We captured fish owls from eight territories in three geographical regions (Olga, Ternei and Amgu; see Fig. S1 in Supporting Information) from 2007 to 2010 primarily using the methods of Slaght, Avdeyuk & Surmach (2009). Briefly, we placed live fish or frogs in an enclosure set within a stream to lure owls to a trap set near the enclosure. We marked adult, territorial fish owls in 2008–2010 with GPS data loggers (40 and 90 g models, Sirtrack Tracking Solutions, Havelock North, New Zealand), which were attached with 1·10 cm Teflon-coated ribbon as a harness (Bally Ribbon Mills, Pennsylvania, USA) following methods of Kenward (2001). Data loggers required recapture of the birds to recover location data. Therefore, any animal that died or dispersed resulted in loss of data. We programmed 90 g data loggers to record one location every 11 h and 40 g units every 23 h to conserve battery power. All GPS data loggers weighed ≤3% of both sexes (mean male mass was 3·10 ± 0·03 kg [mean ± SE, n = 7 owls], and mean female mass was 3·25 ± 0·12 kg [n = 5]), which was within recommended limits (Kenward 2001). We estimated GPS location quality using GPS fix success rate, proportion of 2-D vs. 3-D fixes and location error (Cain et al. 2005). We eliminated GPS locations with 2-D fixes and those with horizontal dilution of precision values >5 because they may be unreliable (Dussault et al. 2001). We partitioned our data into four phenological seasons (winter = 1 December–31 March, spring = 1 April–14 June, summer = 15 June–14 September and autumn = 15 September–30 November; see Slaght 2011).
Data Analysis and Model Development
We estimated home range size and within-home range resource selection (equivalent to Johnson's (1980) ‘third-order selection’) using a synoptic model of space use (Horne, Garton & Rachlow 2008; example code provided in Appendix S1 in Supporting Information), which ameliorated some limitations of standard home range estimators by allowing estimation of both home range and resource selection within the same modelling process. The structure of the synoptic model was based on a weighed distribution that is used to predict a species’ probability of use of a given area (Lele & Keim 2006; Horne, Garton & Rachlow 2008; Johnson et al. 2008). Each individual's space use (i.e. home range) was modelled as follows:
where fu(x) is the probability density of being at spatial location x, fo(x) is the null distribution of space use which models the probability of use in the absence of habitat selection and w(x) is a selection function that transforms fo(x) to fu(x)by selectively weighing different areas based on habitat attributes at location x. For our analysis, we defined fo(x) = N (θ), a bivariate normal distribution with five parameters, symbolized by θ, describing the means and variances in the x and y dimensions and the covariance. We used a bivariate normal distribution as our null model, as this distribution links use with a central place (Horne, Garton & Rachlow 2008). This is an appropriate (i.e. biologically meaningful) null model for fish owls because they are nonmigratory and centre their territories on a nest tree used for multiple seasons (Slaght 2011). We defined the selection function as
where H (x) is a vector of covariate values describing the habitat at location x and β is a vector of parameters (i.e. selection coefficients) to be estimated. To accommodate temporally changing habitat covariates (e.g. distance to open water), we generalized eqn (eqn 2) to depend on the values of the covariates at time t. Thus, the time-specific resource selection function was
If all areas were equally available across the landscape, eqn (eqn 3) would be analogous to a ‘resource selection function’ (i.e. a function that is proportional to the probability of a resource unit being used given knowledge of its habitat characteristics; Manly et al. 2002). However, the synoptic model allows the values of the availability distribution fo (x) to vary across the landscape. Thus, while eqn (eqn 3) is similar in spirit to a resource selection function (i.e. it multiplicatively transforms the availability distribution into the use distribution), its interpretation as well as the associated values of the selection coefficients must include consideration of the availability distribution (see explanation below).
The value of the estimated selection coefficients can be interpreted via probability ratios. In general, we want to understand how the probability of occurrence would change at a given location x with covariate values H(a) compared with an alternative location with covariate values H(b). The probability ratio quantifying how much more or less likely an animal is expected to be at a location with covariate values H(a) vs. covariate values H(b) is
where K is the integral in the denominator of eqn (eqn 1). Importantly, eqn (eqn 4) assumes location x is equally available for subsequent selection in both hypothetical areas a and b (i.e. the role played by fo (x) in both the numerator and denominator). For example, suppose elevation is one of the covariates in our model with values that range from 1000 to 3000 in our study area. For estimation purposes, we standardize the covariate to range from 0 to 1, and we subsequently estimate the selection coefficient to be . To interpret this value, we are interested in how much more likely the animal is to occur at an elevation of 2200 vs. 2000 (i.e. standardized values of 0·6 and 0·5, respectively). From eqn (eqn 4), we can calculate this value as
Thus, given equal availability (i.e. accessibility) within the home range, the animal is twice as likely to be at an elevation of 2200 vs. 2000. Note that this value will be the same for any 200-unit increase in elevation (e.g. 200 vs. 0, 850 vs. 650, etc.). Also note that because eqn (eqn 4) is based on the ratio of probabilities, this interpretation corrects the assertion by Horne, Garton & Rachlow (2008) that eqn (eqn 4) is an ‘odds ratio’.
