�� 2006 The Author DOI: 10.1111/j.1366-9516.2006.00243.x Journal compilation �� 2006 Blackwell Publishing Ltd www.blackwellpublishing.com/ddi 269 Diversity and Distributions, (Diversity Distrib.) (2006) 12 , 269���276 SPECIAL FEATURE ABSTRACT Resource selection functions (RSFs) are statistical models defined to be proportional to the probability of use of a resource unit. My objective with this review is to identify how RSFs can be used to unravel the influence of scale in habitat selection. In wildlife habitat studies, including radiotelemetry, RSFs can be estimated using a variety of statistical methods, all of which can be used to explore the role of scale. All RSFs are bounded by the resolution of data and the spatial extent of the study area, but also allow predictor covariates to be measured at a variety of scales. Conditional logistic regression permits designs (e.g. matched case) that relate the process of habitat selection to a limited domain of resource units that might better characterize what is truly ���available��� to the animal. Scale influences the process of habitat selection, e.g. food resources are often selected at fine spatial scales, whereas landscape patterns at much larger scales typically influence the location of home ranges. Scale also influences appropriate sampling in many ways: (1) heterogeneity might be obliterated (transmutation) if resolution or grain size is too large, (2) variance of habitat characteristics might be undersampled if extent or domain is too small, (3) timing and duration of observations can influence RSF models, and (d) both spatial and temporal autocorrelations can vary directly with the intensity of sampling. Using RSFs, researchers can examine habitat selection at multiple scales, and predictive models that bridge scales can be estimated. Using Geographical Information Systems, predictor covariates in RSF models can be measured at different scales easily so that the predictive ability of models at alternative spatial and temporal domains can be explored by the investigator. Identification of the scale that best explains the data can be evaluated by comparing alternative models using information-theoretic metrics such as Akaike Information Criteria, and predictive capability of the models can be assessed using k -fold cross validation. Keywords Extent, grain, habitat selection, logistic regression, resource selection functions, scale. INTRODUCTION Resource selection functions (RSFs) can be used to characterize the distribution and abundance of organisms (Boyce & McDonald, 1999 Manly et al ., 2002 Nielsen et al ., 2005). More broadly, overlays of RSFs for multiple species can be used to predict species diversity at a site (Nielsen et al ., 2003). Likewise, species interactions in space can be modelled using RSF (Johnson et al ., 2000 Hirzel & Le Lay, 2006). For example, RSFs have been used to map a predator and prey on the same landscape to identify habitats where encounters are likely to occur between predator and prey (Hebblewhite et al ., 2005). Scale is a fundamental consideration in RSF studies because (1) the scale of the sam- pling scheme influences the strength of habitat associations, and (2) ecological processes including habitat selection can occur on different spatio-temporal scales. RSFs are especially convenient structures for studying the influence of scale on habitat selection because they offer a framework that can be used to bridge spatio- temporal scales. A RSF is defined as any function that is proportional to the probability of use (Manly et al ., 2002). In context of scale, RSFs allow a mixture of sampling scales for covariates to be included in the same model. In the extremes, scale must be defined relative to: (1) resolution or grain, and (2) domain or extent (Turner et al ., 2001). Resolution reflects how finely a resource unit or covariate is measured and often is limited by available data, e.g. a 30-m pixel. Resolution clearly limits the precision of spa- tial predictions, which appears to be especially important for Department of Biological Sciences, University of Alberta, Edmonton T6G 2E9, Canada Corresponding author. Mark S. Boyce, Department of Biological Sciences, University of Alberta, Edmonton T6G 2E9, Canada. Tel.: 780-492-0081 Fax: 780-492-9234 E-mail: boyce@ualberta.ca Blackwell Publishing Ltd Scale for resource selection functions Mark S. Boyce

M. S. Boyce �� 2006 The Author 270 Diversity and Distributions , 12 , 269���276, Journal compilation �� 2006 Blackwell Publishing Ltd landscape-structure variables. The availability of data and feasi- bility of data collection can limit the resolution at which an investigation might take place. Domain or extent is the size of the area under investigation. In some cases consistent patterns of habitat selection occur across spatial domains (Schaefer & Messier, 1995 Resetarits, 2005), but in other instances RSFs might vary substantially among scales, and the particular choice of domain depends on the objectives of the study (Boyce et al ., 2003). Fish predators have been shown to influence habitat selection by tree frogs at both regional and local scales leading Resetarits (2005) to conclude that habitat selection is ���a critical link between local communities and the regional dynamics of metacommunities in complex landscapes���. However, I caution that the scale at which habitat selection is measured can influence apparent species interactions. For example, mule deer ( Odocoileus hemionus ) and white-tailed deer ( Odocoileus virgin- ianus ) interactions were studied