Predator–vole interactions in northern Europe: the role of small mustelids revised

Abstract

The cyclic population dynamics of vole and predator communities is a key phenomenon in northern ecosystems, and it appears to be influenced by climate change. Reports of collapsing rodent cycles have attributed the changes to warmer winters, which weaken the interaction between voles and their specialist subnivean predators. Using population data collected throughout Finland during 1986–2011, we analyse the spatio-temporal variation in the interactions between populations of voles and specialist, generalist and avian predators, and investigate by simulations the roles of the different predators in the vole cycle. We test the hypothesis that vole population cyclicity is dependent on predator–prey interactions during winter. Our results support the importance of the small mustelids for the vole cycle. However, weakening specialist predation during winters, or an increase in generalist predation, was not associated with the loss of cyclicity. Strengthening of delayed density dependence coincided with strengthening small mustelid influence on the summer population growth rates of voles. In conclusion, a strong impact of small mustelids during summers appears highly influential to vole population dynamics, and deteriorating winter conditions are not a viable explanation for collapsing small mammal population cycles.

1. Introduction

Trophic interactions have a profound impact on population dynamics [1]. Population cycles, in particular, are commonly thought to arise from trophic interactions, which can introduce a delay in the regulation of population growth [1]. Boreal voles of Eurasia are a well-studied example of species in which predation can cause delayed density dependence of population growth and cyclic population dynamics [2,3]. Voles are often the most abundant mammals in boreal and subarctic regions, and an indispensable food source for numerous avian and mammalian predators [4,5]. The interaction between the vole and the predator communities, and the cyclic population dynamics observed in both, are key phenomena in northern Eurasian ecosystems.

During recent years, there have been reports of collapsing rodent cycles with potentially detrimental effects on the predator community [6,7]. The loss of cyclicity has been attributed to milder and shorter winters, which are thought to increase density-independent winter mortality, and decrease the influence of delayed density dependence [6,7]. However, we recently showed that mild winters are not associated with collapsing cyclicity among boreal vole populations [8]. Furthermore, it is not known how the interactions between voles and predators vary temporally and geographically, so the attribution of causality to altered predator–vole interactions is far from clear.

Practically all terrestrial carnivores in northern Europe consume voles at least occasionally, and the following predators show a clear preference for voles: the small mustelids [9], the red fox [10], the pine marten [11] and several owl and raptor species [12,13]. The small mustelids, the least weasel (Mustela nivalis nivalis) and the stoat (Mustela erminea) are key predators in the boreal vole cycle [2]. They are small and highly adapted to preying on voles even in their nests and under the snow cover, and can be the main cause of mortality in vole populations [14]. They depend almost exclusively on voles [9], but have a much lower intrinsic growth rate than their prey, and hence a strong but delayed numerical response to vole densities, resulting in delayed density-dependent predation pressure on vole populations [9,15]. Of the two species, the stoat is considered to be more of a generalist than the least weasel [9].

Generalist predators, exploiting a variety of food sources, are thought to have a stabilizing effect on the prey populations, preying on voles during the peak phase of the cycle, and switching to alternative prey when vole densities are low [16,17]. Because of this, the generalists have the ability to transmit the cyclic population dynamics of voles to their alternative prey populations [18,19]. According to diet analyses, the red fox (Vulpes vulpes) and the pine marten (Martes martes) are generalist predators in Fennoscandia [10,11]. They are thus expected to have a cycle-dampening effect [17].

Birds of prey may dampen or enhance cyclicity in their prey. Nomadic species are able to travel long distances and nest where vole densities are high, i.e. have a direct numerical response and dampen the vole cycle [13,20]; on the other hand, migratory birds are not able to survey vole densities during the winter, and may rely on last season's information to decide where to nest [21]. The reproductive effort and success of the resident raptors is dependent on current vole densities [22,23]. Therefore, avian predators might respond to vole densities of the previous autumn (decision on where to nest, recruitment of last year's young), spring (reproductive effort) or the current summer (survival of fledglings).

