1 Journal of Animal Ecology 2010, 79, doi: /j x Inference from habitat-selection analysis depends on foraging strategies Guillaume Bastille-Rousseau 1, Daniel Fortin 1 * and Christian Dussault 2 1 Universite Laval, De partement de Biologie, 1045 Av. de la Me decine, pavillon Alexandre Vachon, Universite Laval, Que bec QC G1V 0A6, Canada; and 2 Ministe`re des Ressources naturelles et de la Faune, Direction de l expertise sur la faune et ses habitats, 880 chemin Sainte-Foy, Que bec QC G1X 4X4, Canada Summary 1. Several methods have been developed to assess habitat selection, most of which are based on a comparison between habitat attributes in used vs. unused or random locations, such as the popular resource selection functions (RSFs). Spatial evaluation of residency time has been recently proposed as a promising avenue for studying habitat selection. Residency-time analyses assume a positive relationship between residency time within habitat patches and selection. We demonstrate that RSF and residency-time analyses provide different information about the process of habitat selection. Further, we show how the consideration of switching rate between habitat patches (interpatch movements) together with residency-time analysis can reveal habitat-selection strategies. 2. Spatially explicit, individual-based modelling was used to simulate foragers displaying one of six foraging strategies in a heterogeneous environment. The strategies combined one of three patch-departure rules (fixed-quitting-harvest-rate, fixed-time and fixed-amount strategy), together with one of two interpatch-movement rules (random or biased). Habitat selection of simulated foragers was then assessed using RSF, residency-time and interpatch-movement analyses. 3. Our simulations showed that RSFs and residency times are not always equivalent. When foragers move in a non-random manner and do not increase residency time in richer patches, residencytime analysis can provide misleading assessments of habitat selection. This is because the overall time spent in the various patch types not only depends on residency times, but also on interpatchmovement decisions. 4. We suggest that RSFs provide the outcome of the entire selection process, whereas residencytime and interpatch-movement analyses can be used in combination to reveal the mechanisms behind the selection process. 5. We showed that there is a risk in using residency-time analysis alone to infer habitat selection. Residency-time analyses, however, may enlighten the mechanisms of habitat selection by revealing central components of resource-use strategies. Given that management decisions are often based on resource-selection analyses, the evaluation of resource-use strategies can be key information for the development of efficient habitat-management strategies. Combining RSF, residency-time and interpatch-movement analyses is a simple and efficient way to gain a more comprehensive understanding of habitat selection. Key-words: foraging strategies, habitat selection, individual-based model, interpatch movement, movement biases, residency-time analysis, resource selection function Introduction Several statistical methods have been proposed to characterize habitat selection. Most methods compare habitat attributes at animal locations with attributes at unused or at random locations (Aebischer, Robertson & Kenward 1993; *Correspondence author. Boyce & Mcdonald 1999; Manly et al. 2002; Calenge, Dufour & Maillard 2005). Resource selection functions (RSFs), for example, provide relative probabilities of occurrence in habitat units based on this comparison (Johnson et al. 2006; Lele & Keim 2006; Mcloughlin et al. 2010). Alternatively, some authors have proposed that habitat selection could sometimes be inferred from the relative intensity of use of habitat patches (Fauchald & Tveraa 2003; Ó 2010 The Authors. Journal compilation Ó 2010 British Ecological Society
2 1158 G. Bastille-Rousseau, D. Fortin & C. Dussault Suryan et al. 2006; Trathan et al. 2008). Recently, Freitas et al. (2008) suggested that the risk of departure from a habitat patch decreases with the preference for that patch. In other words, they argued that habitat selection could sometimes be determined without the need to define availability. Traditionally, however, a resource is considered as selected when usage exceeds availability (Johnson 1980; Boyce et al. 2002). Manly et al. (2002) even suggest: [ ] used resources should be compared to available (or unused) resources in order to reach valid conclusions concerning resource selection. A potential problem with inferring habitat selection based only on