at different scales in Colorado (Whittaker & Lindzey, 2004). Although one might have con- cluded potential competitive interaction based on fine-scale selection of diet, seasonal spatial segregation at a larger scale showed that there was little potential for competitive interaction between the two species. Beyond the scale components of resolution and extent, sample units can include covariates measured within buffers of arbitrary size. For example, we might characterize vegetation type as a discrete variable within a 30-m pixel, but road density within a 1-km radius buffer as a continuous variable. Such buffers can be useful for characterizing the context of a resource unit, for ex- ample, the configuration of vegetation patches can be quantified using ��������������������������� (McGarigal & Marks, 1995) or other spatial pat- tern metrics (Perry et al ., 2002), and these context metrics can be used as covariates in the RSF model. For organisms with large area requirements, buffers might need to be large depending on the scale of the ecological processes influencing the use of a resource unit and the spatial pattern in vegetation (Johnson et al ., 2004b). For example, landscape heterogeneity measured at large spatial scales, even larger than the home range, appears to be neces- sary to characterize habitat selection by mule deer (Kie et al ., 2002). My objective in this paper is to highlight the importance of scale in RSF investigations and to suggest some analysis protocols that allow efficient examination of the role of both temporal and spatial scales in habitat studies. Although in my outline I discuss temporal and spatial scales separately, these two dimensions are not independent. For example, body size is related to home- range area and longevity (Calder, 1984), i.e. space and time, so we might expect investigations for large animals to require large spatial and long temporal scales. Integrating time and space con- siderations, methods have been proposed to use movement rates to identify appropriate spatial scales of analysis for RSFs (Nams, 2005), e.g. identifying habitats used for foraging vs. interpatch movement (Johnson et al ., 2002). SAMPLING DESIGNS The scale of an RSF and the appropriate statistics for analysis are fundamentally tied to the sampling design. Manly et al . (2002) provide a comprehensive review of alternative sampling designs for estimating RSFs. I will focus discussion on two designs that are most common in wildlife habitat studies: (1) used/unused or presence/absence designs, and (2) use/availability or presence/ pseudo-absence designs (Pearce & Boyce, 2006). Scale can be studied using either of the two designs ��� primary differences relate to the feasibility of field sampling and the particular data available. In the first design, a random sample of resource units is drawn, and each is inspected for the presence (= 1) or absence (= 0) of a species. Typically a generalized linear model (GLM) or a general- ized additive model (GAM) would be used to estimate a resource selection function (Manly et al ., 2002 Hirzel & Le Lay, 2006). A special case of presence/absence is the case-control design where intensity of sampling of used and unused resource units is not random (Keating & Cherry, 2004). One of the common difficulties with a presence/absence design is called an ���asymmetry of errors��� where presence is observed and thereby known with certainty, but absence can be difficult to evaluate (MacKenzie, 2005). Temporal scale of sam- pling can be crucial to the correct detection of absences, because repeated sampling over a longer time might result in the detec- tion of a presence in a resource unit where the species was ini- tially absent (Johnson et al ., 2006). This may not a problem if the spatial and temporal domains of the study are carefully specified. For example, birds might be sampled using time���area counts for 12 min at sampling locations visited once during the month of June. But having to restrict the domain of application for the RSF might limit applications, for example if the objective is to charac- terize the habitats used by a species for purposes of distribution mapping. Problems associated with accurately characterizing unused resource units or absences often are thought to be a particular problem for animals because they move around. However, I believe that the same problems exist for modelling plant dis- tributions, typically at a much slower temporal scale. Many plants can exist for years in the seed bank, germinating after heavy rains or when conditions are otherwise favourable. Likewise many species of plants may exist undetected until a major disturbance resets the successional process. Clearly detection error can influ- ence estimates of RSF models based upon presence/absence data (Gu & Swihart, 2004), and in some circumstances adjustments for detection bias are possible (Frair et al ., 2004). The second design involves contrasting a sample of resource units where the species is known to occur (= 1) with a random sample of ���available��� resource units (= 0) drawn without replace- ment within the domain of the area of study. We often assume an exponential or log-linear structure for an RSF: (1) for a vector x of k predictor covariates. The model coefficient, �� i , for the i -th habitat covariate, x i , can be estimated using the corre- sponding coefficient from logistic regression so long as used resource units are relatively rare on the landscape (Manly et al ., 2002). RSF ( ) exp( ... ) = = + + + w x x x xk �� �� ��k 1 1 2 2