The interactions between the vole and the predator communities of northern Europe have been studied with mechanistic models and phenomenological time-series analyses [2,17,24] and large-scale, yet local, manipulative experiments (reviewed by [25,26]), but they are not well described on a large temporal and geographical scale, let alone using observational data. Predator–vole interactions are likely to depend on environmental conditions and may thus be subject to spatial and temporal variation: e.g. snow cover may influence the availability of voles to avian and larger mammalian predators [23], temperatures may affect the energy requirements of predators [23,27]; and food availability to voles will influence the relative contribution of predation on vole population growth rates [28].

In this study, we aim to characterize the interactions between voles and the specialist mammalian, the generalist mammalian and the avian predators using animal population monitoring data collected throughout Finland during 23 years. We will estimate the time lags in the predator responses to vole densities as well as the predator effects on vole population growth rates. Specifically, we test the hypothesis that weakening vole-specialist predator interactions during winters are associated with the collapse of the vole cycle. Finally, we use the data-derived parameter estimates to simulate vole population dynamics under a number of scenarios to gauge the roles of different predators in the boreal vole cycle.

2. Material and methods

(a). Vole population data

Vole populations were censused using biannual snap trapping (in spring before the reproductive season of voles in mid-March to mid-June and in autumn after the reproductive season in mid-August to mid-October (both times dependent upon geographical location and seasonal phenology)) in forest and old-field habitats in 32 locations during 1986–2011 (figure 1; electronic supplementary material, figure S1). Voles of the genera Microtus and Myodes were included in the analyses. On average, each trapping session included 289 trap nights (range 30–1800). Trapping was conducted with standard metal mouse snap traps. At each location, a mean of 50–100 traps were set either (i) in a line, in clusters of three traps with an inter-trap distance of 1–2 m and an inter-cluster distance of 10–20 m, or (ii) according to the small quadrat method [29]. Traps were set for one to four nights and checked and re-set if necessary once a day. Regardless of the number of traps used per session, or the number of consecutive trap nights, each trap effectively traps a standard-size area. Since the density of traps (traps per unit area) does not change between sites or over time, our trapping indices from different areas and times are comparable.

Figure 1.

Data collection locations: (a) vole trapping locations, (b) mammalian predator snow-track-monitoring locations, and (c) avian predator monitoring areas. Letters in map a denote the three regions from which results were summarized (N, north; SW, southwest; E, east).

The vole data comprise the following species: Microtus agrestis (28%), Microtus levis (5%) and Microtus oeconomus (6%), and Myodes glareolus (57%), Myodes rutilus (3%) and Myodes rufocanus (1%). Density indices were calculated as N = log ((total number of voles trapped + 1)/trap nights × 100). Seasonal vole population growth rates were calculated as S_t − A_{t − 1} (winter) and A_t − S_t (summer), where S denotes spring vole density, A autumn vole density and t denotes year. Each vole time series was standardized to mean = 0 to correct for potential trapping-site quality bias. We decided to pool all vole species despite the ecological differences between Myodes and Microtus voles. We have analysed the variation in the spatio-temporal dynamics separately for Microtus voles in their principal habitat (old fields) and for Myodes voles in forests. The spatio-temporal patterns in the population dynamics of the different genera parallel each other, and those obtained with the pooled vole densities (see table 1 in [8]). Furthermore, the different species are known to fluctuate in synchrony [8,30] and be subject to predation by the same predators [31,32]. Therefore, the pooled data allow us to answer the study questions more clearly than the genus-specific results would.

