjonsberg, J. Toews, and two anonymous re-viewers for comments on earlier drafts. We also acknowledgethe considerable work completed by the Warden Service ofKluane National Park and Reserve in carrying out theDall’s sheep surveys since 1974 and, in particular, the con-tribution of R. Greer in identifying a pattern that he feltmust be important. Thanks also to C. Krebs for providing thesnowshoe hare data. This study was supported by the ParksCanada Agency and the Kluane Ecological Monitoring Project.

ReferencesArthur, S.M. 2003. Interrelationships of Dall sheep and predators in

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