The return of the vole cycle in southern Finland refutesthe generality of the loss of cycles through‘climatic forcing’

J O N E . B R O M M E R *, H A N N U P I E T I A I N E N *, K A R I A H O L A w , PA T R I K K A R E L L *,

T E U V O K A R S T I N E N z and H E I K K I K O L U N E N §

*Bird Ecology Unit, Department of Biological and Environmental Sciences, PO Box 65 (Viikinkaari 1), FI-00014 University of

Helsinki, Helsinki, Finland, wTornihaukantie 8D 72, FI-02620 Espoo, Finland, zJuusinkuja 1, FI-02700 Kauniainen, Finland,

§Nikkarinkatu 52, FI-15500 Lahti, Finland

Abstract

Multiannual cycles in the abundance of voles and other animals have been collapsing in

the last decades. It has been proposed that this phenomenon is ‘climatically forced’ by

milder winters. We here consider the dynamics of bank and field voles during more than

two decades in two localities (170 km apart) in southern Finland. Using wavelet analysis,

we show that a clear 3-year cycle disappeared in the mid 1990s. However, the vole cycle

returned in both localities after about 5 years despite winters becoming increasingly

milder. In both localities, vole cycles were mainly determined by bank voles after the

period of noncyclic dynamics, whereas field voles were dominant before this irregularity.

Wavelet coherency analysis shows that spatial synchrony temporarily broke down

during the period of noncyclic dynamics, but was fully restored afterwards. The return

of the cycle despite ongoing rapid climate change argues against ‘climatic forcing’ as a

general explanation for loss of cycles. Rather, the population-dynamical consequences of

climate change may be dependent on the local species composition and mechanism of

delayed density dependence.

Keywords: boreal ecosystem, cycle, population dynamics, vole, wavelet analysis

Received 16 February 2009; revised version received 15 May 2009 and accepted 23 May 2009

Introduction

Cyclic population dynamics are a profound feature of

animals living in the boreal zone, including several

species of mammals, grouse and Lepidoptera (Lindstrom

et al., 2001). Because of their central position in the food

chain, the cyclic fluctuations in the abundance of these

consumers reverberate across much of the ecosystem as a

whole (Linden, 1988; Ims & Fuglei, 2005). Perhaps the

best-studied example of cyclic population dynamics is

provided by the Fennoscandian vole cycle, which has

been documented for both a long temporal period and

over a large spatial area (Hansson & Henttonen, 1985;

Hanski et al., 1991). In essence, voles show cyclic dy-

namics above 601 northern latitude (Hansson & Hentto-

nen, 1985). Although there is evidence of cyclic

fluctuations also in a number of central European local-

ities (see e.g. Lindstrom et al., 2001; Lambin et al., 2006),

the Fennoscandian vole cycle has a number of features

that differentiate it from cycles in more southern local-

ities. Most importantly, the Fennoscandian vole cycle is

characterized by cycles that occur synchronously over

hundreds of kilometers (Korpimaki et al., 2005b).

Starting in the mid 1980s to early 1990s, irregularities

in the vole cycle (mainly expected peak abundances that

did not occur) were recorded in several localities in

northern Fennoscandia (Henttonen et al., 1987; Lind-

strom & Hornfeldt, 1994; Hanski & Henttonen, 1996;

Steen et al., 1996; Hornfeldt, 2004). The recent fading of

cycles is not restricted to small mammals, but is a

phenomenon that occurs in several taxa across a wide

geographical area (Ims et al., 2008). In terms of the

Fennoscandian vole cycle, Ims et al. (2008) interpret

the evidence to date as a loss of cycles over large areas,

in particular in forested habitat, leading to a shift in the

geographical border between cyclic and noncyclic

populations and a shrinking geographic region where

the cyclic dynamics prevail. A reduction in the durationCorrespondence: Jon E. Brommer, e-mail: jon.brommer@helsinki.fi

Global Change Biology (2010) 16, 577–586, doi: 10.1111/j.1365-2486.2009.02012.x

r 2009 Blackwell Publishing Ltd 577

of winter snow cover (Bierman et al., 2006) and/or

repeated melting–freezing of the existing snow cover

(Aars & Ims, 2002; Solonen, 2004) induces greater

winter mortality. The ‘climatic forcing’ scenario ex-

plains the loss of vole cycles as a decrease in delayed

density dependence caused by milder winter conditions

(Yoccoz et al., 2001; Bierman et al., 2006; Ims et al., 2008;

Kausrud et al., 2008).

Although the evidence for recent fading of cycles in

the population dynamics of small mammals and other

organisms is convincing, inferring climate change as the

causal agent relies on a descriptive association between

changes in cycles and in climate. In some cases, the

evidence of a recent anomaly and a link with climate is

strong. For example, reconstruction of a 1200-year time

series shows that regular outbreaks in the bud larch

moth Zeiraphera diniana abundance only stopped during

the last decades (Esper et al., 2007). Most time series,

however, are relatively short, which makes the associa-

tion between climate and change in cycles less power-

ful. Importantly, both general models of cyclic

dynamics (Royama, 1992) and more mechanistic mod-

els (Hanski & Henttonen, 1996) predict that periods of

noncyclic dynamics may occur in an otherwise cyclic

system. Short time series will fail to correctly separate

such intrinsic irregularities from ‘climatic forcing’, and

experimental verification of climate change as a causal

agent in dampening population cycles is highly challen-

ging. Nevertheless, climate warming is a large-scale

phenomenon that has occurred during the last three

decades, and is forecasted to continue (IPCC, 2007).

