The study was conducted in the county of Sogn og Fjordane, Norway (Supporting Information, Fig. S1). The vegetation on the west coast of Norway is mostly in the boreonemoral zone. Natural forests are dominated by deciduous (mainly birch Betula spp. L. and alder Alnus incana L.) and pine forest (Pinus sylvestris L.), with juniper (Juniperus communis L.), bilberry (Vaccinium myrtillus L.) and heather (Calluna vulgaris L.). Norway spruce Picea abies L. has been planted on a large scale, and is an important winter habitat for red deer. On flatter and more fertile grounds in the bottom of valleys, areas have been cleared for cultivation. These areas are used mostly as pastures and meadows for grass production. The topography is mountainous, and is characterized by steep hills, valleys, streams and fiords, and the slope increase from coast to inland. In general, temperature and precipitation decline from coast to inland, while snow depth and duration of snow cover increases (Mysterud et al. 2000).
Red deer data
Data derive from 47 female red deer caught by darting on winter feeding sites during 2005–2007, after a procedure approved by the Norwegian national ethical board for science (‘Forsøksdyrutvalget’, http://www.fdu.no). The deer were fitted with Televilt Basic ‘store-on-board’ GPS (Global Positioning System) collars or Televilt Basic GPS collars with GSM (Global System for Mobile Communications) option for transfer of data via cell phone network (Televilt TVP Positioning AB, Lindesberg, Sweden). The GPS collars were programmed to record hourly positions, and to release a drop-off mechanism after approximately 10 months (tracking period ranged from 6 to 12 months). Locations taken during the first 24 hours of tracking and all locations where the animal had moved at a speed of >40 km per hour or a distance >10 km between fixes were removed, as these are most likely erroneous. In total, only 0·5% of the locations were removed as outliers. As some locations (very few) were preceded and succeeded by missing locations, the distance or speed rule was not able to identify these as outliers. To remove these we performed a visual inspection of locations from each individual, to see if any obvious outliers were still retained (N = 27, 0·000098 of locations). If ever in doubt to remove a location based on visual inspection, the location was retained. As the home range concept applies only to stationary space use patterns, and also because migration behaviour is very different from the normal home range behaviour, we removed all locations within and partly overlapping with the migration periods. Deer in our area either stay year round in one area or migrate quickly in spring and autumn between clearly separated seasonal home ranges, with intermediate strategies being rare. We plotted for each individual the distance from the first location by time (Julian date). Individuals displaying distinct migration periods in this plot were classified as migratory, and the rest were classified as stationary (see Supporting Information, Fig. S2). We used piecewise regression (library ‘segmented’ in the statistical software R; Muggeo 2008; R Development Core Team. 2008) to identify migration periods. The aim of the method is applying least-squares methods to identify breakpoints by fitting broken-line relationships between the response and predictor variable. Using Julian date as predictor and distance from first location as the response, we identified when migration started and ended in spring and autumn for each migratory individual and removed data from these periods.
Location error – defined as the distance between estimated and true position – is a common source of error for GPS data. To correct for this, we used the method presented by Börger et al. (2006b). Details on this can be found in the Supporting Information.
Local climate variables
Data on temperature, precipitation and snow depth were taken from meteorological stations located within the study area (http://eklima.met.no/). Temperature was available from seven stations, and precipitation and snow depth from 18 stations (Supporting Information, Fig. S1). For each GPS location recorded from the animals, the closest meteorological station was identified and the daily precipitation, snow depth and temperature value from this station was assigned to the location. We calculated growing degree days (GDD) from hourly temperature measures, which were available from five of the seven temperature stations, as it is expected to be a more direct determinant of plant productivity (Woodward 1987). We estimated GDD according to Molau & Mølgaard (1996), by summing up hourly temperatures for each day when the temperature was above a threshold of 5 °C, and dividing the sum by 24. Day lengths in the study area were downloaded from the U.S. Naval Observatory (http://www.usno.navy.mil/USNO).
