Popul Ecol (2003) 45:165–173 DOI 10.1007/s10144-003-0164-6

FORUM

Takashi Saitoh Æ Nils Chr. Stenseth Hildegunn Viljugrein Æ Marte O. Kittilsen

Mechanisms of density dependence in fluctuating vole populations: deducing annual density dependence from seasonal processes

Received: 4 July 2002 / Accepted: 11 November 2003 / Published online: 11 December 2003
The Society of Population Ecology and Springer-Verlag Tokyo 2003

Abstract Based on recent advances in time-series analyses of ecological dynamics using statistical and mathematical models, we summarise our recent results on the seasonal processes in the annual population dynamics of the grey-sided vole Clethrionomys rufocanus (Sundevall, 1846) in Hokkaido, Japan, and report additional analyses on annual and seasonal density dependence. Annual direct density dependence was strong in almost all populations. In contrast, delayed density dependence was generally weak, although clear delayed density dependence was detected in some of the studied populations. Although seasonal density dependence was observed both in winter and summer, direct density dependence was much more profound during winter; thus, winter density dependence contributed most to the overall annual direct density dependence. We found no correlation between the seasonal components of annual direct density dependence; however, the corresponding seasonal components for annual delayed density dependence were positively correlated. We conclude that winter conditions influence the strength of annual direct density dependence most profoundly. Moreover, we conclude that direct density dependence during summer and winter may be generated by different mechanisms, whereas delayed density dependence seems to be generated by a common mechanism. Candidate mechanisms are discussed in relation to general knowledge of northern rodent populations and to specific insights provided by earlier studies of grey-sided voles in Hokkaido.

T. Saitoh (&) Field Science Center, Hokkaido University, North 11, West 10, Sapporo 060-0811, Japan e-mail: [email protected] Tel.: +81-11-7062590 Fax: +81-11-7063450 N. C. Stenseth Æ H. Viljugrein Æ M. O. Kittilsen Center for Ecological and Evolutionary Synthesis (CEES), Department of Biology, University of Oslo, Oslo, Norway

Keywords Clethrionomys rufocanus Æ Cycle Æ Hokkaido Æ Rodents Æ Seasonal density dependence

Introduction The broad spectrum of population dynamics observed in small rodents, including periodic fluctuations (so-called
rodent cycles), has fascinated ecologists ever since Eltons (1924) pioneering paper (see Stenseth and Ims 1993a, b; Stenseth 1995). Recently, statistical and mathematical modelling of time-series data have provided new and valuable results. For example, linear autoregressive models have demonstrated that a variety of population dynamical patterns, including cycles, may be caused by a set of particular combinations of direct and delayed density-dependence in a generic sense (Royama 1992; Stenseth 1999). As such, geographic gradients of fluctuation patterns may be understood as a result of the changing relative strengths of direct and delayed density dependence (Bjørnstad et al. 1995; Stenseth and Saitoh 1998; Stenseth 1999; Tkadlec and Stenseth 2001). Much of the available information on population cycles has been accumulated both in Fennoscandia and in Hokkaido (Stenseth and Saitoh 1998; Stenseth 1999). Although the structure of density dependence differs somewhat between these regions, some general features have been found. Periodicity and variability of population fluctuations are particularly evident in colder areas of both regions. In Fennoscandia, direct density dependence becomes weaker toward the north, while delayed density dependence remains fairly constant. In Hokkaido, however, both direct and delayed density dependence are stronger in colder areas. Although we have greatly improved our understanding of the generic relationships between the structures of density dependence and the patterns of population dynamics, it remains difficult to interpret the observed density dependence structures in more mechanistic terms, since a variety of mechanisms (such

