Understanding scales of movement: animals ride waves and ripples of environmental change

Authors

  • Bram van Moorter,

    Corresponding author
    1. Terrestrial Department, Norwegian Institute for Nature Research (NINA), Trondheim, Norway
    • Centre for Conservation Biology, Department of Biology, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
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  • Nils Bunnefeld,

    1. Department of Wildlife, Fish and Environmental Studies, Swedish University of Agricultural Sciences, Umea, Sweden
    2. Biological and Environmental Sciences, School of Natural Sciences, University of Stirling, Stirling, UK
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  • Manuela Panzacchi,

    1. Terrestrial Department, Norwegian Institute for Nature Research (NINA), Trondheim, Norway
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  • Christer M. Rolandsen,

    1. Centre for Conservation Biology, Department of Biology, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
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  • Erling J. Solberg,

    1. Terrestrial Department, Norwegian Institute for Nature Research (NINA), Trondheim, Norway
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  • Bernt-Erik Sæther

    1. Centre for Conservation Biology, Department of Biology, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
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Correspondence author. E-mail: Bram.Van.Moorter@gmail.com

Summary

  1. Animal movements are the primary behavioural adaptation to spatiotemporal heterogeneity in resource availability. Depending on their spatiotemporal scale, movements have been categorized into distinct functional groups (e.g. foraging movements, dispersal, migration), and have been studied using different methodologies. We suggest striving towards the development of a coherent framework based on the ultimate function of all movement types, which is to increase individual fitness through an optimal exploitation of resources varying in space and time.
  2. We developed a novel approach to simultaneously study movements at different spatiotemporal scales based on the following proposed theory: the length and frequency of animal movements are determined by the interaction between temporal autocorrelation in resource availability and spatial autocorrelation in changes in resource availability. We hypothesized that for each time interval the spatiotemporal scales of moose Alces alces movements correspond to the spatiotemporal scales of variation in the gains derived from resource exploitation when taking into account the costs of movements (represented by their proxies, forage availability NDVI and snow depth respectively). The scales of change in NDVI and snow were quantified using wave theory, and were related to the scale of moose movement using linear mixed models.
  3. In support of the proposed theory we found that frequent, smaller scale movements were triggered by fast, small-scale ripples of changes, whereas infrequent, larger scale movements matched slow, large-scale waves of change in resource availability. Similarly, moose inhabiting ranges characterized by larger scale waves of change in the onset of spring migrated longer distances.
  4. We showed that the scales of movements are driven by the scales of changes in the net profitability of trophic resources. Our approach can be extended to include drivers of movements other than trophic resources (e.g. population density, density of related individuals, predation risk) and may facilitate the assessment of the impact of environmental changes on community dynamics and conservation.

Introduction

Movements are the main means allowing animals to alter the environmental settings which they are exposed to. Whereas in spatially heterogeneous and temporally stable environments movements would be selected against (Hastings 1983), in natural ecosystems spatial and temporal changes in food availability (Charnov, Orians & Hyatt 1976; Boone, Thirgood & Hopcraft 2006), predation risk (Mitchell & Lima 2002) or intraspecific relationships (Hamilton & May 1977) drive the evolution of movement. Therefore, movements are the primary behavioural adaptation to dynamic resource landscapes (McPeek & Holt 1992; Mueller & Fagan 2008), and play a central role in evolutionary biology (Ravigné, Dieckmann & Olivieri 2009), ecology (Nathan et al. 2008) and conservation (Bolger et al. 2008). However, movements are a relatively poorly understood individual and population process, and the development of a general theory of movement is still in its infancy (Mueller & Fagan 2008; Nathan et al. 2008).

Movements can be described by their spatial and temporal scales, which refer to the distance moved over a given time interval (Schneider 2001). Spatial and temporal scales are often positively correlated, as animals move short distances in a short time and longer distances over longer periods. However, returns to previously visited areas can lead to shorter displacements over a longer time interval (Van Moorter et al. 2009). The scales of movements vary among species, within species, but also within individuals through time. However, the relationship between movements at different spatiotemporal scales has received surprisingly little attention in ecological studies (Morales & Ellner 2002). Movements are typically categorized into distinct functional groups ranging from frequent, small-scale foraging movements to infrequent, large-scale migrations or dispersal (Fryxell et al. 2008; Nathan et al. 2008) and several studies investigated the different proximate physiological, behavioural and cognitive mechanisms triggering each movement type (Dingle 1996; Russel, Bauer & Johnson 2005; Dingle & Drake 2007). To promote the further development of the theoretical basis of movement ecology, we suggest focusing on the underlying mechanisms common to all movement types irrespective of their spatiotemporal scale.