Hence, the critical prediction of climate change as a

causal agent for dampening cycles is that we should see

more and more independent systems loosing cycles and

that this loss will be irreversible in the foreseeable

future. Such a coherent, large-scale pattern could be

considered strong evidence of the effects of climate

change (cf. Parmesan & Yohe, 2003).

Here, we study time series of vole abundance in two

localities in southern Finland. These localities are on the

southern edge of the realm of cyclic vole populations in

Finland (Sundell et al., 2004). We employ wavelet ana-

lysis, a technique for signal analysis that has been

mostly used in the study of cycles in meteorological

and geophysical science (e.g. the El Nino-Southern

Oscillation, Torrence & Compo, 1998), but has recently

been employed also in ecological analyses (reviewed in

Cazelles et al., 2008). In contrast to more traditional

techniques (such as auto-regressive analysis), wavelet

analysis does not depend on the assumption of station-

ary dynamics, but can deal with both stationary and

nonstationary features in the same time series. The

technique can be extended to consider the relationship

between two time series, and is ideally suited to de-

scribe changes in cycles over time (Cazelles et al., 2008).

Using wavelet analysis, we show that the 3-year vole

cycle in our study populations was lost in the mid

1990s, consistent with the dominant pattern of the

collapses in Fennoscandian vole cycles, and occurring

in a period of warming winters. Importantly, we docu-

ment, for the first time to our knowledge, that the loss of

population cycles are regained after a noncyclic period

of 3–5 years, without any evidence of winters getting

colder again. In addition, we use wavelet coherency to

study spatial synchrony, the main characteristic of the

Fennoscandian vole cycle, during this period.

Material and methods

Vole data

Voles were snap-trapped biannually in May–early June

(early summer) and late September–October (autumn)

in two areas in southern Finland. The landscape in

southern Finland is mainly determined by agriculture

and forestry, and consists of fields, meadows, clearcuts

and differently aged plantations. We concentrated our

trapping effort on the dominant two small vole species

that occur in this region; field voles (Microtus agrestis)

and bank voles (Myodes glareolus). The former species

occurs in open habitat, whereas the bank vole mainly is

a forest species. It is hence important to trap in both

habitats in order to get estimates of vole abundance.

In the municipality of Heinola (611130N, 26110E),

trapping was carried out from autumn 1986 onwards

following the general design of Myllymaki et al. (1971).

Traps (n 5 300) were set in squares with three traps at

each corner (12 traps per square). A variable number of

trapping squares were located in three separate sites

(with eight, nine and eight squares per area) that were

about 5 km apart. The permanent squares were mainly

in clearcuts or young plantations and in forested habi-

tat. It should be noticed that due to felling, open habitat

was always represented although not necessarily in the

same proportion each year.

In Kirkkonummi (601150 241150), trapping was carried

out from early summer 1981 onwards. Traps (n 5 192)

were placed in two sites about 20 km apart. In each site,

groups of three traps were set as two lines with 16

trapping spots each (15 m between) and where one line

covered open habitat (meadow) and one line covered

forest habitat. When the open habitat started to become

covered by small trees, both lines were moved to a new

site, chosen to be as close as possible to the former site.

Ordinary metal snap traps baited with fresh bread

were reset after the first night such that each trap was

active for two nights. In total, there were 600 trapnights

in Heinola and 384 trapnights in Kirkkonummi per one

578 J . E . B R O M M E R et al.

r 2009 Blackwell Publishing Ltd, Global Change Biology, 16, 577–586

trapping event. Vole abundance was expressed as the

proportion of voles caught per 100 trapnights.

Analysis of changes in the vole cycle

We used wavelet analysis to study the changes in the

cycles of vole abundance. Wavelet analysis is a tool for

detecting a signal (i.e. a recurring periodic pattern with a

certain frequency) in a time series. It is ideal for the

purpose of detecting changes in ecological time series

dynamics as it has been developed to deal with time

series that may have a varying length of the signal period

and that show changes in the variance across time (Saitoh

et al., 2006; Cazelles et al., 2008; Zhang et al., 2009). We

here adhere to the guidelines provided by Torrence &

Compo (1998). All wavelet analyses were performed

using software implemented in MATLAB (The MathWorks

Inc.) provided by Aslak Grinsted at URL: http://

www.pol.ac.uk/home/research/waveletcoherence/.

Details on the approach can be found in Torrence & Compo

(1998), Grinsted et al. (2004), and Cazelles et al. (2008).

Here, we provide only a brief overview of the approach.