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as interactions with predators, food availability, pathogens, and conspecifics) could explain the observed structures. Predator-prey interactions are often highlighted in attempts at explaining the fluctuations and the observed geographic gradients in periodicity and amplitude among Fennoscandian populations (e.g., Hansson and Henttonen 1985, 1988; Henttonen et al. 1985; see also Klemola et al. 2003). The predator-prey community in northern and central Fennoscandia, where delayed density dependence dominates over direct density dependence and cyclic populations prevail, is characterised by specialist predators having few alternative prey species. In southern parts of Fennoscandia, where non-cyclic populations are common, direct density dependence is relatively strong; the predator community in that region is much more diverse, with a great variety of generalists as well as specialist predators. Mechanistic models based on predator-prey interactions support these explanations (Hanski et al. 1991, 2001; Turchin and Hanski 1997; Klemola et al. 2003). However, in Scotland, where cyclic fluctuations occur, the role of specialist predators is unclear (e.g., Graham and Lambin 2002), while for Hokkaido, the underlying mechanisms that generate the population cycles and the observed gradients in dynamic patterns remain unclear. We therefore need to consider alternative mechanisms to the commonly assumed specialist-predator hypothesis. Observed annual dynamics must necessarily emerge as a result of processes within and between seasons. Different mechanisms may operate during different seasons. Incorporating seasonality into time-series models (e.g., as done by Stenseth et al. 2002, 2003) may improve our ability to gain insight into rodent dynamics. Since multi-annual cycles of small rodents are typically observed in northern temperate and subarctic regions that show strong seasonality, the rodent cycle may be an ideal phenomenon for reducing annual dynamics into their seasonal components (e.g., Hanski et al. 1993; Burkey and Stenseth 1994; Hanski and Korpima¨ki 1995; Turchin and Ostfeld 1997; Stenseth et al. 1998; Hansen et al. 1999; Klemola et al. 2003). In particular, the grey-sided vole Clethrionomys rufocanus (Sundevall, 1846) in Hokkaido, Japan, is an ideal species for the study of the relationship between annual and seasonal dynamics, because its life history is very well documented, and we have access to a good time-series database covering the entire island, which has both cyclic and non-cyclic populations (see papers in Stenseth and Saitoh 1998; see also Saitoh 1987; Bjørnstad et al. 1996, 1998; Stenseth et al. 1996a, 1998; Saitoh et al. 1998). Furthermore, Hokkaido, which is the northernmost island of Japan, exhibits strong seasonality (with longer winters in the northeast than in the southwest). Finally, second-order autoregressive models (including both direct and delayed density dependence) describe the dynamics of these populations rather well (Stenseth et al.1996a, 1998; see also Saitoh et al. 1997, 1998; Stenseth 1999).

In a companion study on the grey-sided vole in Hokkaido (Stenseth et al. 2003), we have statistically reduced the annual density dependence structures of 84 populations in the northern part of the island into their seasonal components (summer and winter). The specific aim of this paper is to summarise—in biological and more mechanistic terms—our recent results on the seasonal processes of annual dynamics in the grey-sided vole of Hokkaido, as well as to report additional analyses of the relationships between seasonal components. By doing so, we aim to increase biological insight into density dependence. Based on our knowledge of fluctuating small rodent populations in northern regions and earlier studies on the grey-sided vole in Hokkaido, we discuss candidate mechanisms to explain the observed patterns.

Study animals and data Hokkaido is the northernmost island (41 24¢– 45 31¢ N, 139 46¢–14549¢ E) of Japan and covers 78,073 km2. It neighbours the Asian continent and is surrounded by the Sea of Okhotsk, the Pacific, and the Sea of Japan (Fig. 1). Hokkaido represents the easternmost extent of the geographic distribution of greysided voles (C. rufocanus); the westernmost edge of their range lies in Fennoscandia (see Kaneko et al. 1998). This species is considered a pest in plantations of larch (Larix leptolepis) and todo-fir (Abies sachalinensis) in Hokkaido. Since 1954, the Forestry Agency of the Japanese government has therefore conducted censuses of vole populations for management purposes in forests all across Hokkaido. The censuses have provided 225 time-series datasets of varying lengths [see Saitoh et al. (1998) for census methods]; the richest dataset (84 time series), including both spring and autumn for 30 years (1963–1992), is available for Asahikawa (Fig. 1), a region that includes both cyclic and non-cyclic vole populations (Bjørnstad et al. 1998; Saitoh et al. 1998). The seasonal dynamics of the grey-sided vole in Hokkaido are quite regular (Fig. 2), such that populations typically increase during the summer and decrease during the winter. The breeding season is generally from April to October, although the pregnancy rate is higher in spring and autumn than in the middle of the summer (Kaneko et al. 1998). Although winter breeding has been reported (Kaikusalo and Tast 1984; Nakata 1987; Saitoh 1989), it is a rare phenomenon (Ota 1984). Thus, the winter population growth rate, i.e., from the preceding autumn to the spring of year t (Rwt), is typically negative, whereas the summer population growth rate, from spring to autumn (Rst), is generally positive. Spring and autumn census data are therefore considered best suited for the study of seasonal and annual dynamics of vole populations. Indeed, spring and autumn data have been used for seasonal analyses (Stenseth et al. 2003).

