Global change biology Congruent responses to weather variability in high arctic herbivores Audun Stien 1, *, Rolf A. Ims 3 , Steve D. Albon 4 , Eva Fuglei 2 , R. Justin Irvine 4 , Erik Ropstad 5 , Odd Halvorsen 6 , Rolf Langvatn 7,8 , Leif Egil Loe 9,10 , Vebjørn Veiberg 7 and Nigel G. Yoccoz 3 1 Norwegian Institute for Nature Research, and 2 Norwegian Polar Institute, Fram Centre, 9296 Tromsø, Norway 3 University of Tromsø, 9037 Tromsø, Norway 4 The James Hutton Institute, Aberdeen AB15 8QH, UK 5 Norwegian School of Veterinary Science, 0033 Oslo, Norway 6 Natural History Museum, University of Oslo, 0318 Oslo, Norway 7 Norwegian Institute for Nature Research, 7485 Trondheim, Norway 8 University Centre in Svalbard, 9171 Longyearbyen, Norway 9 Norwegian University of Life Sciences, 1432 Aas, Norway 10 CEES, Institute of Biology, University of Oslo, 0316 Oslo, Norway *Author for correspondence ([email protected]). Assessing the role of weather in the dynamics of wildlife populations is a pressing task in the face of rapid environmental change. Rodents and rumi- nants are abundant herbivore species in most Arctic ecosystems, many of which are experiencing particularly rapid climate change. Their different life-history characteristics, with the exception of their trophic position, suggest that they should show different responses to environmental vari- ation. Here we show that the only mammalian herbivores on the Arctic islands of Svalbard, reindeer (Rangifer tarandus) and sibling voles (Microtus levis), exhibit strong synchrony in popu- lation parameters. This synchrony is due to rain-on-snow events that cause ground ice and demonstrates that climate impacts can be similarly integrated and expressed in species with highly con- trasting life histories. The finding suggests that responses of wildlife populations to climate variabil- ity and change might be more consistent in Polar regions than elsewhere owing to the strength of the climate impact and the simplicity of the ecosystem. Keywords: arvicolinae; caribou; ungulate 1. INTRODUCTION Assessing the role of climatic variation in the dynamics of wildlife populations has become a pressing task in the face of current rapid climate change, particularly in the Arctic [1]. However, quantifying climate impacts on populations in order to derive generally applicable pre- dictions is often hampered by strongly nonlinear responses modified by species-specific life histories [2] and/or ecosystem complexity [3,4]. Nonetheless, the simplicity of terrestrial high Arctic ecosystems could provide evidence of consistent responses among wildlife species leading to potentially powerful predictions of the likely consequences of future climate change. Reindeer (Rangifer sp.) and small rodents are abundant components of the arctic ecosystem that often show large fluctuations in population densities [5,6]. While their trophic position is similar, they are fundamentally different in most other traits. Reindeer are large-sized (60 – 200 kg) and long-lived (typically max. 10–20 years) with a maximum of one calf per year. By contrast, rodents are small-sized (0.03–0.2 kg) and short-lived (typically max. 1 – 2 years) with several large litters per year. Such differing life-history traits have been suggested to cause different responses to environmental variation [7 – 9]. Arctic rodents often show population cycles that are thought to be driven by predator–prey interactions or grazing- induced food quantity cycles [5], while population dynamics of reindeer in predator-free Arctic environments are in general thought to be driven by competition for food, with additional between-year variation in vital rates caused by climatic effects on the quantity and quality of food available [10 – 13] and/or parasite abundances [14]. A phenomenon that has the potential to affect both species is ground ice that encases the vegetation and thereby limits access to forage in winter [15,16], with effects propagating through their population dynamics [17 – 20], and ultimately the web of interactions these her- bivores are driving in Arctic ecosystems [3,10,18,21]. Rain-on-snow (ROS) events in the Arctic result in ground ice when the rain water percolates through the snow and freezes as it meets the frozen ground [17,22], although the empirical evidence for the importance of such events has been questioned [23]. Here, we report the results from two long-term studies in the high Arctic that for the first time show evidence for strong temporal synchrony in the population dynamics of reindeer and small rodents. This synchrony is caused by climate forcing, of which ROS events is a main component. 2. MATERIAL AND METHODS On the island of Spitsbergen, Svalbard, Norway at 788 N, Svalbard reindeer (Rangifer tarandus platyrhynchus) and sibling voles (Microtus levis) are the only herbivorous mammals. The voles inhabit steep slopes associated with coastal bird cliffs [24] while the reindeer pre- dominantly use inland valleys. Strong interspecific competition for forage resources between the reindeer and vole populations is there- fore unlikely. Furthermore, reindeer and rodents share no predators or parasites that are likely to synchronize their dynamics. We surveyed the populations annually in July–August in two adjacent locations on Nordenskio ¨ld Land peninsula, Spitsbergen (see the electronic supplementary material, figure S1). In a small study area, we monitored the vole population size (1996–2007, n ¼ 12 years), whereas monitoring of reindeer population size and the proportion of female reindeer with a calf occurred in neighbour- ing valleys (1995– 2011, n ¼ 17 years). Calves per female was chosen as the focal demographic parameter for reindeer as it is estimated with higher precision than population size, is known to be sensitive to environmental variation [14], and is positively related to the growth rate of the population (r ¼ 0.59). Daily precipitation and temperature data come from the meteoro- logical station at the airport in the nearby settlement Longyearbyen (see the electronic supplementary material, figure S1). From these data, we calculated the amount of precipitation that fell at a tempera- ture above 18C, between 1 November and 30 April, as our measure of the extent of ROS. We used generalized linear models to investigate the impact of ROS and population size the previous summer on reindeer fertility and vole population sizes. In the analysis of the reindeer fertility data, we assumed a logit link function, and in the analysis of vole popu- lation sizes we assumed a log link function. Owing to overdispersion in the data in relation to the natural distributional assumptions the models were fitted using quasi-likelihood methods ([25], see the electronic supplementary material for details on data and analyses). 3. RESULTS Vole population sizes and calves per female reindeer varied extensively over the study period. The estimated Electronic supplementary material is available at http://dx.doi.org/ 10.1098/rsbl.2012.0764 or via http://rsbl.royalsocietypublishing.org. Biol. Lett. (2012) 8, 1002–1005 doi:10.1098/rsbl.2012.0764 Published online 26 September 2012 Received 17 August 2012 Accepted 5 September 2012 1002 This journal is q 2012 The Royal Society on November 13, 2012 rsbl.royalsocietypublishing.org Downloaded from
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on November 13 2012rsblroyalsocietypublishingorgDownloaded from
Biol Lett (2012) 8 1002ndash1005
doi101098rsbl20120764
Published online 26 September 2012
Global change biology
Congruent responsesto weather variability in
high arctic herbivoresAudun Stien1 Rolf A Ims3 Steve D Albon4Eva Fuglei2 R Justin Irvine4 Erik Ropstad5Odd Halvorsen6 Rolf Langvatn78 Leif Egil Loe910Vebjoslashrn Veiberg7 and Nigel G Yoccoz3
1Norwegian Institute for Nature Research and 2Norwegian PolarInstitute Fram Centre 9296 Tromsoslash Norway3University of Tromsoslash 9037 Tromsoslash Norway4The James Hutton Institute Aberdeen AB15 8QH UK5Norwegian School of Veterinary Science 0033 Oslo Norway6Natural History Museum University of Oslo 0318 Oslo Norway7Norwegian Institute for Nature Research 7485 Trondheim Norway8University Centre in Svalbard 9171 Longyearbyen Norway9Norwegian University of Life Sciences 1432 Aas Norway10CEES Institute of Biology University of Oslo 0316 Oslo NorwayAuthor for correspondence (audunstienninano)
Assessing the role of weather in the dynamics ofwildlife populations is a pressing task in the face ofrapid environmental change Rodents and rumi-nants are abundant herbivore species in mostArctic ecosystems many of which are experiencingparticularly rapid climate change Their differentlife-history characteristics with the exception oftheir trophic position suggest that they shouldshow different responses to environmental vari-ation Here we show that the only mammalianherbivores on the Arctic islands of Svalbardreindeer (Rangifer tarandus) and sibling voles(Microtus levis) exhibit strong synchrony in popu-lation parameters This synchrony is due torain-on-snow events that cause ground ice anddemonstrates that climate impacts can be similarlyintegrated and expressed in species with highly con-trasting life histories The finding suggests thatresponses of wildlife populations to climate variabil-ity and change might be more consistent in Polarregions than elsewhere owing to the strength of theclimate impact and the simplicity of the ecosystem
Keywords arvicolinae caribou ungulate
1 INTRODUCTIONAssessing the role of climatic variation in the dynamics ofwildlife populations has become a pressing task in theface of current rapid climate change particularly in theArctic [1] However quantifying climate impacts onpopulations in order to derive generally applicable pre-dictions is often hampered by strongly nonlinearresponses modified by species-specific life histories [2]andor ecosystem complexity [34] Nonetheless thesimplicity of terrestrial high Arctic ecosystems couldprovide evidence of consistent responses among wildlifespecies leading to potentially powerful predictions ofthe likely consequences of future climate change
Reindeer (Rangifer sp) and small rodents are abundantcomponents of the arctic ecosystem that often show large
Electronic supplementary material is available at httpdxdoiorg101098rsbl20120764 or via httprsblroyalsocietypublishingorg
Received 17 August 2012Accepted 5 September 2012 1002
fluctuations in population densities [56] While theirtrophic position is similar theyare fundamentally differentin most other traits Reindeer are large-sized (60ndash200 kg)and long-lived (typically max 10ndash20 years) with amaximum of one calf per year By contrast rodents aresmall-sized (003ndash02 kg) and short-lived (typically max1ndash2 years) with several large litters per year Such differinglife-history traits have been suggested to cause differentresponses to environmental variation [7ndash9] Arcticrodents often show population cycles that are thought tobe driven by predatorndashprey interactions or grazing-induced food quantity cycles [5] while populationdynamics of reindeer in predator-free Arctic environmentsare in general thought to be driven by competition forfood with additional between-year variation in vital ratescaused by climatic effects on the quantity and quality offood available [10ndash13] andor parasite abundances[14] A phenomenon that has the potential to affect bothspecies is ground ice that encases the vegetation andthereby limits access to forage in winter [1516] witheffects propagating through their population dynamics[17ndash20] and ultimately the web of interactions these her-bivores are driving in Arctic ecosystems [3101821]Rain-on-snow (ROS) events in the Arctic result inground ice when the rain water percolates through thesnow and freezes as it meets the frozen ground [1722]although the empirical evidence for the importance ofsuch events has been questioned [23] Here we reportthe results from two long-term studies in the high Arcticthat for the first time show evidence for strong temporalsynchrony in the population dynamics of reindeer andsmall rodents This synchrony is caused by climateforcing of which ROS events is a main component
2 MATERIAL AND METHODSOn the island of Spitsbergen Svalbard Norway at 788 N Svalbardreindeer (Rangifer tarandus platyrhynchus) and sibling voles (Microtuslevis) are the only herbivorous mammals The voles inhabit steepslopes associated with coastal bird cliffs [24] while the reindeer pre-dominantly use inland valleys Strong interspecific competition forforage resources between the reindeer and vole populations is there-fore unlikely Furthermore reindeer and rodents share no predatorsor parasites that are likely to synchronize their dynamics