A wavelet function is defined in both time and fre-

quency space. Because we are interested in changes in the

wavelet amplitude over time, we used the Morlet wave-

let. For this wavelet (and other complex wavelet func-

tions), the wavelet transform for the nth time step in a

time series at wavelet scale s [Wn(s)] has a real and

imaginary part, containing both information on ampli-

tude [|Wn(s)|] and on the wavelet phase (a function of

the real and imaginary parts of the wavelet transform

separating positive from negative deviations of the

mean). The wavelet power spectrum [|Wn(s)|2] now

indicates the scale at which the strongest signal is de-

tected. Conceptually, the wavelet power spectrum can be

thought of as a variance decomposition, indicating which

period length explains most of the variance in the time

series, for each point in time. For a random (white noise)

process, |Wn(s)|2 is equal to the variance at all n and s (no

signal). For a time series that shows periodicity during

some time step(s), the wavelet power spectrum will be a

distribution with a peak at a certain wavelet scale (in-

dicating the period length) during those time steps.

The significance of the wavelet power spectrum can

be calculated by comparing it with an assumed red-

noise background spectrum (Torrence & Compo, 1998).

We here distinguish a signal from noise in case the

wavelet power is significantly above the 95% confi-

dence interval of a red-noise spectrum. We have an a

priori expectation of a 3-year cycle (Brommer et al., 2002;

Sundell et al., 2004). Royama (1992) analysed the proper-

ties of a second-order model where population size x at

time t is given xt 5 a 1 b xt�1 1 c xt�2 1 en, with en a

Gaussian error term. In this model, a 3-year cycle occurs

when c 5�sqrt(1 1 b) and b � �1. Following Torrence

& Compo (1998: p. 69), we estimated the lag�1 auto-

correlation as |(b 1 sqrt(c))/2| � 0.5. Note, however,

that a range of values for the lag�1 autocorrelation

around this value produces qualitatively the same

result. The region where data are insufficient to allow

inferences on which wavelet periodicity provides the

best fit lies below the ‘cone of influence’ (Torrence &

Compo, 1998). The ‘cone of influence’ was calculated

following Torrence & Compo (1998) and is shown in all

wavelet plots in order to aid in interpretation.

We initially study the dynamics of the two vole

species (bank and field vole) separately using wavelet

analysis. Wavelet analysis can be readily extended to

consider the relationship between two time series (Tor-

rence & Compo, 1998; Torrence & Webster, 1999). We

calculate the cross-wavelet spectrum to study the dy-

namics that is common to both species. A cross wavelet

of two time series is calculated as the product of the

wavelet transform of one time series with the complex

conjugate of the wavelet transform of the other time

series. We calculated the cross-wavelet spectrum in-

stead of performing a wavelet analysis on the pooled

data, because the cross-wavelet spectrum allows to both

identify regions in time-frequency space that are shared

by two time series and to quantify the degree by which

these two time series covary. Because the Morlet wave-

let includes information on the phase, the direction of

synchrony between the time series (i.e. which time

series is leading) can be expressed in terms of degrees

in a plane. Significance testing was based on the same

lag�1 (red noise) coefficient as described above, using a

Monte Carlo simulation to describe the wavelet coher-

ence transform of the null model. For details on the

method, see Grinsted et al. (2004).

The Fennoscandian vole cycle is characterized by

large-scale spatial synchrony. Because we study fluctua-

tions in vole abundance in two localities, we can quan-

tify whether these fluctuations and the possible changes

in any periodicity occur in synchrony. We calculated

wavelet coherency of the time series of both vole species

pooled in the two localities. Wavelet coherency quanti-

fies the degree by which these two time series covary

independently of the power of the periodicity in the

time series. Wavelet coherency is a value between 0 and

1, where the latter indicates perfect synchrony. Testing

the statistical significance of wavelet coherency was

done following the same approach as outline above

for the cross-wavelet spectrum.

Analysis of the trend in winter climate

Daily weather data (temperature and snow depth) were

obtained from the Finnish Meteorological Institute. To

T H E R E T U R N O F T H E V O L E C Y C L E 579

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characterize the winter weather in the Kirkkonummi

locality, we considered data from the weather station in

Vantaa (ca. 20 km east), and for the Heinola locality we

used average data from the stations in Lahti and Mik-

keli (ca. 40–60 km south and north of the trapping site,

respectively).

We characterized the winter weather during three

periods assumed to describe ‘winter’, 1 October to 31

March (6 months), 1 November to 28 February

(4 months) and 1 December to 31 January (2 months).

Annual winter weather during these periods was quan-

tified using three variables; the average daily tempera-

ture, the average snow cover and the number of times

the daily average temperatures fluctuated between

freezing and thawing. Snow cover was shown to be

associated with the loss of the field vole cycle in the

United Kingdom (Bierman et al., 2006). Repeatedly

thawing and freezing was shown to be detrimental for

vole survival with possible population dynamical con-

sequences (Aars & Ims, 2002).

Results

Loss and return of a 3-year cycle

Visual inspection of the data on vole abundances shows

clearly a number of regular cycles in both localities

(Fig. 1a and c). Global wavelet analysis of the dynamics

of the two vole species combined revealed a highly

significant 3-year cycle in both populations (Fig. 1b and d).