167 Fig. 1 Map of the study area. Hokkaido is the northern-most island of Japan. The 84 studied populations reside in the northern region of the island, in which national forests are managed by the Asahikawa Regional Office (Forestry Agency of the Japanese government). Solid symbols indicate the 74 populations for which the seasonal parameters were successfully estimated. For the remaining ten populations (open symbols), seasonal parameters were not obtained. Stars indicate the two populations highlighted in Fig. 2 (left Takinoshita, right Mitsumata). Major towns and cities are indicated by double circles

Ecological model and parameter estimations We let xt correspond to the log-transformed
true abundance in the spring of year t, and yt-1 correspond to the log-transformed true population abundance in the preceding autumn. According to Hansen et al. (1999), the net winter growth rate, Rwt (=xt)yt-1), and the net summer growth rate, Rst (=yt)xt), were defined as: Rwt ¼ xt
yt
1 ¼ aw1 yt
1 þ aw2 xt
1 þ aw3 yt
2 þ aw4 xt
2 þ ewt ;

ð1Þ

and Rst ¼ yt
xt ¼ as1 xt þ as2 yt
1 þ as3 xt
1 þ as4 yt
2 þ est ; ð2Þ where ewt and est are density-independent factors during winter and summer, respectively, having a normal distribution with a mean of zero and standard deviation rw or rs. Typically, small rodent populations exhibit an ordertwo autoregressive structure on an annual basis (e.g., Stenseth et al. 1996a, b; Stenseth 1999). This corresponds to a model of the form: Rt ¼ yt
yt
1 ¼ a1 yt
1 þ a2 yt
2 þ et ;

ð3Þ

where et is a density-independent factor during the year (normally distributed with a mean of zero and variance r2). The annual net growth rate Rt=yt)yt-1 may also be defined by rewriting the combined Eqs. 1 and 2 as a model in y only (see Hansen et al. 1999). Then, ignoring higher-order terms, the parameters a1 and a2 (defining the annual direct and delayed density dependence) may be expressed in the seasonal density dependence as:

Fig. 2a, b Examples of population fluctuation patterns. a The population at Mitsumata showed direct and delayed density dependence for the annual population growth rates and exhibited a cycle of 3–5 years. b The population at Takinoshita exhibited only direct density dependence and its fluctuations seemed to be irregular. Open circles spring abundance index (Xt), solid circles autumn abundance index (Yt) of 150 trap-nights. The averaged census-value for 150 trap-nights in natural forests generated by the Ranger Office was used as the abundance index (for details, see Saitoh et al. 1997, 1998, 1999)

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a1 ¼ aw1 þ as1 þ aw2 þ as2 þ aw1 as1 ;

ð4Þ

and a2 ¼ aw3 þ as3 þ aw4 þ as4 þ aw1 as3 þ as1 aw3
aw2 as2 : ð5Þ The presence of sampling error may lead to substantial bias in estimates of density dependence (e.g., Kuno 1973; Bulmer 1975; Rothery 1998; Shenk et al. 1998; Solow 2001). In our companion paper (Stenseth et al. 2003), sampling error was explicitly accounted for by incorporating both an ecological process model and an observation model [i.e., a state-space model (see de Valpine and Hastings 2002)]. Using the WinBUGS software package (Spiegelhalter et al. 1999), a Bayesian approach was taken to estimate parameters for both annual and seasonal density dependence [for detailed methodology, see Stenseth et al. (2003) as well as http:// www.mrc-bsu.cam.ac.uk/bugs for the software package]. Here, we used the mean of the posterior distributions as representatives of the parameters obtained by Stenseth et al. (2003). Assuming that a density-dependent population has a negative parameter, the probability of density dependence is at least 95% if the upper limit of the 95% credible interval (the Bayesian alternative to the confidence interval) is less than zero. In this paper, we use the term ‘‘significant density dependence’’ at a 5% level (the one-tailed test) if the upper limit of the 95% credible interval is negative.

