Journal of Mammalogy, 86(2):380–385, 2005
HIGH GENETIC VARIABILITY DESPITE HIGH-AMPLITUDE
POPULATION CYCLES IN LEMMINGS
DOROTHEE EHRICH* AND PER ERIK JORDE
Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biology, University of Oslo,
P.O. Box 1050, Blindern, N-0316 Oslo, Norway
Lemmings are a classic example of animals with strong population cycles. High-amplitude density fluctuations
with low numbers during the low phase are expected to lead to strong genetic drift, which erodes genetic
variability. By compiling data on mitochondrial DNA polymorphism for 72 lemming populations from 5 species,
we found no evidence for this erosive mechanism. On the contrary, high levels of haplotype diversity (average h
of 0.75 for samples of the genus Lemmus) were observed in many populations. Although the effective size
determines the level of genetic diversity in closed populations, diversity is primarily determined by immigration
in open populations. Simulations of genetic drift in open populations fluctuating in density confirmed the
independence of genetic variability from local effective size, and predicted a deficit of rare alleles, as observed in
lemming samples. High genetic variability thus implies high gene flow over a considerable area for lemmings,
but does not provide information about the local effective size of populations. Examination of empirical data
suggests that high genetic diversity may be the rule rather than the exception in cyclic populations.
Key words:
Dicrostonyx, gene flow, genetic diversity, Lemmus, migration, population cycles
INTRODUCTION
the low phase, reported amplitudes must be considered with
caution (Boonstra et al. 1998).
The low phase of the population cycle typically lasts several
(2–4) years. During this period, a field worker has the
impression that lemmings have virtually disappeared, and no
animals are caught in traps. Such low densities are typical for
populations of the Norwegian lemming (Lemmus lemmus) in
the alpine tundra of Fennoscandia (Framstad et al. 1993).
Despite a considerable amount of research on cyclic populations, little is known about this low phase, which is very difficult
to investigate with conventional methods (Boonstra et al. 1998).
Thus, it is still unclear which factors are responsible for
delaying population growth after a decline (Stenseth and Ims
1993). Also, little is known about the spatial distribution and
movement of animals at low density (Shchipanov et al. 1990).
Although the causes of population fluctuations in lemmings
remain a long-standing subject for discussion (Chernyavski
2002; Stenseth 1999; Turchin and Hanski 2001), Elton (1924),
in his pioneering work, predicted low genetic variability for
cyclic populations of lemmings. According to population
genetic theory, strong fluctuations in numbers lead to loss of
genetic variability within populations because of drift during
the low phase (Nei et al. 1975; Wright 1978). In fluctuating
populations, the multigenerational effective size, which
determines the overall amount of genetic drift and the rate of
loss of diversity, corresponds to the harmonic mean size over
time and is thus close to the size during the low phase (Motro
and Thomson 1982). After a sudden reduction in population
Arctic lemmings of the genera Lemmus and Dicrostonyx,
which have a circumpolar distribution throughout the tundra
regions, are classical examples of cyclic species. The amplitude
of population density change ranges from 25- to 200-fold and
the periodicity of the cycles ranges from 3 to 5 years (Stenseth
and Ims 1993). Most lemming populations studied so far
experience periodic fluctuations to some extent (Krebs 1993).
Fluctuations of particularly high amplitude and very low
densities during the low phase are characteristic for true
lemmings (Lemmus—Boonstra et al. 1998; Bunnell et al. 1975;
Chernyavski and Tkachev 1982; Framstad et al. 1993), and
noncyclic populations have so far not been reported for this
genus. Also in collared lemmings (Dicrostonyx), most
populations experience periodic fluctuations (Chernyavski
and Tkachev 1982; Pitelka and Batzli 1993; Sittler 1995);
only a single exception of a noncyclic low-density population
has been reported for Dicrostonyx (Krebs et al. 1995; Reid
et al. 1997). In general, the amplitude of density fluctuations
seems somewhat higher for Lemmus than for Dicrostonyx, but
because it is particularly difficult to estimate densities during
* Correspondent: dorothee@bio.uio.no
Ó 2005 American Society of Mammalogists
www.mammalogy.org
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EHRICH AND JORDE—GENETIC DIVERSITY IN LEMMINGS
381
TABLE 1.—Literature survey of mitochondrial DNA (mtDNA) diversity estimates in populations of Arctic lemmings. In the different studies,
mtDNA diversity has been estimated from partial sequences of the control region (CR) or on the basis of restriction fragment length polymorphism
(RFLP). References are given for genetic data as well as for information about population dynamics of lemmings in the particular study regions.