residency time lays in the fact that an animal can use a given patch type more than expected based on availability not only by remaining relatively longer in patches of that type, but also by moving selectively between patches of that type (i.e. without necessarily displaying residency time variation among patch types). Residency-time analysis would detect selection only in the first case. Although Freitas et al. (2008) provide unquestionably a powerful approach to identify environmental factors influencing the risk of animals leaving an area, the link between residency time and habitat selection is less obvious. There is a need to clarify situations under which methods based on useavailable comparisons, such as RSFs, and methods based on residency time provide convergent and divergent results. We argue that concordance between the two approaches strongly depends on foraging strategies. Habitat selection is an adaptive behavioural process shaped by multiple cost-benefit tradeoffs (food acquisition, risk of predation, reproductive success, etc.). Different foraging strategies may thus be favoured in different contexts (Brown & Kotler 2004; Fortin et al. 2005; Mao et al. 2005; Fortin, Morris & Mcloughlin 2008; Kaczensky et al. 2008). First, the strategy may involve a given patch-departure rules (Iwasa, Higashi & Yamamura 1981). For example, Valone & Brown (1989) found that mourning doves Zenaida macroura L. and Gambel s quail Callipepla gambelii Gambel follow a fixed-time strategy, with birds spending the same amount of time in the different patches. Conversely, kangaroo rats Dipodomys merriami Mearns, round-tailed ground squirrels Spermophilus tereticaudus Baird, and Arizona pocket mice Perognathus amplus Osgood follow a fixed-quitting-harvestrate strategy, which closely corresponds to leaving a patch after searching without success for a fixed amount of time (Valone & Brown 1989). This strategy would result in individuals staying longer in richer patches. Finally, many frugivorous bird species leave fruit patches once they have consumed a fixed quantity of fruit (Saracco et al. 2005), which result in individuals staying longer in poorer patches. For example, morphological or physiological constraints can induce satiation, which in turn can trigger patch departure (Brown & Morgan 1995). In addition to different patch-departure rules, a foraging strategy may involve non-random interpatch movements (Farnsworth & Beecham 1999). Animals use area-concentrated search when switching from short and tortuous moves within rich areas to long and linear moves across poor areas (Benhamou 1992; Fortin 2003; Pinaud 2008). Animals may also use spatial memory or visual cues to orient their trajectories towards rich patches (Edwards et al. 1997). For example, zebras Equus burchelli antiquorum Smith can orient their movements towards foraging patches that are located as far away as 3Æ7 km (Brooks & Harris 2008). Also, elk Cervus canadensis Erxleben selectively make movements ending in an aspen stand or in conifer forests, depending on predation risk (Fortin et al. 2005). Although interpatch movements are an important element of the habitat-selection process, most habitat-selection analyses do not explicitly account for movement biases (but see, e.g. Fortin et al. 2005; Moorcroft & Barnett 2008). In this paper, we used spatially explicit, individual-based modelling to simulate animals living in the same virtual landscape, but using different foraging strategies. Habitat-selection strategies involved different patch-departure rules and interpatch-movement decisions. These strategies represent only a subset of all the possible ones, but they have been considered in theoretical studies (Iwasa, Higashi & Yamamura 1981; Schultz & Crone 2001) and they are known to occur in nature (Valone & Brown 1989; Saracco et al. 2005). We contrasted space-use patterns of simulated foragers using these different strategies with RSF, residency time and interpatchmovement analyses. Our general objective was to show how inferences from habitat-selection analyses are contingent upon foraging strategies, as well as to demonstrate the complementary nature and usefulness of the three analyses when used in combination. Materials and methods INDIVIDUAL-BASED MODELS Spatially explicit, individual-based models were created using the Spatially Explicit Landscape Event Simulator (SELES, Fall & Fall 2001). The simulated landscape (4000 cells by 4000 cells) contained three patch types of equal number and size (6000 patches of 40 cells in diameter) randomly distributed within a foodless matrix (MATRIX). The three patch types