Following evolutionary theory, the ultimate function of all types of movements is to increase individual fitness through an optimal exploitation of resources, which vary in space and time (Owen-Smith, Fryxell & Merrill 2010). Based on this theory, recent studies investigated the relationship between movements and spatiotemporal heterogeneity within a given spatiotemporal frame: for example, Mueller et al. (2011) focused on annual movements and documented long migrations for species inhabiting areas with large-scale spatial heterogeneity in primary productivity and shorter movements for species inhabiting ranges with little spatial heterogeneity. We further built upon this theory and developed a novel approach for the simultaneous study of movements performed by individuals, populations or species at different spatiotemporal scales. We propose the following theory: the length and frequency of animal movements is determined by the interaction between temporal autocorrelation in resource availability and spatial autocorrelation in changes in resource availability (Fig. 1). In particular, focusing on the former (i.e. time; rows in Fig. 1), we hypothesize that for a given spatial scale the frequency of movements increases with the frequency of changes in resource availability (Hypothesis 1). Focusing on the latter (i.e. space; columns in Fig. 1), we hypothesized that for any given time interval the distance moved increases with the spatial scale of changes in resource availability (Hypothesis 2). In a realistic scenario, however, the costs associated with movements can prevent individuals from closely tracking changes in resource availability, and hence the distance moved is expected to result from trade-offs between benefits and costs of movements. Note that when the costs of tracking resources are too high (e.g. frequent long movements, Fig. 1) animals have to adopt alternative, non-movement-based tactics such as hibernation (Pearse 1922).

Figure 1.

According to the proposed theory, the length and frequency of animal movements are determined by the interaction between temporal autocorrelation in resource availability (i.e. how fast do resources change; rows) and spatial autocorrelation in changes in resource availability (i.e. how such changes are distributed in space; columns). When changes in resource availability are slow, animals are expected to move infrequently; on the contrary, fast changing resources are expected to trigger frequent animal movements (Hypothesis 1). If spatial autocorrelation in changes in resource availability is low, fine-scale changes in resource availability occur, and animals are expected to move shorter distances; on the contrary, high spatial autocorrelation implies large-scale changes in resource availability and longer distances moved (Hypothesis 2). In addition, in realistic situations the costs of movements can prevent animals from closely tracking changes in resource availability by decreasing the frequency and/or length of movements; hence, frequent, long movement is not likely to occur. We tested both hypotheses under the cost case scenario (see Predictions for details).

Moose (Alces alces) in Norway is a well-suited study species for testing our hypothesis, as within the same population GPS-monitored individuals range from sedentary to long-distance migrants (Bunnefeld et al. 2011) moving between 10 and 150 km to spend summers at higher altitudes (Rolandsen et al. 2010). Furthermore, GPS locations are available at both small (2 h) and large (2–3 years) temporal scales. Moose feed mainly on browse, but also on crops and grasses (Mysterud 2000). Therefore, the net primary productivity – measured by the Normalized Difference Vegetation Index (NDVI; Pettorelli et al. 2011) – is a good proxy of forage availability and was selected to measure variation in benefits to be gained through movements in the snow-free period of the year (Pettorelli et al. 2011). Bjørneraas (2011) showed moose movements track the spring green-up measured with NDVI. During winter moose move to areas with less snow (Ball, Nordengren & Wallin 2001), as deep snow can both limit access to food and hamper movements (Sweeney & Sweeney 1984). Therefore, low snow depth was also chosen to quantify variation in the benefits to be gained by moving to a target location, whereas high snow depth was chosen as a proxy to measure friction hindering movements towards the target location. Hence, we expected that the distance moved by moose resulted from a trade-off between snow depth and the scale of change in NDVI.

Environmental heterogeneity can be detected at different spatial and temporal scales (Levin 1992). In analogy with the frequencies of visible light (Halley 1996), environmental changes occurring over large spatial scales have been termed red, whereas changes affecting only small areas, blue. In real ecosystems landscape heterogeneity often results from a mixture of both large- and small-scale spatial changes, resulting in pink landscapes (sensu Halley 1996; Storch, Gaston & Cepák 2002). In general, a positive association between spatial and temporal scales of change in the environment can be detected (Holling 1992; Southworth et al. 2006), i.e. red changes are slower than blue. However, the relationship between spatial and temporal scale is not constant throughout the year or through space. For instance, during spring landscape-scale wide waves of vegetation greening in temperate regions (Beck et al. 2006, 2007) result in faster red changes than during summer. Also, geographic differences may exist in synchrony of events; for example, the start of the spring greening after the snow melt (i.e. the onset of spring; Beck et al. 2007) may vary within one region due to marked topographical gradients, but it may be highly synchronous in another region lacking such gradients. Thus, in real landscapes both temporal and spatial differences exist in the scales of environmental changes.

