Improving rigour and efficiency of use-availability habitat selection analyses with systematic estimation of availability

Authors


Summary

  1. Animal habitat selection analyses often rely on comparisons of habitat use and availability to infer selection. Random locations are commonly used to assess availability despite inefficiency and potential uncertainty associated with random sampling. Herein, I propose a systematic approach to estimate habitat availability to reduce sampling error and computing time associated with GIS-based estimation of habitat availability using random locations.
  2. I used Euclidean distance analysis (EDA) as a model technique to demonstrate the sensitivity of use-availability analyses to insufficient random sampling and to evaluate the proposed systematic approach. I re-analysed data from a previous study of habitat selection of Florida panthers (Puma concolor coryi) and compared results of analyses in which distance-based habitat availability (i.e. expected distance) was estimated with a range in sample sizes of random locations, and also systematically.
  3. My results demonstrate that expected distances and statistical results of EDA based on random sampling can be unreliable with low and arbitrary numbers of random points, vary if increasing numbers of points are used, and approach results obtained systematically at greater numbers of points (i.e. with sufficient sampling).
  4. The systematic approach efficiently measures habitat availability by making calculations from all possible locations, at a specified resolution, across the scale of interest. Thus, it eliminates uncertainty due to sampling error and is considerably faster. The systematic approach improves rigour and efficiency of animal habitat selection analyses that rely on comparisons of habitat use and availability and ensures repeatability of results for practical and theoretical applications.

Introduction

Statisticians have long debated the relative merits of systematic vs. random sampling (Barbacki & Fisher 1936; Gossett 1938; Yates 1939; Greenberg 1951). In the early 20th century, two statistical pioneers debated this issue as R.A. Fisher was a staunch proponent of strict randomization designs (Fisher 1926; Barbacki & Fisher 1936), whereas W.S. ‘Student’ Gossett criticized Fisher's views and argued that systematic approaches were superior (Gossett 1936, 1938). Hurlbert (1984) reviewed this debate and concluded that Gossett's (1938) basic arguments regarding the strengths of systematic designs seemed irrefutable. However, Hurlbert (1984) also noted that Fisher's views (e.g. Barbacki & Fisher 1936; Fisher 1971), despite being somewhat irrational in terms of his intolerance for any departure from strict randomization, had a more profound influence on the statistical literature of the subject, partly because he outlived Gossett and published much more extensively. A central argument against systematic approaches is that they may lead to a sampling bias if there is a systematic pattern (periodicity) in the variation being studied (Yates 1939; Greenberg 1951). Currently, environmental variation is often sampled using Geographic Information Systems (GIS) where fine-scale sampling is more feasible than it was with traditional field-based sampling efforts, making the potential for confounding periodicity less of a concern. Indeed, with GIS it is often possible to systematically assess environmental variation at a fine-scale such that it can hardly be considered sampling at all, as complete knowledge of the variation of interest is attained at the appropriate resolution.

Quantifying animal habitat selection by comparing habitats used with those available is a fundamental analytical framework for studies of wildlife-habitat relationships (e.g. Neu, Byers & Peek 1974; Johnson 1980; Aebischer, Robertson & Kenward 1993; Manly et al. 2002; Beyer et al. 2010). Conner & Plowman (2001) and Conner, Smith & Burger (2003) proposed a Euclidean distance-based approach for the comparison of animal habitat use with habitat availability to determine specific habitats that are selected and/or avoided. Use of Euclidean Distance Analysis (EDA) has since become widespread in practical and theoretical studies of animal habitat selection (Appendix S1), likely because of several analytical advantages of distance-based analyses relative to classification-based techniques (Conner & Plowman 2001; Conner, Smith & Burger 2003, 2005; but see Dussault, Oeullet, & Courtois 2005; Bingham, Brennan & Ballard 2010). As originally described, EDA relies on random sampling in a GIS environment to determine mean distances to each habitat, which are then compared with distances from animal locations to these habitats to assess whether animal locations are closer (implying selection) and/or farther (implying avoidance) than random locations (Conner & Plowman 2001; Conner, Smith & Burger 2003). The mean distances from random locations to each habitat are used as the estimate of habitat availability (in a distance-based context) and are referred to as expected distances (i.e. distances expected under a null hypothesis of no selection; Conner & Plowman 2001; Conner, Smith & Burger 2003). Conner & Plowman (2001) stated that numerous random locations should be generated throughout the appropriate scale of selection and that numerous should be defined by stability in the mean distances to each habitat type. Clearly, these mean distances will vary when smaller numbers of random points are used depending on their random placement in relation to habitat features, but should stabilize at some unknown threshold number of points above which the distances will not change appreciably if greater numbers of points are used.