We evaluated the availability of four different habitat types within the red deer home ranges. The dominant habitat type within each home range was determined by using digital land resource maps provided by the Norwegian Forest and Landscape Institute, with scale 1:5000 and a resolution of 50 × 50 m. The digital resource maps were divided into five habitat types, by merging of habitat classes from the original maps (as in Godvik et al. 2009). ‘Forest of high productivity’ and ‘pastures’ are considered forage-rich, and ‘forest of low productivity’ and areas deficient in shelter and forage plants (mainly mountains and marshes, defined as ‘other’ in figures and tables; Godvik et al. 2009) are considered forage-poor. The fifth category contained lakes, sea and uncharted areas, and was thus not of interest. In any case that this was the dominant habitat type, we used the second most abundant habitat type in the analysis.
Home range estimation
To be able to evaluate and compare the results, we estimated home ranges by two different methods. The methods were fixed-kernel (the currently most popular method) using the reference method for calculation of the smoothing factor h (Kernohan, Gitzen & Millspaugh 2001) and minimum convex polygon (MCP, traditionally the most used method). MCP home ranges were estimated using the library ‘adehabitat’ (Calenge 2006) implemented in the statistical software R version 2.10.1 (R Development Core Team. 2009), and kernel home ranges were estimated using the Animal Movement extension in ArcView GIS 3.3 (ESRI, USA). We only estimated home ranges if the individual had at least 95% coverage of the given time interval, and at least 16 GPS locations. Home ranges were estimated at four different temporal scales; daily, weekly, two weeks (biweekly) and monthly. To investigate if the effect of a factor varied for different home range density isopleths (i.e. affected ‘core’ area more than full home range), we always estimated the 90%, 70% and 50% home range for each individual.
To examine variation in home range size we used the method developed by Börger et al. (2006b). We fitted linear mixed-effects models (Pinheiro & Bates 2004), using the library ‘nlme’ (Pinheiro et al. 2009) implemented in R (R Development Core Team. 2009). The response variable in the model was log-transformed home range size (ha), and only individuals with repeated home range estimates during the particular temporal scale were used in the analysis. Five covariates were fitted as fixed effects; temperature, precipitation, day length, dominant habitat type and spatial GPS error (Supporting Information, Table S1), including all combinations of two-way interactions. The climatic variables temperature and precipitation were fitted as residuals obtained from a linear regression against day length to remove the seasonal trend. We fitted separate models for the winter season, defined as 1st December–31st March, where snow depth (residuals obtained in the same way as above) was included as a covariate. We fitted separate models for summer, where growing degree days (GDD) was included as a covariate. Summer was defined differently for stationary and migratory individuals. For stationary individuals summer was defined as 1st May–31st August. If migratory individuals started spring migration after 1st May, the date of arrival was used, and the start date of autumn migration defined the end of summer if this was before 31st August.
As random terms we fitted random intercepts for each individual. When dealing with a random sample of individuals with varying numbers of corresponding home range estimates, coefficient estimates will be biased towards individuals with the largest amount of estimates and/or individuals with extreme home range sizes (Follmann & Lambert 1989; Pinheiro & Bates 2004). If a random intercept is needed, this implies variation in home range size within individuals is smaller than between individuals. The random intercept added to the model accounts for this individual variability by adjusting the overall average home range size, allowing inference to be extended to the entire population (Neter et al. 1996).