Based on this theoretical background, we expected the spatial scales of changes in NDVI and in snow depth to vary both throughout the year and through space, and we expected moose to track such changes both temporally and spatially, when taking into account the cost of movements. When changes in resource availability occur at a fine-scale, we predict the frequency of animal movements to increase with increasing frequency of changes in resource availability. More explicitly, we predict more frequent daily movements of moose with increasing fine-scale forage depletion and regrowth patterns (Prediction 1; left column, Fig. 1). For changes in resource availability over larger time intervals, we predict the distance moved by animals to increase with increasing spatial scale of change in resource availability. More explicitly, we predict longer 16-day moose displacements following larger scale environmental changes such as vegetation greening, browning and snow fall (Prediction 2; bottom row, Fig. 1). Similarly, we predict that animals inhabiting regions experiencing larger waves of change in the onset of spring migrate longer distances (i.e. longer 6-month displacement) compared with animals living in more synchronized environments (Prediction 3; see Mueller et al. 2011).

Material and methods

Study site

We conducted our study in Nord-Trøndelag, northern parts of Sør-Trøndelag and southern parts of Nordland counties (c. 23 100 km2), in central Norway (64°32′ N, 12°15 E). The biomes include mountains, boreal forest and cultivated land (Moen 1999). The forested part is dominated by Norway spruce Picea abies L., downy birch Betula pubescens L. and Scots pine Pinus sylvestris L. (Moen 1999). Cultivated land occurs particularly in the lower part of the study area, mostly on the west coast and along the fjords (Moen 1999). The study area covers large climatic gradient with substantial variation in both onset of spring (ranging from early-April to June; Beck et al. 2007) and yearly maximum snow depth (ranging from < 25 to > 400 cm; http://senorge.no, accessed October 2011).

Movement data

In 2006, 2007 and 2008, 169 moose (119 females and 50 males, ≥ 8 months old) were captured during February, March and November, and fitted with GPS-collars (Bjørneraas et al. 2010). Locations were obtained for each animal every second hour, but due to satellite acquisition failure and to the deletion of erroneous locations (Bjørneraas et al. 2010), 1% of the locations were missing. Reproductive rates were high, as more than 90% of adult females gave birth. Nine per cent of locations fell in Sweden, and were not considered in analyses involving snow as snow depth maps were only available for Norway. Only individuals with at least 6 months of data were retained for analysis (75 females, 25 males).

Quantifying scales of movement

We examined whether the frequency or length of movements was related to the corresponding temporal or spatial scale of change in environmental variables representing benefits and costs of movement (Hypotheses 1 and 2). We quantified the frequency and spatial scale of change in environmental variables, and we linked them to the frequency and length of moose displacements using mixed models. We also regressed individual displacements after 6 months against the spatial scale of regional waves in the onset of spring. To assess the frequency or length of movements, for each individual we calculated the Net Displacements, ND (i.e. the straight line distance between two locations separated by a given time interval), travelled in 1 day, 16 days and 6 months. The 16-day interval corresponds to the temporal resolution of our environmental data (see below); note that we assessed sensitivity of the main results to this time interval by testing also a 32-day interval, but our conclusions remained unaltered. Then, within a 16-day moving window we determined for each individual the average ND at 1 and 16 days: ND(Δt = 1 day) and ND(Δt = 16 days). Note that the average ND(Δt = 1 day) calculated within a 16-day moving window effectively measures the daily frequency of movements during that period. Females and males were tracked for on average 24- (SD = 8) and 25- (SD = 10) 16-day periods respectively. The 6-month displacement is the maximum distance between locations from winter to summer and from summer to winter, i.e. for both 6-month periods we determined the maximum distance among locations during this period, MD(Δt = 6 months).