(b). Mammalian predator data

We obtained density indices for the mammalian predators from the Finnish Game and Fisheries Research Institute [33]. Mammalian predator densities were monitored by counting snow tracks on previously marked transects in winter (mid-January to mid-March) during 1989–2011. Triangles consisting of three 4 km transects were surveyed and all mammal tracks crossing the transect were counted and identified to species 1 or 2 days after a pre-check or snowfall. Annually, ca 800 triangles are monitored (figure 1 and electronic supplementary material, figure S1). As weather conditions could influence the visibility of the snow tracks, the protocol set by the Finnish Game and Fisheries Research Institute rigorously defines the environmental circumstances under which the snow track counts may be conducted. First, the transect must be walked or skied twice—first to mark all existing tracks, then at least 24 h later to count all new tracks. This time of track accumulation cannot include extreme cold temperatures, heavy winds or snowfall. Alternatively, tracks may be counted without a preliminary marking round, 24–48 h after a snowfall. In both cases, the snow cover must be fine and soft enough to enable the smallest recordable animals, least weasels, to leave identifiable tracks. These strict guidelines ensure that the weather conditions during the snow track count are geographically and temporally consistent. The degree of detectability of tracks is thus unlikely to differ between geographical areas.

The density index for a given species is calculated as , where the n_i,t is the number of tracks observed per 10 km of survey route at location i and year t, n_min is the minimum observed non-zero n, and d is the number of days during which the tracks accumulated. We included the densities of four mammalian predators and aggregated the predator species into two groups based on their behaviour and morphology: the small mustelids (the least weasel and the stoat) formed the specialist predator group, and the larger mammalian predators (the red fox and the pine marten) the generalist predator group [17]. Density indices of both groups were calculated for each vole trapping location by distance-weighted averaging (using all data points, with weight decreasing by distance²). The mammalian predator data were globally standardized to mean = 0 to render the values of the different predator groups comparable.

(c). Avian predator data

The data for avian predators were obtained from the Finnish Museum of Natural History [34]. The monitoring scheme is organized in 25 areas (figure 1; electronic supplementary material, figure S1), which together cover all of Finland. In each area, all known raptor territories are visited each spring and summer, and checked for nests from which eggs and later the chicks are counted. Raptor monitoring data were available from 1986 to 2011. We included data on the following species, which prey on voles and which are relatively abundant in our study area: the nomadic or migratory species Asio flammeus, Asio otus, Aegolius funereus, Glaucidium passerinum, Falco tinnunculus, Circus cyaneus and Buteo lagopus; and the resident species Strix uralensis, Strix aluco, Bubo bubo and Buteo buteo. Although it is known that these species react slightly differently to vole abundances and differ in their specialization in voles, their densities showed strong correlations (r > 0.8), which justified the calculation of a total avian predator density index as , where n_i,t refers to the number of nesting pairs in area i and year t, c_i,t to the average number of chicks per nest in area i and year t, and s_i,t to the number of territories surveyed in area i and year t. The avian predator density index was calculated for each vole-trapping site by averaging over all raptor monitoring areas within a 50 km distance. Prior to combining the avian time series, they were de-trended, as some showed potentially artificial increasing trends owing to increased nest-box availability. The avian predator density was calculated for each vole-trapping site by averaging over all raptor monitoring areas within a 50 km distance.

(d). Influence of predators on vole population growth rates

To estimate the spatial and temporal variation in the impact of the different predator groups on vole populations, we modelled vole population growth rates during winter (model 1) and summer (model 2) as a function of vole and predator indices. Mammalian predator indices were measured in winter, and avian predator indices in summer. We assumed the linear models:

where P₁ refers to the density index of the small mustelids, P₂ to the generalist mammalian predators and P₃ to the avian predators.

Because we had no a priori knowledge of the geographical and temporal variation in predator–vole interactions, we began with a very flexible model, and then simplified the model based on the data. Initially, we allowed the parameters a–f to vary with time and space by including a latitude × longitude × (year + year²) interaction. After fitting these models, we simplified the models using Akaike information criterion (AIC; [35]): all terms whose elimination would have resulted in an increase in AIC were retained in the final model.