Any sampling regime will require some minimum level of effort to adequately capture the variation of interest; however, the importance of determining the sufficient number of random points needed to estimate expected distances for EDA has apparently not been recognized by most researchers. I conducted a literature search yielding 41 studies published from 2003 to 2011 (see Appendix S1) that used EDA to study animal habitat use. Only 5 (12%) reported testing to determine whether a sufficient number of random points were used (Van Etten, Wilson & Crabtree 2007; Moyer, McCown & Oli 2008; Obbard et al. 2010; Onorato et al. 2011) or otherwise accounted for variability due to random sampling (Parra 2006), whereas 9 (22%) did not even report the number of random locations used (Appendix S1). Most researchers seem to have arbitrarily selected a number of random points to use for the analysis and assumed this number was numerous sensu Conner & Plowman (2001). Thus, the potential sensitivity of EDA to sampling error associated with low and arbitrary numbers of random locations has not been adequately addressed by the majority of researchers employing the technique. Exhaustive testing (i.e. for each animal and all habitat types) is necessary to ensure that robust (i.e. repeatable) expected distances are produced, but this is computationally intensive and extremely time consuming, which probably explains why most studies have not done so.

Herein, I propose a systematic approach for calculating habitat availability for habitat selection studies that eliminates the uncertainty associated with random sampling and the need for time-consuming testing. To demonstrate the sensitivity of use-availability analyses to the number of random points used, investigate the potential for spurious results with insufficient random sampling, and evaluate the systematic approach, I re-analysed data from a previous study employing EDA to study habitat selection of the highly endangered Florida panther (Puma concolor coryi) by Kautz et al. (2006). Specifically, I conducted EDA with the same panther location data, but with increasing numbers of random points and the systematic approach to calculate expected distances. I hypothesized that: (i) expected distances based on different sets and sample sizes of random points would vary, and this variation would lead to different statistical results in EDA; (ii) mean expected distances from random sampling would stabilize (sensu Conner & Plowman 2001) at greater numbers of points and would approach expected distances calculated with the proposed systematic approach; (iii) statistical results with greater numbers of random points (i.e. once random sampling was sufficient) would be similar to those obtained using the systematic approach. My results will provide guidance to future studies to ensure that rigorous, repeatable results can be efficiently obtained when employing use-availability habitat selection analyses such as EDA.

Materials and methods

Euclidean Distance Analysis (EDA) with Random or Systematic Approaches

Euclidean distance analysis (EDA) utilizes observed animal locations and compares distances from these locations to each habitat type of interest with the mean distance to these habitats across the area considered available to the animal at the scale of interest. Johnson's (1980) 3rd order habitat selection is achieved with EDA by comparing distances from animal locations to each habitat type with distances from random locations distributed across each animal's home range to the same habitat types (Conner & Plowman 2001; Conner, Smith & Burger 2003). Johnson's (1980) 2nd order habitat selection is achieved with EDA by comparing distances to habitat types from random locations distributed across the individual animal home ranges to distances from random locations distributed across the study area to the same habitat types (Conner & Plowman 2001). As discussed above, it is important to determine the number of random points needed to achieve stable mean expected distances, which can be a time-consuming process that has only rarely been done in previous studies employing EDA (Appendix S1).

Alternatively, I propose that random points, and associated testing, are unnecessary and that robust expected distances can be obtained by systematically calculating the mean distance to each habitat type across the home ranges or study areas using gis software. This can be done by creating a raster (map composed of pixels) for each of the habitat types across the study area and calculating the distance from the centre of each pixel to the closest representation of that habitat type. Then, animal home ranges or the entire study area can be intersected with the distance raster for each habitat type to calculate mean expected distances to each habitat type for 3rd and/or 2nd order analyses, respectively. Thus, with the systematic approach, distances from the centre of evenly distributed pixels replace the distances from randomly distributed points. If conducted with a pixel size matching the resolution of the habitat layer, this method produces robust mean expected distances suitable for EDA, in which distance measurements are made from every pixel across the habitat map. Creating distance rasters with pixel sizes lower than the minimum pixel size of habitat features, will not provide additional realistic information, but can greatly increase computing time.

