Here we build on previous work to demonstrate a new technique for visualizing potential ETs and their uncertainty: we apply a partitioning method to limited and initially spatially autocorrelated Andean bear data from the Cordillera de Mérida to generate partially independent subsets, and fit a previously developed spatial model of poaching probability for the species (Sánchez‐Mercado et al ., 2008 ) to the first subset. We then combine replicates of this with replicates of the best of several models of occurrence probability (fit and validated with the remaining partitions) to identify potential traps. In addition to demonstrating a novel technique for identifying potential ETs and their uncertainty by applying it to a real case, we aimed to consider the implications of our results for managing taxa where ETs may be present. We focused on the Cordillera de Mérida in Venezuela because it is the only portion of the Andean bear range for which a compiled database of hunting records and species presence exist (Sánchez‐Mercado et al ., 2008 ), and because an analysis at this scale is also useful for national‐level conservation planning (Yerena et al ., 2007 ).

The Andean bear Tremarctos ornatus is an example of a threatened species whose conservation depends greatly on the appropriate management of both its habitat and one of its principal threats, poaching (Rodríguez et al ., 2003 ). Despite the global impacts of hunting on animal populations (Fa, Peres & Meeuwig, 2002 ) and the recognition that hunting can create ETs by increasing mortality in preferred habitats (Martínez‐Abraín et al ., 2007 ; Abrams et al ., 2012 ), hunting has been little studied as a cause of ETs. Like the grizzly bear Ursus arctos , which has little perception of hunting risk (Nielsen et al ., 2006 ), Andean bears may be susceptible to ETs. However, their low population density, elusive behavior and remote habitat have hampered efforts to identify critical habitat and areas with high poaching pressure (García‐Rangel et al ., 2008 ). SDMs developed to date for the Andean bear have been restricted to small areas (Cuesta, Peralvo & Sánchez, 2000 ; Ríos‐Uzeda, Gómez & Wallace, 2006 ), whereas distribution maps across larger areas have been based only on expert opinion (e.g. Peralvo, Cuestas & van Manen, 2005 ), ignoring spatial variation in bear occurrence.

Spatial modeling techniques that combine maps of anthropogenic threats with SDMs present one promising means of identifying both potential ETs – patches with both high threat and occurrence probability – as well as potentially safe harbors (SHs), or patches with reduced threat but high occurrence probability (Nielsen, Stenhouse & Boyce, 2006 ). However, previous studies using this general approach have focused on short time spans relative to both anthropogenic threats and the study species' lifespan (Nielsen et al ., 2006 ), have inappropriately combined anthropogenic threats and SDMs fit to different spatial regions (Nielsen et al ., 2006 ), have failed to quantify fitness costs associated with anthropogenic activity, or have provided no explicit estimate of spatial uncertainty in the distribution of trap habitats (Naves et al ., 2003 ; Northrup, Stenhouse & Boyce, 2012 ).

ETs are known to threaten the persistence of affected populations (Fletcher, Orrock & Robertson, 2012 ), but identifying them is a challenge. Obtaining replicated empirical evidence illustrating an inverse relationship between habitat preference and fitness in focal habitat patches can be logistically difficult, time consuming and expensive, particularly at larger spatial scales (Robertson & Hutto, 2006 ). Techniques are needed to visualize the spatial distribution of potential ETs across entire landscapes such that management actions can be strategically applied to manage ETs under financial constraints and with a full understanding of potential uncertainties. Such methods ideally should be robust to small datasets, which are common in regions where field capacity and funds are limited.

Predicting species distributions is fundamental to conservation planning (Johnson & Gillingham, 2005 ). Potential distributions may be estimated using species distribution models (SDMs), which associate species occurrence with biophysical and ecological variables, and presume that areas with high occurrence probabilities predict high‐quality habitat (Guisan & Thuiller, 2005 ). However, anthropogenic effects such as poaching may increase mortality in these areas in ways that animals are unable to detect (Battin, 2004 ; Abrams et al ., 2012 ). If a species actively selects its habitat, but environmental cues do not reflect this increased mortality (e.g. Martínez‐Abraín et al ., 2007 ), high‐quality habitat can become an attractive sink, or ecological trap (ET; Schlaepfer, Runge & Sherman, 2002 ).