Quantifying scales of environmental change

As it is implausible that a moose would experience the environmental conditions in the whole study area, we assumed that individuals respond to environmental conditions within their ranges. Hence, environmental variables were measured within the square area centred on the barycentre of the locations during 16 days. The area of this quadrat (144 km2) equalled the size of the average circular 16-day range (including 95% of locations); note that we obtained similar results using a 33% larger area. The NDVI (Fig. 2a) was obtained from MODIS satellites at 16-day intervals with a spatial resolution of about 230 m (NASA Earth Data – Land Processes Distributed Active Archive Center. Retrieved September 10, 2010, from https://lpdaac.usgs.gov/); due to cloud coverage only NDVI images as 16-day composites were regularly available. Snow depth was estimated with a spatial resolution of 1 km2 based on measurements from meteorological stations and interpolation based on a precipitation/degree-day type snow model (Tveito et al. 2002; Engeset et al. 2004). We selected one map every 16 days to match the temporal resolution of the NDVI.

Figure 2.

Flowchart of the analyses, in which we explain the distance moved by moose at smaller (1 day, f) and larger (16 days, g) temporal scales with proxies of the spatial scale of changes in forage (NDVI, left) and travel cost (snow depth, right) during the same time span (i.e. 1 day: meanNDVI and mean Snow; 16 days: slopeNDVI and slopeSnow). To obtain these proxies, first we identified the 16-day range for each individual as the square centred on the barycentre of each moose locations during each 16-day intervals (a). For each range, we calculated the mean (math formula and math formula) and the difference (ΔNDVI and Δsnow) between two consecutive NDVI and snow depth images at time t and t + 16 days (b). After, ΔNDVI and Δsnow were Fourier transformed into a power spectrum (c). Fourth, we calculated meanNDVI and meanSnow by averaging all pixels composing math formula and math formula, whereas we regressed the wavelength against the power spectrum (i.e. power = α + β × wavelength + ε), and to obtain the slope, β (d). To avoid multi co-linearity, we performed a regression between meanNDVI and meanSnow (meanNDVI = α + β × meanSnow + ε), and we extracted the residuals (e). Finally, we performed a linear mixed model to explain the distance moved by moose after 1 day (f) and 16 days (g) by the residuals of the two NDVI measures and by the two snow measures when accounting for individual differences in movements and temporal autocorrelation.

The first step to quantify changes in NDVI (ΔNDVI) and in snow depth (Δsnow) at 16-day intervals (Fig. 2b) was to calculate differences in the pixel score of two consecutive NDVI or snow images. Next, we quantified the spatial scale of change in NDVI and in snow depth by applying Fourier transforms (Fig. 2c). Fourier transforms are traditionally used to quantify the scale of variation in a 1-dimensional data series (e.g. time series or transect) by decomposing it as a sum of regular waves (sine and cosine) characterized by wavelength (i.e. the scale of variation) and amplitude (i.e. its magnitude, the relative importance of different scales; Wittemyer et al. 2008). Following Prum & Torres (2003), we used a 2-D extension of this method to quantify the spatial scale of change in NDVI and in snow depth by applying Fourier transforms to the ΔNDVI and Δsnow maps (Fig. 2c). Thus, the spatial scales of those 2-dimensional images are quantified by the power spectrum of each wavelength. Then, to quantify the relative importance of smaller and larger scale spatial variation we regressed the wavelength against the power spectrum, and we extracted the slope (Storch, Gaston & Cepák 2002). The resulting variables, slopeNDVI and slopeSnow (Fig. 2d) were used as proxies of large- vs. small-scale changes in the net environmental profitability during 16 days. A slope = 0 indicates that red and blue changes (i.e. larger and smaller scale changes, respectively) are equally important; a slope > 0 indicates a prevalence of red changes, and a slope < 0, which is unrealistic, would indicate a prevalence of blue changes. Note that the changes we found in the relative importance of different spatial scales were also supported by variograms (Fig. S1, Supporting Information).

While we could directly quantify environmental changes occurring at 16-day intervals, we could not estimate directly 1-day changes in the cost benefits of the environment, as these data were not available at sufficiently fine spatiotemporal resolution. However, as during such small temporal scales no large-scale changes in the environment are expected (Holling 1992; Southworth et al. 2006), we needed proxies of frequency of 1-day change only at fine spatial scales. The dynamics of the perceived cost benefit of the environment at such small temporal scale are driven by local processes, such as depletion and renewal (Schreiner et al. 1996; Adler, Raff & Lauenroth 2001; Weisberg & Bugmann 2003). The Marginal Value Theorem (Charnov 1976; Stephens & Krebs 1986) states that the giving-up time is lower in highly productive environments (e.g. goats: De Knegt et al. 2007) and when the travel cost is small (e.g. moose: Astrom, Lundberg & Danell 1990; cattle: Utsumi et al. 2009). As both giving-up time and renewal are positively correlated with productivity and negatively correlated with snow depth, these two variables will, respectively, increase or decrease the frequency of change in the cost benefit from the environment for an animal. Hence, we used the average value of all pixels from two consecutive NDVI images (meanNDVI) and from two consecutive snow maps (meanSnow) as proxies of changes in resource profitability at fine spatial scale, at 1 day (Fig. 2b–c).