We surveyed the populations annually in JulyndashAugust in twoadjacent locations on Nordenskiold Land peninsula Spitsbergen(see the electronic supplementary material figure S1) In a smallstudy area we monitored the vole population size (1996ndash2007n frac14 12 years) whereas monitoring of reindeer population size andthe proportion of female reindeer with a calf occurred in neighbour-ing valleys (1995ndash2011 n frac14 17 years) Calves per female was chosenas the focal demographic parameter for reindeer as it is estimatedwith higher precision than population size is known to be sensitiveto environmental variation [14] and is positively related to thegrowth rate of the population (r frac14 059)
Daily precipitation and temperature data come from the meteoro-logical station at the airport in the nearby settlement Longyearbyen(see the electronic supplementary material figure S1) From thesedata we calculated the amount of precipitation that fell at a tempera-ture above 18C between 1 November and 30 April as our measure ofthe extent of ROS We used generalized linear models to investigate theimpact of ROS and population size the previous summer on reindeerfertility and vole population sizes In the analysis of the reindeer fertilitydata we assumed a logit link function and in the analysis of vole popu-lation sizes we assumed a log link function Owing to overdispersionin the data in relation to the natural distributional assumptionsthe models were fitted using quasi-likelihood methods ([25] see theelectronic supplementary material for details on data and analyses)
3 RESULTSVole population sizes and calves per female reindeervaried extensively over the study period The estimated
This journal is q 2012 The Royal Society
0
50
100
150
200
250
300
350
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02
04
06
08
10volesreindeerrain-on-snow
calv
es p
er f
emal
e
(a)
0
50
100
150
200
250
300
0 04 08
vole
pop
ulat
ion
vole
pop
ulat
ion
calves per female
(b)
1995 2000 2005 2010
0
50
100
150
200250
300
350
rain-on-snow (mm)
0 1 5 15 50
(c)
0
02
04
06
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er f
emal
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(d)
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rain
-on-
snow
(m
m)
vole
pop
ulat
ion
Figure 1 Annual estimates of sibling vole population sizes calves per female Svalbard reindeer and ROS (a) Time series of
annual estimates (+ 95 CI) of sibling vole population sizes (red colour 1996ndash2007) Svalbard reindeer fecundities(calves per female (blue colour 1995ndash2011) and ROS (black colour mm 1995ndash2011) (b) Estimated vole population sizesplotted against calves per female reindeer (c) Vole population sizes plotted against ROS (d) Calves per female reindeer plottedagainst ROS Regression lines for the univariate relationships with 95 confidence envelopes (dashed lines) are given in (c) and
(d) with ROS along the x-axis plotted on log(x thorn 1) scale
Table 1 Parameter estimates (with 95 CI) QAICc and R2-values for GLMs for the impact of rain-on-snow (ROS) and
previous yearrsquos population size (DD) on calves per female reindeer and vole population sizes QAICc values for the best fitmodels are in bold
response model
parameter estimates (95 CI)
intercept ROS (mm) DD QAICc R2-values
calves per intercept 028 (202 08) 628femalea ROS 18 (09 27) 2075 (2118 2037) 422 057
DD 38 (21 57) 20010 (20015 20005) 400 039ROS thornDD 37 (22 52) 2046 (2084 2011) 20007 (20012 20002) 367 068
vole intercept 51 (48 54) 632
populationb ROS 58 (55 60) 20084 (2013 2005) 255 081DD 55 (47 62) 20098 (2024 007) 617 015ROS thornDD 59 (55 63) 20083 (2013 2005) 20036 (2012 005) 295 083
aROS fitted as log(ROS thorn 1) in the modelsbDD fitted as log(DD thorn 1) in the models
Synchrony in Arctic herbivores A Stien et al 1003
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
vole population size fluctuated between 0 and 286individuals with no evidence of population cycleswhile calves per female reindeer varied between 016and 080 (figure 1a) The fluctuations in vole popu-lation size and calves per female reindeer were highlycongruent (figure 1b r frac14 095 p 0001) Thissuggests that both the reindeer and vole populationwere responding to a common environmental stimulusin this high Arctic ecosystem
Biol Lett (2012)
ROS had a strong negative effect on both vole popu-lation sizes (figure 1c and table 1) and calves per femalereindeer (figure 1d and table 1) The lowest observationsof vole population sizes and calves per female reindeerwere all associated with more than 15 mm ROS(figure 1cd) When the effect of ROS was controlledfor statistically there was little evidence for a negativeeffect of previous yearrsquos population size on vole popu-lation sizes (table 1) but a clear effect of previous
1004 A Stien et al Synchrony in Arctic herbivores
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
yearrsquos reindeer population size on calves per femalereindeer (table 1) The full models had high R2-values(table 1) however there was still evidence for additionalunexplained covariance between the species in theresiduals from these models (r frac14 075 p frac14 0005)
4 DISCUSSIONThis study demonstrates a strong population dynamicsynchrony between voles and reindeer in a high Arcticecosystem that is predominantly due to the extent ofjoint climatic forcing Ground ice caused by ROSevents has previously been shown to affect reindeer[17] while there has been less evidence for an effecton high Arctic small rodents [3] Our study is thefirst to show a strong impact on both ecosystem com-ponents in the same arctic ecosystem Climatechange is expected to increase the frequency of ROSevents in large parts of the Arctic [2226] and ourresults suggest that these extreme weather eventsmight increasingly become a main determinant of thestructure and functioning of arctic ecosystems
After correcting for the effects of ROS and densitydependence there was still some evidence for residualcorrelation between the species This suggests that ourestimator of ROS does not capture all the climaticvariation that impacts the two herbivores A betterunderstanding of the processes that generate groundice as well as direct measures of ground ice mightallow improved predictions Alternatively there mightbe additional climatic factors that affect the food qual-ity and quantity available for both voles and reindeer inthis ecosystem
We are aware of only one previous study that hasdemonstrated climate-induced interspecific synchronyamong arctic animals Post amp Forchhammer [27]found that populations of musk oxen (Ovibos moschatus)and caribou (Rangifer tarandus) were synchronized byregionalized weather patterns across Greenland Inthat case the two focal herbivores were both large ungu-lates with similar life histories Thus our study adds tothe knowledge about the population dynamics of Arcticherbivores by providing a compelling demonstrationthat climate impacts can be integrated and expressedsimilarly in species with highly contrasting life histories
There are two contexts of the high Arctic environmentthat might facilitate the extraordinary interspecific con-gruent responses One is the extreme variability of thewinter climate on Svalbard with frequent and profoundROS events [22] a pattern seen over extensive areas inthe Arctic [2226] The other is the simplicity of theterrestrial food web at Svalbard in particular withoutspecialized predators that could drive multi-annualpopulation cycles due to delayed density dependence[5] It could be expected that populations with differentand strong density dependence would be less prone toclimate-induced interspecific synchrony [28] Conse-quently responses of wildlife populations to climatevariability and change might indeed be more consistentand more predictable in the most extreme environmentsof the Polar regions than terrestrial ecosystems elsewhere
We thank numerous field assistants and the technical staff atthe Norwegian Polar Institute and UNIS for supporting the
Biol Lett (2012)
field campaigns Olav Strand for the use of monitoring dataon reindeer population sizes and Marco Festa-Bianchet andtwo anonymous referees for commenting on the manuscriptThe work was mainly supported by grants from UK NaturalEnvironment Research Council the Norwegian ResearchCouncil and the Macaulay Development Trust Additionaleconomic support has come from the Norwegian Institute forNature Research Centre for Ecology and Hydrology UNISThe Macaulay Institute the Norwegian School of VeterinaryScience the Amundsen Foundation Arctic Field Grant theFrench Polar Institute and the Governor of Svalbard
1 ACIA 2004 Impacts of a warming Arctic Arctic climateimpact assessment London UK Cambridge University
Press2 Coulson T Catchpole E A Albon S D Morgan
B J T Pemberton J M Clutton-Brock T HCrawley M J amp Grenfell B T 2001 Age sex densitywinter weather and population crashes in Soay sheep
Science 292 1528ndash1531 (doi101126science29255211528)
3 Gilg O Sittler B amp Hanski I 2009 Climate changeand cyclic predatorndashprey population dynamics in thehigh Arctic Glob Change Biol 15 2634ndash2652 (doi10
1111j1365-2486200901927x)4 Stenseth N C Mysterud A Ottersen G Hurrell
J W Chan K S amp Lima M 2002 Ecological effectsof climate fluctuations Science 297 1292ndash1296(doi101126science1071281)
5 Ims R A amp Fuglei E 2005 Trophic interaction cycles intundra ecosystems and the impact of climate changeBioscience 55 311ndash322 (doi1016410006-3568(2005)055[0311ticite]20co2)
6 Vors L S amp Boyce M S 2009 Global declines of car-ibou and reindeer Glob Change Biol 15 2626ndash2633(doi101111j1365-2486200901974x)
7 Caughley G amp Krebs C J 1983 Are big mammalssimply small mammals writ large Oecologia 59 7ndash17
(doi101007BF00388066)8 Krebs C J 2009 Population dynamics of large and small
mammals Graeme Caughleyrsquos grand vision Wildl Res36 1ndash7 (doi101071wr08004)
9 Morris W F et al 2008 Longevity can buffer plant and
animal populations against changing climatic variabilityEcology 89 19ndash25 (doi10189007-07741)
10 Post E et al 2009 Ecological dynamics across the Arcticassociated with recent climate change Science 3251355ndash1358 (doi101126science1173113)
11 Solberg E J Jordhoy P Strand O Aanes R LoisonA Saether B E amp Linnell J D C 2001 Effects ofdensity-dependence and climate on the dynamics of aSvalbard reindeer population Ecography 24 441ndash451
(doi101034j1600-05872001d01-200x)12 Tyler N J C Forchhammer M C amp Oritsland N A
2008 Nonlinear effects of climate and density in thedynamics of a fluctuating population of reindeer Ecology89 1675ndash1686 (doi10189007-04161)
13 Aanes R Saether B E Smith F M Cooper E JWookey P A amp Oritsland N A 2002 The Arctic Oscil-lation predicts effects of climate change in two trophiclevels in a high-arctic ecosystem Ecol Lett 5 445ndash453(doi101046j1461-0248200200340x)
14 Albon S D Stien A Irvine R J Langvatn RRopstad E amp Halvorsen O 2002 The role of parasitesin the dynamics of a reindeer population Proc R SocLond B 269 1625ndash1632 (doi101098rspb20022064)
Synchrony in Arctic herbivores A Stien et al 1005
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
15 Korslund L amp Steen H 2006 Small rodent winter survivalsnow conditions limit access to food resources J Anim Ecol75 156ndash166 (doi101111j1365-2656200501031x)
16 Stien A Loe L E Mysterud A Severinsen TKohler J amp Langvatn R 2010 Icing events triggerrange displacement in a high-arctic ungulate Ecology91 915ndash920 (doi10189009-00561)
17 Hansen B B Aanes R Herfindal I Kohler J ampSaether B E 2011 Climate icing and wild arctic rein-deer past relationships and future prospects Ecology 921917ndash1923 (doi10189011-00951)
18 Kausrud K L et al 2008 Linking climate change to
lemming cycles Nature 456 93ndash97 (doi101038nature07442)
19 Aars J amp Ims R A 2002 Intrinsic and climatic determi-nants of population demography the winter dynamics of
tundra voles Ecology 83 3449ndash3456 (doi1023073072093)
20 Miller F L amp Gunn A 2003 Catastrophic die-off ofPeary caribou on the western Queen Elizabeth IslandsCanadian High Arctic Arctic 56 381ndash390
21 Ims R A Henden J A amp Killengreen S T 2008 Col-lapsing population cycles Trends Ecol Evol 23 79ndash86(doi101016jtree200710010)
Biol Lett (2012)