Seasonal components of annual density dependence

Fig. 3 Frequency distributions of the parameter estimates (a1 and a2 in Eq. 3) for annual direct and delayed density dependence, obtained by incorporating an observation model [and thus incorporating sampling variance; data from Stenseth et al. (2003)]. Shaded parts indicate populations that exhibited ‘‘significant’’ density dependence

Using the data set and methods of analysis described above, Stenseth et al. (2003) estimated both the annual direct dependence and delayed density dependence [a1 and a2 in Eq. 3] for all 84 time-series. The annual direct density dependence was estimated to be around )1 for all populations (mean=)0.93, SD=0.267; Fig. 3). All but one population (98.8%) exhibited ‘‘significant’’ direct density dependence. Annual delayed density dependence was found to be relatively weak (mean=)0.14, SD=0.292; Fig. 3), although it was ‘‘significant’’ in 19 populations (22.6%). These results relating to the annual density dependence confirm the earlier conclusions reported by Saitoh et al. (1997) using a different approach, which did not consider sampling variance. For the seasonal model (Eqs. 1, 2), parameters were assessed to converge appropriately for 74 out of 84 series (Stenseth et al. 2003). Annual density dependence (a1¢ and a2¢), estimated from the seasonal components using Eqs. 4 and 5, corresponded well with the estimates (a1 and a2) for annual density dependence obtained directly from Eq. 3, although the variance of a1¢ and a2¢ increased, as compared to that of a1 and a2. The relationship between these estimates was linear, and direct estimates were well fitted by regression to the following equations: a1=0.417a1¢)0.597 (r2=0.417,

F=52.21, P<0.0001) and a2=0.633a2¢)0.035 (r2= 0.523, F=81.08, P<0.0001). The seasonal parameters for the annual direct density dependence (see Eq. 4) are shown in Fig. 4. The parameter aw1, which relates abundance in the preceding autumn to winter growth rate (Rwt), was typically around )1 (mean=)0.85, SD=0.453). For most populations (62.2%), this effect was ‘‘significant’’. The parameter as1, which relates abundance in the current spring to summer growth rate (Rst), was also negative (mean=)0.18, SD=0.436); for 33.8% of these populations, this effect was ‘‘significant’’. The strength of seasonal density dependence was higher in winter (aw1) than in summer [as1 (for the t-test, t=9.55, P<0.001)]. The other parameters of direct seasonal density dependence were essentially zero (mean=0.12, SD=0.484 for aw2; mean=)0.04, SD=0.409 for as2). The percentage of populations for which these two parameters (aw2 and as2) were ‘‘significantly’’ less than zero did not differ from what was expected by chance alone (5.4% for aw2; 4.1% for as2). The seasonal parameters of delayed density dependence (see Eq. 5) are shown in Fig. 5. All of these parameters were around zero (mean=)0.04, SD=0.393 for aw3; mean=)0.20, SD=0.420 for aw4; mean=)0.15,

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(2.7% for aw3; 12.2% for aw4; 13.5% for as3; 9.5% for as4), the ‘‘significance’’ was not biased toward a specific season.

Relationships between seasonal processes

Fig. 4 Frequency distributions of the seasonal parameters for direct density dependence (see Eq. 4), estimated by incorporating an observation model [and thus incorporating sampling variance; data from Stenseth et al. (2003)]. Shaded parts indicate populations with a parameter that was ‘‘significantly’’ less than zero

Fig. 5 Frequency distributions of the seasonal parameters for delayed density dependence (see Eq. 5), estimated by incorporating an observation model [and thus incorporating sampling variance; data from Stenseth et al. (2003)]. Shaded parts indicate populations with a parameter that was ‘‘significantly’’ less than zero

SD=0.473 for as3; mean=)0.003, SD=0.305 for as4). Although there were some populations for which some of these four parameters were ‘‘significantly’’ negative

Pair-wise correlations were examined between seasonal parameters for direct and delayed density dependence using the Pearson correlation coefficient (Fig. 6). Strong negative correlations were found between aw1 and aw2, as well as between as1 and as2, for direct density dependence. These are not surprising results, because these parameters were estimated using Eq. 1 or Eq. 2, in which aw1 and aw2 (or as1 and as2) had an additive relationship. Thus, we were interested in the relationships of coefficients between different seasons. No significant correlations were found for direct density dependence. However, for delayed density dependence, we did find a significant positive correlation between aw3 and as3. The strength of direct density dependence was significantly higher during winter (aw1) than during summer (as1). This suggests a major contribution by aw1 to the overall annual direct density dependence. Annual direct density dependence corresponds to the effects of the previous autumn abundance (yt-1) on the current autumn abundance (yt), which emerges through both winter and summer processes. The parameter aw1 represents the indirect effects of yt-1 on yt through xt (see Eq. 1), while those of as2 directly incorporate effects of yt-1 on yt (see Eq. 2). In spite of this, effects of aw1 were stronger than those of as2. It should be noted that a considerable number of populations exhibited ‘‘significant’’ density dependence in summer processes (as1), although relatively weakly, and that there was no correlation between aw1 and as1 (r=0.08, P=0.51). This suggests that seasonal density dependence may operate through different mechanisms of winter and summer processes of direct density dependence. Strong density dependence was not found in any seasonal component for delayed density dependence, in contrast to direct density dependence, but aw3 and as3 were positively correlated (Fig. 6; r=0.25, P=0.03). Since these coefficients were independently estimated using Eqs. 1 and 2, this relationship is not an artefact. This positive relationship suggests that the same factor may operate on winter and summer processes of delayed density dependence.