Relating temporal variation in scales of movement to environmental change

The relationships between productivity, snow depth and movements were assessed using linear mixed models. As moose are partially migratory in our study area, and environmental factors triggering spring and fall movements could be different, we allowed the relationships between movements and NDVI/snow depth to be dependent on period of the year. Therefore, we split our time-series analysis between the first half of the year (hereafter called greening period) starting in March after the peak in snow depth, and the second half (i.e. browning period) starting in August after the peak in vegetation greenness. The analyses were conducted separately for both sexes.

The Net Displacement ND of moose after 1 day (Equation in Fig. 2f) and after 16 days (Fig. 2g) was modelled as a function of meanNDVI and meanSnow, and of slopeNDVI and slopeSnow. We would consider Prediction 1 to be supported if meanNDVI and meanSnow have a larger effect on ND(Δt = 1 day) than slopeNDVI and slopeSnow. Prediction 2 would be supported if slopeNDVI and slopeSnow have a larger effect on ND(Δt = 16 days), than meanNDVI and meanSnow.

When in a model meanNDVI and meanSnow occurred together, we took the residuals from a linear regression between NDVI and snow depth to avoid problems with co-linearity (meanNDVI and meanSnow have an r2 = 0.41). Other correlations did not seem problematic (r2 < 0.15). A linear mixed model with random intercept was used to account for individual differences in ND's travelled. We accounted for temporal autocorrelation in the residuals using an autoregressive moving average correlation structure for the residuals in all analyses – we estimated the order for the autoregressive and for the moving average part using AIC (i.e. ARMA[p, q]; Pinheiro & Bates 2000). To facilitate the comparison of the beta-coefficients all variables were standardized by sex (z-transform) prior to inclusion in the regression analysis. We investigated all combinations of the environmental variables (i.e. meanNDVI, slopeNDVI, meanSnow, slopeSnow) and parameters from the ARMA[p, q]. Models were selected using Akaike's Information Criterion (AIC; Burnham & Anderson 2002). We used the Singer (1998) approach to quantify the contribution of the fixed and random effects on the variance explained (i.e. assessing the increase in the residual variance after omitting the fixed effects from the best model).

Relating individual difference in movements to spatial differences in environmental change

To better understand individual variation in our previous analyses, we calculated the correlation coefficients between individual differences in distance moved at 1 and 16 days during the greening and browning period. Individual differences were represented by the Best Linear Unbiased Predictor for each individual from the random effects used in the above described mixed models (Fig. 2f–g). We then tested Prediction 3, i.e. that individual differences in movement tactics – from resident to long-distant migrants – are explained by regional differences in the spatial scale of the variation in onset of spring. The continuum in movement distances was quantified by measuring the maximum displacement (MD) after 6 months, matching the greening-browning period separation from the previous analyses. The individual range, which was used for the assessment of the spatial scale of variation in the onset of spring, was defined as the square area centred on the barycentre of the locations during 6 months [20 × 20 km; 20 km corresponds to the mean MD(Δt = 6 months)]. The onset of spring was derived from NDVI data with ground-truthing (Beck et al. 2006, 2007), with a spatial resolution of 1 km2, and the spatial scale of variation in onset of spring (slopeOoS) was quantified using wave theory as previously described. We could not repeat the same analyses for snow depth, as the sample size was too small. We used ordinary linear regression of the log-transformed distances to test the effect of slopeOoS on individual displacement.

All analyses were performed in R (R Development Core Team 2009), with library ‘nlme’ (Pinheiro & Bates 2000) for the mixed models and ‘adehabitat’ (Calenge 2006) and ‘sp’ (Bivand, Pebesma & Gómez-Rubio 2008) for the manipulation of maps and animal movement paths. The 2D Fast Fourier Transform and the radial average of the power spectrum calculations were performed in Matlab, using an adaptation of the function written by E. Ruzanski (http://www.mathworks.com/matlabcentral/fileexchange/23636, accessed May 2009).

