This study examines the relationship between snowshoe hare densities and Dall's sheep lamb numbers in Yukon, Canada. The researchers analyzed correlations between lamb counts and hare densities over different phases of the 10-year hare cycle. They found significant correlations with 1-2 year time lags, suggesting the populations are indirectly linked through shared predators. When hare densities are high, lamb population growth is inversely related to hare density. During low hare phases, lamb growth fluctuates independently of density. The researchers hypothesize that the inverse relationship between lamb growth and hare density is mediated by predators switching between the two prey sources as densities change.

1. Correlated cycles of snowshoe hares and Dall’s
sheep 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 (Ovis
dalli Nelson, 1884) population on Sheep Mountain, Yukon, Canada, is correlated to the density of snowshoe hares (Lepus
americanus Erxleben, 1777) in the surrounding boreal forest. We examined correlations between the number of lambs
and 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 numbers
also 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 indirectly
by shared predators.
Re´sume´ : Nous e´valuons l’hypothe`se selon laquelle le nombre d’agneaux survivants recense´s en mi-e´te´ dans une popula-
tion de mouflons de Dall (Ovis dalli Nelson, 1884) sur Sheep Mountain, Yukon, Canada, est en corre´lation avec la densite´
des lie`vres d’Ame´rique (Lepus americanus Erxleben, 1777) dans la foreˆt bore´ale avoisinante. Nous examinons les corre´la-
tions entre les nombres d’agneaux et de lie`vres dans les diffe´rentes phases du cycle de 10 ans du lie`vre d’Ame´rique. Il y a
des corre´lations croise´es significatives entre le rapport nume´rique des agneaux sur les moutons de nursery, d’une part, et
les densite´s de lie`vres, d’autre part, mais avec des de´calages temporels de 1 et 2 ans. Les nombres d’agneaux subissent
aussi une rotation dans le sens des aiguilles d’une montre par rapport aux densite´s de lie`vres lorsque les points sont re´unis
chronologiquement. Des mode`les de´mographiques simples indiquent plusieurs relations possibles: lorsque les densite´s de
lie`vres sont e´leve´es, les taux de croissance des populations d’agneaux sont inversement proportionnels aux densite´s de lie`-
vres. Dans la phase minimale du cycle de´mographique des lie`vres, les taux de croissance des populations d’agneaux subis-
sent des fluctuations inde´pendantes de la densite´. En l’absence de preuves incontestables d’interactions directes entre les
mouflons de Dall et les lie`vres, nous avanc¸ons l’hypothe`se selon laquelle la relation inverse qui existe entre la croissance
de la population d’agneaux et la densite´ des lie`vres s’e´tablit indirectement par l’interme´diaire de pre´dateurs communs.
[Traduit par la Re´daction]
Introduction
Population cycles in natural communities have long been
of both theoretical and empirical interest for ecologists
(Elton 1924; Chitty 1960; Kendall et al. 1999; Berryman
2002). 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). In
communities containing one or more cycling populations, di-
rect links either between predators and prey (Norrdahl and
Korpimaki 1996; Korpimaki and Norrdahl 1998) or between
sympatric 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 spatially
distinct populations should be possible either where shared
predators range widely (Ostman and Ives 2003) or where ex-
ternal, large-scale, and periodic control is exerted on food
resources (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 snowshoe
hare and some of the research conducted on this cycle. Re-
peating approximately every 8–11 years, the cycle consists
of a gradual increase in the hare population followed by a
sudden decline and then 3–4 years of low hare densities.
The main predators of snowshoe hares have a similar cycle
with a 1- to 2-year time lag behind the hares.
A striking characteristic of the snowshoe hare cycle is the
degree of synchrony that occurs in this cycle across the bor-
eal forest of North America (Krebs et al. 2001a; Henry
2002). A recently completed long-term experiment in the
Kluane 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).
736
Can. J. Zool. 84: 736–743 (2006) doi:10.1139/Z06-051 # 2006 NRC Canada

2. 2001b). However, the factors (likely food and predation)
that contribute to the 10-year timing of the cycle (Ruesink
et al. 2002), the exact causes of the sustained low phase
after the crash (Boonstra et al. 1998; Hodges et al. 1999),
and the phenomena that synchronize the cycle across the
boreal forest region of North America (Sinclair and Gosline
1997) have yet to be conclusively determined. It is clear that
the hare cycle itself is an important driver of biotic interac-
tions in the boreal forest (Krebs et al. 2001b). From the
lagged cycling of their terrestrial predators, such as the lynx
(Lynx canadensis Kerr, 1792) and coyote (Canis latrans
Say, 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 forest
trees (Bryant 1981; Henry 2002), the ebb and flow of the
hare population influences many species in the boreal forest
community (Krebs et al. 2001b).