differed in terms of food availability, with the RICH patch type offering the highest food abundance and the POOR patch type, the least. This simple landscape eliminated potential confounding effects of landscape structure, and ensured that patterns detected by habitat-selection analyses were the direct result of foraging strategies. Virtual foragers were travelling in this landscape following six strategies that differed in terms of patch-departure rules and interpatch-movement biases. Patch-departure rules included: (i) fixedtime, (ii) fixed-quitting-harvest-rate and (iii) fixed-amount-strategy (Iwasa, Higashi & Yamamura 1981; Brown & Morgan 1995). These different strategies translated into differences in the adjustment of residency time to local food abundance. Individuals using the fixedtime strategy systematically spent four successive time steps in each patch, regardless of food availability. Individuals using the fixedquitting-harvest-rate-strategy spent five time steps in the RICH patches, two time steps in the MEDIUM patches and one in POOR patches (i.e. forager did not stop). Finally, individuals using the fixed-amount strategy spent one time step in the RICH patches, three time steps in the MEDIUM patches and five time steps in POOR
3 Inferences from habitat-selection analyses 1159 patches. Each time step corresponds to a new location. Foragers could only leave a patch once they have accomplished the predetermined number of time steps. After staying this amount of time in a patch, foragers moved randomly inside the patch changing direction using an angle drawn from a uniform distribution (0, 359) and a steplength drawn from a normal distribution with a mean of 20 cells and variance of 10. Following this rule, foragers usually reached the matrix after making one additional step inside the patch. To complete individual strategies, each patch-departure rule was combined with one of two interpatch-movement rules: random movements vs. directional movements biased towards RICH patches. Foragers moved in the matrix, following a correlatedrandom walk, with turning angles drawn from a normal distribution with a mean of 0 and variance of 25, and step-lengths drawn from a normal distribution with a mean of 15 cells and variance of 8. For directional movements, we considered a biased-correlated-random walk (Schultz & Crone 2001) where the turning angles were directed, on average, towards the nearest RICH patch, but also with variance of 25 around this mean direction. Step-length was again drawn from a normal distribution with a mean of 15 cells and variance of 8. The stochastic nature of this movement rule was such that, despite this bias towards RICH patches, simulated individuals ended up in each patch other than a RICH one about 20% of the time. For each foraging strategy, 250 virtual foragers were followed for 1000 consecutive moves. RESOURCE SELECTION FUNCTION We used RSFs to describe the relationships between the probability of occurrence of simulated individuals and landscape composition. We estimated RSFs by comparing habitat characteristics at observed (i.e. one location per time step) and random locations (1 : 1 ratio) with logistic regressions. We drew random locations for a given forager within its 100% minimum-convex polygon (MCP) (third-order selection; Johnson 1980). The RSF took the form: wðxþ ¼expðb MATRIX X MATRIX þ b POOR X POOR þ b RICH X RICH Þ eqn 1 where w(x) represents the RSF scores, and b u is the selection coefficient for patch X u, where u is one of the three patch types or the matrix. In our model, the MEDIUM patch type represented the reference type. The use of mixed-effects models was not necessary because all foragers considered for a given analysis had the same movement rules, and moved the same number of steps in the landscape types (although with different starting locations). We thus simply relied on fixed-effects models. Other RSF designs can be used to assess habitat selection at different scales (see e.g. Ciarniello et al. 2007; Fortin et al. 2009; Mcloughlin et al. 2010). To test whether our conclusions were robust of variations in scales, we also built RSFs based on a paired design. Each observed location was then linked to 10 random locations drawn within a 25-cell radius circle, which encompassed 90% of the distances observed between two successive locations. These RSFs were estimated with conditional logistic regression. RESIDENCY TIME We used the methodology proposed by Freitas et al. (2008), which is based on First-passage time (FPT), to identify the intensity of use of each patch based on residency times (hereafter simply referred to