In the Kirkkonummi population, there was no strong

evidence of a bank vole cycle until 1999 (Fig. 2a). In

contrast, field vole abundance showed a clear cycle

from the beginning of the time series, and initially

showed a trend of increasing periodicity after which it

shifted to a cycle with a periodicity shorter than 3 years

after 1994 and then disappeared (Fig. 2b). Cross-wavelet

analysis (combining the dynamics of the two species)

showed an absence of 3-year cycles in 1994–2000,

although there was some evidence of cycles at a peri-

odicity lower than 3 years. Hence, 3-year cycles re-

turned after an irregularity of about 5 years, when

especially bank vole cycles were strong (Fig. 2a). In-

vestigation of the time series clearly showed strongly

reduced maximal field vole abundances after the irre-

gularity (Fig. 1a). The field vole cycle was, although

marginally significant, less pronounced after the irre-

gularity than before (Fig. 2b).

Significance for the 3-year cycle in both bank voles

and field voles was lost in 1996 in the Heinola popula-

tion (Fig. 3a and b). Cross-wavelet analysis showed that

a 3-year cycle returned in 2002 (Fig. 3c), but this signal

was clearly mostly due to bank vole dynamics (Fig. 3a)

rather than field vole dynamics (Fig. 3b). In the Heinola

population, there was no apparent shift in the periodi-

city of the cycles before the irregularity in the dynamics

(Fig. 3). Analyses of spring vole abundances lead to

qualitatively the same conclusions regarding the pre-

sence of a period of noncyclic dynamics (supporting

information Appendix S1).

In the Heinola population, bank vole dynamics were

leading ahead of field vole dynamics before, but not

after, the irregularity (the arrows in the cross-wavelet

analysis (Fig. 3c) indicate the degree the dynamics of

the two species are in phase). This pattern was also

apparent in the time-series data (Fig. 1c, years 1993 and

1996). In contrast, the dynamics of the two species were

phase-locked both before and after the irregularity in

the Kirkkonummi population (Figs 2c and 1a).

Changes in spatial synchrony

The pattern of variation in vole abundance in the two

localities showed clear similarities. We explicitly con-

sidered the relationship between the two time series by

calculating wavelet coherence (indicating synchrony of

the time series, irrespective of wavelet power). This

analysis showed that synchrony at the frequency band

of a 3-year cycle broke down during the period of

irregular dynamics (Fig. 4). There was evidence for

synchrony between the two time series for periods

longer than 4 years (Fig. 4), but periodicity at this

frequency explained only a low part of the total var-

iance in each time series (i.e. wavelet power was low,

Figs 2 and 3). Wavelet coherence was particularly strong

after the period of irregular dynamics (Fig. 4). Wavelet

coherence allowed investigation of the extent the two

time series were in phase (indicated by the arrows in

Fig. 4). There was clear phase locking of the vole

dynamics in these two localities after the irregularity

was over (indicated by arrows pointing right over a

wide range of frequencies considered).

Climate and cycles

We tested which characterization of winter weather

showed the clearest temporal trend, while allowing

for nonlinear trends. As a description of climate during

the study period, we considered average temperature,

average snow cover and the number of times during

winter the temperature crossed 0 1C (freezing–thawing

effect). In addition, we considered three possible winter

periods. We performed a second-order polynomial re-

gression (i.e. y 5 a 1 b x 1 c x2) of all winter weather

variables on zero-mean standardized year and its

square and ranked the fits according to their adjusted

R2. Of these six different descriptions of winter weather,

the strongest time trend was a linear decrease of

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0.5–0.7 cm yr�1 in the snow cover during 1 December to

31 January (Fig. 5; Kirkkonummi: a 5 8.9 � 1.5, t 5 5.8,

Po0.001; b 5�0.52 � 0.13, t 5�4.1, Po0.001;

c 5 0.001 � 0.018, t 5 0.1, P 5 0.95, R2 5 0.36; Heinola:

a 5 20.3 � 2.7, t 5 7.5, Po0.001; b 5�0.71 � 0.22,

t 5�3.2, P 5 0.004; c 5 0.030 � 0.031, t 5 0.96, P 5 0.35,

R2 5 0.25). Snow cover and temperature during this

period were clearly correlated (r 5�0.51; Po0.01) for

both localities.

Discussion

Vole cycles and global warming

Over most of Finland, a 3-year vole cycle is the norm

(Sundell et al., 2004). Here, we show that in two local-

ities in southern Finland that are 170 km apart, 3-year

cycles have temporarily disappeared in the latter half of

the 1990s. We believe that loss of vole cycles during this

period was a phenomenon that occurred on the scale of

southern Finland. In addition to this event occurring in

our two study sites (601150 and 611130), wavelet analysis

of vole data published by Korpimaki et al. (2005a) from

the western part of central Finland (631 northern lati-

tude) also shows evidence of a temporary loss of a

3-year cycle in 1994–1998 (supporting information

Appendix S2). A strong, large amplitude vole cycle

returned in our two study localities about 4–5 years

after the irregularity started.