Species and region
Lemmus lemmus Fennoscandia
L. lemmus Norway
L. sibiricus Eurasian Arctic
L. sibiricus Taimyr (Russia)
L. trimucronatus Canadian Arctic
Dicrostonyx torquatus Eurasian Arctic
D. groenlandicus Canadian Arctic
Number
of samples
mtDNA
marker
5
2
9a
20a
CR
CR
RFLP
CR
7
10
19
CR
RFLP
CR
References
Genetic data
Fedorov and Stenseth 2001
J. E. Stacy, in litt.
Fedorov et al. 1999b
Ehrich and Stenseth 2001;
D. Ehrich, in litt.
Ehrich et al. 2001b;
D. Ehrich, in litt.
Fedorov et al. 1999a
Ehrich et al. 2001a
Data on population dynamics
Framstad et al. 1993; Henttonen and Kaikusalo 1993
Framstad et al. 1993
Chernyavski and Tkachev 1982; Erlinge et al. 1999
Orlov 1980; Sdobnikov 1957
Ehrich et al. 2001b; C. J. Krebs, unpublished
Chernyavski and Tkachev 1982
Wilson et al. 1999; Ehrich et al. 2001a; Predavec et al. 2001
a
Two samples from the study by Fedorov et al. (1999b) also were analyzed by Ehrich and Stenseth (2001); because the latter authors analyzed a larger number of individuals, their
estimate is included in this study.
size, the number of different alleles is reduced more rapidly
than gene diversity measured as heterozygosity because rare
alleles are lost 1st (Maruyama and Fuerst 1985). A heterozygosity excess relative to the level expected at mutation–drift
equilibrium for the number of alleles present can thus be
considered a signature of genetic bottlenecks (Cornuet and
Luikart 1996).
In closed populations, the loss of genetic diversity is
counteracted by mutations, which occur typically at a low
rate, and possibly by selection (Coltman et al. 1999). In open
populations, on the contrary, gene flow prevents loss of
diversity (Hedrick 2000). As a well-known general rule it was
stated that 1 immigrant per generation is enough to maintain
some genetic variability within populations (Mills and
Allendorf 1996). High levels of gene flow, either mediated
through migration among extant populations or through
recolonization of extinct ones, are typical of metapopulations
(Hanski and Gilpin 1997). Although mutation and gene flow
both retard the loss of genetic variation, these 2 forces lead to
different levels of local differentiation. Gene flow acts as
a homogenizing force, whereas mutation may lead to more
differentiation.
Here we assemble genetic data on lemmings from the
literature to test for evidence of low genetic diversity and for
a bottleneck signature in these cyclic populations. Then we
present simulations that highlight the importance of gene flow
in determining the level of genetic variability in local
populations, and investigate the relation between the number
of different alleles and heterozygosity in populations with
strong drift and high levels of gene flow. Finally, implications
of the findings on genetic diversity for the population biology
of lemmings are suggested.
MATERIALS AND METHODS
All estimates of local genetic variability in fluctuating lemming
populations we are aware of are included. Samples were in general
collected over areas less than 3 km in diameter. Multiannual density
fluctuations have been reported from all sample localities or from
nearby areas (Table 1). The data represent 2 genera and 5 species of
true lemmings (Lemmus trimucronatus in North America, L. lemmus
in Fennoscandia, and L. sibiricus in Russia) and collared lemmings
(Dicrostonyx groenlandicus in North America and D. torquatus in
Russia). In total, 72 samples with an average size of 10.4 (SD ¼ 4.5,
range: 4–24) were available. The large number of samples and the
wide geographic area covered makes this study of genetic diversity
representative of Arctic lemming populations, despite relatively small
sample sizes.
Because most of the studies were based on mitochondrial DNA
(mtDNA), we estimated genetic variability for this molecular marker
only. Because mtDNA is haploid and in general maternally transmitted,
it is particularly sensitive to loss of genetic variability in small populations (Birky et al. 1983). A drawback of the exclusive use of mtDNA is
that it represents only a single locus. The studies present either partial
sequences of the mtDNA control region, or restriction fragment length
polymorphism analyses of the entire mtDNA genome. In the following,
we used data generated by both techniques equally, although the
restriction fragment length polymorphism approach may result in lower
diversity estimates than control region sequencing. Three estimates of
genetic diversity were calculated: Nei’s unbiased haplotype diversity
(h, the probability of 2 randomly drawn haplotypes being different—Nei
1987:260), the number of different haplotypes observed (a), and allelic
richness (R, an estimate of the number of alleles corrected for sample
size after the rarefaction method—El Mousadik and Petit 1996).