Indirect effects of the snowshoe hare cycle have not been
extensively studied. In Stenseth et al.’s (1997) illustration of
the links to snowshoe hares in the boreal food web (Boutin
et al. 1995; Krebs et al. 1995), the golden eagle (Aquila
chrysaetos L., 1758), American kestrel (Falco sparverius
L., 1758), moose (Alces alces L., 1758), spruce grouse
(Canachites canadensis L., 1758), and willow ptarmigan
(Lagopus lagopus L., 1758) were the only animal species
identified with indirect links. Boutin et al. (1995) found that
only the population changes of spruce grouse and willow
ptarmigan correlated with changes in snowshoe hare den-
sities. Golden eagles are known to predate snowshoe hares
in parts of their range (Scotton 1997; Arthur 2003; Prugh
2005), so their interaction with snowshoe hares in the
Kluane region may also be direct.
Dall’s sheep (Ovis dalli Nelson, 1884) have not been pre-
viously considered as a species interacting with snowshoe
hares 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 study
area, suggest that low counts on the nursery range (where
ewes, lambs, and non-breeding yearlings aggregate after
lambing season) consistently follow peak densities of snow-
shoe hares (Greer 2004). Here, we use time-series analysis
to verify the consistency of this observation and, using sur-
vey data, we test three hypotheses that could account for this
observation. First, we test the hypothesis that there is direct
competition between these two populations. This hypothesis
predicts that there should be evidence for shared use of a
limiting resource (e.g., food, mineral licks), little or no time
lag between the population dynamics of hares and sheep,
and a negative relationship between hare densities and lamb
counts. Second, we test the hypothesis that the populations
are responding to a common external cue, such as weather
(Ranta et al. 1999) or a celestial event (Sinclair and Gosline
1997), that may be synchronizing the population patterns of
nursery sheep and hares without there being any interaction
between these two populations. This hypothesis predicts that
the population responses will be simultaneous and that their
highs 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 predicts
that there should be a time lag between the dynamics of
one population and those of the other as the predator
switches from one food source to another (Pech and Hood
1998) 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 greater
Kluane ecosystem in the Yukon Territory, Canada, since
1974. In most years, aerial Dall’s sheep surveys were con-
ducted on Sheep Mountain (61803’N, 139835’W) in the
Kluane National Park and Reserve of Canada (KNPR) dur-
ing mid-summer, when dependent lambs are discernable
from 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 these
surveys, the number of individuals in each of three sex/age
classes (rams, young-of-year, and nursery groups) was re-
corded. Nursery groups consist of females and immature
males that are closely associated and are indistinguishable
from the air. Throughout this study we refer to sheep from
this group as nursery sheep (NS).
Since 1977, snowshoe hare surveys have been conducted
in 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 were
surveyed using livetrapping techniques on the experimental
and control plots that made up the Kluane Boreal Forest
Ecosystem Project 1986–1996 (Krebs et al. 2001b). Live-
trapping of hares was conducted on eight grids, each 60 ha
in size, located within the study area. Between 1977 and
2004, trapping has been conducted twice annually (spring
and fall) and the density estimate calculated as the mean of
the two annual trapping events (Krebs et al. 2001c). Hare
densities were calculated from the livetrapping data using
Jolly–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 through
correlative and graphical analyses, and we examined the
predictions of the hypothesis using population models. All
analyses were conducted on hare densities (number/ha) and
the number of lambs counted during the Sheep Mountain
aerial surveys. Lamb counts were log-transformed for analy-
ses, but we found no significant relationship between lamb
and NS counts (P = 0.954), meaning that we did not have
to 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 compared
hare 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 linear
and significant quadratic trends in the direct relationship
between 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
Wilmshurst et al. 737
# 2006 NRC Canada

3. 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 of
snowshoe hare densities and lamb numbers at time lags
from 0 to 10 years for three 10-year snowshoe hare popula-
tion cycles. We tested first for temporal trends in the data
before 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 (external
control) 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 points
were connected to show the continuous temporal sequence
of hare density and lamb numbers. Population cycles may
have distinct increasing, decreasing, high, and low phases
for which mechanistic explanations are commonly sought
(Boonstra et al. 1998). While time-series analysis and gen-
eral linear modelling are effective at identifying the strength
of the interaction between study populations, they do not
highlight the simultaneous behaviour of each population.