22 Rennert K J Roe G Putkonen J amp Bitz C M 2009Soil thermal and ecological impacts of rain on snow
events in the circumpolar Arctic J Climate 222302ndash2315 (doi1011752008jcli21171)
23 Tyler N J C 2010 Climate snow ice crashes anddeclines in populations of reindeer and caribou (Rangifertarandus L) Ecol Monogr 80 197ndash219 (doi10189009-10701)
24 Henttonen H Fuglei E Gower C N Haukisalmi VIms R A Niemimaa J amp Yoccoz N G 2001 Echinococcusmultilocularis on Svalbard introduction of an intermediatehost has enabled the local life-cycle Parasitology 123
547ndash552 (doi101017s0031182001008800)25 Venables W N amp Ripley B D 1999 Modern applied
statistics with S-Plus 3rd edn New York NY Springer26 Liston G E amp Hiemstra C A 2011 The changing
cryosphere Pan-Arctic snow trends (1979ndash2009)J Climate 24 5691ndash5712 (doi101175jcli-d-11-000811)
27 Post E amp Forchhammer M C 2002 Synchronization ofanimal population dynamics by large-scale climateNature 420 168ndash171 (doi101038nature01064)
28 Moran P A P 1953 The statistical analysis of the Cana-dian lynx cycle II Synchronization and meteorologyAust J Zool 1 291ndash298 (doi101071ZO9530291)
1
Electronic supplementary material
Congruent responses to weather variability in high-arctic herbivores
Audun Stien1 Rolf A Ims2 Steve D Albon3 Eva Fuglei4 R Justin Irvine3 Erik
Ropstad5 Odd Halvorsen6 Rolf Langvatn78 Leif Egil Loe910 Vebjoslashrn Veiberg7 Nigel
G Yoccoz2
1 Norwegian Institute for Nature Research Fram Centre NO-9296 Tromsoslash Norway
2 University of Tromsoslash NO-9037 Tromsoslash Norway
3 The James Hutton Institute Aberdeen AB15 8QH UK
4 Norwegian Polar Institute Fram Centre NO-9296 Tromsoslash Norway
5 Norwegian School of Veterinary Science NO-0033 Oslo Norway
6 Natural History Museum University of Oslo NO-0318 Oslo Norway
7 Norwegian Institute for Nature Research NO-7485 Trondheim Norway
8 University Centre in Svalbard NO-9171 Longyearbyen Norway
9 Norwegian University of Life Sciences NO-1432 Aas Norway
10 CEES Institute of Biology University of Oslo NO-0316 Oslo Norway
Author for correspondence (audunstienninano)
1 Materials and methods
The studies were carried out annually in July-August on Nordenskioumlld Land peninsula on
Spitsbergen At one location the vole population size was estimated whereas the total
reindeer population size and the proportion of female reindeer with a calf were estimated in a
2
neighbouring area (Fig S1) The reindeer study area included Colesdalen Semmeldalen parts
of Reindalen and their adjacent side valleys covering approximately 285 km2 (Fig S1)
Female reindeer have been individually marked in the study population since 1994 [see 1]
During the period 1995-2011 the study area have been surveyed each year in July-August
Marked females have been registered and the presence of a calf associated with them noted
Svalbard reindeer have reduced calving rates at less than 3 years of age To remove potential
bias due to age structure we only included females of 3 years and older in the analyses The
number of marked female reindeer observed in the surveys varied between 36 and 151
between years Reindeer population size was estimated as the number of animals observed
along a transect line going through Colesdalen and Semmeldalen each year 1994-2011 The
reindeer population size varied between 210 and 510 animals (mean=342 SD=79)
Voles
Reindeer
LongyearbyenBarentsburg
78
80
79
77
10 20 30
Figure S1 The study areas for the Svalbard reindeer and sibling vole monitoring on the Nordenskioumlld Land
peninsula Spitsbergen Svalbard Norway The coastline (black line) and 150 m contour lines (grey line) are
given together with locations of the two main human settlements Longyearbyen and Barentsburg The inserted
map shows the position of Nordenskioumlld Land peninsula (rectangle) on Svalbard
3
The sibling vole population was monitored within an area of less than 1 km2 by the
abandoned mining town Grumant at the coast of Isfjorden 10 km north of the study area for
the Svalbard reindeer (Fig S1) In 1996-2007 five fixed trapping grids with a total of 139
Ugglan traps (24 25 and 3 times 30 traps per grid) were checked 6 hours after the traps were
set and up to 2 times per day over a period from 4-6 consecutive days during the first 10 days
of August giving 7-10 trapping occasions each year In addition trapping was done in one of
the trapping grids (30 traps) in 1995 An estimate of the vole population size in the extensive
trapping grid for 1995 was obtained using prediction from a linear regression model for the
relationship between the vole population size in the single trapping grid and the vole
population size in the extensive trapping grid (estimated vole population size in 1995 = 281
SE=23) The estimated population size for 1995 was only used in the model that included
previous yearrsquos vole population size as predictor Trapped animals were marked on first
capture and the identity checked before release on subsequent capture occasions Vole
population sizes were estimated via sample coverage [2] using program CARE-2 and a closed
capturendashrecapture model that include both between individual and capture occasion
heterogeneity in capture probabilities (model Mht in CARE-2) In 1996 and 2002 not a single
vole was trapped in the trapping grids For these years we report the estimated zero population
size with no confidence limits
Daily precipitation and temperature data were obtained from the meteorological station at the
airport in the nearby settlement Longyearbyen (httpeklimametno Fig S1) From these
data we calculated the amount of precipitation that fell at a temperature above one degree C
between 1 November and 30 April as our measure of the extent of rain-on-snow [for a similar
approach see 3] The average annual rain-on-snow since records beginning at Longyearbyen
airport in 1976 has been 136 mm (SD=175 median=7 mm 75 quantile=184 mm) and in
4
the three 12 year periods from 1976 to 2011 the number of years with more than 15 mm of
rain-on-snow has been 3 (1976-1987) 4 (1988-1999) and 4 (2000-2011) suggesting that
heavy rain-on-snow was relatively common also in the first 12 year period (every 4th year on
average) We note that most of the rain-on-snow has tended to come in the early part of the
winter (on average 68 in November-January) In particularly this has been true in the years
with severe rain-on-snow events (gt15 mm) when on average 86 of the rain-on-snow has
come in November to January The correlation between the annual estimates of rain-on-snow
for November-January and for November-April is therefore high (r=097) This pattern
implies that there is too little information in the data to allow an evaluation of whether the
effect of rain-on-snow on voles and reindeer differ between early and late winter rain-on-
snow events Whether we use November-January or November-April as the measurement
period for rain-on-snow has no significant impact on analyses or conclusions
The dataset is given in Table S1 We report Pearson correlation coefficients for simple
correlations As a measure of the predictive power of the regression models we report R2-
values estimated as the squared correlation between the annual point estimates of the response
variables and predicted values of the selected regression model [4] Initially we used
generalised linear models as implemented in R 2150 [5] to investigate the impact of rain-on-
snow and population size the previous summer on reindeer fecundity and vole population
sizes Calves per female reindeer were modelled assuming a logit link function and binomial
error distribution and the rain-on-snow predictor variable was fitted as log(rain-on-snow+1)
to reduce non-linearities Vole population sizes were modelled assuming a log link function
A Poisson error distribution was chosen as initial analyses showed that the estimates of the
sampling variance in the annual point estimates increased with the value of the point estimate
with a ratio of the variance to the mean close to 1 (average value of variancemean=11)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
0
50
100
150
200
250
300
350
0
02
04
06
08
10volesreindeerrain-on-snow
calv
es p
er f
emal
e
(a)
0
50
100
150
200
250
300
0 04 08
vole
pop
ulat
ion
vole
pop
ulat
ion
calves per female
(b)
1995 2000 2005 2010
0
50
100
150
200250
300
350
rain-on-snow (mm)
0 1 5 15 50
(c)
0
02
04
06
08
10
0 1 5 15 50
calv
es p
er f
emal
e
(d)
rain-on-snow (mm)
rain
-on-
snow
(m
m)
vole
pop
ulat
ion
Figure 1 Annual estimates of sibling vole population sizes calves per female Svalbard reindeer and ROS (a) Time series of
annual estimates (+ 95 CI) of sibling vole population sizes (red colour 1996ndash2007) Svalbard reindeer fecundities(calves per female (blue colour 1995ndash2011) and ROS (black colour mm 1995ndash2011) (b) Estimated vole population sizesplotted against calves per female reindeer (c) Vole population sizes plotted against ROS (d) Calves per female reindeer plottedagainst ROS Regression lines for the univariate relationships with 95 confidence envelopes (dashed lines) are given in (c) and
(d) with ROS along the x-axis plotted on log(x thorn 1) scale
Table 1 Parameter estimates (with 95 CI) QAICc and R2-values for GLMs for the impact of rain-on-snow (ROS) and
previous yearrsquos population size (DD) on calves per female reindeer and vole population sizes QAICc values for the best fitmodels are in bold
response model
parameter estimates (95 CI)
intercept ROS (mm) DD QAICc R2-values
calves per intercept 028 (202 08) 628femalea ROS 18 (09 27) 2075 (2118 2037) 422 057
DD 38 (21 57) 20010 (20015 20005) 400 039ROS thornDD 37 (22 52) 2046 (2084 2011) 20007 (20012 20002) 367 068
vole intercept 51 (48 54) 632
populationb ROS 58 (55 60) 20084 (2013 2005) 255 081DD 55 (47 62) 20098 (2024 007) 617 015ROS thornDD 59 (55 63) 20083 (2013 2005) 20036 (2012 005) 295 083
aROS fitted as log(ROS thorn 1) in the modelsbDD fitted as log(DD thorn 1) in the models
Synchrony in Arctic herbivores A Stien et al 1003
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
vole population size fluctuated between 0 and 286individuals with no evidence of population cycleswhile calves per female reindeer varied between 016and 080 (figure 1a) The fluctuations in vole popu-lation size and calves per female reindeer were highlycongruent (figure 1b r frac14 095 p 0001) Thissuggests that both the reindeer and vole populationwere responding to a common environmental stimulusin this high Arctic ecosystem
Biol Lett (2012)
ROS had a strong negative effect on both vole popu-lation sizes (figure 1c and table 1) and calves per femalereindeer (figure 1d and table 1) The lowest observationsof vole population sizes and calves per female reindeerwere all associated with more than 15 mm ROS(figure 1cd) When the effect of ROS was controlledfor statistically there was little evidence for a negativeeffect of previous yearrsquos population size on vole popu-lation sizes (table 1) but a clear effect of previous
1004 A Stien et al Synchrony in Arctic herbivores
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
yearrsquos reindeer population size on calves per femalereindeer (table 1) The full models had high R2-values(table 1) however there was still evidence for additionalunexplained covariance between the species in theresiduals from these models (r frac14 075 p frac14 0005)
4 DISCUSSIONThis study demonstrates a strong population dynamicsynchrony between voles and reindeer in a high Arcticecosystem that is predominantly due to the extent ofjoint climatic forcing Ground ice caused by ROSevents has previously been shown to affect reindeer[17] while there has been less evidence for an effecton high Arctic small rodents [3] Our study is thefirst to show a strong impact on both ecosystem com-ponents in the same arctic ecosystem Climatechange is expected to increase the frequency of ROSevents in large parts of the Arctic [2226] and ourresults suggest that these extreme weather eventsmight increasingly become a main determinant of thestructure and functioning of arctic ecosystems
After correcting for the effects of ROS and densitydependence there was still some evidence for residualcorrelation between the species This suggests that ourestimator of ROS does not capture all the climaticvariation that impacts the two herbivores A betterunderstanding of the processes that generate groundice as well as direct measures of ground ice mightallow improved predictions Alternatively there mightbe additional climatic factors that affect the food qual-ity and quantity available for both voles and reindeer inthis ecosystem