For my analyses, after systematically and/or randomly sampling expected distances to each habitat type across the study area, I created distance ratios (mean observed distance/mean expected distance) for each individual animal in relation each habitat type and tested the hypothesis that observed habitat use did not differ from a random or systematic pattern using multivariate analysis of variance (manova) as described by Conner & Plowman (2001) and Conner, Smith & Burger (2003). If these distance ratios differed from a vector of 1′s (i.e. manova was significant at < 0·05), then I used univariate t-tests on the distance ratios of each habitat to determine which were significantly different than 1. Distance ratios < 1 indicated selection, whereas ratios > 1 indicated avoidance for a given habitat (Conner & Plowman 2001; Conner, Smith & Burger 2003). Finally, I created a habitat ranking matrix using univariate paired t-tests between individual habitat types to rank habitats in order of preference (Conner & Plowman 2001; Conner, Smith & Burger 2003). All statistical analyses were performed in sas v9·0 (SAS Institute Inc., Cary, NC, USA) using the code provided in Conner & Plowman (2001).

Re-Analysis of Euclidean Distance Analysis (EDA) of Kautz et al

Kautz et al. (2006) generated 5000 random points within a 13546·8 km2 minimum convex polygon (MCP) created with panther telemetry data from 79 Florida panthers > 2 years old to calculate expected distances to 16 habitat types in south Florida across the occupied range of the Florida panther. I generated eight sets of 5000 random points using the ‘genrandompnts’ command in Geospatial Modelling Environment v0·5·4 beta within the same MCP used by Kautz et al. (2006). If the 5000 random points used in the original analysis were a sufficient sampling effort then the expected distances calculated with different sets of 5000 random points should have produced similar results. If the results were not similar, this would be evidence of insufficient random sampling, highlighting the importance of either testing with greater numbers of random points or using the proposed systematic approach. I used distances from panther locations (observed data) calculated by Kautz et al. (2006) for my analyses to ensure that any differences between our results were due to changes in mean expected distances rather than changes in animal location data. I used the same GIS landcover layer of south Florida described in Kautz et al. (2006) with 16 habitat types and a 30 m pixel size for my analyses. For all analyses with random points, I calculated mean distances from random locations to the closest representation of each habitat type using the ‘Near’ function in the ‘Analysis (Proximity)’ extension for arcgis 10 (ESRI, Redlands, CA, USA) to construct the distance ratios needed for EDA. I recorded distances from points falling within a given habitat type to that same habitat type as 0 following Conner & Plowman (2001) and Conner, Smith & Burger (2003).

Kautz et al. (2006) reported that they included data from all panthers (= 79) for which > 50 telemetry locations were available, and excluded data from panthers for which < 50 locations were available. However, while extracting data for analysis using the panther telemetry database and sas code provided by Kautz et al. (2006), it came to my attention that an error in their sas procedure resulted in data from eight panthers with < 50 locations being included (range 11–47) and data from eight panthers with > 50 locations being excluded in their original analysis. The authors have acknowledged this error (R. Kautz, Breedlove, Dennis and Associates Inc., and R. Kawula, Florida Fish and Wildlife Conservation Commission, personal communications). Therefore, I conducted separate EDAs with 5000 random points using their original panther data set (including the database error, hereafter referred to as the actual data set) and the panther data set described in the methods (without the database error, hereafter referred to as the intended data set). Given that I was interested in using these analyses to evaluate methodology, rather than test biological hypotheses, using both the actual and intended data sets was useful because it allowed me to observe differences in the results of analyses with slightly different data sets.

To test my hypotheses, I first calculated mean expected distances to each of the 16 habitat types for eight separate sets of 5000 random points, generated within the MCP described by Kautz et al. (2006) and plotted the results for each habitat type to visually assess variation in results. Next, I used mean distances from the actual and intended data sets, calculated by Kautz et al. (2006), and combined them with expected distances from each set of 5000 random points to create observed/expected ratios and conducted separate EDAs with the two data sets. The variability between results of my analyses with 5000 random points and those of Kautz et al. (2006) was much greater than variability between results of the multiple EDA's conducted with sets of 5000 random points that I generated (see Appendix S2). These disparities represented more drastic differences than those due only to changes in methodology for generating expected distances, suggesting additional errors in the analysis or interpretation of results by Kautz et al. (2006; see Appendix S2 for additional details). My objective was to evaluate methodology for calculating expected distances, rather than to evaluate the analyses of Kautz et al. (2006) per se. Therefore, I tested my hypotheses and based all inferences regarding the relative strengths of systematic and random sampling of expected distances on analyses with different sets of expected distances that I generated [rather than to the results reported by Kautz et al. (2006)]. This was done to ensure that any differences could be attributed definitively to methodology for calculating expected distances, rather than to other (unknown) sources of error.