The models were checked for unequal variance structures of the within-group errors by investigation of relevant model diagnostic plots (plots of residuals vs. fitted values for the relevant model and variable; Pinheiro & Bates 2004) and by comparing models with and without different variance functions, using likelihood ratio tests. If selected, we implemented variance functions in the models, as according to Pinheiro & Bates (2004). The variance functions tested for were either a general function specifying the fitted values as variance covariates, a function with different variance parameters for each level of the variable specifying the dominant habitat type, or with different variance parameters for migratory and stationary individuals. These were fitted using the ‘varPower’-function in library ‘nlme’, which models cases where there is an increase or decrease in variance with the absolute value of the covariate (Pinheiro et al. 2009). We also checked for any remaining dependencies among the within-group errors after the fixed and random effects were fitted. If present, these were modelled using correlation structures. We tried fitting either a spatial or a temporal correlation function. Spatial autocorrelation between home ranges was corrected by using the mean coordinates of the home ranges, and temporal autocorrelation was corrected by giving the home range estimates for each individual continuous integers starting with 1 for the first home range estimate. Both spatial and temporal correlation were for all models fitted inside an exponential correlation structure using Euclidean distances as distance metric (function ‘corExp’ in the library ‘nlme’; Pinheiro et al. 2009), as this provided the best fit based on investigation of diagnostic plots (plots of residuals vs semivariogram) and likelihood ratio tests of models without and including the different spatial correlation structures (‘corStruct’-classes) available in the ‘nlme’-library (see Pinheiro & Bates 2004, pp 226–249). As it is not possible to fit spatial and temporal correlation structures together in the same model, we proceeded with the most parsimonious model based on diagnostic plots and likelihood ratio tests. Spatial correlation structure was best for 92% of all models. The likelihood ratio tests and diagnostic plots of the three models selecting temporal correlation over spatial correlation structures showed no distinct improvement, suggesting that the inclusion of a temporal correlation structure is not critical. Therefore, if a correlation structure was needed, we always used a spatial correlation structure.
We always checked, based on likelihood ratio tests, if a random intercept was required to enhance model fit. If the mixed-effects model was not significantly better than a linear model without a random intercept, we checked for unequal variances and dependencies among within-group errors, which can be corrected for by utilizing generalized least squares (GLS) models, but without having to add complexity by including unnecessary random effects to the model (Pinheiro & Bates 2004). In no case was such correction needed (thus GLS models were never required) so in cases where no random intercept was required, we fitted a basic linear model (LM).
When the initial model structure was determined and model assumptions met, fixed effects model selection was conducted by backwards selection of variables from the full model (Murtaugh 2009). Model comparison between the reduced and the more complicated model was by likelihood ratio tests (Pinheiro & Bates 2004). During comparison of mixed-effects models with different fixed effects, parameter values must be obtained using maximum likelihood estimation (Pinheiro & Bates 2004). After model selection, the final model was fitted using restricted maximum likelihood estimates.
All these analyses were performed for full year, summer and winter models, both home range estimation methods, all home range density isopleths, and all temporal scales. Kernel and MCP estimates of home range size were generally in agreement. The models showed the same trends, but with MCP estimates being somewhat larger than the kernel estimates. Also, the different models run for each of the three density isopleths (90%, 70% and 50%) showed similar results. For a summary of descriptive statistics of the data set, home range sizes at the different temporal scales, effects of individual differences, spatial autocorrelation and variance explained in the models, see Supporting Information, Tables S2–S4.
We report results obtained from models fitted on home range sizes estimated by the kernel method, due to both kernel and MCP models showing similar trends, but also due to earlier studies comparing these two methods of home range estimation concluding with kernel methods performing better (Worton 1987; Börger et al. 2006a). If not explicitly stated, the results refer to all density isopleths, and for predictions made with the dominant habitat type ‘forest of high productivity’ as reference, as this is the most common dominant habitat type. Except for monthly winter models (70% and 50% density isopleths), models including random intercepts for individuals were always more parsimonious. The monthly 70% and 50% kernel winter models were fitted as basic linear models, as no correlation structures or variance functions were necessary. Final models are in many cases quite complicated, with several interactions retained (Supporting Information Tables S5–S12 and S15). When presenting the results, we focus on the interactions considered biologically significant, not presenting results including the variable ‘error’ and interactions with this variable, as this variable is included in the models for corrective purposes only (see Materials and Methods).