We are aware of only one previous study that hasdemonstrated climate-induced interspecific synchronyamong arctic animals Post amp Forchhammer [27]found that populations of musk oxen (Ovibos moschatus)and caribou (Rangifer tarandus) were synchronized byregionalized weather patterns across Greenland Inthat case the two focal herbivores were both large ungu-lates with similar life histories Thus our study adds tothe knowledge about the population dynamics of Arcticherbivores by providing a compelling demonstrationthat climate impacts can be integrated and expressedsimilarly in species with highly contrasting life histories
There are two contexts of the high Arctic environmentthat might facilitate the extraordinary interspecific con-gruent responses One is the extreme variability of thewinter climate on Svalbard with frequent and profoundROS events [22] a pattern seen over extensive areas inthe Arctic [2226] The other is the simplicity of theterrestrial food web at Svalbard in particular withoutspecialized predators that could drive multi-annualpopulation cycles due to delayed density dependence[5] It could be expected that populations with differentand strong density dependence would be less prone toclimate-induced interspecific synchrony [28] Conse-quently responses of wildlife populations to climatevariability and change might indeed be more consistentand more predictable in the most extreme environmentsof the Polar regions than terrestrial ecosystems elsewhere
We thank numerous field assistants and the technical staff atthe Norwegian Polar Institute and UNIS for supporting the
Biol Lett (2012)
field campaigns Olav Strand for the use of monitoring dataon reindeer population sizes and Marco Festa-Bianchet andtwo anonymous referees for commenting on the manuscriptThe work was mainly supported by grants from UK NaturalEnvironment Research Council the Norwegian ResearchCouncil and the Macaulay Development Trust Additionaleconomic support has come from the Norwegian Institute forNature Research Centre for Ecology and Hydrology UNISThe Macaulay Institute the Norwegian School of VeterinaryScience the Amundsen Foundation Arctic Field Grant theFrench Polar Institute and the Governor of Svalbard
1 ACIA 2004 Impacts of a warming Arctic Arctic climateimpact assessment London UK Cambridge University
Press2 Coulson T Catchpole E A Albon S D Morgan
B J T Pemberton J M Clutton-Brock T HCrawley M J amp Grenfell B T 2001 Age sex densitywinter weather and population crashes in Soay sheep
Science 292 1528ndash1531 (doi101126science29255211528)
3 Gilg O Sittler B amp Hanski I 2009 Climate changeand cyclic predatorndashprey population dynamics in thehigh Arctic Glob Change Biol 15 2634ndash2652 (doi10
1111j1365-2486200901927x)4 Stenseth N C Mysterud A Ottersen G Hurrell
J W Chan K S amp Lima M 2002 Ecological effectsof climate fluctuations Science 297 1292ndash1296(doi101126science1071281)
5 Ims R A amp Fuglei E 2005 Trophic interaction cycles intundra ecosystems and the impact of climate changeBioscience 55 311ndash322 (doi1016410006-3568(2005)055[0311ticite]20co2)
6 Vors L S amp Boyce M S 2009 Global declines of car-ibou and reindeer Glob Change Biol 15 2626ndash2633(doi101111j1365-2486200901974x)
7 Caughley G amp Krebs C J 1983 Are big mammalssimply small mammals writ large Oecologia 59 7ndash17
(doi101007BF00388066)8 Krebs C J 2009 Population dynamics of large and small
mammals Graeme Caughleyrsquos grand vision Wildl Res36 1ndash7 (doi101071wr08004)
9 Morris W F et al 2008 Longevity can buffer plant and
animal populations against changing climatic variabilityEcology 89 19ndash25 (doi10189007-07741)
10 Post E et al 2009 Ecological dynamics across the Arcticassociated with recent climate change Science 3251355ndash1358 (doi101126science1173113)
11 Solberg E J Jordhoy P Strand O Aanes R LoisonA Saether B E amp Linnell J D C 2001 Effects ofdensity-dependence and climate on the dynamics of aSvalbard reindeer population Ecography 24 441ndash451
(doi101034j1600-05872001d01-200x)12 Tyler N J C Forchhammer M C amp Oritsland N A
2008 Nonlinear effects of climate and density in thedynamics of a fluctuating population of reindeer Ecology89 1675ndash1686 (doi10189007-04161)
13 Aanes R Saether B E Smith F M Cooper E JWookey P A amp Oritsland N A 2002 The Arctic Oscil-lation predicts effects of climate change in two trophiclevels in a high-arctic ecosystem Ecol Lett 5 445ndash453(doi101046j1461-0248200200340x)
14 Albon S D Stien A Irvine R J Langvatn RRopstad E amp Halvorsen O 2002 The role of parasitesin the dynamics of a reindeer population Proc R SocLond B 269 1625ndash1632 (doi101098rspb20022064)
Synchrony in Arctic herbivores A Stien et al 1005
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
15 Korslund L amp Steen H 2006 Small rodent winter survivalsnow conditions limit access to food resources J Anim Ecol75 156ndash166 (doi101111j1365-2656200501031x)
16 Stien A Loe L E Mysterud A Severinsen TKohler J amp Langvatn R 2010 Icing events triggerrange displacement in a high-arctic ungulate Ecology91 915ndash920 (doi10189009-00561)
17 Hansen B B Aanes R Herfindal I Kohler J ampSaether B E 2011 Climate icing and wild arctic rein-deer past relationships and future prospects Ecology 921917ndash1923 (doi10189011-00951)
18 Kausrud K L et al 2008 Linking climate change to
lemming cycles Nature 456 93ndash97 (doi101038nature07442)
19 Aars J amp Ims R A 2002 Intrinsic and climatic determi-nants of population demography the winter dynamics of
tundra voles Ecology 83 3449ndash3456 (doi1023073072093)
20 Miller F L amp Gunn A 2003 Catastrophic die-off ofPeary caribou on the western Queen Elizabeth IslandsCanadian High Arctic Arctic 56 381ndash390
21 Ims R A Henden J A amp Killengreen S T 2008 Col-lapsing population cycles Trends Ecol Evol 23 79ndash86(doi101016jtree200710010)
Biol Lett (2012)
22 Rennert K J Roe G Putkonen J amp Bitz C M 2009Soil thermal and ecological impacts of rain on snow
events in the circumpolar Arctic J Climate 222302ndash2315 (doi1011752008jcli21171)
23 Tyler N J C 2010 Climate snow ice crashes anddeclines in populations of reindeer and caribou (Rangifertarandus L) Ecol Monogr 80 197ndash219 (doi10189009-10701)
24 Henttonen H Fuglei E Gower C N Haukisalmi VIms R A Niemimaa J amp Yoccoz N G 2001 Echinococcusmultilocularis on Svalbard introduction of an intermediatehost has enabled the local life-cycle Parasitology 123
547ndash552 (doi101017s0031182001008800)25 Venables W N amp Ripley B D 1999 Modern applied
statistics with S-Plus 3rd edn New York NY Springer26 Liston G E amp Hiemstra C A 2011 The changing
cryosphere Pan-Arctic snow trends (1979ndash2009)J Climate 24 5691ndash5712 (doi101175jcli-d-11-000811)
27 Post E amp Forchhammer M C 2002 Synchronization ofanimal population dynamics by large-scale climateNature 420 168ndash171 (doi101038nature01064)
28 Moran P A P 1953 The statistical analysis of the Cana-dian lynx cycle II Synchronization and meteorologyAust J Zool 1 291ndash298 (doi101071ZO9530291)
1
Electronic supplementary material
Congruent responses to weather variability in high-arctic herbivores
Audun Stien1 Rolf A Ims2 Steve D Albon3 Eva Fuglei4 R Justin Irvine3 Erik
Ropstad5 Odd Halvorsen6 Rolf Langvatn78 Leif Egil Loe910 Vebjoslashrn Veiberg7 Nigel
G Yoccoz2
1 Norwegian Institute for Nature Research Fram Centre NO-9296 Tromsoslash Norway
2 University of Tromsoslash NO-9037 Tromsoslash Norway
3 The James Hutton Institute Aberdeen AB15 8QH UK
4 Norwegian Polar Institute Fram Centre NO-9296 Tromsoslash Norway
5 Norwegian School of Veterinary Science NO-0033 Oslo Norway
6 Natural History Museum University of Oslo NO-0318 Oslo Norway
7 Norwegian Institute for Nature Research NO-7485 Trondheim Norway
8 University Centre in Svalbard NO-9171 Longyearbyen Norway
9 Norwegian University of Life Sciences NO-1432 Aas Norway
10 CEES Institute of Biology University of Oslo NO-0316 Oslo Norway
Author for correspondence (audunstienninano)
1 Materials and methods
The studies were carried out annually in July-August on Nordenskioumlld Land peninsula on
Spitsbergen At one location the vole population size was estimated whereas the total
reindeer population size and the proportion of female reindeer with a calf were estimated in a
2
neighbouring area (Fig S1) The reindeer study area included Colesdalen Semmeldalen parts
of Reindalen and their adjacent side valleys covering approximately 285 km2 (Fig S1)
Female reindeer have been individually marked in the study population since 1994 [see 1]
During the period 1995-2011 the study area have been surveyed each year in July-August
Marked females have been registered and the presence of a calf associated with them noted
Svalbard reindeer have reduced calving rates at less than 3 years of age To remove potential
bias due to age structure we only included females of 3 years and older in the analyses The
number of marked female reindeer observed in the surveys varied between 36 and 151
between years Reindeer population size was estimated as the number of animals observed
along a transect line going through Colesdalen and Semmeldalen each year 1994-2011 The
reindeer population size varied between 210 and 510 animals (mean=342 SD=79)
Voles
Reindeer
LongyearbyenBarentsburg
78
80
79
77
10 20 30
Figure S1 The study areas for the Svalbard reindeer and sibling vole monitoring on the Nordenskioumlld Land
peninsula Spitsbergen Svalbard Norway The coastline (black line) and 150 m contour lines (grey line) are
given together with locations of the two main human settlements Longyearbyen and Barentsburg The inserted
map shows the position of Nordenskioumlld Land peninsula (rectangle) on Svalbard
3
The sibling vole population was monitored within an area of less than 1 km2 by the
abandoned mining town Grumant at the coast of Isfjorden 10 km north of the study area for
the Svalbard reindeer (Fig S1) In 1996-2007 five fixed trapping grids with a total of 139
Ugglan traps (24 25 and 3 times 30 traps per grid) were checked 6 hours after the traps were
set and up to 2 times per day over a period from 4-6 consecutive days during the first 10 days
of August giving 7-10 trapping occasions each year In addition trapping was done in one of
the trapping grids (30 traps) in 1995 An estimate of the vole population size in the extensive
trapping grid for 1995 was obtained using prediction from a linear regression model for the
relationship between the vole population size in the single trapping grid and the vole
population size in the extensive trapping grid (estimated vole population size in 1995 = 281
SE=23) The estimated population size for 1995 was only used in the model that included
previous yearrsquos vole population size as predictor Trapped animals were marked on first
capture and the identity checked before release on subsequent capture occasions Vole
population sizes were estimated via sample coverage [2] using program CARE-2 and a closed
capturendashrecapture model that include both between individual and capture occasion
heterogeneity in capture probabilities (model Mht in CARE-2) In 1996 and 2002 not a single
vole was trapped in the trapping grids For these years we report the estimated zero population
size with no confidence limits
Daily precipitation and temperature data were obtained from the meteorological station at the
airport in the nearby settlement Longyearbyen (httpeklimametno Fig S1) From these
data we calculated the amount of precipitation that fell at a temperature above one degree C
between 1 November and 30 April as our measure of the extent of rain-on-snow [for a similar
approach see 3] The average annual rain-on-snow since records beginning at Longyearbyen
airport in 1976 has been 136 mm (SD=175 median=7 mm 75 quantile=184 mm) and in
4
the three 12 year periods from 1976 to 2011 the number of years with more than 15 mm of
rain-on-snow has been 3 (1976-1987) 4 (1988-1999) and 4 (2000-2011) suggesting that
heavy rain-on-snow was relatively common also in the first 12 year period (every 4th year on
average) We note that most of the rain-on-snow has tended to come in the early part of the
winter (on average 68 in November-January) In particularly this has been true in the years
with severe rain-on-snow events (gt15 mm) when on average 86 of the rain-on-snow has
come in November to January The correlation between the annual estimates of rain-on-snow
for November-January and for November-April is therefore high (r=097) This pattern