Cyclic population dynamics are driven by a combina-

tion of direct and delayed density dependence (Roya-

ma, 1992). Global warming has been hypothesized to

stabilize cyclic vole dynamics through a reduction in

the delayed density dependence caused either by a

shortening of the winter season (Bierman et al., 2006)

or by reducing vole winter survival to such a low level

that the lagged numerical response of the specialized

predator(s) is hampered (Ims et al., 2008). For example,

the absence of lemming cycles during the last decades

could be explained by a modifying effect of snow

conditions on the functional response of the lemmings’

predators (Kausrud et al., 2008). The global climate is

projected to continue to warm, especially in northern

latitudes (IPCC, 2007). Hence, the ‘climate forcing’

hypothesis predicts that vole cycles will fade and will

remain absent in the foreseeable future. In contrast to

the prediction of the ‘climate forcing’ hypothesis, we

here observe ongoing cyclic dynamics of voles in south-

ern Finland. In particular, we find that especially during

the last two decades, mid-winter snow cover has

Fig. 1 Time series of the abundance of two vole species based on snap trapping in autumn in Kirkkonummi (a, 1981–2008) and Heinola

(c, 1986–2008), respectively. Vole abundance is standardized to zero mean and unit standard deviation. Bank vole abundance is plotted

with a filled diamond connected by a dashed line, and field vole abundance as an open circle connected by a solid line. The global

wavelet spectrum (with 5% confidence level indicated with a dashed line) for the dynamics of the two species combined for

Kirkkonummi (b) and Heinola (d) indicate that the dominant signal stems from a 3-year cycle.

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dramatically declined by 0.5–0.7 cm yr�1. Despite these

milder winters with less snow, the vole cycle has

returned from being absent for a few years. We believe

that this return of the vole cycle during a period of

rapidly warming winters provides strong evidence to

falsify the climatic forcing hypothesis as a general

explanation for the loss of vole cycles.

A period of irregular dynamics in the vole cycle

Ecological time series, including ours, are typically

fairly short. Murdoch et al. (2002) argued that 25 years

of data with a period length of one-third of the time

series is sufficient for drawing statistical inferences on

periodicity. By comparing analysis with 50 or 100 simu-

lated data points over a same period of time, Cazelles

et al. (2008) have shown that wavelet analysis leads to

the same conclusions regarding population cycles de-

spite the shortness of the time series. The lengths of our

time series (28 and 23 years, respectively) are consid-

ered marginally sufficient by Cazelles et al. (2008),

although the length of our time series (7 three-year

periods) is considered sufficient by the criteria of Mur-

doch et al. (2002). However, we believe that the period

of noncyclic dynamics that we detected is not due to

low power of our time series, because (1) we detected a

clear global signal (a single spike) of a 3-year cycle that

is highly significant; (2), the disappearance of this

3-year cycle falls approximately in the middle of our

time series, well within the ‘cone of influence’, and is

flanked by periods that show clear evidence of 3-year

cycles. A time series that is too short is expected to

produce the converse pattern.

We are not aware of any other evidence showing first

fading vole cycles, followed by a return of the vole cycle

Fig. 2 Wavelet analysis of the autumn vole abundance in the

Kirkkonummi population in southern Finland (presented in Fig.

1a). Wavelet power spectrum for the dynamics of (a) the bank vole

(b) the field vole. (c) The cross-wavelet transform for the dynamics

of both species. For each point in time and for each period length,

wavelet power is indicated with darker red indicating higher

power and darker blue lower power. The region where the wavelet

power is significantly different from red noise is delineated by a

thick black line. Because of truncation effect at the edges of the time

series, inferences cannot be made below the ‘cone of influence,’

which is indicated by a thin black line and a change in the

brightness of the colours. For the cross-wavelet transform (c), the

direction the arrows are pointing indicates whether the two

wavelets are in-phase (pointing right), anti-phase (pointing left)

or whether the bank vole dynamics (pointing down) or field vole

dynamics (pointing up) are leading. The direction in which the

arrows point is indicative of the angle between the wavelets

(pointing straight down or up equals 901).

Fig. 3 Wavelet analysis of the autumn vole abundance in the

Heinola population (data presented in Fig. 1c). Wavelet power

spectrum for the dynamics of (a) the bank vole (b) the field vole.

(c) The cross-wavelet transform for the dynamics of both species

combined. For explanation, see caption of Fig. 2.

582 J . E . B R O M M E R et al.

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in the same locality during the recent decades in which

climatic change has been pronounced. We observed this

phenomenon in two independent localities at approxi-

mately the same time, and we found that the dynamics

in the two localities showed a clear correspondence

both before and after the irregular period. Hence,

locally noncyclic dynamics were also linked to a tem-

porary loss of spatial synchrony (cf. Henden et al., 2009).