We validated the models by dividing the dataset randomly into a training set (50% of the data points) and a test set (50%), refitting the models to the training data and using these models to predict the test data; this was repeated 50 times (electronic supplementary material, figure S2). In addition, we assessed the performance of the models by simulating vole and predator dynamics using parameter estimates from the models; adequate models should be able to create realistic dynamics.

Based on the models, we calculated the relative contributions of the different predator groups and of the non-predation-attributable density dependence to the variation in vole population growth rates for each trapping site and year as a fraction of the total variation. To do so, we decomposed the total variance (example for model 1) as:

where the variances and covariances are calculated from the whole dataset, σ² is the variance of the residual term ɛ and the model parameter values a–f depend on sampling location and year.

To simplify the interpretation of the results, rather than considering the relative contributions of covariances separately, we decided to treat the covariances by assigning half of the covariances to each of the terms involved. As an example, the variance explained by the small mustelids was calculated as:

These values were summarized to represent three regions by averaging over the trapping locations in each: northern Finland (above the 66th latitude), southwestern (less than 64th latitude and less than 25th longitude) and eastern (more than 27th longitude) Finland (figure 1).

(e). Influence of vole population densities on predator abundance indices

Using the same initial spatio-temporal structure as in models 1 and 2, we modelled the predator indices as a function of current and past vole densities to determine the magnitude of and the time lags in the predators' responses:

We did not include previous predator densities in the predator models because after accounting for the vole-cycle-attributable autocorrelation, no temporal autocorrelation was left in the predator time series. AIC-determined model reduction was performed as explained above. The relative contributions of vole densities at different time lags to the predator densities were calculated as:

The values were summarized to regions (figure 3) as explained earlier.

Figure 3.

Relative contributions of vole densities at different time lags to predator densities, estimated with models (a) (mammalian predators) and (b) (avian predators) and averaged to northern, southwestern and eastern Finland, as in figure 1. Mammalian predator densities were monitored in winter, and therefore the time lags presented are around five months (vole density in autumn_{t −1}), around 10 months (vole density in spring_{t −1}), and around 17 months (vole density in autumn_{t −2}). Avian predator densities were monitored in summer, and the time lags are around two months (vole density in spring_t), around nine months (vole density in autumn_{t −1}), and around 14 months (vole density in spring_{t − 1}).

(f). Roles of the different predators in the boreal vole cycle: simulation

We used the parameter estimates from models 1–3 to simulate vole and predator population dynamics. The simulations were used both for model validation, i.e. to confirm that the models were capable of reproducing the population dynamics observed in different locations and time points, and for scenario simulations, i.e. to investigate the roles of the different predators in vole population dynamics. We focused on three geographical regions, which we had previously discovered to exhibit distinctly different vole population dynamics: the north, the southwest and the east [8]. Using the parameter estimates for the geographical locations and the year 2011 (the last available year with full data records), we simulated 1000 years of vole and predator time series under eight different scenarios in which one, two or all predator groups were removed by setting their density to the minimum observed value in the dataset.

We estimated the direct and delayed density dependence of vole population growth rates in the simulated time series by regressing the seasonal vole population growth rates against the current and the 1-year-lagged vole densities [8]. To assess the variability in the model predictions, we divided the 1000-year time series into 25-year sections, and fitted autoregressive models to each section. Consensus density dependence values were obtained by averaging over the results from the 40 sections, and annual density dependence was calculated from the seasonal density dependence values as in [8]. From each 25-year section, we calculated the standard deviation of the population densities (s-index) as an index of amplitude, and seasonality as the difference between the average summer and average winter population growth rates, and averaged these over all sections. The type of population dynamics was inferred from the density dependence values, autocorrelation values and from visual inspection of the time series. All statistical analyses were conducted with R [36].