implies that there is too little information in the data to allow an evaluation of whether the
effect of rain-on-snow on voles and reindeer differ between early and late winter rain-on-
snow events Whether we use November-January or November-April as the measurement
period for rain-on-snow has no significant impact on analyses or conclusions
The dataset is given in Table S1 We report Pearson correlation coefficients for simple
correlations As a measure of the predictive power of the regression models we report R2-
values estimated as the squared correlation between the annual point estimates of the response
variables and predicted values of the selected regression model [4] Initially we used
generalised linear models as implemented in R 2150 [5] to investigate the impact of rain-on-
snow and population size the previous summer on reindeer fecundity and vole population
sizes Calves per female reindeer were modelled assuming a logit link function and binomial
error distribution and the rain-on-snow predictor variable was fitted as log(rain-on-snow+1)
to reduce non-linearities Vole population sizes were modelled assuming a log link function
A Poisson error distribution was chosen as initial analyses showed that the estimates of the
sampling variance in the annual point estimates increased with the value of the point estimate
with a ratio of the variance to the mean close to 1 (average value of variancemean=11)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
1004 A Stien et al Synchrony in Arctic herbivores
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
yearrsquos reindeer population size on calves per femalereindeer (table 1) The full models had high R2-values(table 1) however there was still evidence for additionalunexplained covariance between the species in theresiduals from these models (r frac14 075 p frac14 0005)
4 DISCUSSIONThis study demonstrates a strong population dynamicsynchrony between voles and reindeer in a high Arcticecosystem that is predominantly due to the extent ofjoint climatic forcing Ground ice caused by ROSevents has previously been shown to affect reindeer[17] while there has been less evidence for an effecton high Arctic small rodents [3] Our study is thefirst to show a strong impact on both ecosystem com-ponents in the same arctic ecosystem Climatechange is expected to increase the frequency of ROSevents in large parts of the Arctic [2226] and ourresults suggest that these extreme weather eventsmight increasingly become a main determinant of thestructure and functioning of arctic ecosystems
After correcting for the effects of ROS and densitydependence there was still some evidence for residualcorrelation between the species This suggests that ourestimator of ROS does not capture all the climaticvariation that impacts the two herbivores A betterunderstanding of the processes that generate groundice as well as direct measures of ground ice mightallow improved predictions Alternatively there mightbe additional climatic factors that affect the food qual-ity and quantity available for both voles and reindeer inthis ecosystem
We are aware of only one previous study that hasdemonstrated climate-induced interspecific synchronyamong arctic animals Post amp Forchhammer [27]found that populations of musk oxen (Ovibos moschatus)and caribou (Rangifer tarandus) were synchronized byregionalized weather patterns across Greenland Inthat case the two focal herbivores were both large ungu-lates with similar life histories Thus our study adds tothe knowledge about the population dynamics of Arcticherbivores by providing a compelling demonstrationthat climate impacts can be integrated and expressedsimilarly in species with highly contrasting life histories
There are two contexts of the high Arctic environmentthat might facilitate the extraordinary interspecific con-gruent responses One is the extreme variability of thewinter climate on Svalbard with frequent and profoundROS events [22] a pattern seen over extensive areas inthe Arctic [2226] The other is the simplicity of theterrestrial food web at Svalbard in particular withoutspecialized predators that could drive multi-annualpopulation cycles due to delayed density dependence[5] It could be expected that populations with differentand strong density dependence would be less prone toclimate-induced interspecific synchrony [28] Conse-quently responses of wildlife populations to climatevariability and change might indeed be more consistentand more predictable in the most extreme environmentsof the Polar regions than terrestrial ecosystems elsewhere
We thank numerous field assistants and the technical staff atthe Norwegian Polar Institute and UNIS for supporting the
Biol Lett (2012)
field campaigns Olav Strand for the use of monitoring dataon reindeer population sizes and Marco Festa-Bianchet andtwo anonymous referees for commenting on the manuscriptThe work was mainly supported by grants from UK NaturalEnvironment Research Council the Norwegian ResearchCouncil and the Macaulay Development Trust Additionaleconomic support has come from the Norwegian Institute forNature Research Centre for Ecology and Hydrology UNISThe Macaulay Institute the Norwegian School of VeterinaryScience the Amundsen Foundation Arctic Field Grant theFrench Polar Institute and the Governor of Svalbard
1 ACIA 2004 Impacts of a warming Arctic Arctic climateimpact assessment London UK Cambridge University
Press2 Coulson T Catchpole E A Albon S D Morgan
B J T Pemberton J M Clutton-Brock T HCrawley M J amp Grenfell B T 2001 Age sex densitywinter weather and population crashes in Soay sheep
Science 292 1528ndash1531 (doi101126science29255211528)
3 Gilg O Sittler B amp Hanski I 2009 Climate changeand cyclic predatorndashprey population dynamics in thehigh Arctic Glob Change Biol 15 2634ndash2652 (doi10
1111j1365-2486200901927x)4 Stenseth N C Mysterud A Ottersen G Hurrell
J W Chan K S amp Lima M 2002 Ecological effectsof climate fluctuations Science 297 1292ndash1296(doi101126science1071281)
5 Ims R A amp Fuglei E 2005 Trophic interaction cycles intundra ecosystems and the impact of climate changeBioscience 55 311ndash322 (doi1016410006-3568(2005)055[0311ticite]20co2)
6 Vors L S amp Boyce M S 2009 Global declines of car-ibou and reindeer Glob Change Biol 15 2626ndash2633(doi101111j1365-2486200901974x)
7 Caughley G amp Krebs C J 1983 Are big mammalssimply small mammals writ large Oecologia 59 7ndash17
(doi101007BF00388066)8 Krebs C J 2009 Population dynamics of large and small
mammals Graeme Caughleyrsquos grand vision Wildl Res36 1ndash7 (doi101071wr08004)
9 Morris W F et al 2008 Longevity can buffer plant and
animal populations against changing climatic variabilityEcology 89 19ndash25 (doi10189007-07741)
10 Post E et al 2009 Ecological dynamics across the Arcticassociated with recent climate change Science 3251355ndash1358 (doi101126science1173113)
11 Solberg E J Jordhoy P Strand O Aanes R LoisonA Saether B E amp Linnell J D C 2001 Effects ofdensity-dependence and climate on the dynamics of aSvalbard reindeer population Ecography 24 441ndash451
(doi101034j1600-05872001d01-200x)12 Tyler N J C Forchhammer M C amp Oritsland N A
2008 Nonlinear effects of climate and density in thedynamics of a fluctuating population of reindeer Ecology89 1675ndash1686 (doi10189007-04161)
13 Aanes R Saether B E Smith F M Cooper E JWookey P A amp Oritsland N A 2002 The Arctic Oscil-lation predicts effects of climate change in two trophiclevels in a high-arctic ecosystem Ecol Lett 5 445ndash453(doi101046j1461-0248200200340x)
14 Albon S D Stien A Irvine R J Langvatn RRopstad E amp Halvorsen O 2002 The role of parasitesin the dynamics of a reindeer population Proc R SocLond B 269 1625ndash1632 (doi101098rspb20022064)
Synchrony in Arctic herbivores A Stien et al 1005
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
15 Korslund L amp Steen H 2006 Small rodent winter survivalsnow conditions limit access to food resources J Anim Ecol75 156ndash166 (doi101111j1365-2656200501031x)
16 Stien A Loe L E Mysterud A Severinsen TKohler J amp Langvatn R 2010 Icing events triggerrange displacement in a high-arctic ungulate Ecology91 915ndash920 (doi10189009-00561)
17 Hansen B B Aanes R Herfindal I Kohler J ampSaether B E 2011 Climate icing and wild arctic rein-deer past relationships and future prospects Ecology 921917ndash1923 (doi10189011-00951)
18 Kausrud K L et al 2008 Linking climate change to
lemming cycles Nature 456 93ndash97 (doi101038nature07442)
19 Aars J amp Ims R A 2002 Intrinsic and climatic determi-nants of population demography the winter dynamics of
tundra voles Ecology 83 3449ndash3456 (doi1023073072093)
20 Miller F L amp Gunn A 2003 Catastrophic die-off ofPeary caribou on the western Queen Elizabeth IslandsCanadian High Arctic Arctic 56 381ndash390
21 Ims R A Henden J A amp Killengreen S T 2008 Col-lapsing population cycles Trends Ecol Evol 23 79ndash86(doi101016jtree200710010)
Biol Lett (2012)
22 Rennert K J Roe G Putkonen J amp Bitz C M 2009Soil thermal and ecological impacts of rain on snow
events in the circumpolar Arctic J Climate 222302ndash2315 (doi1011752008jcli21171)
23 Tyler N J C 2010 Climate snow ice crashes anddeclines in populations of reindeer and caribou (Rangifertarandus L) Ecol Monogr 80 197ndash219 (doi10189009-10701)
24 Henttonen H Fuglei E Gower C N Haukisalmi VIms R A Niemimaa J amp Yoccoz N G 2001 Echinococcusmultilocularis on Svalbard introduction of an intermediatehost has enabled the local life-cycle Parasitology 123
547ndash552 (doi101017s0031182001008800)25 Venables W N amp Ripley B D 1999 Modern applied
statistics with S-Plus 3rd edn New York NY Springer26 Liston G E amp Hiemstra C A 2011 The changing
cryosphere Pan-Arctic snow trends (1979ndash2009)J Climate 24 5691ndash5712 (doi101175jcli-d-11-000811)
27 Post E amp Forchhammer M C 2002 Synchronization ofanimal population dynamics by large-scale climateNature 420 168ndash171 (doi101038nature01064)
28 Moran P A P 1953 The statistical analysis of the Cana-dian lynx cycle II Synchronization and meteorologyAust J Zool 1 291ndash298 (doi101071ZO9530291)
1
Electronic supplementary material
Congruent responses to weather variability in high-arctic herbivores
Audun Stien1 Rolf A Ims2 Steve D Albon3 Eva Fuglei4 R Justin Irvine3 Erik
Ropstad5 Odd Halvorsen6 Rolf Langvatn78 Leif Egil Loe910 Vebjoslashrn Veiberg7 Nigel
G Yoccoz2
1 Norwegian Institute for Nature Research Fram Centre NO-9296 Tromsoslash Norway
2 University of Tromsoslash NO-9037 Tromsoslash Norway
3 The James Hutton Institute Aberdeen AB15 8QH UK
4 Norwegian Polar Institute Fram Centre NO-9296 Tromsoslash Norway
5 Norwegian School of Veterinary Science NO-0033 Oslo Norway
6 Natural History Museum University of Oslo NO-0318 Oslo Norway
7 Norwegian Institute for Nature Research NO-7485 Trondheim Norway
8 University Centre in Svalbard NO-9171 Longyearbyen Norway
9 Norwegian University of Life Sciences NO-1432 Aas Norway
10 CEES Institute of Biology University of Oslo NO-0316 Oslo Norway
Author for correspondence (audunstienninano)
1 Materials and methods
The studies were carried out annually in July-August on Nordenskioumlld Land peninsula on
Spitsbergen At one location the vole population size was estimated whereas the total
reindeer population size and the proportion of female reindeer with a calf were estimated in a
2
neighbouring area (Fig S1) The reindeer study area included Colesdalen Semmeldalen parts
of Reindalen and their adjacent side valleys covering approximately 285 km2 (Fig S1)
Female reindeer have been individually marked in the study population since 1994 [see 1]
During the period 1995-2011 the study area have been surveyed each year in July-August
Marked females have been registered and the presence of a calf associated with them noted
Svalbard reindeer have reduced calving rates at less than 3 years of age To remove potential
bias due to age structure we only included females of 3 years and older in the analyses The
number of marked female reindeer observed in the surveys varied between 36 and 151
between years Reindeer population size was estimated as the number of animals observed
along a transect line going through Colesdalen and Semmeldalen each year 1994-2011 The
reindeer population size varied between 210 and 510 animals (mean=342 SD=79)
Voles
Reindeer
LongyearbyenBarentsburg
78
80
79
77
10 20 30
Figure S1 The study areas for the Svalbard reindeer and sibling vole monitoring on the Nordenskioumlld Land