as residency time). We calculated FPT the time required for an animal to cross a circle of a given radius for each forager at regular distance intervals (see Fauchald & Tveraa 2003). We tested radii ranging from 4 to 200 distance units, with 2-unit increments, and identified the radius maximizing the variance of the FPT (log-transformed). We then calculated the FPT at regularly spaced intervals using this radius (6-cell radius). We used a Cox Proportional Hazards (CPH) model (Cox 1972) to quantify how FPT at a given location was influenced by the associated patch type. FPT radius was smaller than our patch size, and in almost all cases, contained only one patch type or the matrix. We attributed to each FPT circle the attribute of the patch type falling in the middle of the circle (which represented the dominant patch type). The CPH model then took the form: hðtþ ¼expðb MATRIX X MATRIX þ b POOR X POOR þ b RICH X RICH Þh0ðtÞ; eqn 2 where h(t) is the hazard function, i.e. the risk that an individual leaves an area at time t. b u is the regression coefficient for patch type X u. MEDIUM patch types were used as the baseline. Therefore, the risk of leaving a MEDIUM patch (i.e. the baseline hazard at time t) was represented by h0(t). INTERPATCH MOVEMENTS For each forager, we classified the transition between two successively visited patches by taking into account patch richness (POOR, MEDIUM, RICH). We tallied the frequency of each type of transition (i.e. POOR-POOR, POOR-MEDIUM, POOR-RICH, etc.). We created a contingency table from all these possibilities of interpatch movements. We compared observed and expected frequencies using G-tests (Sokal & Rohlf 1995). All transitions had the same likelihood when individuals moved randomly because patch locations within the landscape were completely random and all patch types were equally abundant. We displayed partial G-test values for all possible interpatch transitions. Negative values indicated that observed values were smaller than expected, whereas positive values indicated that observed values were greater than expected. Results Regardless of the foraging strategy, the matrix was consistently used less than expected by random chance, and it had the lowest residency time. Coefficients for the matrix were therefore not presented in Fig. 1 for simplicity. RSF, residency-time analysis and interpatch-movement analysis detected different selection or avoidance of the different food patch types, depending on the strategy. Complete results of the analyses are given in Table S1 (Supporting information). RSF results were robust to changes in the spatial extent used to define availability (Table S2, Supporting information). FORAGING STRATEGIES INVOLVING RANDOM INTERPATCH MOVEMENTS Because all patch types were equally available in individual home ranges, RSF identified patches in which foragers spent the most total time as selected. In contrast, residency-time analysis based on FPT identified the selected patches as being those in which foragers remained for the longest time periods during any given visit. Residency-time analysis thus correctly identified each of the three patch-departure rules (Fig. 1).
4 1160 G. Bastille-Rousseau, D. Fortin & C. Dussault Random movements Biased movements Resource selection function Coefficient Poor Rich Poor Rich Poor Rich Poor Rich Poor Rich Poor Rich Residency time Coefficient Poor Rich Poor Rich Poor Rich Poor Rich Poor Rich Poor Rich Interpatch movement partial G-value ( 10³) Poor- Rich- Poor- Rich- Poor- Rich- Poor- Rich- Poor- Rich- Poor- Rich- Poor Rich Poor Rich Poor Rich Poor Rich Poor Rich Poor Rich Fig. 1. Main results of resource selection function, residency-time and interpatch-movement analyses for 250 virtual foragers following one of the six resource-use strategies. The strategies involve a combination of patch-departure rules [-quitting-harvest-rate (), -time and -amount] and interpatch movements (Random and Biased). For RSF and residency-time analyses, selection was evaluated with respect to medium-quality patches (results for the matrix were not represented but always resulted in avoidance). A positive coefficient for the RSF implied relative selection, whereas a negative coefficient indicated relative avoidance. For residency-time analysis, a positive coefficient indicated a relatively high probability of leaving a patch of a given type (hence, a relatively short residency time), whereas a negative coefficient revealed a relatively low probability of patch departure. For interpatch-movement analyses, partial G-values of POOR-POOR and RICH- RICH transitions were represented for each strategy. Positive partial G-values for a given interpatch transition indicated more frequent movements than expected randomly, whereas a negative value meant less frequent movements.