Results

Yearly changes in NDVI and snow depth at two temporal scales

We found a non-linear relationship for both NDVI (Fig. 3a) and snow depth (Fig. 3b) between the spatial scale of their 16-day change (i.e. the slope of their power spectrums; slopeNDVI and slopeSnow) and their daily change (i.e. their mean value; meanNDVI and meanSnow). SlopeNDVI and slopeSnow responded similarly throughout the year: low values in the winter months, high in spring, low in summer and high in fall. MeanNDVI and meanSnow responded similarly through the year: meanNDVI increased from winter to summer and decreased from summer to winter, whereas meanSnow changed in the opposite way.

Figure 3.

Annual changes in the scales of environmental variability and moose displacements. Panel (a) and (b) depict changes in NDVI, on the left, and in snow depth, on the right. The mean values are on the x-axis, whereas the slope of the power spectrum of the difference is on the y-axis (see main text for further details). Panel (c) and (d) show, for females and males, respectively, the Net Displacement over 1-day intervals on the x-axis and over 16-day intervals on the y-axis (note the scale difference in the movements between both sexes). Grey bars indicate the standard errors associated with individual variations (for clarity not all months are labelled in the figure).

Yearly changes in Net Displacement travelled at two temporal scales

The Net Displacement travelled by female (Fig. 3c) and male moose (Fig. 3d) during 16 days and 1 day showed a non-linear relationship. In winter, moose travelled only short distances on either temporal scale. During early spring both sexes increased their movements at both 16-day and 1-day intervals; males travelled longer ND(Δt = 16 days) than females. During late spring and early summer, moose decreased their ND(Δt = 16 days), and increased it again in fall. During this period males moved longer distances at both temporal scales than females. As winter approached, ND decreased at both temporal scales, eventually reaching similar values for both sexes.

Relationship between Net Displacement and temporal dynamics of NDVI and snow depth

In all selected models individual effects were significant (see Tables S1 and S2 in Supporting Information for the contribution of the fixed and random effects to the explained variance).

During greening (March to July) the most parsimonious models (Table S1, Supporting Information) showed that ND(Δt = 1 day) were more affected by mean values in environmental parameters (meanNDVI or meanSnow), than by their spatial scale of change in 16 days (slopeNDVI or slopeSnow), hence supporting Prediction 1. ND(Δt = 1 day) increased for both sexes with meanNDVI (females: β ± SE: 0.54 ± 0.04, DF = 743; males: 0.70 ± 0.06, DF = 211). We also detected a positive relationship between ND(Δt = 1 day) and slopeNDVI for females, but the β-coefficient was nearly 80% smaller (females: β ± SE: 0.11 ± 0.03; males: not significant) compared with those of meanNDVI. Snow depth had no statistically significant effect on ND(Δt = 1 day) in spring.

For explaining the ND(Δt = 16 days) of females the spatial scale of change in the environmental variables became relatively more important than their mean: ND(Δt = 16 days) was positively affected by slopeNDVI (β ± SE: 0.10 ± 0.03, DF = 745). However, we did not detect a statistically significant effect of slopeNDVI on males. Hence, Prediction 2 was only supported for females. Male ND(Δt = 16 days) were only affected by the meanNDVI (β ± SE 0.30 ± 0.07), even though its effect was more than 50% smaller than for ND(Δt = 1 day). Snow depth did not significantly affect ND(Δt = 16 days) in either sex.

During browning (August to February) ND(Δt = 1 day) were negatively affected by meanSnow (females: β ± SE: −0.33 ± 0.03, DF = 1008; males: β ± SE: −0.54 ± 0.08, DF = 231), with a more than 50% lower effect from slopeSnow on these movements in females (β ± SE: 0.16 ± 0.04) and no statistically significant effect on males. In addition to snow depth, ND(Δt = 1 day) of both sexes during the browning period was also positively affected by meanNDVI (females: β ± SE: 0.19 ± 0.03; males: β ± SE: 0.24 ± 0.06) but not by slopeNDVI; thus supporting Prediction 1.

ND(Δt = 16 days) of females were only affected by slopeSnow (females: β ± SE: 0.21 ± 0.04, DF = 1010). For males the best model (i.e. with lowest AIC) was an only-intercept model (see Table S1 in Supporting Information). Hence, Prediction 2 was again supported only for females.