Mechanisms Taking into account sampling variance, we found annual direct density dependence to be strong in almost all studied populations. Annual delayed density dependence was also found in a significant proportion of populations, and both of these results are consistent with

170 Fig. 6 Correlation matrix for seasonal parameters of direct (upper right) and delayed density dependence (lower left). The Pearson correlation coefficient (r) is shown for each combination. Statistical significance is indicated by asterisks (*P<0.05, **P<0.01, ***P<0.001). Ellipses indicate density ellipses that contain the specific mass of points, as determined by the probability (95%). Significant relationships are shown by a bold ellipse

earlier findings that did not account for sampling variance (see Saitoh et al. 1997). By dividing the annual growth rates into seasonal components (summer and winter), we were able to demonstrate that the observed strong annual direct density dependence emerged through both winter and summer processes; however, the contribution of winter processes was stronger (see also Stenseth et al. 2003). Stenseth et al. (2002) indirectly estimated seasonal density dependence using only autumn abundance data (a dataset that covered a larger part of Hokkaido than the present data sets). That study also supported the profound contribution of winter processes to annual direct density dependence. Together, these results point to the importance of winter processes. However, the empirical study of direct density dependence has, at least until fairly recently, focused on the summer season. One mechanism that is expected to account for observed annual density dependence is social suppression of reproduction (e.g., Stenseth et al. 1996b; Saitoh et al. 1997, 1998, 1999). Microtine rodents, particularly the genus Clethrionomys, exhibit strong spatial and social organisation (for reviews, see Bondrup-Nielsen and Karlsson 1985; Bujalska 1985; Gipps 1985; Ishibashi et al. 1998a; for a more general treatment, see Cockburn 1988). Female grey-sided voles often establish breeding territories, and at high densities, when they cannot easily obtain territories, they exhibit delayed maturation. In Hokkaido,

territoriality among grey-sided voles is common (Saitoh 1985), and maturation rates are reduced at high densities (Abe 1976; Saitoh 1981; Nakata 1989; but see Saitoh 1991). Density dependence for summer processes (as1), which was detected in a significant proportion of studied populations (Fig. 4), may indeed reflect social suppression of reproduction. However, the estimated seasonal density dependence was much stronger during winter (aw1) than during summer. Since no correlations between seasonal density dependence coefficients were found (Fig. 6), another mechanism is expected to operate during the winter season. In Hokkaido, the main food items of grey-sided voles during winter are the leaves of bamboo grasses (Sasa spp.). Although there are plenty of bamboo grasses available, the leaves are not particularly nutritious during winter, implying that food availability may serve as a mechanism of density dependence. If resources during winter (e.g., food or wintering sites) are restricted, and if resources are stable from year to year, a similar number of voles would be expected to survive winter, regardless of their abundance during the previous autumn. This may bring about a density-dependent decrease in winter growth rates. Although there are many generalist predators (snakes, birds, and mammals) in Hokkaido (Henttonen et al. 1992), their activity under snow cover is restricted. The least weasel, Mustela nivalis, is the most important