We used maximum likelihood to estimate the parameters governing the null model of home range (θ) and the selection coefficients(β). We approximated the integral in eqn (eqn 1) by placing an ‘availability grid’ (a grid of points) spaced 50 m apart over each fish owl region (mean size was an 818 295-point grid across a 2111 km2 area; n = 3). We chose this grid size as a trade-off between spatial resolution and processing speed.
We developed habitat covariates based either on our knowledge or the literature on fish owls (Slaght & Surmach 2008; Slaght 2011). We used a covariate (VALLEY) to assess important landform features within the home range (Takenaka 1998; Slaght 2011). VALLEY was a continuous variable estimated using a topographic position index (TPI) in Land Facet Corridor Designer (a module in ESRI ArcGIS; v. 9.3, Redlands, CA, USA), where negative values indicate valleys locations, values near 0 indicate low slopes, and positive values indicate high slopes or ridge tops (Jenness, Brost & Beier 2012). In our study landscape, TPI values distinguished valleys (TPI < −0·62) from slopes (−0·62 < TPI < 0·90) and ridges (TPI >0·90). We also generated a covariate depicting neighbouring owl territories (NEIGH), which we created with a minimum convex polygon to bound home ranges of neighbouring owls; otherwise, the synoptic model would include all nearby suitable habitat, which is not realistic for this territorial species.
We created seven continuous covariates: distance to water (D_WAT), distance to patches of permanently open water; that is, river stretches that remain unfrozen in winter (D_WWAT), amount of deciduous forest (DEC_213), amount of riparian old-growth forest (RO_213) and open space (i.e. young forest, field, road, talus slope; OPEN_213) within a 213-m buffer. We also measured the amount of open water in winter (WWAT_213). We included a covariate for channel complexity (i.e. number of river channels; CHAN_213) and one interactive term (RO*DWAT), which evaluated the interaction between riparian old-growth forest and distance to water covariates. Fish owls appeared to be closely associated with water (Slaght & Surmach 2008); therefore, we chose a 213-m buffer to sample resources because this was the mean distance (plus two standard deviations) of all fish owl locations to water.
We used remotely sensed data to create a cover type map of the study area. We identified five cover types: coniferous forest, deciduous forest, riparian old-growth forest, water (river, lake) and open space (bare surfaces, settlements, agriculture, other open areas). We used SPOT five imagery (Satellite Pour l'Observation de la Terre) because high spatial resolution (10 m) facilitated mapping open water (particularly in winter) and some cover types. We used 30 m Landsat TM data (Sioux Falls, SD; http://glovis.usgs.gov/) from September 2007 because we could not reliably distinguish old-growth forest using SPOT. We enhanced Landsat TM images for analysis using a variety of techniques and assessed map accuracy following Congalton & Green (1999) with some modification (see Slaght 2011). Overall classification accuracy was 85%, with a Kappa statistic (a measure of agreement between our classified map and reference data; Titus, Mosher & Williams 1984) of 0·82 (see Slaght 2011). We conducted all remote sensing analyses using ESRI ArcGIS and ERDAS Imagine (v. 9.3; Norcross, GA).
To assess within-home range resource selection by fish owls, we developed 14 a priori additive and interactive models using the above nine covariates (see Slaght 2011). Prior to analysis, we tested covariates for colinearity and removed highly correlated covariates (r ≥ 0·7). In such cases, we retained the covariate that made the most sense, given our knowledge of fish owl biology and ecology. Half of the models (50%, n = 7) were variants of what we called the ‘literature’ model, which included the covariates VALLEY, D_WWAT and RO_213. An additional four models were variants of what we called the ‘multi-channel’ model, which had similar components to the ‘literature’ model but also included D_WAT and CHAN_213.
We selected the best synoptic model from the candidate set based on Akaike's information criterion corrected for small sample sizes (AICC; Burnham & Anderson 2002; Horne, Garton & Rachlow 2008). We drew inference from models based on AICC weights (Burnham & Anderson 2002) and strength of parameter estimates (85% confidence intervals [CI]; Arnold 2010). If individual fish owl data sets had sufficient sample size (i.e. if the best model was anything but the null model [bivariate normal distribution]), we included them in seasonal analysis. We excluded data for home range size analysis from an unpaired owl from autumn because its movement patterns indicated that it did not have a stable home range. However, we retained its location data for parameter estimation of resource selection.
We averaged parameter estimates from all top models across individuals to generate seasonal parameter estimates and averaged seasonal estimates to derive an annual estimate (similar to ‘two-stage’ methods; Fieberg et al. 2010). For annual estimates, we weighed parameter estimates for each season by its relative proportion of the year (i.e. spring was 75 days long, so spring selection coefficients were weighed by 0·21).
We modelled six additional home range estimators including the exponential power distribution, bivariate normal, a two-mode bivariate circular normal mix, a two-mode bivariate normal mix, and fixed kernel and adaptive kernels. We determined the best of these using the likelihood cross-validation criterion (CVC; Horne & Garton 2006), in program Animal Space Use (v. 1.3; Horne & Garton 2007). Computation time, involving numerical maximum likelihood, prevented us from calculating CVC for the synoptic model. However, to provide a general comparison of the performance of the synoptic model vs. the alternatives, we compared the AICC score of the best synoptic model with the CVC score of the best alternative estimator (Stone 1977; Horne & Garton 2006). We executed the synoptic model using program R (v. 2.11, R Development Core Team, www.r-project.org) using code written by D. Johnson and J.S.H.