To test for a deficit of rare alleles that would indicate bottlenecks
(Cornuet and Luikart 1996), we calculated the haplotype diversity
expected in an equilibrium population for the observed number of
haplotypes and sample sizes, by using Ewens’s sampling formula
(hEwens—Ewens 1972). The expected haplotype diversity thus calculated was compared to the value of h estimated for each sample. If
lemming populations had as many rare alleles as expected at mutation–
drift equilibrium, on average over samples the 2 estimates should be
equal. This approach is analogous to the homozygosity test for neutrality
(Watterson 1978), but tests for a general deviation from neutral
expectations over samples instead of testing within each sample.
Genetic drift was simulated by a Monte Carlo process to illustrate the
change in genetic variability over time in closed and open populations
with lemminglike dynamics, and to assess the importance of stochastic
variation in mtDNA diversity estimates. Simulated populations initially
had 50 different haplotypes at equal frequencies—an arbitrary number
of haplotypes illustrating high diversity. The population cycle consisted
of 8 generations (assuming 2 generations per year), 6 generations at low
density, 50 times more individuals in the 7th generation, and 100 times
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JOURNAL OF MAMMALOGY
FIG. 1.—Distribution of genetic diversity in 29 samples of
Dicrostonyx (left) and 43 samples of Lemmus (right). The upper
panels show the distribution of allelic richness (R; standardized for
a sample size of 4) and the lower panels show the distribution of
haplotype diversity (h).
more in the 8th generation (for the shape of the cycle, see Boonstra et al.
[1998], Krebs [1993], and Stenseth and Ims [1993]). Each new
generation was created by randomly choosing with replacement the
desired number of haplotypes among those of the parent generation.
Because little is known about the number of generations per year in
lemmings, simulations also were performed with 1 generation per year
and with 3 generations during the low phase and 2 generations during the
peak. The number of generations only influenced the outcome in so far as
it changed the harmonic mean of population sizes over the cycle (i.e., the
multigenerational effective size). Immigration (deterministic) was
simulated by adding immigrants to the population each generation (for
Nm ¼ 1 or 2) or every other generation (Nm ¼ 0.5). Immigrants were
chosen at random from a fixed source population that had either 100
different haplotypes (high diversity), 5 equally frequent haplotypes
(moderate diversity), or was at mutation–drift equilibrium with 2Nl ¼ 5.
Mutations were simulated so that every mutation created a new allele
(infinite allele model) and mutation rate was set to 7 105 per fragment
per generation. This corresponds to the divergence rate of 17% per
million years estimated for the mtDNA control region in lemmings
(Fedorov and Stenseth 2001). Because of the high mutation rate chosen,
the simulated data should be considered as mtDNA control region
haplotypes. Using a lower rate would lead to somewhat lower diversity
in all simulations. Haplotype diversity and the number of different
haplotypes within populations were estimated from simulated samples
of 10, corresponding to the average sample size of the field studies.
RESULTS
Empirical data.— Contrary to Elton’s (1924) expectations,
most populations of Lemmus harbor extensive genetic variability
and almost one-third (14/43) of populations have estimates of
haplotype diversity, h, that are at or above 0.9. On average for
43 samples, h was 0.75 (SD ¼ 0.24; Fig. 1). This is nearly twice
as large as the average for Dicrostonyx, which, in general, is
less strongly fluctuating (average over 29 samples: h ¼ 0.39,
Vol. 86, No. 2
FIG. 2.—Simulations of loss of genetic diversity at 1 haploid locus
in closed populations with periodic fluctuations in size. Minimum
sizes were 25 (upper panels) and 50 (lower panels), respectively, and
maximum sizes were 2,500 (upper) and 5,000 (lower). The curve
represents the average of 200 iterations and the upper and lower lines
indicate the 95% confidence interval.