peninsula Spitsbergen Svalbard Norway The coastline (black line) and 150 m contour lines (grey line) are
given together with locations of the two main human settlements Longyearbyen and Barentsburg The inserted
map shows the position of Nordenskioumlld Land peninsula (rectangle) on Svalbard
3
The sibling vole population was monitored within an area of less than 1 km2 by the
abandoned mining town Grumant at the coast of Isfjorden 10 km north of the study area for
the Svalbard reindeer (Fig S1) In 1996-2007 five fixed trapping grids with a total of 139
Ugglan traps (24 25 and 3 times 30 traps per grid) were checked 6 hours after the traps were
set and up to 2 times per day over a period from 4-6 consecutive days during the first 10 days
of August giving 7-10 trapping occasions each year In addition trapping was done in one of
the trapping grids (30 traps) in 1995 An estimate of the vole population size in the extensive
trapping grid for 1995 was obtained using prediction from a linear regression model for the
relationship between the vole population size in the single trapping grid and the vole
population size in the extensive trapping grid (estimated vole population size in 1995 = 281
SE=23) The estimated population size for 1995 was only used in the model that included
previous yearrsquos vole population size as predictor Trapped animals were marked on first
capture and the identity checked before release on subsequent capture occasions Vole
population sizes were estimated via sample coverage [2] using program CARE-2 and a closed
capturendashrecapture model that include both between individual and capture occasion
heterogeneity in capture probabilities (model Mht in CARE-2) In 1996 and 2002 not a single
vole was trapped in the trapping grids For these years we report the estimated zero population
size with no confidence limits
Daily precipitation and temperature data were obtained from the meteorological station at the
airport in the nearby settlement Longyearbyen (httpeklimametno Fig S1) From these
data we calculated the amount of precipitation that fell at a temperature above one degree C
between 1 November and 30 April as our measure of the extent of rain-on-snow [for a similar
approach see 3] The average annual rain-on-snow since records beginning at Longyearbyen
airport in 1976 has been 136 mm (SD=175 median=7 mm 75 quantile=184 mm) and in
4
the three 12 year periods from 1976 to 2011 the number of years with more than 15 mm of
rain-on-snow has been 3 (1976-1987) 4 (1988-1999) and 4 (2000-2011) suggesting that
heavy rain-on-snow was relatively common also in the first 12 year period (every 4th year on
average) We note that most of the rain-on-snow has tended to come in the early part of the
winter (on average 68 in November-January) In particularly this has been true in the years
with severe rain-on-snow events (gt15 mm) when on average 86 of the rain-on-snow has
come in November to January The correlation between the annual estimates of rain-on-snow
for November-January and for November-April is therefore high (r=097) This pattern
implies that there is too little information in the data to allow an evaluation of whether the
effect of rain-on-snow on voles and reindeer differ between early and late winter rain-on-
snow events Whether we use November-January or November-April as the measurement
period for rain-on-snow has no significant impact on analyses or conclusions
The dataset is given in Table S1 We report Pearson correlation coefficients for simple
correlations As a measure of the predictive power of the regression models we report R2-
values estimated as the squared correlation between the annual point estimates of the response
variables and predicted values of the selected regression model [4] Initially we used
generalised linear models as implemented in R 2150 [5] to investigate the impact of rain-on-
snow and population size the previous summer on reindeer fecundity and vole population
sizes Calves per female reindeer were modelled assuming a logit link function and binomial
error distribution and the rain-on-snow predictor variable was fitted as log(rain-on-snow+1)
to reduce non-linearities Vole population sizes were modelled assuming a log link function
A Poisson error distribution was chosen as initial analyses showed that the estimates of the
sampling variance in the annual point estimates increased with the value of the point estimate
with a ratio of the variance to the mean close to 1 (average value of variancemean=11)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
Synchrony in Arctic herbivores A Stien et al 1005
on November 13 2012rsblroyalsocietypublishingorgDownloaded from
15 Korslund L amp Steen H 2006 Small rodent winter survivalsnow conditions limit access to food resources J Anim Ecol75 156ndash166 (doi101111j1365-2656200501031x)
16 Stien A Loe L E Mysterud A Severinsen TKohler J amp Langvatn R 2010 Icing events triggerrange displacement in a high-arctic ungulate Ecology91 915ndash920 (doi10189009-00561)
17 Hansen B B Aanes R Herfindal I Kohler J ampSaether B E 2011 Climate icing and wild arctic rein-deer past relationships and future prospects Ecology 921917ndash1923 (doi10189011-00951)
18 Kausrud K L et al 2008 Linking climate change to
lemming cycles Nature 456 93ndash97 (doi101038nature07442)
19 Aars J amp Ims R A 2002 Intrinsic and climatic determi-nants of population demography the winter dynamics of
tundra voles Ecology 83 3449ndash3456 (doi1023073072093)
20 Miller F L amp Gunn A 2003 Catastrophic die-off ofPeary caribou on the western Queen Elizabeth IslandsCanadian High Arctic Arctic 56 381ndash390
21 Ims R A Henden J A amp Killengreen S T 2008 Col-lapsing population cycles Trends Ecol Evol 23 79ndash86(doi101016jtree200710010)
Biol Lett (2012)
22 Rennert K J Roe G Putkonen J amp Bitz C M 2009Soil thermal and ecological impacts of rain on snow
events in the circumpolar Arctic J Climate 222302ndash2315 (doi1011752008jcli21171)
23 Tyler N J C 2010 Climate snow ice crashes anddeclines in populations of reindeer and caribou (Rangifertarandus L) Ecol Monogr 80 197ndash219 (doi10189009-10701)
24 Henttonen H Fuglei E Gower C N Haukisalmi VIms R A Niemimaa J amp Yoccoz N G 2001 Echinococcusmultilocularis on Svalbard introduction of an intermediatehost has enabled the local life-cycle Parasitology 123
547ndash552 (doi101017s0031182001008800)25 Venables W N amp Ripley B D 1999 Modern applied
statistics with S-Plus 3rd edn New York NY Springer26 Liston G E amp Hiemstra C A 2011 The changing
cryosphere Pan-Arctic snow trends (1979ndash2009)J Climate 24 5691ndash5712 (doi101175jcli-d-11-000811)
27 Post E amp Forchhammer M C 2002 Synchronization ofanimal population dynamics by large-scale climateNature 420 168ndash171 (doi101038nature01064)
28 Moran P A P 1953 The statistical analysis of the Cana-dian lynx cycle II Synchronization and meteorologyAust J Zool 1 291ndash298 (doi101071ZO9530291)
1
Electronic supplementary material
Congruent responses to weather variability in high-arctic herbivores
Audun Stien1 Rolf A Ims2 Steve D Albon3 Eva Fuglei4 R Justin Irvine3 Erik
Ropstad5 Odd Halvorsen6 Rolf Langvatn78 Leif Egil Loe910 Vebjoslashrn Veiberg7 Nigel
G Yoccoz2
1 Norwegian Institute for Nature Research Fram Centre NO-9296 Tromsoslash Norway
2 University of Tromsoslash NO-9037 Tromsoslash Norway
3 The James Hutton Institute Aberdeen AB15 8QH UK
4 Norwegian Polar Institute Fram Centre NO-9296 Tromsoslash Norway
5 Norwegian School of Veterinary Science NO-0033 Oslo Norway
6 Natural History Museum University of Oslo NO-0318 Oslo Norway
7 Norwegian Institute for Nature Research NO-7485 Trondheim Norway
8 University Centre in Svalbard NO-9171 Longyearbyen Norway
9 Norwegian University of Life Sciences NO-1432 Aas Norway
10 CEES Institute of Biology University of Oslo NO-0316 Oslo Norway
Author for correspondence (audunstienninano)
1 Materials and methods
The studies were carried out annually in July-August on Nordenskioumlld Land peninsula on
Spitsbergen At one location the vole population size was estimated whereas the total
reindeer population size and the proportion of female reindeer with a calf were estimated in a
2
neighbouring area (Fig S1) The reindeer study area included Colesdalen Semmeldalen parts
of Reindalen and their adjacent side valleys covering approximately 285 km2 (Fig S1)
Female reindeer have been individually marked in the study population since 1994 [see 1]
During the period 1995-2011 the study area have been surveyed each year in July-August
Marked females have been registered and the presence of a calf associated with them noted
Svalbard reindeer have reduced calving rates at less than 3 years of age To remove potential
bias due to age structure we only included females of 3 years and older in the analyses The
number of marked female reindeer observed in the surveys varied between 36 and 151
between years Reindeer population size was estimated as the number of animals observed
along a transect line going through Colesdalen and Semmeldalen each year 1994-2011 The
reindeer population size varied between 210 and 510 animals (mean=342 SD=79)
Voles
Reindeer
LongyearbyenBarentsburg
78
80
79
77
10 20 30
Figure S1 The study areas for the Svalbard reindeer and sibling vole monitoring on the Nordenskioumlld Land
peninsula Spitsbergen Svalbard Norway The coastline (black line) and 150 m contour lines (grey line) are
given together with locations of the two main human settlements Longyearbyen and Barentsburg The inserted
map shows the position of Nordenskioumlld Land peninsula (rectangle) on Svalbard
3
The sibling vole population was monitored within an area of less than 1 km2 by the
abandoned mining town Grumant at the coast of Isfjorden 10 km north of the study area for
the Svalbard reindeer (Fig S1) In 1996-2007 five fixed trapping grids with a total of 139
Ugglan traps (24 25 and 3 times 30 traps per grid) were checked 6 hours after the traps were
set and up to 2 times per day over a period from 4-6 consecutive days during the first 10 days
of August giving 7-10 trapping occasions each year In addition trapping was done in one of
the trapping grids (30 traps) in 1995 An estimate of the vole population size in the extensive
trapping grid for 1995 was obtained using prediction from a linear regression model for the
relationship between the vole population size in the single trapping grid and the vole
population size in the extensive trapping grid (estimated vole population size in 1995 = 281
SE=23) The estimated population size for 1995 was only used in the model that included
previous yearrsquos vole population size as predictor Trapped animals were marked on first
capture and the identity checked before release on subsequent capture occasions Vole
population sizes were estimated via sample coverage [2] using program CARE-2 and a closed
capturendashrecapture model that include both between individual and capture occasion
heterogeneity in capture probabilities (model Mht in CARE-2) In 1996 and 2002 not a single
vole was trapped in the trapping grids For these years we report the estimated zero population
size with no confidence limits
Daily precipitation and temperature data were obtained from the meteorological station at the
airport in the nearby settlement Longyearbyen (httpeklimametno Fig S1) From these
data we calculated the amount of precipitation that fell at a temperature above one degree C
between 1 November and 30 April as our measure of the extent of rain-on-snow [for a similar
approach see 3] The average annual rain-on-snow since records beginning at Longyearbyen
airport in 1976 has been 136 mm (SD=175 median=7 mm 75 quantile=184 mm) and in
4
the three 12 year periods from 1976 to 2011 the number of years with more than 15 mm of
rain-on-snow has been 3 (1976-1987) 4 (1988-1999) and 4 (2000-2011) suggesting that
heavy rain-on-snow was relatively common also in the first 12 year period (every 4th year on
average) We note that most of the rain-on-snow has tended to come in the early part of the
winter (on average 68 in November-January) In particularly this has been true in the years
with severe rain-on-snow events (gt15 mm) when on average 86 of the rain-on-snow has
come in November to January The correlation between the annual estimates of rain-on-snow
for November-January and for November-April is therefore high (r=097) This pattern
implies that there is too little information in the data to allow an evaluation of whether the
effect of rain-on-snow on voles and reindeer differ between early and late winter rain-on-