Materials and methods

Study area The Andean bear is classified as Vulnerable globally (IUCN, 2010) and is found only in the Andes, in South America. In Venezuela, this mountain range consists of the Cordillera de Mérida and the Sierra de Perijá, where the Andean bear is Endangered because of poaching and habitat loss (Fig. 1a; García‐Rangel et al., 2008). Given the scarcity of bear observations in the Sierra de Perijá, we focused only on the Cordillera de Mérida. The study area of 43 296 km2 (i.e. 10 821 ∼ 2 × 2‐km cells) spanned the range of altitudes (250–5000 m) and habitat types (a complex mosaic of wet and dry forests including montane meadows, or páramo) known to be used by Andean bears (García‐Rangel, 2012). Protected areas presently cover 25% of the region (Fig. 1b; Yerena, 1998), with towns, roads and agricultural development concentrated at lower altitudes (Vila, Brito Figueroa & Cárdenas, 1965). Human population density exceeds 163 individuals/km2 and is growing rapidly (INE, 2011). We used a 4‐km2 resolution because it was similar to or smaller than home range sizes reported for the species (Castellanos, 2011) and was sufficiently fine to divide the study area into a large number of cells and to ensure that the entire range of values reported for predictive variables was represented (data not shown). Figure 1 Open in figure viewerPowerPoint (a) Cordillera de Mérida (>250 m, shaded) relative to national borders. Light gray lines indicate state boundaries. (b) Cordillera de Mérida, showing study area (light gray) and towns >5000 people (black points). Protected areas (medium gray): (1) Terepaima, (2) Yacambú, (3) El Guache, (4) Dinira, (5) Guaramacal, (6) Teta de Niquitao‐Güirigay, (7) Sierra Nevada, (8) La Culata, (9) Tapo Caparo, (10) Páramos Batallón and La Negra, (11) Chorro El Indio, (12) El Tamá.

Poaching and occurrence data We compiled 844 bear reports as described in detail in Sánchez‐Mercado et al. (2008). Reports comprised poaching events, direct sightings and signs, and physical remains of natural deaths. Briefly, these came from scientific publications spanning 1940–2004, unpublished field and interview data from S. G.‐R., and from interviews with D. Torres (Fundación AndígenA, Mérida) and H. Zambrano (EcoVida, Táchira). We then discarded records without detailed location information, with no date or from before 1960 (when predictor variables were unavailable; Hijmans et al., 2005). This left us with 196 georeferenced reports from 1960 to 2005. To use records for poaching estimates, we assigned each a value of 1 or 0 for the variable poach, which identified it as being an event of poaching (1) or not (0). To use records for occurrence estimates, all were considered as records of presence, whether they pertained to poaching events or not. Our bear data were not only limited but they were also spatially autocorrelated (at distances below 40.3 km; Sánchez‐Mercado et al., 2008). To generate independent estimates for our models, as well as to explicitly consider the uncertainty generated by small sample size, we applied a stratified random sampling to the reports and repeatedly partitioned them into three independent subsets: a poaching probability estimation subset, an occurrence probability calibration subset and an occurrence validation subset (Fielding & Bell, 1997). To do this, we first set a spatial grid matching the scale of previously detected spatial autocorrelation and considered each cell in the grid as a stratum. Then, we choose a random sample balanced across strata. This resulted in a small, dispersed sample from within each stratum, and it minimized (without completely avoiding) the selection of records that were separated by less than 40 km (Segurado, Araújo & Kunin, 2006; Peterson et al., 2011). The poaching risk subset contained 100 reports and was used to fit a poaching probability model as described below. The occupancy calibration subset was used to fit SDMs as described below and consisted of 40 reports, a size that produced predictions as reliable as larger sample sizes, but left sufficient remaining data for a validation subset (see Supporting Information Appendix S1 for details). The third subset (30 reports) was then used to validate SDM performance, as described in ‘Occurrence probability modeling’ section below. We repeated this three‐way partitioning 10 times, which created replicates allowing us to directly evaluate data heterogeneity (Diniz‐Filho et al., 2009).

Poaching probability modeling The model of poaching probability described in detail in Sánchez‐Mercado et al. (2008) is based on logistic regression and captures the categorical response of a dependent binomial variable, poach (described earlier), as a function of seven continuous independent spatial, ecophysical and anthropogenic variables (latitude, longitude, altitude, vegetation index, human population density, distance to nearest road and to the nearest protected area; details in Sánchez‐Mercado et al., 2008). The resulting output estimates the historical/cumulative poaching probability across the study area, as a function of these variables. We fit this previously developed poaching probability model to replicates of the first data partition, as described earlier, in order to generate poaching probability estimates that were at least partially independent from occurrence probability estimates (below). We took the poaching probability at any given location to be the median of estimates across the 10 replicates at that location and measured uncertainty as the maximum absolute deviation among replicates.