5 Inferences from habitat-selection analyses 1161 Given that interpatch transitions were simply random, patch-transition analysis did not contribute at explaining the overall selection of patches, and RSF and residency-time analysis provided consistent results (Fig. 1): foragers displaying fixed-quitting-harvest-rate selected rich patches, whereas those leaving patches following the acquisition of a specific amount of food selected poor patches. FORAGING STRATEGIES INVOLVING BIASED INTERPATCH MOVEMENTS Biases in interpatch movements were such that virtual foragers spent more total time in rich patches than they did when patch transitions were simply random (Fig. 1). According to RSFs, these changes translated into a systematic selection for RICH over MEDIUM patches, regardless of the patchdeparture strategy. Residency-time analysis correctly identified the three patch-departure rules, but did not detect any difference in patch selection resulting from interpatch-movement biases (Fig. 1). Results were then qualitatively similar between RSF and residency-time analyses only when foragers followed a fixed-quitting-harvest-rate strategy (Fig. 1). By informing an alternative strategy of patch utilization, interpatch-movement analysis provided the missing link between RSF and residency-time analyses. Foragers moved selectively towards RICH patches, which explain that more time was globally spent in RICH patches as compared to when movements were random, even though the time spent by a forager in a given patch was independent of interpatchmovement decisions. Understanding the entire process of patch selection outlined by RSF thus required results from both residency-time and interpatch-movement analyses. Discussion Many management decisions rely on the interpretation of habitat-selection analyses. Residency-time analysis based on FPT has recently emerged as a promising avenue for studying habitat selection without the need to quantify resource availability (Freitas et al. 2008). Using a simple individual-based modelling approach, however, we demonstrated how inferences from this quantitative method were not sensitive to non-random interpatch movements [as discussed by Freitas et al. (2008)]. This lack of sensitivity can potentially bias habitat-selection assessments when animals do not stay longer in preferred area, and can lead analyses to violate the main assumption of Freitas et al. s (2008) methodology. There is increasing evidence that animals commonly bias their movements with respect to habitat structure and composition (Börger, Dalziel & Fryxell 2008). A priori knowledge of the validity of Freitas et al. s (2008) assumption is not always available, and we thus suggest that the use of multiple methods to evaluate habitat selection can avoid such potential issues. Selection towards a given patch type can emerge from different foraging strategies. For example, animals can stay longer in preferred areas or they can just return more frequently to this area without adjusting their residency time. Residency-time analysis would only detect selection in the case of the first strategy (i.e. longer stays in preferred areas). Our simulations thus showed that RSF and residency-time analysis are not equivalent and that they display different levels of sensitivity to foraging strategies. We suggest that RSFs characterize the overall selection process, whereas residency-time and interpatch-movement analyses can reveal mechanisms behind the selection process. The selection process can be represented by patch-departure rules varying among and within animal species, which could be modelled with various movement algorithms and yield different patterns of habitat selection. Here we used simulations based on simple foraging strategies supported by empirical observations (Valone & Brown 1989; Edwards et al. 1997; Saracco et al. 2005; Brooks & Harris 2008). We found that residency-time analysis yielded similar insights on habitat selection compared to RSF when virtual foragers moved randomly within the patch network, regardless of the patch-departure rule. When foragers oriented their movements towards specific patches, however, RSF and residencytime analysis can provide different results because RSFs are sensitive to both patterns of residency times and of transitions among patches, whereas residency-time analysis is unaffected by interpatch-movement decisions. This lack of sensitivity may have important consequences for