Relating individual differences in displacement to spatial differences in environmental change

All individual effects from the previous linear mixed models were highly correlated among each other (min(r) > 0.60; Table S3 in Supporting Information). Moreover, these individual effects were highly correlated with MD(Δt = 6 months) (min(r) ≥ 0.50; Table S3, Supporting Information). We found a positive relationship between slopeOoS and the MD(Δt = 6 months) for both sexes and seasons (r2 during spring = 0.29 and 0.24, for resp. females and males; r2 during fall = 0.20 and 0.23, for resp. females and males), i.e. both sexes moved longer distances with increasing slopeOoS (Fig. 4; females during greening: β ± SE: 3.2 ± 0.7, DF = 56, < 0.001; males during greening: β ± SE: 1.9 ± 0.8, DF = 16, < 0.05; females during browning: β ± SE: 2.3 ± 0.6, DF = 60, < 0.001 and males during browning: β ± SE: 3.2 ± 1.4, DF = 16, < 0.05). Hence, Prediction 3 was supported for both sexes. Note that the ND(Δt = 6 months) were highly correlated between the greening and browning period for both females (= 0.96) and males (= 0.92); thus, animals moving the longest distances in the greening period also moved the longest distances in the browning period.

Figure 4.

Maximum individual distance moved during 6 months [MD(Δt = 6 months)] in relation to local differences in the spatial scale of variation in the onset of spring (slopeOoS), on log-scale. Panel (a) refers to the spring season, panel (b) to the fall. Females are represented by open circles and males by filled triangles. The dotted line shows the regression slope for females, the continuous line for males.

Discussion

We propose an integrative approach for explaining the continuum ranging from smaller to larger scales of movements based on their common underlying function, i.e. to exploit resources varying in space and time. Previous studies have demonstrated a relationship between ungulate migration and variation in net primary productivity (Albon & Langvatn 1992; Mysterud et al. 2001a; Boone, Thirgood & Hopcraft 2006; Hebblewhite, Merrill & McDermid 2008) or snow depth (Ball, Nordengren & Wallin 2001; Sabine et al. 2002; Luccarini et al. 2006). The novel approach we developed – based on wave theory – allowed us to explain variation in spatiotemporal scales of moose movements throughout the year based on corresponding variation in the scales of environmental change. For a given time interval, the frequency and length of moose movements tracked the spatiotemporal scale of changes in the main factors associated with the benefits and costs of movements, i.e. forage availability and snow depth. Overall, large-scale waves of change in NDVI and snow depth triggered larger scale movements such as longer distances covered during 16 days or migrations (Prediction 2), whereas small-scale ripples of environmental changes led to frequent foraging movements on a daily basis (Prediction 1). However, marked individual differences in movement patterns were detected. Whereas some moose performed long-distance migrations during spring and fall (up to 120 km), others migrated only short distances, or were highly sedentary (c. 1 km/season; Fig. 4). Our results show that individual differences in scales of movements are largely explained by spatial differences in the scale of environmental changes (Prediction 3). Hence, short-distance movements were typically performed by individuals inhabiting regions characterized by little spatial variation in yearly phenology, whereas long-distance movements were performed by individuals experiencing marked spatial variation in annual phenology. Mueller et al. (2011) found similar results by comparing migration behaviour in contrasting landscapes for different species.

We thus found support for the proposed theory on the relationship between the spatiotemporal scale of animal movement and the spatiotemporal scale of environmental change. Our results support Hypothesis 1 by showing that whereas in fast changing environment (i.e. low temporal autocorrelation, Fig. 1) animal movement frequency increases, in slow changing environments (i.e. high temporal autocorrelation) it decreases. Hypothesis 2 is also supported, as when environmental changes are highly synchronized in space (i.e. high spatial autocorrelation), animals have to move longer distances to track those waves of environmental changes. In contrast, short-distance movements suffice to allow animals to benefit from ripples of environmental changes, in habitat with low spatial autocorrelation.

At small spatial scales, the Marginal Value Theorem predicts that an optimally foraging animal exploiting heterogeneous resources should leave high-resource areas faster, when the time to travel between such areas decreases and/or the environment increases in productivity (Charnov 1976; Stephens & Krebs 1986). In agreement with this prediction, an increase in primary productivity led to more frequent movements, whereas snow depth had a strong negative effect on movement frequency. In summer, however, the longer daily movements did not lead to longer displacement after 16 days, probably due to high forage regrowth rates which led to an increased return rates to previously visited areas (Van Moorter et al. 2009; Van Beest et al. 2010). Thus, in highly productive environments the fast (i.e. low temporal autocorrelation) fine-scale changes in resource availability (i.e. low spatial autocorrelation of the change) result in more frequent movements at shorter time lags and shorter movements at longer time lags. During winter, on the contrary, movement is costly, forage is poor and partly covered by snow, and there is no regrowth. Because of the high costs of movements together with limited and slow (i.e. high temporal autocorrelation) small-scale environmental changes (i.e. relatively low spatial autocorrelation of the change), we recorded the most infrequent daily movements in winter. However, forage depletion and the lack of regrowth lead to low return rates (Van Beest et al. 2010) and, accordingly, the distances covered at 16-day lags were relatively similar to those recorded in summer, when the daily movement frequency was much higher.