While this does not provide a statistical test of the data, it
does give important insights into the temporal pattern of the
hare and sheep interaction that, by replicating with models,
can point to mechanisms, if any, that could be responsible
for the observed cycles.
Finally, to identify the key variables in the sheep–hare in-
teraction, we constructed three simple population models in
Visual BASIC1 (Microsoft Corporation 2001). Because our
purpose was to understand the interactions that are key to
the 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 oscillating
hare 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 population
was high (‡300). These parameter values accomplished the
goal of having two oscillating (cycling) but stationary (no
long-term increase or decrease) populations. In the second
model we modified the hare dynamics by imposing a 5-year
low phase before a return to higher growth rates at low hare
densities. During the low, the hare population fluctuated ran-
domly, with a l between 0.96 and 1.01, and we made the
lamb population density-dependent by inversely relating it
to its own density at low hare densities. In the third model
we removed all density dependence in the lamb population
and allowed it to vary between 0.8 and 1.27 (mean slightly
greater that 1.0) at the low phase of the hare cycle, simulat-
ing density-independent dynamics.
Results and discussion
Snowshoe hare densities peaked in the Kluane area in
1980–1981, 1988–1990, and 1997–1998 (Fig. 1). After each
peak, the hare population declined abruptly and remained
low for 3–4 years before increasing again (Fig. 1). Lamb
numbers showed more erratic dynamics with time but,
nevertheless, peaks and valleys appeared. Although peaks
were 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 and
lamb 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). This
result is consistent with the indirect competition hypothesis
but 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 the
sheep (P = 0.765) population had an increasing or decreasing
trend over the study period. Analysis of the lamb numbers
for autocorrelation revealed a positive correlation at 9 years
approaching 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 our
lamb data set. A partial autocorrelation plot revealed a sig-
nificant positive correlation at 9 years (Fig. 2b), reflecting
direct density dependence in the cycling pattern of the
lambs, and a negative correlation at 10 years that ap-
proached significance. This reflects a degree of delay in
the density-dependent interaction (Williams et al. 2004).
Time-series analysis of hares and lambs revealed signifi-
cant cross-correlations between the hare densities and lamb
numbers that exceeded an absolute Pearson’s coefficient of
0.5 with 1- and 2-year lags (Fig. 3). One to two years prior
to the hare peak, lamb densities are also increasing, while
lamb densities decline 1–2 years after hare densities begin
to decline. Thus, time-series analysis confirmed what the
raw data plots suggested; that is, during most years lamb
numbers are highest before the hare population peaks (as
hare densities are increasing) and lowest in the 2 years di-
rectly after the hare population peaks. This supports the ob-
1974 1984 1994 2004
YEAR
0
1
2
3
0
25
50
75
100
HAREDENSITY(no./ha)
LAMBCOUNT
Fig. 1. Snowshoe hare (Lepus americanus) densities from the
Kluane Boreal Forest Project study area (solid line) and Dall’s
sheep (Ovis dalli) lamb counts from annual Sheep Mountain aerial
surveys (dashed line). Hare data are mean annual counts from
spring and fall livetrapping events and are available from http://
www.zoology.ubc.ca/~krebs.
738 Can. J. Zool. Vol. 84, 2006
# 2006 NRC Canada

4. 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 lack
of 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 we
cannot reject is that of indirect competition.
Plotting lamb numbers against hare densities in phase
plane diagrams revealed clockwise cycling of hare densities
versus lamb numbers with a periodicity of approximately 9
years (Fig. 4). Clockwise cycling of lamb numbers with re-
spect to hare densities signifies predominantly negative in-
teractions between populations. When hare densities were
high, lamb numbers consistently declined from one year to
0.0
0.5
1.0
(a)
0.5
1.0
(b)
LAG (Years)
LAG (Years)
PEARSONCORRELATIONPEARSONCORRELATION
Fig. 2. Autocorrelation (a) and partial autocorrelation (b) plots of Dall’s sheep lamb counts from 1977 to 2004. Bars represent the ordinary
Pearson’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.
0.5
1.0
0.0
-0.5
0.5
-1.0
-20 -10 0 10 20
LAG (Years)
PEARSONCORRELATION
Fig. 3. Cross-correlation plot of the ordinary Pearson’s correlation (r) for snowshoe hare densities and Dall’s sheep lamb numbers plotted
against annual time lags. Bars that cross the horizontal lines above and below the y-axis have significant cross-correlations.