the assessment of habitat selection by animal populations in natural systems. Many studies have demonstrated the ability of animals to direct their movements towards certain areas while adopting an extensive search mode (Fortin et al. 2005; Brooks & Harris 2008). For example, wood mice Apodemus sylvaticus L. and white-footed mice Peromyscus leucopus Rafinesque can orient their movements towards their home-range core area and forested patches, respectively (Jamon & Benhamou 1989; Zollner & Lima 1997). Given that animals commonly display non-random interpatch movements, it is of primary importance to base habitat-selection assessments on analyses that account not only for time spent in individual patches, but also for movement biases. In that respect, RSFs estimated at the scale of interest (hence with the appropriate design; Boyce 2006), or an approach combining residency-time and interpatch-movement analyses would appear suitable. Analysis of the total time spent in an area (e.g. Barraquand & Benhamou 2008), instead of the time spent during each individual visit, should yield results closer to those provided by an RSF analysis. UNCOVERING HABITAT-SELECTION STRATEGIES BY COMBINING STATISTICAL APPROACHES We suggest that a combination of residency-time and interpatch-movement analyses could efficiently unveil key mechanisms of habitat selection, and therefore, inform on adaptive behavioural decisions. Our simulations based on a fixedamount strategy revealed that RSF and residency-time analyses can gain by being combined with interpatch-movement analyses. When there was no bias towards the richest patches,
6 1162 G. Bastille-Rousseau, D. Fortin & C. Dussault both RSF and residency-time analyses identified the poorest patches as being selected. The interpretation differed, however, when animals move selectively among patches. Foragers ended up spending the same amount of time in rich and poor patches and the selection for these patch types was therefore similar. Only the combination of analyses thus provides a clear picture of the overall habitat-selection process. A few studies have already combined RSF and residencytime analysis. For example, Anderson, Forester & Turner (2008) found that elk did not display longer residency times in areas identified as selected by RSF. They concluded that space use by elk was driven by individuals returning frequently to favourable patches, and that variation in residency times by elk could reduce predation risk by making their presence more difficult to predict. Fortin et al. (2009) found that bison Bison bison L. selected meadows more strongly when part of a large rather than a small group. To explain the difference, they showed that smaller groups displayed shorter residency times in meadows than larger groups. Thus, bison departure from meadows appeared unlikely to result from a depression in food-intake rate, but was rather associated with a predator-avoidance strategy. The combination of different habitat-selection analyses thus appears particularly useful for the study of predator-prey interactions. Considering the behaviour of both the prey and the predator is necessary when developing conservation plans for threatened or endangered species (Quinn & Cresswell 2004; Courbin et al. 2009). More generally, the combination of these different statistical techniques can provide an efficient quantitative framework to enlighten our understanding of animal distribution by providing clues about environment forces driving habitat selection. Conclusion Our study points out that, unlike previous contentions, residency-time analysis does not provide the same insights as RSF in terms of habitat selection. Our study warns about the risk of choosing just any approach for studying habitat selection without having adequate knowledge of the system because the different approaches can not be considered as equivalent. We suggest that RSF, interpatch-movement and residency-time analyses can, altogether, provide the information necessary to gain a comprehensive understanding of the habitat-selection process. Understanding habitat selection is the key to the development of sound management practices that not only reflect animal distributions, but also integrate behavioural considerations. Acknowledgements This study was funded by the Natural Sciences and Engineering Research Council of Canada and the Ministère des Ressources naturelles et de la Faune du Québec. G. Bastille-Rousseau was supported by scholarships from the Natural Sciences and Engineering Research Council of Canada and the Fonds Québécois de la recherche sur la nature et les technologies. We thank