The most parsimonious explanation of the pattern we

have documented here is that it is due to stochastic

processes. Periods of noncyclic dynamics are a well-

known feature of a cyclic system with both direct and

delayed density dependence and environmental sto-

chasticity (Royama, 1992). In addition to changes in

the cycle being associated with stochastic processes,

certain deterministic processes may also drive an irre-

gularity in the vole cycle. One example for an intrinsic

factor that could cause noncyclic dynamics would be a

disturbance in the community of vole species and their

mustelid predators that temporarily causes erratic dy-

namics (Hanski & Henttonen, 1996; Henttonen, 2000).

The irregularity in the vole cycle we here detected

lasted only a few years, thereby allowing us to detect

it using a relatively short time series. In general, how-

ever, irregular periods can last longer. For example, in

their analysis of fox bounty data as a proxy of small

mammal fluctuations from 1880 to 1976, Henden et al.

(2009) found that seven of the 11 localities with cycles

above 601 northern latitude showed long periods when

cycles were absent. Hence, periods of noncyclic dy-

namics in the fluctuations of small mammals probably

existed also prior to the unprecedented climatic warm-

ing of the last decades and temporary loss of cycles

need not be causally linked to climate warming.

Supracyclic variation in the vole community

In both populations, field vole dynamics were strongly

cyclic before the irregularity, but the cyclic dynamics of

bank voles were more pronounced when the vole cycle

returned. This pattern was accompanied by a propor-

tional decrease in the amplitude of the fluctuations (and

hence average abundance) of field voles after the irre-

gularity. Clearly, the patterns in the data we document

here cannot be used to infer causality, but it is worth

noting that a change in the composition of the vole

community may be caused by a number of factors. (1)

Species-specific consequences of climate change may

cause a shift in the community. Milder winters are

expected to especially be detrimental for the food

Fig. 4 Wavelet coherency transform between vole abundance

in Kirkkonummi and Heinola for the time period common to

both time series (1986–2008). For each point in time and for each

period length, the wavelet coherence shows the extent by which

the two time series covary. Values lie between 0 and 1, with

larger values indicated by colours shifting to red (see legend on

the right-hand side). Significant regions in time-frequency space

are indicated by a thick line. Inferences outside the cone of

influence (black line) are less strong, and this region is indicated

by its paler colour. The direction the arrows are pointing

indicates whether the two wavelets are in-phase (pointing right),

anti-phase (pointing left), or whether the vole abundance in

Kirkkonummi (pointing down) or Heinola (pointing up) are

leading. The direction in which the arrows point is indicative

of the angle between the wavelets (pointing straight down or up

equals 901).

Fig. 5 The change in the mean snow cover in the localities

Kirkkonummi (open squares, dashed line) and Heinola (filled

dots, solid line) for the period 1 December to 31 January. Fitted

lines are regression lines. The trends over time had a significant

linear term in both localities (statistical details reported in the

text).

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quality of the grass-eating field vole, while the grani-

vorous bank vole is expected to be less affected. The

recent dominance of the bank vole in the vole commu-

nity, which we observe in both our study populations, is

consistent with this notion. It is even possible that the

bank vole has enjoyed a release from competition with

the larger field vole in the recent decade; (2) Species-

specific population dynamical consequences may also

stem from other changes in the environment. For ex-

ample, a disease may have species-specific conse-

quences; and (3) Least weasels, which are thought to

drive the Fennoscandian vole cycle, prefer to prey on

field voles above bank voles (Hanski & Henttonen,

1996). Stochastic differences in the vole – least weasel

community are predicted to lead to both within- and

supracycle changes in the relative abundance of the two

vole species. Explicit consideration of the dynamics of

vole predators could provide further insight in this

hypothesis.

Conclusions

Cycles in the abundance of small mammals and other

animals are a profound feature of the boreal ecosystem.

The fading out of these cycles is projected to have

cascading effects both towards lower trophic levels

(e.g., mosses, Rydgren et al., 2007), and to higher trophic

levels (avian predators, Hornfeldt et al., 2005). If the loss

of cycles is due to climatic warming the forecast for the

boreal ecosystem as a whole is a grim one, indeed as it

predicts that the loss of cycles will be permanent for the

foreseeable future. We have here provided the first

empirical evidence that the Fennoscandian vole cycle

can temporarily disappear and return to its former

state, including its special feature of large-scale spatial

synchrony. We show that such a return of the vole cycle

can occur despite an ongoing decrease in winter snow

cover. This observation does not imply that snow con-

ditions are not involved in the observed loss of vole

cycles in the United Kingdom or (semi-)Arctic Fennos-

candian localities. Rather, we suggest that there is

context dependency with respect to how climate affects

population dynamics. Such context dependency may

stem from the fact that the species composition of the

vole community differs between regions (Hanski &

Henttonen, 1996), combined with the expectation that

some species are more sensitive to climate change than

others. For example, our results indicate that the return

of the vole cycle in southern Finland is largely deter-

mined by bank vole dynamics, whereas field vole

dynamics was dominant before. In addition, the cycle

generating mechanism (i.e. the mechanism behind the

delayed density dependence) is likely to differ from

place to place. For example, evidence is accumulating

that disease causes delayed density dependence in field

voles in the United Kingdom (Burthe et al., 2008; Smith

et al., 2008), whereas predation by small mustelids is

thought to play this role in Fennoscandia (Korpimaki

et al., 2005b). Ongoing climate change may affect such

mechanisms differently leading to varying population-

dynamical outcomes. Ecological time-series data will

play an increasingly important role in sharpening our

understanding of the interplay between climate change

and population dynamics.