3. Results

(a). Model validation

Our models performed well in model validation: they produced realistic predator–vole dynamics capturing the spatial and temporal variation in vole population dynamics (compare figure 4 to [8]). When refitted with 50% of the data points, they predicted the remaining 50% fairly well (electronic supplementary material, figure S2). Only the small mustelid model's performance was somewhat unsatisfactory, as the correlation between the observed and the predicted small mustelid indices was only 0.42. The final best models based on the model selection are presented in the electronic supplementary material, tables S1–S4.

Figure 4.

Results of simulations. Parameter estimates from models 1–3 were used to simulate vole (shown in figure) and predator (not shown) population dynamics under different predation scenarios. The full model scenario refers to a simulation with all parameters included in the model, and thus represents the model prediction for current population dynamics. In the different predation scenarios, the densities of the different predator groups were set to the minimum observed value. Panels (a–c) show the simulated vole time series in density dependence space. Multiannual cycles exist under the parabola with cycle length increasing from left to right, and irregular dynamics above the parabola. Panels (d–f) show the s-indices (mean ± s.d.) and panels (g–i) show the seasonality in vole population growth rates, calculated as the difference between mean summer and mean winter population growth rates.

(b). Spatio-temporal variation in predator–vole interactions

The relative influences of the different predator groups on vole population growth rates showed substantial variation over the years and regions (figure 2). In the north, the influence of the small mustelids on vole populations showed an increasing temporal trend during both seasons, and they are currently estimated to be the strongest force affecting the winter population growth rates of voles (figure 2a,b). According to our models, the generalist predators influenced vole populations only during summers in the north, and the relative impact of the avian predators was declining, particularly during winters (figure 2a,b).

Figure 2.

Relative contributions of predators and non-predation-attributable density dependence (‘delayed DD’ and ‘direct DD’) to the summer and winter population growth rates of voles, estimated with models 1 and 2 and averaged to northern, southwestern and eastern Finland, as in figure 1.

Predators were estimated to have a modest impact on the winter population growth rates of voles in the southwest (figure 2c). However, the relative contribution of the small mustelids on the summer population growth rates of voles appeared to have increased considerably (figure 2d). The generalist predators were estimated to have very little impact on vole populations in the southwest, and the avian predators to have a modest, and possibly declining, impact during both seasons (figure 2c,d).

The factors affecting the winter population growth rates of voles in the east were similar to those in the north: a strong avian predator influence substituted in the recent years by a rapidly increasing small mustelid influence (figure 2e). However, during summers, the generalist and avian predators were estimated to be a stronger force than the small mustelids (figure 2f).

The dependence of the predator indices on vole population densities tended to be strongest, and the delays longest, in the north (figure 3). Particularly in the north and southwest, there appeared to be a temporal trend of shortening delays in the numerical responses of the predators. The small mustelids responded to all vole densities measured during the previous 18 months, the longest delay being the weakest. The larger mammalian predators responded to vole densities with a 10 month delay in the north, and with a five-month delay in the south. The avian predators responded to vole densities with a time lag of 2–10 months.

(c). Is predation necessary for cyclic vole population dynamics?

Our model correctly predicted a regular, high-amplitude 5-year cycle in the north for the year 2011 (figure 4a,b, black symbol; electronic supplementary material, figure S3). Removing either the small mustelids or the avian predators weakened the delayed density dependence (figure 4a, pink and light blue symbols) and amplitude (figure 4b), and weakened the cycle (electronic supplementary material, figure S3). The seasonality disappeared in the absence of the small mustelids, regardless of which predators remained (figure 4c, pink, orange, dark blue and grey symbols), suggesting that the major cause of winter mortality in the north is predation by the small mustelids (figure 2a). Removing both the avian predators and the small mustelids, with or without the larger mammalian predators, weakened the delayed density dependence to the extent that the vole cycle collapsed (figure 4a, orange and grey symbols; electronic supplementary material, figure S3), and the amplitude was clearly reduced (figure 4b). The generalist mammalian predators did not influence vole population dynamics to a great extent in the north (figure 4a–c, yellow symbols).