SD ¼ 0.34; Fig. 1). In Dicrostonyx, one-third of the population apparently lacks genetic diversity, with only 1 haplotype
observed in samples (10/29). The same general pattern of higher
genetic variability in Lemmus is evident from the number of
haplotypes in populations: allelic richness for a reference sample
size of 4 was on average 2.97 (SD ¼ 0.84) for Lemmus and 1.88
(SD ¼ 0.75) for Dicrostonyx. Despite large sample variances
associated with estimates of mtDNA diversity, the difference
between the 2 genera is significant (Wilcoxon test: Z ¼ 4.38,
P , 0.001 for h and Z ¼ 4.71, P , 0.001 for R). Note that if
cyclic fluctuations in population density were causing reduced
genetic variability in lemmings, we would expect the more
strongly fluctuating genus to have lower variability.
Haplotype diversity was on average larger than expected in
samples of the same size with the same number of haplotypes
taken from populations at equilibrium. However, the observed
heterozygosity excess was small. In Lemmus, the mean of the
difference between h and hEwens was 0.020 (median ¼ 0.017,
SD ¼ 0.046, Wilcoxon test for mean ¼ 0: Z ¼ 2.73, P ¼
0.006), whereas in Dicrostonyx it was 0.018 (median ¼ 0,
SD ¼ 0.08; Wilcoxon test: Z ¼ 1.69, P ¼ 0.09).
Simulations.— Simulations of genetic drift at 1 locus in closed
populations with high-amplitude density fluctuations illustrated
the expected rapid rate of loss of genetic diversity and the high
stochastic variability of mtDNA diversity estimates (Fig. 2).
Note that the simulated effective sizes during the low phase were
not extremely small (Ne ¼ 25 or 50), considering that for most
species the genetically effective size is considerably lower than
the census population size (Frankham 1995) and that for
mtDNA only the effective number of females is relevant. Still,
genetic diversity was lost after only a few generations in the
simulations, so that this closed population model can be rejected
for lemmings over longer periods of time.
In open populations, in the contrast, the level of genetic
diversity within samples depends primarily on the number of
immigrants entering the local population. This dependence of
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EHRICH AND JORDE—GENETIC DIVERSITY IN LEMMINGS
383
populations where genetic diversity is mainly influenced by
immigration. Such an excess in heterozygozity is thus not only
a signature of a recent bottleneck (Cornuet and Luikart 1996),
but is also characteristic of populations subject to strong drift,
with immigration balancing the loss of diversity.
DISCUSSION
FIG. 3.—Simulations of loss of genetic diversity (number of
different alleles in a sample of 10 haplotypes and haplotype diversity)
at 1 locus in open populations with periodic fluctuations in size and 1
immigrant every other generation from a source population with high
diversity. Minimum sizes were 25 (upper panels) and 50 (lower
panels), respectively, and maximum sizes were 2,500 (upper) and
5,000 (lower). The curve represents the average of 200 runs and the
upper and lower lines indicate the 95% confidence interval.
diversity on gene flow is evident from the equilibrium
expectation of genetic diversity at mutation–migration–drift
equilibrium (Hedrick 2000):
EðhÞ52Nef ðm1lÞ=½2Nef ðm1lÞ11
where Nef is the effective number of females (corresponding to
the effective size for mtDNA), m is the migration rate, and l is
the mutation rate. When l is small compared to m, h depends
only on Nef m, the effective number of immigrants. This relation
assumes that each mutation creates a new haplotype, and that
each immigrant carries a new haplotype. Simulated populations
with Nm ¼ 0.5 and a high-diversity source population indeed
reached the predicted level of h of approximately 0.5
independently of their effective size (Fig. 3). Obviously,
a model assuming an infinitely diverse source population cannot be applied to natural populations. In reality, local diversity
is determined both by the diversity in the source population and
the rate of immigration. Populations simulated with Nm ¼ 0.5
from a moderately diverse source (5 haplotypes, h ¼ 0.8)
reached equilibrium diversity at approximately 0.4. The effective population size determined only the speed at which the
equilibrium diversity was reached (also, in a large population
fluctuating between 500 and 50,000 with Nm ¼ 0.5 from a
high-diversity source, diversity decreased to a level of 0.5, but
did so very slowly). The same equilibrium level was reached
for simulations starting with monomorphic populations.