Acknowledgements

This is report number 7 of Kimpari Bird Projects. We thank theother members of KBP – Juhani Ahola, Pentti Ahola, Bo Ekstam,Arto Laesvuori and Martti Virolainen – for the many hours spentconducting fieldwork. Author contributions: data were collectedmainly by K. A. and T. K. (Kirkkonummi) and H. P. and H. K.(Heinola). Analyses and writing by J. E. B., assisted by H. P. andP. K. Fieldwork was supported by the Academy of Finland (H. P.,J. E. B.). P. K. was supported by the Academy of Finland (project1118484 and to J. E. B. 1131390) and J. E. B. was employed as anAcademy Researcher.

References

Aars J, Ims RA (2002) Intrinsic and climatic determinants of

population demography: the winter dynamics of tundra voles.

Ecology, 83, 3449–3456.

Bierman SM, Fairbairn JP, Petty SJ, Elston DA, Tidhar D, Lambin

X (2006) Changes over time in the spatiotemporal dynamics of

cyclic populations of field voles (Microtus agrestis L.). American

Naturalist, 167, 583–590.

Brommer JE, Pietiainen H, Kolunen H (2002) Reproduction and

survival in a variable environment: Ural owls and the three-

year vole cycle. Auk, 119, 194–201.

Burthe S, Telfer S, Begon M, Bennett M, Smith A, Lambin X

(2008) Cowpox virus infection in natural field vole Microtus

agrestis populations: significant negative impacts on survival.

Journal of Animal Ecology, 77, 110–119.

Cazelles B, Chavez M, Berteaux D, Menard F, Vik JO, Jenouvrier

S, Stenseth NC (2008) Wavelet analysis of ecological time

series. Oecologia, 156, 287–304.

Esper J, Buntgen U, Frank DC, Nievergelt D, Liebholt A (2007)

1200 years of regular outbreaks in alpine insects. Proceedings of

the Royal Society B, 274, 671–679.

Grinsted A, Moore JC, Jevrejeva S (2004) Application of the cross

wavelet transform and wavelet coherence to geophysical time

series. Nonlinear Processes in Geophysics, 11, 561–566.

Hanski I, Hansson L, Henttonen H (1991) Specialist predators,

generalist predators, and the microtine rodent cycle. Journal of

Animal Ecology, 60, 353–367.

Hanski I, Henttonen H (1996) Predation on competing rodent

species: a simple explanation of complex patterns. Journal of

Animal Ecology, 65, 220–232.

Hansson L, Henttonen H (1985) Gradients in density variations

of small rodents: the importance of latitude and snow cover.

Oecologia, 67, 394–402.

584 J . E . B R O M M E R et al.

r 2009 Blackwell Publishing Ltd, Global Change Biology, 16, 577–586

Henden J-A, Ims RA, Yoccoz NG (2009) Nonstationary spatio-

temporal small rodent dynamics: evidence from long-term

Norwegian fox bounty data. Journal of Animal Ecology, 78,

636–645.

Henttonen H (2000) Long-term dynamics of the bank vole

Clethrionomys glareolus at Pallasjarvi, northern Finnish taiga.

Polish Journal of Ecology, 48 (Suppl.), 87–96.

Henttonen H, Oksanen T, Jortikka A, Haukisalmi V (1987) How

much do weasels shape microtine cycles in the northern

Fennoscandian taiga. Oikos, 50, 353–365.

Hornfeldt B (2004) Long-term decline in numbers of cyclic voles

in boreal Sweden: analysis and presentation of hypotheses.

Oikos, 107, 376–392.

Hornfeldt B, Hipkiss T, Eklund U (2005) Fading out of vole and

predator cycles? Proceedings of the Royal Society B, 272,

2045–2049.

Ims RA, Fuglei E (2005) Tropic interaction cycles in tundra

ecosystems and the impact of climate change. Bioscience, 55,

311–322.

Ims RA, Henden J-A, Killengreen ST (2008) Collapsing popula-

tion cycles. Trends in Ecology and Evolution, 23, 79–86.

Intergovernmental Panel on Climate Change (IPCC) (2007). Climate

Change 2007: Synthesis Report. Fourth Assessment Report. Avail-

able at http://www.ipcc.ch/(accessed 15 January 2009).

Kausrud KL, Mysterud A, Steen H et al. (2008) Linking climate

change to lemming cycles. Nature, 456, 93–98.

Korpimaki E, Norrdahl K, Huitu O, Klemola T (2005a) Predator-

induced synchrony in population oscillations of coexisting

small mammal species. Proceedings of the Royal Society B, 272,

193–202.

Korpimaki E, Oksanen L, Oksanen T, Klemola T, Norrdahl K,

Banks PB (2005b) Vole cycles and predation in temperate and

boreal zones in Europe. Journal of Animal Ecology, 74,

1150–1159.