Next, I generated 7500, 10 000, 25 000, 50 000, 75 000, 100 000, 200 000 and 400 000 random points within the study area. I calculated expected distances from each set of points, combined them with the actual and intended observed panther distances, and conducted two sets of eight EDAs with the increasing numbers of points. I conducted two final EDAs, using the actual and intended panther data sets as observed distances, with the systematic approach described above to generate mean expected distances. Specifically, I generated distance rasters with a 30 m pixel size to match the resolution of the habitat map using the ‘Euclidean Distance’ tool in the ‘Spatial Analyst (Distance)’ extension in arcgis 10. Then, I intersected the MCP of the study area with distance rasters for each habitat type using the clip function in the ‘raster processing’ tool of the ‘Data Management Tools (Raster)’ extension in arcgis 10 (Fig. 1). This resulted in distance rasters of the study area for each habitat type with associated mean expected distances based on measurements from 1111 systematic locations within every 1 km2 across the study area (> 15 million distance measurements to each habitat type total). As with random points, all systematic points falling within a given habitat type were given a distance of 0 to that habitat type. I compared the results of all EDA based on random or systematic sampling of expected distances to investigate variability of statistical results.

Figure 1.

Process for systematically calculating the mean expected distance to a given habitat type across a study area in ArcGis 10. (i) Begin with a raster or shapefile of a given habitat type (e.g. cypress) from your habitat layer. (ii) Create a distance raster of the habitat type using the ‘Euclidean distance’ tool in the ‘Spatial Analyst (distance)’ extension. (iii) Intersect the cypress distance raster with the study area polygon using the ‘clip’ function in the ‘raster processing’ tool in the ‘Data Management (raster)’ extension. (iv) The result is a distance raster with mean expected distance to cypress across the entire study area at a specified resolution.

Raster-based distance calculations, such as those made with the ‘Euclidean Distance’ tool in arcgis 10, are made from the centre of each pixel (systematic points) to the centre of the outermost pixel of the nearest patch of the habitat feature of interest, rather than to the edge of the habitat feature as described in the original EDA technique (Conner & Plowman 2001; Conner, Smith & Burger 2003). The small amount of additional distance to the centre of the pixel did not represent a problem on its own as it was below the resolution of the habitat map. However, because measurements from random points were made to habitat edges, I adjusted the systematic measurements to eliminate this discrepancy and avoid biasing estimates of systematic expected distances high relative to random expected distances (see details in Appendix S3). Methodology for these corrections will also be useful for researchers wishing to standardize observed and expected distances (see Appendix S3).

Calculation of Computing Time

I recorded the processing time of expected distances for Euclidean distance analyses (EDA) using both random and systematic approaches to compare the computing time required for these methods. For the systematic method, I recorded the amount of time it took to: (i) generate a distance raster map for each of the 16 habitat types and (ii) clip the distance raster with the study area MCP (which automatically calculates average distance to the habitat feature). For the random approach, I recorded the time it took to: (i) generate a sample of random points of a given size and (ii) calculate the average distance from these points to each of the 16 habitat types. I used a Toshiba Qosmio notebook (Toshiba America Information Systems, Inc., Irvine, CA, USA) with the windows 7 (64-bit version) operating system, a 2·0 GHZ clock speed and 8 GB memory for all analyses.

Results

Results of manova tests for all EDA were highly significant (Wilk's λ = 0·029–0·035, F16,63 = 110·1–132·5, all < 0·001), indicating panthers exhibited habitat selection in each analysis. Mean expected distances were variable with different sets of 5000 random points generated within the study area (Fig. 2a,b). Mean expected distances also varied with increasing numbers of random points, but stabilized (sensu Conner & Plowman 2001) with greater numbers of points and approached expected distances obtained with the systematic approach (Fig. 3a,b). The variability in expected distances manifested in different statistical results, as results of EDA with 5000 and 7500 points differed from results with greater numbers of points, and the systematic approach, regarding which habitat types panthers were significantly closer to or farther from for both the intended (Table 1) and actual (Appendix S2, Table 2) data sets. Specifically, there were differences in results and conclusions regarding panther use of freshwater marsh, barren land and open water habitat types for analyses of intended data set with < 10 000 random points (Table 1). Results from paired t-tests used to determine relative preference of habitat types were also variable with < 200 000 and < 10 000 random points for the actual (Table 2) and intended (data not shown) panther data sets, respectively.