Even though moose responded strongly to changes in the environment at a wide range of scales, they were obviously not able to respond to variation occurring at the largest scales, e.g. the whole study area, c. 23 100 km2. The range over which scales of changes in foraging opportunities are perceived and responded to can vary dramatically depending on an animal's cognitive and physiological capacities, as well as the costs associated with the response (e.g. increased mortality: Hebblewhite & Merrill 2007). Indeed, due to the higher energetic cost of walking compared with flying or swimming, terrestrial animals cover considerably shorter migration distances compared with flying or swimming animals (reviewed in Alexander 1998, 2002; Hein, Hou & Gillooly 2012).

Even though the overall annual movement patterns were similar between sexes (Fig. 3c and d), males moved longer daily and 16-day distances than females during most of the year and we could not detect an effect of waves of environmental change on the 16-day travel distances in males. The longer travel distances at all temporal scales support the hypothesis that the larger spatial requirements of males arise from their higher body mass, higher energetic requirements (Shipley et al. 1994; Mysterud, Pérez-Barbería & Gordon 2001b) and lower movement costs (Garland 1983; Hein, Hou & Gillooly 2012). During spring, the peak wave in vegetation greening occurs around mid-April (Fig. 3a), which is when females travel the longest 16-day distances (Fig. 3c), whereas males are lagging nearly a month behind (Fig. 3d). Also Bunnefeld et al. (2011) found a delayed spring migration in males compared with females. We can speculate that males delay their large-scale movements to benefit from more vegetation growth and higher forage quantity, which they require for their larger body size (Demment & Van Soest 1985). Such sex differences could also be caused by the reduced movement of females with a calf at heel in May–June (Testa, Becker & Lee 2000).

The coarser spatial resolution of the snow data (1 km2) compared with NDVI data (250 m2) limited our ability to quantify small-scale variations in snow depth, and partially explains why we found smaller effects of snow compared with NDVI on moose movements. In addition, due to the coarse temporal resolution of our environmental data (i.e. 16 days), we had to rely on proxies instead of actual measures of spatial variation in environmental change in 1 day. Such proxies were based on the assumption that no large-scale spatial variation occurs in 1 day. Although this assumption is plausible for plant productivity, it might not always hold for snow depth, as a large snow dump can create large-scale environmental changes in a few days. However, such snow dump would likely affect the 16-day changes too, and would thus lead the spatial scale of the 16-day change in snow depth to affect the 1-day movements, which is indeed the case for females in fall. The coarse nature of our environmental data probably led us to underestimate the importance of the relationships between the scales of environmental change and those of moose displacements. We expect that with ongoing technological developments future studies could further test and develop the conceptual framework we proposed.

As movements are an adaptation to dynamic resource landscapes (McPeek & Holt 1992), we recommend investigating the continuum from smaller to larger scale movements by focusing on the ultimate function and drivers of movements. We assumed that moose movements were primarily driven by forage availability and hampered by snow cover, and we succeeded in relating the scales of variation in such parameters to the scales of movements. However, movements can be driven by factors other than trophic resources: dispersal movements can occur to avoid kin competition, mate competition or to escape density dependence (Clobert, Danchin & Dhondt 2001; Long et al. 2008), whereas small-scale movements can allow for access to refugia (Panzacchi et al. 2010). Our approach can be readily extended to include drivers of movements other than trophic resources, such as population density, density of related individuals or predation risk. Relating the scales of movement to environmental variance may facilitate the assessment of the impact of changes in the environment (e.g. climate change, habitat fragmentation, population density, predation risk) for community dynamics.

Acknowledgements

We are grateful to K.-A. Høgda from the Northern Research Institute (NORUT) who kindly helped us with the acquisition of the MODIS-NDVI data, to I. Herfindal for further screening and formatting of these data and to F. Hanssen for the snow depth data. The lead author was financially supported by an intra-European Marie Curie fellowship and the Norwegian Research Council's PredClim grant to B.-E. Saether, whereas N. Bunnefeld was funded by the SLU thematic programme Wildlife and Forest. We are grateful to T. Falldorf for fruitful suggestions, and to J.-M. Gaillard and two anonymous referees for comments on earlier version of this manuscript.

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