snow events Whether we use November-January or November-April as the measurement
period for rain-on-snow has no significant impact on analyses or conclusions
The dataset is given in Table S1 We report Pearson correlation coefficients for simple
correlations As a measure of the predictive power of the regression models we report R2-
values estimated as the squared correlation between the annual point estimates of the response
variables and predicted values of the selected regression model [4] Initially we used
generalised linear models as implemented in R 2150 [5] to investigate the impact of rain-on-
snow and population size the previous summer on reindeer fecundity and vole population
sizes Calves per female reindeer were modelled assuming a logit link function and binomial
error distribution and the rain-on-snow predictor variable was fitted as log(rain-on-snow+1)
to reduce non-linearities Vole population sizes were modelled assuming a log link function
A Poisson error distribution was chosen as initial analyses showed that the estimates of the
sampling variance in the annual point estimates increased with the value of the point estimate
with a ratio of the variance to the mean close to 1 (average value of variancemean=11)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
1
Electronic supplementary material
Congruent responses to weather variability in high-arctic herbivores
Audun Stien1 Rolf A Ims2 Steve D Albon3 Eva Fuglei4 R Justin Irvine3 Erik
Ropstad5 Odd Halvorsen6 Rolf Langvatn78 Leif Egil Loe910 Vebjoslashrn Veiberg7 Nigel
G Yoccoz2
1 Norwegian Institute for Nature Research Fram Centre NO-9296 Tromsoslash Norway
2 University of Tromsoslash NO-9037 Tromsoslash Norway
3 The James Hutton Institute Aberdeen AB15 8QH UK
4 Norwegian Polar Institute Fram Centre NO-9296 Tromsoslash Norway
5 Norwegian School of Veterinary Science NO-0033 Oslo Norway
6 Natural History Museum University of Oslo NO-0318 Oslo Norway
7 Norwegian Institute for Nature Research NO-7485 Trondheim Norway
8 University Centre in Svalbard NO-9171 Longyearbyen Norway
9 Norwegian University of Life Sciences NO-1432 Aas Norway
10 CEES Institute of Biology University of Oslo NO-0316 Oslo Norway
Author for correspondence (audunstienninano)
1 Materials and methods
The studies were carried out annually in July-August on Nordenskioumlld Land peninsula on
Spitsbergen At one location the vole population size was estimated whereas the total
reindeer population size and the proportion of female reindeer with a calf were estimated in a
2
neighbouring area (Fig S1) The reindeer study area included Colesdalen Semmeldalen parts
of Reindalen and their adjacent side valleys covering approximately 285 km2 (Fig S1)
Female reindeer have been individually marked in the study population since 1994 [see 1]
During the period 1995-2011 the study area have been surveyed each year in July-August
Marked females have been registered and the presence of a calf associated with them noted
Svalbard reindeer have reduced calving rates at less than 3 years of age To remove potential
bias due to age structure we only included females of 3 years and older in the analyses The
number of marked female reindeer observed in the surveys varied between 36 and 151
between years Reindeer population size was estimated as the number of animals observed
along a transect line going through Colesdalen and Semmeldalen each year 1994-2011 The
reindeer population size varied between 210 and 510 animals (mean=342 SD=79)
Voles
Reindeer
LongyearbyenBarentsburg
78
80
79
77
10 20 30
Figure S1 The study areas for the Svalbard reindeer and sibling vole monitoring on the Nordenskioumlld Land
peninsula Spitsbergen Svalbard Norway The coastline (black line) and 150 m contour lines (grey line) are
given together with locations of the two main human settlements Longyearbyen and Barentsburg The inserted
map shows the position of Nordenskioumlld Land peninsula (rectangle) on Svalbard
3
The sibling vole population was monitored within an area of less than 1 km2 by the
abandoned mining town Grumant at the coast of Isfjorden 10 km north of the study area for
the Svalbard reindeer (Fig S1) In 1996-2007 five fixed trapping grids with a total of 139
Ugglan traps (24 25 and 3 times 30 traps per grid) were checked 6 hours after the traps were
set and up to 2 times per day over a period from 4-6 consecutive days during the first 10 days
of August giving 7-10 trapping occasions each year In addition trapping was done in one of
the trapping grids (30 traps) in 1995 An estimate of the vole population size in the extensive
trapping grid for 1995 was obtained using prediction from a linear regression model for the
relationship between the vole population size in the single trapping grid and the vole
population size in the extensive trapping grid (estimated vole population size in 1995 = 281
SE=23) The estimated population size for 1995 was only used in the model that included
previous yearrsquos vole population size as predictor Trapped animals were marked on first
capture and the identity checked before release on subsequent capture occasions Vole
population sizes were estimated via sample coverage [2] using program CARE-2 and a closed
capturendashrecapture model that include both between individual and capture occasion
heterogeneity in capture probabilities (model Mht in CARE-2) In 1996 and 2002 not a single
vole was trapped in the trapping grids For these years we report the estimated zero population
size with no confidence limits
Daily precipitation and temperature data were obtained from the meteorological station at the
airport in the nearby settlement Longyearbyen (httpeklimametno Fig S1) From these
data we calculated the amount of precipitation that fell at a temperature above one degree C
between 1 November and 30 April as our measure of the extent of rain-on-snow [for a similar
approach see 3] The average annual rain-on-snow since records beginning at Longyearbyen
airport in 1976 has been 136 mm (SD=175 median=7 mm 75 quantile=184 mm) and in
4
the three 12 year periods from 1976 to 2011 the number of years with more than 15 mm of
rain-on-snow has been 3 (1976-1987) 4 (1988-1999) and 4 (2000-2011) suggesting that
heavy rain-on-snow was relatively common also in the first 12 year period (every 4th year on
average) We note that most of the rain-on-snow has tended to come in the early part of the
winter (on average 68 in November-January) In particularly this has been true in the years
with severe rain-on-snow events (gt15 mm) when on average 86 of the rain-on-snow has
come in November to January The correlation between the annual estimates of rain-on-snow
for November-January and for November-April is therefore high (r=097) This pattern
implies that there is too little information in the data to allow an evaluation of whether the
effect of rain-on-snow on voles and reindeer differ between early and late winter rain-on-
snow events Whether we use November-January or November-April as the measurement
period for rain-on-snow has no significant impact on analyses or conclusions
The dataset is given in Table S1 We report Pearson correlation coefficients for simple
correlations As a measure of the predictive power of the regression models we report R2-
values estimated as the squared correlation between the annual point estimates of the response
variables and predicted values of the selected regression model [4] Initially we used
generalised linear models as implemented in R 2150 [5] to investigate the impact of rain-on-
snow and population size the previous summer on reindeer fecundity and vole population
sizes Calves per female reindeer were modelled assuming a logit link function and binomial
error distribution and the rain-on-snow predictor variable was fitted as log(rain-on-snow+1)
to reduce non-linearities Vole population sizes were modelled assuming a log link function
A Poisson error distribution was chosen as initial analyses showed that the estimates of the
sampling variance in the annual point estimates increased with the value of the point estimate
with a ratio of the variance to the mean close to 1 (average value of variancemean=11)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
2
neighbouring area (Fig S1) The reindeer study area included Colesdalen Semmeldalen parts
of Reindalen and their adjacent side valleys covering approximately 285 km2 (Fig S1)
Female reindeer have been individually marked in the study population since 1994 [see 1]
During the period 1995-2011 the study area have been surveyed each year in July-August
Marked females have been registered and the presence of a calf associated with them noted
Svalbard reindeer have reduced calving rates at less than 3 years of age To remove potential
bias due to age structure we only included females of 3 years and older in the analyses The
number of marked female reindeer observed in the surveys varied between 36 and 151
between years Reindeer population size was estimated as the number of animals observed
along a transect line going through Colesdalen and Semmeldalen each year 1994-2011 The
reindeer population size varied between 210 and 510 animals (mean=342 SD=79)
Voles
Reindeer
LongyearbyenBarentsburg
78
80
79
77
10 20 30
Figure S1 The study areas for the Svalbard reindeer and sibling vole monitoring on the Nordenskioumlld Land
peninsula Spitsbergen Svalbard Norway The coastline (black line) and 150 m contour lines (grey line) are
given together with locations of the two main human settlements Longyearbyen and Barentsburg The inserted
map shows the position of Nordenskioumlld Land peninsula (rectangle) on Svalbard
3
The sibling vole population was monitored within an area of less than 1 km2 by the
abandoned mining town Grumant at the coast of Isfjorden 10 km north of the study area for
the Svalbard reindeer (Fig S1) In 1996-2007 five fixed trapping grids with a total of 139
Ugglan traps (24 25 and 3 times 30 traps per grid) were checked 6 hours after the traps were
set and up to 2 times per day over a period from 4-6 consecutive days during the first 10 days
of August giving 7-10 trapping occasions each year In addition trapping was done in one of
the trapping grids (30 traps) in 1995 An estimate of the vole population size in the extensive
trapping grid for 1995 was obtained using prediction from a linear regression model for the
relationship between the vole population size in the single trapping grid and the vole
population size in the extensive trapping grid (estimated vole population size in 1995 = 281
SE=23) The estimated population size for 1995 was only used in the model that included
previous yearrsquos vole population size as predictor Trapped animals were marked on first
capture and the identity checked before release on subsequent capture occasions Vole
population sizes were estimated via sample coverage [2] using program CARE-2 and a closed
capturendashrecapture model that include both between individual and capture occasion
heterogeneity in capture probabilities (model Mht in CARE-2) In 1996 and 2002 not a single
vole was trapped in the trapping grids For these years we report the estimated zero population
size with no confidence limits
Daily precipitation and temperature data were obtained from the meteorological station at the
airport in the nearby settlement Longyearbyen (httpeklimametno Fig S1) From these
data we calculated the amount of precipitation that fell at a temperature above one degree C
between 1 November and 30 April as our measure of the extent of rain-on-snow [for a similar
approach see 3] The average annual rain-on-snow since records beginning at Longyearbyen
airport in 1976 has been 136 mm (SD=175 median=7 mm 75 quantile=184 mm) and in
4
the three 12 year periods from 1976 to 2011 the number of years with more than 15 mm of
rain-on-snow has been 3 (1976-1987) 4 (1988-1999) and 4 (2000-2011) suggesting that
heavy rain-on-snow was relatively common also in the first 12 year period (every 4th year on
average) We note that most of the rain-on-snow has tended to come in the early part of the
winter (on average 68 in November-January) In particularly this has been true in the years
with severe rain-on-snow events (gt15 mm) when on average 86 of the rain-on-snow has
come in November to January The correlation between the annual estimates of rain-on-snow
for November-January and for November-April is therefore high (r=097) This pattern
implies that there is too little information in the data to allow an evaluation of whether the