The model predicted a 3–4-year cycle in southwestern Finland (figure 4d, black symbol; electronic supplementary material, figure S4), with a lower amplitude than in the north (figure 4e). The removal of the small mustelids had a strong impact on vole population dynamics, regardless of whether the predators remained present: both direct and delayed density dependence were weakened to the extent that the vole cycle collapsed (figure 4d, pink, orange, dark blue and grey symbols; electronic supplementary material, figure S4) into completely seasonal (figure 4f), high-amplitude dynamics (figure 4e). The small mustelids were capable of maintaining cyclic vole population dynamics in the absence of the other predators: removing the generalist and the avian predators increased the cycle period (figure 4d, red symbols; electronic supplementary material, figure S4) and weakened the seasonality (figure 4f).

The model predicted irregular dynamics in eastern Finland (figure 4g; electronic supplementary material, figure S5). Predator removal had no effect on the density dependence (figure 4g). Removing the small mustelids reduced and removing the generalist mammals increased the seasonality and the amplitude (figure 4h,i, pink and yellow symbols); whereas removing the avian predators had no influence on vole population dynamics (figure 4h,i, light blue symbols).

(d). Changes within the predator community

A high relative abundance of the stricter vole specialist, the least weasel, in relation to the semi-generalist stoat, coincided with cyclic vole dynamics (electronic supplementary material, figure S6). In western Finland, with continuously cyclic vole dynamics, the least weasel has been more abundant than the stoat; in northern Finland, the relative abundance of the least weasel was very low during the non-cyclic period and is currently increasing together with the strengthening cycle. Most impressively, the relative abundance of the least weasel peaked in synchrony with the vole density peaks in the north: the stoat dominated during cyclic lows, and the least weasel when voles were abundant. A similar pattern was observed in the east, although there the increasing relative abudance of the least weasel was evidently not sufficient to strengthen the vole cycle. One possible explanation is the relative abundance of the generalist mammalian predators, which in eastern Finland was in favour of the pine marten, while the red fox was relatively more abundant in western Finland.

4. Discussion

We analysed predator–vole interactions comprehensively over a large geographical area (ca 300 000 km²) and a long time period (26 years), capturing the return of the high-amplitude vole cycle in the north as well as the collapse of the cycle in the east. Our results show that the predator–vole interactions vary temporally and geographically, and that this variation explains many of the observed changes in vole population dynamics.

Not surprisingly, our model identified the small mustelids as key players in the boreal vole cycle: their numerical response was estimated to be delayed and sufficiently strong to cause negative delayed density dependence in vole populations, supporting earlier results [9,15,24]. Earlier mechanistic modelling studies on vole–predator interactions have suffered from the lack of predator time series to confirm the results. The fact that very different approaches, based on different types of data and models, all lead to the same conclusion offers strong support for the specialist predator hypothesis.

In the north, the small mustelids were estimated to be currently the strongest force affecting the winter population growth rates of voles. However, their influence on vole populations appears not to be restricted to the winter season, but occurs, increasingly, during summers, as well. The increase in summer impact coincides with increasing summer precipitation in the north [8]. In the coastal southwest, where winters are milder and shorter than in the more continental east and in the north, the small mustelids appear to exert their influence on vole populations mainly during summers. Hence, mild winters appear not to weaken the overall impact of the specialist predators on vole populations. Furthermore, as the vole cycle has collapsed in the east despite a strong relative influence of the small mustelids during winters, it appears that predation by the small mustelids in winter is alone not sufficient to create cyclic vole dynamics. Rather, a sufficient impact of the small mustelids during summers may be an elemental part of the vole cycle, contributing to the summer declines which characterize cyclic, but not non-cyclic, vole populations [3,37,38]. In addition to the small mustelids, the avian predators were found to influence vole population dynamics, and to be an important source of delayed density dependence in vole populations (see also [21]).