Excess haplotype diversity was estimated for the simulated
populations in the same way as for the lemming data (h hEwens) and was found to be positive during the diversity decline
as well as at migration–drift equilibrium. For Ne fluctuating
between 25 and 2,500 and Nm ¼ 1 from a source population at
mutation–drift equilibrium (which had no heterozygosity
excess), the difference was approximately 0.05. The haplotype
diversity excess observed on average in the lemming samples
thus corresponds to the results of our simulations for fluctuating
According to classical population genetics, in open populations local genetic diversity is determined by the rate of gene flow
and the diversity among immigrants (Hedrick 2000). Our
simulations confirmed that the level of genetic diversity in
samples from open populations does not provide much information about the local effective population size and is not
affected by cycles with periodically small numbers. In spite of
low densities, lemmings are common animals in the largely
nonfragmented Arctic tundras, and there is a priori no reason to
assume that their populations are isolated. It is thus not surprising to observe high genetic diversity in many populations of
Lemmus and in some populations of Dicrostonyx despite regular
bottlenecks in numbers during the low phase of the cycle. In fact,
low genetic variability in some lemming populations has been
attributed to causes other than dynamics. The low diversity
observed in many samples of Dicrostonyx reflects historical
bottlenecks during a warm period in the Holocene, when a forest
expansion to the north and a higher sea level contracted the
tundra habitat of collared lemmings (Ehrich et al. 2000; Fedorov
1999). Low diversity in brown lemmings in the central Canadian
Arctic has been attributed to the scarcity of brown lemming
habitat in this particular region, leading to a low effective
population size at the regional scale (Ehrich et al. 2001b).
Although the observed high genetic variability does not
allow any conclusions concerning the effective size of populations during the low phase, it shows that there must be
considerable migration into populations from highly variable
sources. For the simulations a source–sink model was assumed,
where immigrants come from a large constant population and
diversity is lost only from the focal population, which is a sink.
However, for most of the sampled lemming populations, at least
on the mainland, having separate source and sink populations is
probably not an adequate description of population structure. In
natural populations in more or less continuous habitats, migration is an exchange with the surrounding area. Over many
generations genes can migrate over large distances, and eventually the whole region, or even the whole species in some cases,
may become a potential source. The level of diversity in this
large source population, which together with the migration rate
determines the local level of diversity, is itself determined by
the interaction of mutation and drift on an evolutionary time
scale (Hedrick 2000).
The substantial gene flow necessary to maintain high genetic
variability in lemmings despite periodic low densities is likely
to lead to low genetic differentiation at the local scale. The
spatial structure is thus predicted to be rather extensive, with
large genetically homogenous areas. Ehrich and Stenseth
(2001) studied the local genetic structure of Siberian lemmings
and found that populations were indeed structured in large
homogeneous patches. These patches extended over at least
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JOURNAL OF MAMMALOGY
8 km on a linear transect (within the patch, samples separated
by 1 km were not significantly differentiated, FST ¼ 0.025 for
mtDNA, P ¼ 0.09 in a permutation test). Considering this the
minimum diameter of a circle would result in an area of at least
50 km2 for a genetically homogenous population, and possibly
more (the sampling design allows no upper limit to be set on
this estimate). On a larger scale, among patches, differentation
was higher (FST ¼ 0.18 for mtDNA data). A rather weak
genetic structuring suggesting high gene flow also was reported
for collared lemmings in the Canadian Arctic (FST ¼ 0.03
between sample localities separated by 10 km in a continuous
habitat, when using microsatellite data—Ehrich et al. 2001a).
Locally, within populations, lemmings may live in small
groups (Shchipanov et al. 1990) and exchange several migrants
every generation. Such high dispersal rates will prevent local
genetic differentiation and effectively join the demes into larger
panmictic units, as observed for Siberian lemmings. Because
local demes are likely to go extinct and be founded again, these
larger units might be interpreted as metapopulations (Hanski and
Gilpin 1997) lacking internal genetic differentiation. During the
low phase, lemming populations may be structured as a loose
network of small breeding groups possibly reassembling every
season. Although the literature is scarce, some ecological findings support such a population model. Seasonal migration is
a well-known trait of Norwegian lemmings (Henttonen and
Kaikusalo 1993), and has been reported on a smaller geographic
scale for Siberian lemmings (Orlov 1980). Furthermore,
during the low phase a considerable amount of movement was
registered within 1 season in Siberian and Norwegian lemmings,
where females may shift home ranges in the course of the summer
(Heske and Jensen 1993; Shchipanov et al. 1990; Travina 1995).