Table 1. Comparison of results of five Euclidean distance habitat analyses for Florida panthers using identical panther dataa with different sets of random points or the systematic approach to generate mean expected distances to each habitat. Shown are P values and conclusions from t-tests to determine which habitats were selected and avoided (α = 0·05). Results for 12 additional habitat types are not shown as results showed strong selection in all analyses (< 0·001). Note variable results for some habitat types with lower numbers of random points and similarity of results with 400 000 random points and systematic approach
 Random points (= 5000)Random points (= 5000)Random points (= 7500)Random points (= 400 000)Systematic approach (30 m pixels)
P Conclusion P Conclusion P Conclusion P Conclusion P Conclusion
  1. a

    Intended panther data set as explained in methods (i.e. 79 panthers with > 50 telemetry locations) calculated by Kautz et al. (2006).

  2. b

    Panthers were not significantly closer or farther from the habitat (P > 0·05).

Freshwater marsh0·131NSb0·023Select0·118NSb0·038Select0·033Select
Barren0·033Select0·086NSb0·036Select0·022Select0·022Select
Scrub0·004Select0·001Select0·002Select0·004Select0·004Select
Open water0·070NSb0·044Avoid0·068NSb0·097NSb0·090NSb
Table 2. Habitat ranking matrix results from EDA reported in Table 1 of Kautz et al. (2006) and re-analyses using the actuala panther data set for observed distances and (i) increasing numbers of random points and (ii) the systematic approach to generate expected distances. Panther use of habitats with the same letter did not differ based on paired t-tests (> 0·05). Results with 400 000 random points did not differ from 200 000 random points or systematic approach and are not shown
 Kautz et al. (2006)5000 points7500 points10 000 points25 000 points50 000 points75 000 points100 000 points200 000 pointsSystematic points
  1. a

    Actual panther data set consisted of distances from panther locations to each habitat type calculated by Kautz et al. (2006) that included 71 panthers with > 50 telemetry locations and eight panthers < 50 locations as described in the methods.

CypressAAAAAAAAAA
PinelandsABAAAAAAAAA
Hardwood swampBCABABABABABABABABAB
Dry-prairieDEBBBBBBBBB
Upland forestCDBCBCBCBCBCBCBBCBC
Pasture/grasslandEFBCBCBCBCBCBCBCBCBC
Unimproved pastureFBCBCBCBCBCBCBCBCBC
Shrub and brushFCDCCCCDCCCC
UrbanGDEDDDDEDDDD
Orchard/citrus groveGEDEDDEDDDD
CroplandGEDEDDEEFDEDDD
Coastal wetlandsGEEFDEDEEFDEDDEDE
Freshwater marshHFFGEFEFFGEFEEFEF
Barren landHFGFFGFEFF
ScrubHFGFFGFEFF
Open waterIGHGGHGFGG
Figure 2.

(a and b) Expected distances to freshwater marsh and open water habitat types with eight separate sets of 5000 random points (5000-1–5000-8), 200 000 (200 K) random points, and the systematic approach. Note variability across different sets of 5000 points [which manifested in variable statistical results in Euclidean distance analysis (EDA)] and similarity between results with 200 000 random points and systematic approach (which yielded identical results in EDA). Variance of mean expected distances is not incorporated into EDA, thus no error bars are shown.

Figure 3.

(a and b) Expected distances to barren land and shrub/brush habitat types in south Florida with increasing numbers of random points and the systematic approach. Variance of mean expected distances is not incorporated into Euclidean distance analysis (EDA), thus no error bars are shown.

The systematic approach was considerably quicker, in terms of computing time, than using random points regardless of the number of points used (Table 3). As the number of random points increased, differences in computing efficiency between the two approaches became much greater (Table 3).