Wilmshurst et al. 739
# 2006 NRC Canada

5. the next, and when hare densities were low, lamb counts
tended 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 the
other way. When lamb numbers were high, hares tended to
increase, and when lamb numbers were low, hares tended to
decrease. Nevertheless, we assumed that the hares are driv-
ing the interaction, given their status as keystone (Sinclair
2003) in the ecosystem, and so we pursued the analysis
from the perspective of the sheep population responding to
hare 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 hare
density at high hare densities, and second, changes in lamb
numbers vary independently of hares at low hare densities.
Using simple growth models, we altered two variables: the
pattern of hare population cycles and the growth rate of the
lamb population at low hare densities. Models that did not
have a lag phase to the hare population cycle did not show
any phase plane rotation but rather simple oscillations be-
tween alternate density states (Fig. 6a). Simulating the long
low phase of the hare cycle improved the model’s ability to
replicate 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 approached
those we observed in our data (Fig. 6b). Indeed, this is likely
the direct and delayed density dependence that the partial
autocorrelation data revealed at 9 and 10 years. Only when
we included three parameters (10-year hare cycles with ex-
tended low phases and punctuated population highs, low
lamb 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 that
we observed in the field data (Fig. 6c). These simulations
suggest 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 enables
the other species to increase before the negative effects of
the dominant species recur. What is also evident is that the
growth rate of the lamb population, in this case, should be
relatively low during the hare population lag and may even
fluctuate haphazardly, perhaps in a density-independent
fashion. Pure density dependence of the lamb population
when 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 lamb
crops, 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 forage
production (Hoefs and Bayer 1983). Hence, it would appear
possible that sheep population growth is influenced by food
availability, at least at peak sheep densities. Additionally,
there is experimental evidence in relation to the snowshoe
hare cycle that herb and shrub growth in the Kluane ecosys-
tem is under donor (nutrient) control rather than control by
grazing herbivores (Turkington et al. 2001).
Portier et al. (1998) found that density-dependent factors
affected the survival of bighorn sheep lambs (Ovis canaden-
sis Shaw, 1804) in Alberta, and they suggested that spring
forage availability was the agent of density dependence.
The feedback between forage availability and survival may
also operate in Dall’s sheep because they share several traits
0.0 0.2 0.4 0.6
1.0
1.2
1.4
1.6
1.8
2.0
77
83
84
85 81
80
82
79
78
(a)
0.0 0.2 0.4 0.6
HARE DENSITY (log )10
LAMBCOUNT(log)10
94
93
86
87
90
88
91
89
92
(b)
0.0 0.2 0.4 0.6
01
95
00
98
99
97
96
(c)
Fig. 4. Symmetrical phase diagrams of Dall’s sheep lamb counts plotted against snowshoe hare densities. Points are joined in sequence by
year and are divided into three panels, each representing a cycle beginning and ending with low hare density.
HARE DENSITY
LAMBCOUNT
Fig. 5. Schematic illustrating the rotation of the lamb and hare cy-
cle. At high hare densities, lamb counts show a downward trend; at
low hare densities, downward pressure is less. However, upward
pressure on lamb numbers is high when lamb densities are low
(density dependence). Therefore, when lamb densities are high and
hare densities are low, upward pressures are weaker, as indicated
by the dashed line.
740 Can. J. Zool. Vol. 84, 2006
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6. with bighorn sheep, namely physical and behavioural adap-
tations for surviving harsh winters and a strong dependency
upon 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 and
shrubs (17%) (Nichols 1978). Hares are predominantly
browsers, with shrubs constituting more than 80% of their
winter diet and more than 50% of their summer diet (forbs
constitute most of the remainder of their summer diet and
are usually plentiful) (Wolff 1980; Sinclair et al. 1982). Ad-
ditionally, Dall’s sheep occupy steep alpine slopes and
meadows in this region (Burles and Hoefs 1984), whereas
snowshoe hares occupy the subalpine and valley-bottom bor-
eal forests (Krebs et al. 2001b). However, it is not unheard
of for hares to compete for food with ungulates (Hulbert and
Andersen 2001), and hares can facilitate food intake by
geese, as found in the Netherlands (van der Wal et al.