Lambin X, Bretagnolle V, Yoccoz NG et al. (2006) Vole population

cycles in northern and southern Europe: is there a need for

different explanations for single pattern? Journal of Animal

Ecology, 75, 340–349.

Linden H (1988) Latitudinal gradients in predator-prey interac-

tions, cyclicity and synchronism in voles and small game

populations in Finland. Oikos, 52, 341–349.

Lindstrom ER, Hornfeldt B (1994) Vole cycles, snow depth and

fox predation. Oikos, 70, 156–160.

Lindstrom J, Ranta E, Kokko H, Lundberg P, Kaitala V (2001)

From arctic lemmings to adaptive dynamics: Charles Elton’s

legacy in population ecology. Biological Reviews, 76, 129–158.

Murdoch WW, Kendall BE, Nisbet RM, Briggs CJ, McCauley E,

Bolser R (2002) Single-species models for many-species food

webs. Nature, 423, 541–543.

Myllymaki A, Paasikallio A, Pankakoski E, Kanervo V (1971)

Removal experiments on small quadrates as a means of rapid

assessment of the abundance of small mammals. Annales

Zoologici Fennici, 8, 177–185.

Parmesan C, Yohe G (2003) A globally coherent fingerprint of

climate change impacts across natural systems. Nature, 421,

37–42.

Royama T (1992) Analytical Population Dynamics. Chapman &

Hall, New York, USA.

Rydgren K, Økland RH, Pico FX, de Kroon H (2007) Moss species

benefit from breakdown of cyclic rodent dynamics in boreal

forest. Ecology, 88, 2320–2329.

Saitoh T, Cazelles B, Vik JO, Viljugrein H, Stenseth NC (2006)

Effects of regime shifts on the population dynamics of the

grey-sided vole in Hokkaido, Japan. Climate Research, 32,

109–118.

Smith MJ, White A, Sherratt JA, Telfer S, Begon M, Lambin X

(2008) Disease effects on reproduction can cause population

cycles in seasonal environments. Journal of Animal Ecology, 77,

378–389.

Solonen T (2004) Are vole-eating owls affected by mild winters

in southern Finland? Ornis Fennica, 81, 65–74.

Steen H, Ims RA, Sonerud GA (1996) Spatial and temporal

patterns of small-rodent population dynamics at a regional

scale. Ecology, 77, 2365–2372.

Sundell J, Huitu O, Henttonen H et al. (2004) Large-scale spatial

dynamics of vole populations in Finland revealed by the

breeding success of vole-eating predators. Journal of Animal

Ecology, 73, 167–178.

Torrence C, Compo GP (1998) A practical guide to wavelet

analysis. Bulletin of the American Meteorological Society, 79,

61–78.

Torrence C, Webster PJ (1999) Interdecadal changes in the ENSO

– monsoon system. Journal of Climate, 12, 2679–2690.

Yoccoz NG, Stenseth NC, Henttonen H, Prevot-Julliard

A-C (2001) Effects of food addition on the seasonal

density-dependent structure of bank vole Clethrionomys

glareolus populations. Journal of Animal Ecology, 70,

713–720.

Zhang Z, Cazelles B, Tian H, Stige LC, Brauning A, Stenseth NC

(2009) Periodic temperature-associated drought/flood drives

locust plagues in China. Proceedings of the Royal Society B, 276,

823–831.

T H E R E T U R N O F T H E V O L E C Y C L E 585

r 2009 Blackwell Publishing Ltd, Global Change Biology, 16, 577–586

Supporting Information

Additional Supporting Information may be found in the online version of this article:

Appendix S1. Analysis of early summer abundance of voles.

Figure SA1. Wavelet analysis of vole trapping carried out in early summer (June) in the Kirkkonummi population. Plotted are the

wavelet power spectra for the dynamics of (panel a) the bank vole, and panel (b) the field vole, and (panel c) the cross-wavelet power

spectrum for both species. See caption of Fig. 2 for a detailed explanation of these plots.

Figure SA2. Wavelet analysis of vole trapping carried out in early summer (June) in the Heinola population. Plotted are the wavelet

power spectra for the dynamics of (panel a) the bank vole, and panel (b) the field vole, and (panel c) the cross-wavelet power

spectrum for both species. See caption of Fig. 2 for a detailed explanation of these plots.

Appendix S2. Wavelet analysis of published data.

Figure SB1. Wavelet analysis of data published by Korpimaki et al. (2005, summation of data in their Fig. 1a and b) on vole

abundance in

western-central Finland from 1977–2003. Plotted are the wavelet power spectra for the dynamics of (panel a) the bank vole, and panel

(b) the field vole, and (panel c) the cross-wavelet power spectrum for both species. See caption of Fig. 2 in the main text for a detailed

explanation of these plots.

Please note: Wiley-Blackwell are not responsible for the content or functionality of any supporting materials supplied by the authors.

Any queries (other than missing material) should be directed to the corresponding author for the article.

586 J . E . B R O M M E R et al.

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