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predator under snow. Although the least weasel is a specialist predator, it could be an agent for direct density dependence, as it thoroughly exploits voles (except individuals that are able to escape to limited refuges) in winter. However, little is known about the ecology of this weasel in Hokkaido. The reduction of immune function caused by cold stress may also facilitate density dependence. Cichon et al. (2002) demonstrated that cold stress may significantly reduce the immune response of mice. Immune function is probably subject to a trade-off over limited energy; it has been experimentally verified in birds that increased activity and reproduction reduce the immune response (Deerenberg et al. 1997; Ra˚berg et al. 2000; Cichon et al. 2001). A trade-off between immune function and thermoregulation may thus occur after an animal has depleted its nutrient reserves (Cichon et al. 2002). Cichon et al. (2002) also showed that suppression of the immune response is elicited by long-lasting cold stress. Thus, voles that are exhausted during and after reproduction, as a result of competitive interactions or exposure to small nutrient reserves (as commonly seen during high-density conditions), are more likely to lose their immune function under cold stress. In the greysided vole, over-wintering populations consist mainly of autumn-born individuals that did not breed in the previous year (Abe 1976; Ota 1984). Ishibashi et al. (1998b) showed in a grey-sided vole population that small individuals could not survive winter. Since a high-density population may hold more individuals that are immunologically weakened (from exhaustion or small body size), a cold winter could cause density-dependent population decreases. In this context, it is worth noting that density dependence is strongest in areas of Hokkaido that have longer winters (Stenseth et al. 1998, 2002). Delayed density dependence is essential to generate cyclic fluctuations (Royama 1992; Stenseth 1999). A positive correlation was found between seasonal density dependence coefficients (aw3 and as3; Fig. 6); thus, the same process generating delayed density dependence may operate both during winter and summer in grey-sided vole populations of Hokkaido. The summer period includes processes of both reproduction and death, but the winter period consists only of death. Therefore, a mechanism of delayed density dependence that is common to both winter and summer processes should be related to death. Specialist predators are the most plausible agents for delayed density dependence. Specialist predators are generally thought to track rodent densities with a time delay (Hassell and May 1986; Hanski et al. 1991; Hanski and Korpima¨ki 1995), and predator-prey interactions are often applied to explain the geographic gradient (from cyclic to stable) in cycling periods and population amplitudes in Fennoscandia (Hansson and Henttonen 1985, 1988; Henttonen et al. 1985). Saitoh et al. (1999) compared the structure of density dependence between the grey-sided vole and two species of wood mouse (Apodemus speciosus and A. argenteus) using time series data from Hokkaido. Direct density

dependence was detected for all three species, but delayed density dependence was found only in the greysided vole. These contrasting results between the greysided vole and the wood mice may be explained by predator-prey interactions. Many predators in Hokkaido specialise on the grey-sided vole; even the red fox, which is a typical generalist predator, selectively preys upon this species (Yoneda 1979). Thus, the influence of predators may be strongly biased toward the grey-sided vole, which corresponds well to the fact that a significant proportion of grey-sided vole populations exhibited delayed density dependence but almost none was observed in wood mice. Microparasites, including viruses, may exhibit behaviour similar to that of specialist predators. Cowpox virus and vole tuberculosis respond to vole dynamics with a 6-month delay (R. Cavanagh, X. Lambin, T. Ergon, I. Graham, D. van Soolingen, M. Begon, personal communication), and these pathogens may give rise to negative effects on the population growth of voles throughout the year (Feore et al. 1997; Telfer et al. 2002). The role of pathogens in rodent cycles has been largely neglected owing to the lack of direct evidence in the field, although their effects have been noticed traditionally and theoretically. However, recent methodological advances require us to re-visit this question. Although intrinsic factors involving changes in individual differences may cause delayed density dependence (for a review, see Krebs 1996), this seems not to be the case for the Hokkaido vole, because hypotheses on intrinsic factors primarily apply to breeding processes, although delayed density dependence should be expected both in summer and winter processes. For instance, a recent maternal-effects model, which is a major hypothesis for an intrinsic factor (Turchin and Hanski 2001), is based on the interactions between resource and population densities during the breeding season (Inchausti and Ginzburg 1998). Based on our assessment of the possible factors that could generate various types of density dependence structures, we suggest a need for more research on the winter ecology of voles, particularly on their interactions with food resources and predators. Studies of immune function may provide valuable new insights regarding mechanisms. Summer ecology should be studied more as a process determining peak densities. Acknowledgments We are indebted to the Forestry Agency of the Japanese Government and to the Forestry and Forest Products Research Institute of Japan (FFPRI) for providing the material analysed in this paper. Grants from the Japan Society for Promotion of Science, the University of Oslo, the Norwegian Research Council (NFR/NT), the Centre for Advanced Study (Oslo, Norway), and FFPRI to N.C.S. and T.S. made it possible to start our project and facilitated our analyses. NFR also supported M.O.K. and H.V. This study was also supported in part by Grantin-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japanese Government (No. 14340240) to TS. Anonymous reviewers and the editor provided valuable comments and suggestions on an earlier version of the paper.

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