The considerable amount of movement and extensive scale of
genetic structure inferred above may contribute to the understanding of the population dynamics of lemmings. Dispersal,
together with predation, has been shown to generate a negative
feedback loop on population dynamics in periodically fluctuating root voles (Microtus oeconomus—Ims and Andreassen
2000). For both voles and lemmings, dispersal has been reported
to be inversely proportional to density (Blackburn et al. 1999;
Ims and Andreassen 2000). In declining densities, risky movements may thus become more frequent, leading to increased
predation and consequently to continued population decline. If
lemmings experience particularly low densities during the low
phase of the cycle compared to other microtine rodents (Stenseth
and Ims 1993), and local genetic variability is maintained by
important migration in spatially large populations, movements
may be a particularly important feature of lemming biology.
Predation during these numerous risky movements may explain
the prolonged low phases observed in lemming cycles.
High genetic mtDNA variability despite fluctuating population densities has been reported previously by Plante et al.
(1989) for meadow voles (Microtus pennsylvanicus) and
explained by strong gene flow in peak years. High microsatellite
variability has been observed for cyclic water voles (Arvicola
terrestris—J. Aars in litt.) in Finland. Burton et al. (2002) also
reported high genetic variability for microsatellite data in cyclic
populations of snowshoe hares (Lepus americanus) in Canada.
As for lemmings, differentiation was low and high gene flow
was inferred. Here we pointed out that in open populations, the
local effective size does not determine the long-term level
of genetic variability within populations and periodic low
densities are thus not expected to reduce diversity. The scale of
the present study including 5 species and samples from several
regions of the Arctic is much larger than that of previous studies.
Together with the reports from other species, our study indicates
that the finding of high genetic variability in periodically
fluctuating arvicoline rodents may be the rule rather than the
exception. One could even go further in suggesting that strong
density fluctuations, which destabilize the spatial organization
of populations, may lead to more migration. This migration
might in turn create a geographically more extensive population
structure with gene flow over large distances and high genetic
diversity at the local scale. Empirical investigation of this
hypothesis would be interesting, for example, by comparing
fluctuating and stable populations of the same species.
ACKNOWLEDGMENTS
We are grateful to N. C. Stenseth, D. Tallmon, and G. Luikart for
valuable comments on earlier versions of the manuscript.
LITERATURE CITED
BIRKY, C. W., T. MARUYAMA, AND P. FUERST. 1983. An approach to
population and evolutionary genetic theory for genes in mitochondria and chloroplasts, and some results. Genetics 103:513–527.
BLACKBURN, G. S., D. J. WILSON, AND C. J. KREBS. 1999. Dispersal of
juvenile collared lemmings (Dicrostonyx groenlandicus) in a highdensity population. Canadian Journal of Zoology 76:2255–2261.
BOONSTRA, R., C. J. KREBS, AND N. C. STENSETH. 1998. Population
cycles in small mammals: the problem of explaining the low phase.
Ecology 79:1479–1488.
BUNNELL, F. L., S. F. MACLEAN, AND J. BROWN. 1975. Barrow, Alaska,
USA. Pp. 73–124 in Structure and function of tundra ecosystems
(T. Rosswall and O. W. Heal, eds.). Ecological Bulletin 20:73–124.
BURTON, C., C. J. KREBS, AND E. B. TAYLOR. 2002. Population genetic
structure of the cyclic snowshoe hare (Lepus americanus) in
southwestern Yukon, Canada. Molecular Ecology 11:1689–1701.
CHERNYAVSKI, F. B. 2002. Population dynamics of lemmings.
Zoologichskii Zhurnal 81:1135–1165 (in Russian, English summary).
CHERNYAVSKI, F. B., AND A. V. TKACHEV. 1982. Population cycles of
Arctic lemmings. Ecological and endocrinological aspects. Nauka,
Moscow, Russia (in Russian, English summary).
COLTMAN, D. W., J. G. PILKINGTON, J. A. SMITH, AND J. M. PEMBERTON.
1999. Parasite-mediated selection against inbred Soay sheep in
a free-living, island population. Evolution 53:1259–1267.
CORNUET, J. M., AND G. LUIKART. 1996. Description and power
analysis of two tests for detecting recent population bottlenecks
from allele frequency data. Genetics 144:2001–2014.
EHRICH, D., V. B. FEDOROV, N. C. STENSETH, C. J. KREBS, AND A. J.
KENNEY. 2000. Phylogeography and mtDNA diversity in North
American collared lemmings (Dicrostonyx groenlandicus). Molecular Ecology 9:329–337.