Table 3. Computing time for calculating expected distances to 16 habitat types in South Florida using different numbers of random points or the proposed systematic approach
 HoursMinutesSeconds
5000 random points03959
7500 random points15347
10 000 random points22222
25 000 random points4751
50 000 random points8294
75 000 random points980
100 000 random points182932
200 000 random points24338
400 000 random points503439
Systematic approach0238

Discussion

Systematic sampling of expected distances to habitat types is an effective and efficient method for generating robust expected average distances for EDA. Distance raster maps with user-specified pixel sizes can be produced easily using GIS software making it possible to quickly generate systematic expected distances across home ranges or study areas, even for animals with large space requirements. The random sampling approach traditionally employed with EDA, and other use-availability analyses, requires time-consuming testing with successive numbers of points and computing time was slow for calculating average expected distances at higher numbers of points. Furthermore, landscapes that require large numbers of random points to achieve stable mean expected distances are essentially achieving quasi-systematic coverage of the study area using a random approach. Indeed, Hurlbert (1984) noted that ad-hoc (non-systematic) efforts to achieve adequate interspersion between sampling points often produce a marked degree of regularity in the experimental layout, such that randomization may produce near-systematic layouts. For estimating habitat availability in GIS, a more direct and efficient approach is to standardize the interspersion between points by systematically sampling at the resolution of the habitat map.

A classical objection to systematic sampling approaches is that there may be some regular-spaced pattern (periodicity) in the variation the researcher is attempting to sample, which can lead to biased results if the sampling grid corresponds with this pattern (Yates 1939; Greenberg 1951). Hurlbert (1984) noted that this risk is quite small in most field studies and periodicity is not relevant to systematic calculation of expected distances as proposed here. The use of a pixel size equal to the smallest habitat patch ensures that a single systematic point will fall in all habitat patches regardless of any periodicity that could exist in the dispersion of habitat types across the landscape. If one considers the grid imposed on the study area using the systematic approach, it is easy to visualize that even intensive random sampling would likely result in multiple points occurring in some grid cells and no points occurring in other cells. Thus, distances from some areas would be oversampled, whereas distances from other areas would not be sampled at all. The systematic approach ensures that distances from a single point in each of these cells would be used to calculate the mean expected distance, resulting in a more efficient and accurate calculation of habitat availability.

Deriving the mean expected distances with the systematic approach at 30 m resolution took < 3 min of computing time and was considerably quicker than achieving stable results with 200 000 and 10 000 random points for the actual and intended panther data sets, respectively. It's worth noting that the computing time associated with using random points will generally be much longer than those reported in Table 3, because one would have no way of knowing that 200 000 or 10 000 random points were sufficient without testing. Thus, testing at a range of random points would further increase computing time and would not produce any results useful for the biological questions of interest. Using the systematic approach eliminates uncertainty and time-consuming testing associated with random sampling by efficiently providing systematic coverage of the study area, requiring only a single run of the analysis.

For habitat maps that are not pixel based, such as those digitized manually along with interpretation of aerial photography, there may not be a specified resolution. In these instances, I would suggest selecting the pixel size equal to the size of the smallest habitat patch defined by the habitat layer. I tried using a pixel size smaller than the resolution of the habitat map (5 m) to compare results with those at 30 m resolution. The expected distances generated with 5 m pixel were very similar (within 0–4 m) to those obtained with a 30 m pixel size results, and the results of EDA were identical (Appendix S4). Thus, although computing time increased substantially with the smaller pixel size, it did not result in any additional information (Appendix S4). However, there were no negative effects of sampling below the resolution of the habitat map beyond the reduced computational efficiency as the results were identical.

In addition to EDA, systematic calculation of habitat availability is appropriate for other habitat selection analyses that utilize random points to estimate habitat availability. For example, it is applicable to resource selection functions (RSF) that have become increasingly prevalent (Manly et al. 2002; McLoughlin et al. 2010). Indeed, while evaluating GIS and statistical approaches relevant to habitat selection studies, Erickson, McDonald & Skinner (1998) used systematic sampling to assess availability in a case study with an RSF, and noted the excellent interspersion achieved by systematic sampling. However, Erickson, McDonald & Skinner (1998) sampled every 13th pixel rather than using all 30 m pixels, citing limitations in computing resources. With advances in technology, computer processing power is no longer an obstacle to thorough pixel-based habitat sampling, as evidenced by my rapid calculation of distances from all 30 m pixels to 16 habitat types across a large study area on a laptop computer. Manly et al. (2002, p. 101) also concluded that systematic sampling would be a valid approach to estimate habitat availability for RSF's and noted the importance of using a large enough sample of available units such that sampling error is negligible. However, despite early recognition that systematic calculation of habitat availability is a valid and effective approach for RSF's, and the subsequent elimination of computer processing limitations associated with advancing technology, random points continue to be the standard approach for RSF's. The methodology I propose could easily be adapted to efficiently derive accurate estimates of habitat availability for use with RSF's and other habitat analyses that employ random points. However, as there are many different ways to conduct RSF's, researchers may need to consider additional details that are not covered here to ensure that the resulting estimates of availability are suitable for use within their specific analytical design. I note that systematic (or random) estimation of habitat availability is not necessary or relevant for classification-based analyses where the proportions of each habitat available can be derived from the habitat map and used directly in the analysis (e.g. compositional analysis; Aebischer, Robertson & Kenward 1993).