effect of rain-on-snow on voles and reindeer differ between early and late winter rain-on-
snow events Whether we use November-January or November-April as the measurement
period for rain-on-snow has no significant impact on analyses or conclusions
The dataset is given in Table S1 We report Pearson correlation coefficients for simple
correlations As a measure of the predictive power of the regression models we report R2-
values estimated as the squared correlation between the annual point estimates of the response
variables and predicted values of the selected regression model [4] Initially we used
generalised linear models as implemented in R 2150 [5] to investigate the impact of rain-on-
snow and population size the previous summer on reindeer fecundity and vole population
sizes Calves per female reindeer were modelled assuming a logit link function and binomial
error distribution and the rain-on-snow predictor variable was fitted as log(rain-on-snow+1)
to reduce non-linearities Vole population sizes were modelled assuming a log link function
A Poisson error distribution was chosen as initial analyses showed that the estimates of the
sampling variance in the annual point estimates increased with the value of the point estimate
with a ratio of the variance to the mean close to 1 (average value of variancemean=11)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
3
The sibling vole population was monitored within an area of less than 1 km2 by the
abandoned mining town Grumant at the coast of Isfjorden 10 km north of the study area for
the Svalbard reindeer (Fig S1) In 1996-2007 five fixed trapping grids with a total of 139
Ugglan traps (24 25 and 3 times 30 traps per grid) were checked 6 hours after the traps were
set and up to 2 times per day over a period from 4-6 consecutive days during the first 10 days
of August giving 7-10 trapping occasions each year In addition trapping was done in one of
the trapping grids (30 traps) in 1995 An estimate of the vole population size in the extensive
trapping grid for 1995 was obtained using prediction from a linear regression model for the
relationship between the vole population size in the single trapping grid and the vole
population size in the extensive trapping grid (estimated vole population size in 1995 = 281
SE=23) The estimated population size for 1995 was only used in the model that included
previous yearrsquos vole population size as predictor Trapped animals were marked on first
capture and the identity checked before release on subsequent capture occasions Vole
population sizes were estimated via sample coverage [2] using program CARE-2 and a closed
capturendashrecapture model that include both between individual and capture occasion
heterogeneity in capture probabilities (model Mht in CARE-2) In 1996 and 2002 not a single
vole was trapped in the trapping grids For these years we report the estimated zero population
size with no confidence limits
Daily precipitation and temperature data were obtained from the meteorological station at the
airport in the nearby settlement Longyearbyen (httpeklimametno Fig S1) From these
data we calculated the amount of precipitation that fell at a temperature above one degree C
between 1 November and 30 April as our measure of the extent of rain-on-snow [for a similar
approach see 3] The average annual rain-on-snow since records beginning at Longyearbyen
airport in 1976 has been 136 mm (SD=175 median=7 mm 75 quantile=184 mm) and in
4
the three 12 year periods from 1976 to 2011 the number of years with more than 15 mm of
rain-on-snow has been 3 (1976-1987) 4 (1988-1999) and 4 (2000-2011) suggesting that
heavy rain-on-snow was relatively common also in the first 12 year period (every 4th year on
average) We note that most of the rain-on-snow has tended to come in the early part of the
winter (on average 68 in November-January) In particularly this has been true in the years
with severe rain-on-snow events (gt15 mm) when on average 86 of the rain-on-snow has
come in November to January The correlation between the annual estimates of rain-on-snow
for November-January and for November-April is therefore high (r=097) This pattern
implies that there is too little information in the data to allow an evaluation of whether the
effect of rain-on-snow on voles and reindeer differ between early and late winter rain-on-
snow events Whether we use November-January or November-April as the measurement
period for rain-on-snow has no significant impact on analyses or conclusions
The dataset is given in Table S1 We report Pearson correlation coefficients for simple
correlations As a measure of the predictive power of the regression models we report R2-
values estimated as the squared correlation between the annual point estimates of the response
variables and predicted values of the selected regression model [4] Initially we used
generalised linear models as implemented in R 2150 [5] to investigate the impact of rain-on-
snow and population size the previous summer on reindeer fecundity and vole population
sizes Calves per female reindeer were modelled assuming a logit link function and binomial
error distribution and the rain-on-snow predictor variable was fitted as log(rain-on-snow+1)
to reduce non-linearities Vole population sizes were modelled assuming a log link function
A Poisson error distribution was chosen as initial analyses showed that the estimates of the
sampling variance in the annual point estimates increased with the value of the point estimate
with a ratio of the variance to the mean close to 1 (average value of variancemean=11)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
4
the three 12 year periods from 1976 to 2011 the number of years with more than 15 mm of
rain-on-snow has been 3 (1976-1987) 4 (1988-1999) and 4 (2000-2011) suggesting that
heavy rain-on-snow was relatively common also in the first 12 year period (every 4th year on
average) We note that most of the rain-on-snow has tended to come in the early part of the
winter (on average 68 in November-January) In particularly this has been true in the years
with severe rain-on-snow events (gt15 mm) when on average 86 of the rain-on-snow has
come in November to January The correlation between the annual estimates of rain-on-snow
for November-January and for November-April is therefore high (r=097) This pattern
implies that there is too little information in the data to allow an evaluation of whether the
effect of rain-on-snow on voles and reindeer differ between early and late winter rain-on-
snow events Whether we use November-January or November-April as the measurement
period for rain-on-snow has no significant impact on analyses or conclusions
The dataset is given in Table S1 We report Pearson correlation coefficients for simple
correlations As a measure of the predictive power of the regression models we report R2-
values estimated as the squared correlation between the annual point estimates of the response
variables and predicted values of the selected regression model [4] Initially we used
generalised linear models as implemented in R 2150 [5] to investigate the impact of rain-on-
snow and population size the previous summer on reindeer fecundity and vole population
sizes Calves per female reindeer were modelled assuming a logit link function and binomial
error distribution and the rain-on-snow predictor variable was fitted as log(rain-on-snow+1)
to reduce non-linearities Vole population sizes were modelled assuming a log link function
A Poisson error distribution was chosen as initial analyses showed that the estimates of the
sampling variance in the annual point estimates increased with the value of the point estimate
with a ratio of the variance to the mean close to 1 (average value of variancemean=11)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
5
Previous years population size was fitted as log(vole population sizet-1 +1) In both analyses
we detected substantial overdispersion in residuals when compared to what expected given
the selected distributional assumptions We approached this problem using two methods
First we fitted the models using quasi ndash likelihood methods where the variance was assumed
to be proportional to micro(1-micro) for the analyses of calves per female and proportional to micro for
the analysis of vole population densities where micro is the expected value of the response
variable given the model [6] The results from these analyses are reported in the result section
of the article As an alternative we modelled the overdispersion by fitting year as a random
effect in generalised linear mixed models (GLMMs) using the lmer function in the lme4
package for R The results from the mixed models are qualitatively the same as those of the
quasi-likelihood models (Table S2) In addition to parameter estimates we report QAICc for
the quasi-likelihood models and AICc for the GLMMs [7 8]
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
6
Table S1 The dataset analysed in the article Ncalves and Nfemales gives the observed number of marked adult females with a calf and the
total number of adult females seen in a given year respectively Nreindeert_1 gives the observed number of reindeer seen during the survey of
Semmeldalen-Colesdalen the previous year Nvoles gives the estimated population size of voles and NvolesLCI and NvolesUCI gives the
lower and upper confidence intervals for Nvoles ROSNov-Jan and ROSNov-Apr gives the mm rain-on-snow in the period November to
January and November to April respectively
year Ncalves Nfemales Nreindeert_1 Nvoles NvolesLCI NvolesUCI ROSNov-Jan ROSNov-Apr 1995 25 38 238 - - - 01 02 1996 6 36 280 0 - - 435 662 1997 67 93 273 2715 24522 31274 41 41 1998 99 122 300 2858 25849 32914 0 0 1999 118 151 276 2549 23445 28809 22 31 2000 49 123 346 1195 10147 15712 66 66 2001 91 112 349 2439 22127 28116 62 8 2002 17 75 446 0 - - 137 186 2003 72 93 212 2149 19905 24156 52 54 2004 42 63 365 1606 14631 1874 02 107 2005 71 101 271 2031 17945 24336 23 43 2006 35 101 415 57 4292 9624 247 265 2007 43 90 389 1935 17329 22807 1 41 2008 7 82 506 - - - 165 165 2009 44 81 354 - - - 29 4 2010 15 50 383 - - - 64 64 2011 27 41 411 - - - 0 31
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
7
Table S2 Parameter estimates and AICc values for GLMMs of the impact of rain-on-snow (ROS) and previous years population size (DD) on
calves per female reindeer and vole population sizes In the models year was fitted as a random effect AICc values for the best fit models in
bold In the models for calves per female ROS was fitted as log(ROS+1) and in the models for vole population sizes DD was fitted as
log(previous years population size+1)
parameter estimates (se) random effect sd
response model intercept ROS (mm) DD year AICc
calves per female intercept 015 (027) 107 716
ROS 163 (040) -071 (017) 073 625
DD 342 (091) -0010 (0003) 077 649
ROS+DD 340 (072) -051 (016) -0006 (0002) 058 598
vole population intercept 427 (064) 218 904
ROS 590 (042) -013 (004) 098 777
DD 576 (142) -0339 (0298) 206 929
ROS+DD 616 (069) -013 (004) -0069 (0145) 096 821
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
8
References
1 Albon SD Stien A Irvine RJ Langvatn R Ropstad E Halvorsen O 2002 The role of parasites in the dynamics of a reindeer population Proc Roy Soc Lond B 269 1625-1632 (doi101098rspb20022064)
2 Lee SM Chao A 1994 Estimating population size via sample coverage for closed capture-recapture models Biometrics 50 88-97 (doi1023072533199)
3 Hansen BB Aanes R Herfindal I Kohler J Saether BE 2011 Climate icing and wild arctic reindeer past relationships and future prospects Ecology 92 1917-1923
4 Zheng BY Agresti A 2000 Summarizing the predictive power of a generalized linear model Statistics in Medicine 19 1771-1781 (doi1010021097-0258(20000715)1913lt1771aid-sim485gt33co2-g)
5 The R development Core Team 2010 R A Language and Environment for Statistical Computing (Vienna Austria R Foundation for Statistical Computing
6 McCullagh P Nelder JA 1989 Generilized linear models Second ed London Chapman amp Hall 511 p
7 Burnham KP Anderson DR 2002 Model selection and multimodel inference a practical information-theoretic approach New York Springer-Verlag
8 Bolker BM Brooks ME Clark CJ Geange SW Poulsen JR Stevens MHH White JSS 2009 Generalized linear mixed models a practical guide for ecology and evolution TREE 24 127-135 (doi101016jtree200810008)
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