EHRICH, D., P. E. JORDE, C. J. KREBS, A. K. KENNEY, J. E. STACY, AND
N. C. STENSETH. 2001a. Spatial structure of lemming populations
(Dicrostonyx groenlandicus) fluctuating in density. Molecular
Ecology 10:481–495.
EHRICH, D., C. J. KREBS, A. J. KENNEY, AND N. C. STENSETH. 2001b.
Comparing the genetic population structure of two species of Arctic
April 2005
EHRICH AND JORDE—GENETIC DIVERSITY IN LEMMINGS
lemmings: more local differentiation in Lemmus trimucronatus than
in Dicrostonyx groenlandicus. Oikos 94:143–150.
EHRICH, D., AND N. C. STENSETH. 2001. Genetic structure of Siberian
lemmings (Lemmus sibiricus) in a continuous habitat: large patches
rather than isolation by distance. Heredity 86:716–730.
EL MOUSADIK, A., AND R. J. PETIT. 1996. High level of genetic
differentiation for allelic richness among populations of the argan
tree [Argania spinosa (L.) Skeels] endemic to Morocco. Theoretical
and Applied Genetics 92:832–839.
ELTON, C. S. 1924. Periodic fluctuations in the number of animals: their
causes and effects. British Journal of Experimental Ecology 2:119–163.
ERLINGE, S., et al. 1999. Asynchronous population dynamics of Siberian
lemmings across the Palearctic tundra. Oecologia 119:493–500.
EWENS, W. J. 1972. The sampling theory of selectively neutral alleles.
Theoretical Population Biology 3:87–112.
FEDOROV, V. B. 1999. Contrasting mitochondrial DNA diversity
estimates in two sympatric genera of Arctic lemmings (Dicrostonyx,
Lemmus) indicate different responses to Quaternary environmental
fluctuations. Proceedings of the Royal Society of London, B.
Biological Sciences 266:621–626.
FEDOROV, V. B., K. FREDGA, AND G. H. JARRELL. 1999a. Mitochondrial
DNA variation and the evolutionary history of chromosome races of
collared lemmings (Dicrostonyx) in the Eurasian Arctic. Journal of
Evolutionary Biology 12:134–145.
FEDOROV, V. B., A. V. GOROPASHNAYA, G. H. JARRELL, AND K. FREDGA.
1999b. Phylogeographic structure and mitochondrial DNA variation
in true lemmings (Lemmus) from the Eurasian Arctic. Biological
Journal of the Linnean Society 66:357–371.
FEDOROV, V. B., AND N. C. STENSETH. 2001. Glacial survival of the
Norwegian lemming (Lemmus lemmus) in Scandinavia: inference
from mitochondrial DNA variation. Proceedings of the Royal
Society of London, B. Biological Sciences 268:809–814.
FRAMSTAD, E., N. C. STENSETH, AND E. ØSTBYE. 1993. Time series
analysis of population fluctuations of Lemmus lemmus. Pp. 97–116
in The biology of lemmings (N. C. Stenseth and R. A. Ims, eds.).
Academic Press, London, United Kingdom.
FRANKHAM, R. 1995. Effective population-size adult-population size
ratios in wildlife—a review. Genetical Research 66:95–107.
HANSKI, I., AND M. GILPIN. 1997. Metapopulation biology. Academic
Press, London, United Kingdom.
HEDRICK, P. W. 2000. Genetics of populations. Jones and Bartlett
Publishers, Sudbury, Massachusetts.
HENTTONEN, H., AND A. KAIKUSALO. 1993. Lemming movements. Pp.
157–186 in The biology of lemmings (N. C. Stenseth and R. A. Ims,
eds.). Academic Press, London, United Kingdom.
HESKE, E. J., AND P. M. JENSEN. 1993. Social structure of Lemmus
lemmus during the breeding season. Pp. 387–396 in The biology of
lemmings (N. C. Stenseth and R. A. Ims, eds.). Academic Press,
London, United Kingdom.
IMS, R. A., AND H. P. ANDREASSEN. 2000. Spatial synchronization of
vole population dynamics by predatory birds. Nature 408:194–196.
KREBS, C. J. 1993. Are lemmings large Microtus or small reindeer? A
review of lemming cycles after 25 years and recommendations for
future work. Pp. 247–260 in The biology of lemmings (N. C. Stenseth
and R. A. Ims, eds.). Academic Press, London, United Kingdom.