C. Freitas, N. Courbin, B. Parsons and an anonymous reviewer for valuable comments on an earlier version of the paper. References Aebischer, N.J., Robertson, P.A. & Kenward, R.E. (1993) Compositional analysis of habitat use from animal radio-tracking data. Ecology, 74, Anderson, D.P., Forester, J.D. & Turner, M.G. (2008) When to slow down: elk residency rates on a heterogeneous landscape. Journal of Mammalogy, 89, Barraquand, F. & Benhamou, S. (2008) Animal movements in heterogeneous landscapes: identifying profitable places and homogeneous movements bouts. Ecology, 89, Benhamou, S. (1992) Efficiency of area-concentrated searching behavior in a continuous patchy environment. Journal of Theoretical Biology, 159, Bo rger, L., Dalziel, B.D. & Fryxell, J.M. (2008) Are there general mechanisms of animal home range behaviour? A review and prospects for future research. Ecology Letters, 11, Boyce, M.S. (2006) Scale for resource selection functions. Diversity and Distributions, 12, Boyce, M.S. & Mcdonald, L.L. (1999) Relating populations to habitats using resource selection functions. Trends in Ecology & Evolution, 14, Boyce, M.S., Vernier, P.R., Nielsen, S.E. & Schmiegelow, F.K.A. (2002) Evaluating resource selection functions. Ecological Modelling, 157, Brooks, C.J. & Harris, S. (2008) Directed movement and orientation across a large natural landscape by zebras, Equus burchelli antiquorum. Animal Behaviour, 76, Brown, J.S. & Kotler, B.P. (2004) Hazardous duty pay and the foraging cost of predation. Ecology Letters, 7, Brown, J.S. & Morgan, R.A. (1995) Effects of foraging behavior and spatial scale on diet selectivity a test with fox squirrels. Oikos, 74, Calenge, C., Dufour, A.B. & Maillard, D. (2005) K-select analysis: a new method to analyse habitat selection in radio-tracking studies. Ecological Modelling, 186, Ciarniello, L.M., Boyce, M.S., Seip, D.R. & Heard, D.C. (2007) Grizzly bear habitat selection is scale dependent. Ecological Applications, 17, Courbin, N., Fortin, D., Dussault, C. & Courtois, R. (2009) Landscape management for woodland caribou: the protection of forest blocks influences wolf-caribou co-occurrence. Landscape Ecology, 24, Cox, D.R. (1972) Regression models and life tables (with discussion). Journal of the Royal Statistical Society, B, 74, Edwards, G.R., Newman, J.A., Parsons, A.J. & Krebs, J.R. (1997) Use of cues by grazing animals to locate food patches: an example with sheep. Applied Animal Behaviour Science, 51, Fall, A. & Fall, J. (2001) A domain-specific language for models of landscape dynamics. Ecological Modelling, 141, Farnsworth, K.D. & Beecham, J.A. (1999) How do grazers achieve their distribution? A continuum of models from random diffusion to the ideal free distribution using biased random walks. American Naturalist, 153, Fauchald, P. & Tveraa, T. (2003) Using first-passage time in the analysis of area-restricted search and habitat selection. Ecology, 84, Fortin, D. (2003) Searching behavior and use of sampling information by free-ranging bison (Bos bison). Behavioral Ecology and Sociobiology, 54, Fortin, D., Morris, D.W. & Mcloughlin, P.D. (2008) Habitat selection and the evolution of specialists in heterogeneous environments. Israel Journal of Ecology and Evolution, 54, Fortin, D., Beyer, H.L., Boyce, M.S., Smith, D.W., Duchesne, T. & Mao, J.S. (2005) Wolves influence elk movements: behavior shapes a trophic cascade in Yellowstone National Park. Ecology, 86, Fortin, D., Fortin, M.-E., Hawthorne, L.B., Duchesne, T., Courant, S. & Dancose, K. (2009) Group-size-mediated habitat selection and group fusion-fission dynamics of bison under predation risk. Ecology, 90, Freitas, C., Kovacs, K.M., Lydersen, C. & Ims, R.A. (2008) A novel method for quantifying habitat selection and predicting habitat use. Journal of Applied Ecology, 45, Iwasa, Y., Higashi, M. & Yamamura, N. (1981) Prey distribution as a factor determining the choice of optimal foraging strategy. American Naturalist, 117, Jamon, M. & Benhamou, S. (1989) Orientation and movement patterns of wood mice (Apodemus sylvaticus) released inside and outside a familiar area. Journal of Comparative Psychology, 103, Johnson, D.H. (1980) The comparison of usage and availability measurements for evaluating resource preference. Ecology, 61,