My analyses show the potential problems associated with using arbitrary and small numbers of random points without adequate testing to ensure that stable expected distances are achieved. The results were variable with respect to which habitats were selected and avoided, and the relative preference of these habitat types by panthers, until a sufficient number of points were used. Inadequate sampling of expected distances introduced a source of error into the analysis that can be eliminated with the systematic approach. When sampling error from expected distances is combined with other sources of error that are more difficult to avoid, and present in virtually all habitat selection studies (e.g. telemetry error, GIS error), the cumulative effect may result in erroneous conclusions with serious theoretical or conservation implications. In the example presented here, results and inferences regarding selection and avoidance of three habitat types (freshwater marsh, barren and open water) varied between significance and insignificance across trials with lower numbers of random points. That, these results have been applied to habitat management efforts for a highly endangered species highlights the potential practical consequences of insufficient random sampling of expected distances in EDA. The results of the EDA conducted by Kautz et al. (2006) are currently used, along with results from other analyses [i.e. Cox, Maehr & Larkin 2006; Land et al. 2008; and other analyses from Kautz et al. (2006)] to guide habitat management for the federally endangered Florida panther on private lands in south Florida (D. Land, Florida Fish and Wildlife Conservation Commission, personal communication). Fortunately, despite problems with their analysis and resulting inaccuracies regarding selection or avoidance of certain habitat types, many of the results of the EDA conducted by Kautz et al. (2006) are consistent with other panther habitat selection studies (e.g. with respect to strong selection for forested habitat types, Cox, Maehr & Larkin 2006; Land et al. 2008; Onorato et al. 2011). These consistencies have likely mitigated potential consequences of the practical application of these results. Nonetheless, future studies employing EDA should use the systematic approach to prevent information based on flawed analyses from being applied to conservation or management efforts.

It is worth noting that Kautz et al. (2006) did not assess habitat selection at a previously described order of selection, but instead compared distances from panther telemetry locations with mean distances from random points distributed across the study area to each habitat type. If the objective was to investigate habitat use based on individual locations of resident panthers (i.e. 3rd order selection), the expected distances should have been calculated within home ranges (Johnson 1980; Conner & Plowman 2001). Alternatively, if the objective was to investigate selection of home ranges from the landscape (i.e. 2nd order selection), the appropriate observed data would be random (or systematic) points distributed throughout the home range (Conner & Plowman 2001). Comparing habitat use based on animal locations restricted to home ranges to habitat availability across the entire south Florida study area, as in the EDA of Kautz et al. (2006), did not assess habitat selection at a meaningful scale, and the results reflected this. When I used the intended observed data and sampled expected distances sufficiently, the results of the EDA designed by Kautz et al. (2006) showed that panthers were significantly closer to 15 of 16 habitat types. The only habitat type that panthers were not significantly closer to was open water. These results would seem to contribute little, if any, useful information to panther habitat conservation efforts in south Florida. Given the insufficient random sampling of expected distances, the poorly defined order of selection, and other problems (see Appendix S2), I recommend that the results of the EDA conducted by Kautz et al. (2006) no longer be applied to panther management efforts. I did not review other analyses conducted by Kautz et al. (2006) that are also used to guide panther management efforts, thus my recommendation applies only to the results of their EDA.

Acknowledgements

R. Kawula provided original panther data from Kautz et al. (2006). Discussions with E. Howe, R. Kawula, D. Land, P. Mahoney, C. Narr, B. Pond, J. Schaefer, J. Smith and A. Walpole improved this work. R. Kautz, R. Kawula, D. Land, C. Narr, B. Patterson, and three anonymous reviewers provided useful comments on earlier drafts of this manuscript.

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