KREBS, C. J., R. BOONSTRA, AND A. J. KENNEY. 1995. Population
dynamics of collared lemming and tundra vole at Pearce Point,
Northwest Territories, Canada. Oecologia 103:481–489.
MARUYAMA, T., AND P. A. FUERST. 1985. Population bottlenecks and
nonequilibrium models in population genetics. 2. Number of alleles
in a small population that was formed by a recent bottleneck.
Genetics 111:657–689.
385
MILLS, L. S., AND F. W. ALLENDORF. 1996. The one-migrant-pergeneration rule in conservation and management. Conservation
Biology 10:1509–1518.
MOTRO, U., AND G. THOMSON. 1982. On heterozygosity and the effective
size of populations subject to size changes. Evolution 36:1059–1066.
NEI, M. 1987. Molecular evolutionary genetics. Columbia University
Press, New York.
NEI, M., T. MARUYAMA, AND R. CHAKRABORTY. 1975. The bottleneck
effect and genetic variability in populations. Evolution 29:1–10.
ORLOV, V. A. 1980. Seasonal migration of Siberian and collared
lemmings in the typical tundra subzone on Taimyr. Pp. 95–99 in
Regulation mechanisms of lemming and vole densities in the far
North. Dal’nevostochnyj nauchnyj centr Akademii Nauk SSSR
Press, Vladivostok, Russia (in Russian).
PITELKA, F. A., AND G. O. BATZLI. 1993. Distribution, abundance and
habitat use by lemmings on the north slope of Alaska. Pp. 213–236
in The biology of lemmings (N. C. Stenseth and R. A. Ims, eds.).
Academic Press, London, United Kingdom.
PLANTE, Y., P. T. BOAG, AND B. N. WHITE. 1989. Microgeographic
variation in mitochondrial DNA of meadow voles (Microtus
pennsylvannicus) in relation to population density. Evolution 43:
1522–1537.
PREDAVEC, M., C. J. KREBS, K. DANELL, AND R. HYNDMAN. 2001.
Cycles and synchrony in the collared lemming (Dicrostonyx
groenlandicus) in Arctic North America. Oecologia 126:216–224.
REID, D. G., C. J. KREBS, AND A. J. KENNEY. 1997. Patterns of predation
on noncyclic lemmings. Ecological Monographs 67:89–108.
SDOBNIKOV, V. M. 1957. Lemmings on northern Taimyr. Trudy Arctic
Research Institute 205:109–125 (in Russian).
SHCHIPANOV, N. A., M. V. KASATKIN, AND V. Y. OLEINICHENKO. 1990.
Spatial distribution of Lemmus sibiricus having low population in
Chaun tundra. Zoologichskii Zhurnal 69:156–159 (in Russian,
English summary).
SITTLER, B. 1995. Response of stoats (Mustela erminea) to a fluctuating
lemming (Dicrostonyx groenlandicus) population in north east
Greenland: preliminary results from a long term study. Annales
Zoologici Fennici 32:79–92.
STENSETH, N. C. 1999. Population cycles in voles and lemmings:
density dependence and phase dependence in a stochastic world.
Oikos 87:427–461.
STENSETH, N. C., AND R. A. IMS. 1993. Population dynamics of
lemmings: temporal and spatial variation—an introduction. Pp. 61–
96 in The biology of lemmings (N. C. Stenseth and R. A. Ims, eds.).
Academic Press, London, United Kingdom.
TRAVINA, I. V. 1995. Spatial structure of lemming populations
(Dicrostonyx vinogradovi, Lemmus sibiricus) of Wrangel Island
in years of their low density. Zoologichskii Zhurnal 78:485–493 (in
Russian, English summary).
TURCHIN, P., AND I. HANSKI. 2001. Contrasting alternative hypotheses
about rodent cycles by translating them into parameterized models.
Ecology Letters 4:267–276.
WATTERSON, G. A. 1978. The homozygosity test of neutrality.
Genetics 88:405–417.
WILSON, D. J., C. J. KREBS, AND T. SINCLAIR. 1999. Limitation of collared
lemming populations during a population cycle. Oikos 87:382–398.
WRIGHT, S. 1978. Evolution and the genetics of populations.
Variability within and among natural populations. University of
Chicago Press, Chicago, Illinois.
Submitted 12 April 2004. Accepted 15 August 2004.
Associate Editor was Eric A. Rickart.