Generalist predators are usually thought to dampen or inhibit cyclic dynamics in their prey populations [17]. However, the red fox is also considered strongly dependent on voles, to the extent that the red fox game bag index has been used as a surrogate for vole density [39]. Yet another view is that vole populations are not influenced by the generalist predators, as previously shown for the red fox [18]. According to our data, the generalists did not depend strongly on voles, nor did they markedly influence vole populations, especially in southern Finland. In the north, however, where alternative food is scarce and where the climate is unfavourable for the red fox [27], the generalist predator index responded occasionally quite strongly to the spring densities of voles and influenced their summer population growth rates. This suggests that in unfavourable environments, voles form a significant food source to fox cubs in their early life. However, the overall impact of the generalists on vole population dynamics was weak.

All predators appear to be responding to vole densities with shortening time lags, which may contribute to increasing direct, and weakening delayed density dependence in vole populations. However, this may not unequivocally be the case. The predator populations are monitored only once a year, which makes it difficult to estimate the time lags in their responses and the timing of their impact on the vole populations. It is possible for example, the small mustelids to be dependent on the spring densities of voles, while influencing the vole populations during the following winter, or to be dependent on the autumn densities of voles and to influence vole populations during the following summer. In both cases, the impact on the density dependence of vole population growth rates would be the same. The changes in the time lags of the predators' numerical responses may also be owing to temporal variations in the relative abundances of the different species. Different raptor species respond to vole densities with different time lags [40], and the stoat responds to vole densities with a shorter time lag than the least weasel [15]. Furthermore, the ability of the predators to track vole abundances and to adjust their reproductive effort accordingly may depend on weather conditions, which could lead to the observed temporal variation in the responses.

The reliability of the snow track indices is a matter of debate, especially with respect to the small mustelids (discussed recently in [15,41]). Our results indicate a marked amount of measurement error in the small mustelid index, as only ca 50% of variation in the index was attributable to the vole abundances, although these predators are known to rely heavily on voles [9]. Furthermore, a large fraction of the variation in vole population growth rates was unexplained by the predator indices, although predation has been shown to be a major cause of mortality in vole populations [14]. The generalist and avian predator indices are likely to be more accurate than the small mustelid index: both indices behaved in our analyses as expected based on earlier studies, the generalists cannot move under the snow cover, and the avian predator index is derived from counts of the animals themselves. Measurement error in the predator indices is likely to weaken, but not strenghten, the estimated interactions between voles and the predators; our estimates are therefore conservative and the interactions may be stronger in reality. Because of the unknown amount of measurement error in the predator indices, some of the unexplained density dependence in vole population growth rates is most likely attributable to predation, although undoubtedly other factors, such as food supply [28], also influence vole populations.

According to our results, predation, by the small mustelids in the southwest and by the whole predator guild in the north, is a necessary contributor to the regular, high-amplitude vole cycle in northern Europe. The small mustelid–vole interaction is not restricted to winters, confirming our previous finding that mild winters do not necessarily lead to a collapse of the vole cycle [8]. The observed strengthening of delayed density dependence in vole populations coincided with strengthening small mustelid influence on the summer population growth rates of voles. A strong impact of the small mustelids during summers appears important to cyclic vole dynamics.

Ethics statement

The trapping methods applied in this study were approved by the Finnish Animal Experiment Board and the Finnish Ministry of the Environment.

Data accessibility

Data are archived in Dryad (doi:10.5061/dryad.h3bt7).

Funding statement

The study was financially supported by the Academy of Finland (grant no. 133495 to O.H., 250709 to E. Kor, 218107 and 257340 to E. Kos, and 250243 and 250444 to O.O.); EU grant FP7–261504 EDENext (H.H.); European Research Council, ERC Starting Grant 205905 (O.O.).