7 Inferences from habitat-selection analyses 1163 Johnson, C.J., Nielsen, S.E., Merrill, E.H., Mcdonald, T.L. & Boyce, M.S. (2006) Resource selection functions based on use-availability data: theoretical motivation and evaluation methods. Journal of Wildlife Management, 70, Kaczensky, P., Ganbaatar, O., Von Wehrden, H. & Walzer, C. (2008) Resource selection by sympatric wild equids in the Mongolian Gobi. Journal of Applied Ecology, 45, Lele, S.R. & Keim, J.L. (2006) Weighted distributions and estimation of resource selection probability functions. Ecology, 87, Manly, B.F.J., Mcdonald, L.L., Thomas, D.L., Mcdonald, T.L. & Erickson, W.P. (2002) Resource Selection by Animals: Statistical Design and Analysis for Field Studies, 2nd edn. Kluwer, Boston. Mao, J.S., Boyce, M.S., Smith, D.W., Singer, F.J., Vales, D.J., Vore, J.M. & Merrill, E.H. (2005) Habitat selection by elk before and after wolf reintroduction in Yellowstone National Park. Journal of Wildlife Management, 69, Mcloughlin, P.D., Morris, D.W., Fortin, D., Vander Wal, E. & Contasti, A.L. (2010) Considering ecological dynamics in resource selection functions. Journal of Animal Ecology, 79, Moorcroft, P.R. & Barnett, A. (2008) Mechanistic home range models and resource selection analysis: a reconciliation and unification. Ecology, 89, Pinaud, D. (2008) Quantifying search effort of moving animals at several spatial scales using first-passage time analysis: effect of the structure of environment and tracking systems. Journal of Applied Ecology, 45, Quinn, J.L. & Cresswell, W. (2004) Predator hunting behaviour and prey vulnerability. Journal of Animal Ecology, 73, Saracco, J.F., Collazo, J.A., Groom, M.J. & Carlo, T.A. (2005) Crop size and fruit neighborhood effects on bird visitation to fruiting Schefflera morototoni trees in Puerto Rico. Biotropica, 37, Schultz, C.B. & Crone, E.E. (2001) Edge-mediated dispersal behavior in a prairie butterfly. Ecology, 82, Sokal, R.R. & Rohlf, F.J. (1995) Biometry: The Principles and Practice of Statistics in Biological Research, 3rd edn. W.H. Freeman, New York. Suryan, R.M., Sato, F., Balogh, G.R., Hyrenbach, K.D., Sievert, P.R. & Ozaki, K. (2006) Foraging destinations and marine habitat use of shorttailed albatrosses: a multi-scale approach using first-passage time analysis. Deep-Sea Research Part II-Topical Studies in Oceanography, 53, Trathan, P.N., Bishop, C., Maclean, G., Brown, P., Fleming, A. & Collins, M.A. (2008) Linear tracks and restricted temperature ranges characterise penguin foraging pathways. Marine Ecology Progress Series, 370, Valone, T.J. & Brown, J.S. (1989) Measuring patch assessment abilities of desert granivores. Ecology, 70, Zollner, P.A. & Lima, S.L. (1997) Landscape-level perceptual abilities in whitefooted mice: perceptual range and the detection of forested habitat. Oikos, 80, Received 14 January 2010; accepted 6 July 2010 Handling Editor: Stan Boutin Supporting Information Additional Supporting Information may be found in the online version of this article. Table S1. Summary of resource selection function, residency-time and interpatch-movement analyses for 250 virtual foragers following one of the six resource-use strategies in a landscape comprised of three patch types (poor, medium, rich) randomly distributed in equal proportions across a foodless matrix. The strategies involve a combination of patch-departure rules [-quitting-harvest-rate (), -time or -amount] and interpatch movements (Random or Biased). For RSF and residency-time analyses, selection was evaluated with respect to medium-quality patches. A positive coefficient for the RSF implied relative selection, whereas a negative coefficient indicated relative avoidance. For residency-time analysis, a positive coefficient indicated a relatively high probability of leaving a patch of a given type (hence, a relatively short residency time), whereas a negative coefficient revealed a relatively low probability of patch departure. For interpatch-movement analyses, partial G-values of transitions were represented for each strategy. Positive partial G-values for a given interpatch transition indicated more frequent movements than expected randomly, whereas a negative value meant less frequent movement Table S2. Resource selection functions of 250 virtual foragers estimated based on a paired design for which 10 random locations were drawn within a 25-cell radius circle of each observed location. Foragers were following one of the six resource-use strategies in a landscape comprised of three patch types (poor, medium, rich) randomly distributed in equal proportions across a foodless matrix. The strategies involve a combination of patch-departure rules [quitting-harvest-rate (), -time and -amount] and interpatch movements (Random and Biased). Selection was evaluated with respect to medium-quality patches. A positive coefficient implied relative selection, whereas a negative coefficient indicated relative avoidance As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.