2000). As well, it is possible that at peak hare densities in
the Kluane region, when high-quality food for hares be-
comes scarce in the valley bottoms, hares may expand their
diet to include non-preferred items that overlap with the
Dall’s sheep diet. We have not observed this, nor could we
find any published reports of this, but such behaviour could
drive 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 adjacent
snowshoe 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 dispersal
or some large-scale external (climatic or celestial) events
serve as either a cue or a driver for population cycles and
explain 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 relevant
to our study of interspecific cycles through its reference to
climatic or celestial cues. It seems reasonable that herbi-
vores of any species should be affected by the same cyclic
variation in the quality or abundance of herbage, even if
their diets do not strongly overlap. However, our analyses
do not support this hypothesis, principally due to the time
lag between the increases and decreases in the lamb and
hare populations. Hence, we conclude that it is unlikely that
the relationships we have documented are due to an external
cue.
Alternatively, indirect interactions between hares and
sheep mediated through common predators seem plausible
(Comins and Hassel 1976; Bety et al. 2002). The dominant
predator of adult Dall’s sheep in the Kluane area is the coy-
ote, whereas coyotes, lynx (Burles and Hoefs 1984; Frid
1997), and golden eagles (C.L. McIntyre, personal commu-
nication) are the main predators of lambs. Both lynx and
coyotes are effective mammalian predators of snowshoe
hares (O’Donoghue et al. 1997), and golden eagle nesting
success may be linked to snowshoe hare densities in Alaska
(Prugh 2005). Frid (1997) reported that predation pressure
from lynx and coyotes on lambs was low during his study,
and he attributed this to low hare densities adjacent to his
study area. Coyote densities undergo wide fluctuations in re-
sponse to snowshoe hare densities across their geographic
distribution (Todd et al. 1981). Hence, conditions exist for
the population dynamics of lambs, as secondary prey of
lynx, coyotes, and eagles, to be affected indirectly by the
population density of snowshoe hares via their common
predators.
That a shared predator of hares and lambs is responsible
for correlated cycles in these two populations implies by def-
inition that the predator is a generalist. However, predator–
prey dynamics involving generalist predators should be
directly 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 a
generalist predator in Kluane? The most prominent cyclic
patterns in the Kluane system occur among the snowshoe
hare, its specialist predators (lynx and great-horned owls
200 250 300 350 400
MODEL HARES
200
220
240
260
280
300
(a)
225 245 265 285 305 325
MODEL HARES
200
235
270
305
340
375
(b)
200 250 300 350
MODEL HARES
60
70
80
90
(c)
MODELLAMBS
Fig. 6. Population model output illustrating three feasible interaction scenarios for snowshoe hares and Dall’s sheep. In panel a, sheep
population growth is inversely related to hare density and hare population growth is strictly density-dependent. In panel b, sheep population
growth at low hare densities has been changed to be self-regulating (density-dependent) and independent of hare densities. In panel c, sheep
population growth is density-independent when hare densities are low. In panels b and c, a 4-year duration of the low phase of the hare
population cycle has been imposed.
Wilmshurst et al. 741
# 2006 NRC Canada

7. (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 predator
population affects not only its primary prey, the snowshoe
hare, but also secondary prey such as Dall’s sheep lambs.
Hence, our reasoning does not rely on a generalist predator
causing cycling in Dall’s sheep lambs, but is based on the
lamb population being affected by the cyclic dynamics of
the 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 a
depressing effect on lamb numbers of high hare densities
with a 1- or 2-year time lag. We hypothesize that this is re-
lated to the abundance of predators that are maintained by
hares but take lambs either as a secondary prey item (when
hares are abundant) or as a primary prey item (when hares
are scarce). To establish this as the mechanism of the cycles
in the Dall’s sheep lamb population (as opposed to alterna-
tives such as shared food resources) will require further study
of the functional responses of predators in this ecosystem.
The second factor is density-independent fluctuations in lamb
numbers (with an increasing tendency) during the relatively
long low phase of the hare population cycle. We contend
that it is more likely a release from predation accompanying
the hare crash rather than any increase in food availability
that permits lamb number increases during this phase.
Acknowledgements
The 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 acknowledge
the considerable work completed by the Warden Service of
Kluane National Park and Reserve in carrying out the
Dall’s sheep surveys since 1974 and, in particular, the con-
tribution of R. Greer in identifying a pattern that he felt
must be important. Thanks also to C. Krebs for providing the
snowshoe hare data. This study was supported by the Parks
Canada Agency and the Kluane Ecological Monitoring Project.
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