Occurrence probability predictor variables Our models of occurrence probability for the Andean bear included a different set of covariates than those used to predict poaching, as specified in Table 1. We rescaled all six predictive variables to a 4‐km2 grain, using the bilinear rescale/resampling options in Geographic Resources Analysis Support System (GRASS; Neteler et al., 2012). Specifically, we aggregated the fine‐scale variables (compound topographic index (CTI), cover forest, BIO15, BIO12 and BIO4) using nearest neighbor resampling, and interpolated the coarse‐scale variable (human population density) using cubic splines. Table 1. Variables associated with Andean bear presence used to predict occurrence probability across the Cordillera de Mérida, Venezuela Attribute Description Original resolution Source Justification Intra‐annual variation in temperature (BIO4) Coefficient of variation based on annual range in temperature, 1960–1990. 1 km2 Hijmans et al., 2005 This and precipitation variables below capture variation in biomass among tropical humid forests, one of the main vegetation types used by Andean bears (Sandoval, 2000 2006 2012 et al., 2012 Annual precipitation (BIO12) Annual precipitation, 1960–1990. 1 km2 Hijmans et al., 2005 As above. In particular, precipitation variables strongly influence the availability of fruits upon which Andean bears depend during the dry season (Cuesta et al., 2003 Intra‐annual variation in precipitation (BIO15) Coefficient of variation based on annual range in precipitation, 1960–1990. 1 km2 Hijmans et al., 2005 As above. Forest cover (forest) Percentage (%) forest cover between November 2000 and November 2001. 0.5 km2 Hansen et al., 2002 This variable captures concentration of food resources and availability of refuge (Sandoval, 2000 2004 2005 2006 2011 et al., 2012 et al., 2011 Compound topographic index (cti) Index of steady state wetness, a function of both slope and upstream watershed area (m per radius). 1 km2 USGS, 2011 This index of soil wetness is expected to influence key food resources as well as bear use of microsites in clear cuts (Nielsen et al., 2010 Human population density (hdens) Individuals per 9 km2 9 km2 Dobson et al., 2000 This variable captures anthropogenic influence on the landscape that is perceptible to bears, and was selected over distance to nearest road (as in previous studies of Andean bears and American black bears Ursus americanus; McLellan & Shackleton, 1988 et al., 2003 We applied a log‐transformation to variables with considerable skew (Quinn & Keough, 2002) and standardized all variables to a zero mean and unit variance, as recommended for the algorithm implemented (below). We evaluated collinearity by calculating Pearson correlation coefficients (r) and variance inflation factors (VIFs) among all pairs of variables. No pairs had correlations above |0.6| or individual VIF scores above 10, so none were considered collinear (Chatterjee & Price, 2000).

Occurrence probability modeling Although we considered other SDM algorithms (see Supporting Information Appendix S1), we chose standard maximum likelihood methods as implemented in MaxLike (Royle et al., 2012) to estimate bear occurrence probability, Ψ, as a function of the covariates described earlier. We chose the MaxLike algorithm because it performed as well as or better than the other algorithms considered (ecological niche factor analysis, Hirzel et al., 2002; and maximum entropy, Phillips, Anderson & Schapire, 2006; see Supporting Information Appendix S1). Furthermore, MaxLike produces direct estimates of occurrence probability, rather than the indirect estimates of habitat suitability produced by other methods; this greatly facilitated combining MaxLike outputs with outputs of the poaching model (above) to identify potential ETs and their uncertainty (below). Although the choice of the algorithm had a minor effect on quantitative outputs, it did not substantially affect conclusions (see Supporting Information Appendix S1 for details; Supporting Information Figure S2). The MaxLike approach is based on logistic regression, but because it employs presence‐only data, it must make strong assumptions; most importantly, it presumes that the probability of detecting the species is uniform across the landscape, and that sampling is random (Royle et al., 2012). In our case, records were accumulated over a long period of time. Thus, it seems likely that sampling effort was extended enough to have detected the species in the areas considered if it was present, leaving detection probability sufficiently uniform to meet stringent assumptions. However, the areas under consideration themselves were clearly not a random sample, even though our dataset included almost all known sources of records (Sánchez‐Mercado et al., 2008). Our spatially stratified subsampling (described earlier) was specifically designed to surmount this problem (Segurado et al., 2006). To select the ‘best’ MaxLike occurrence probability model, we then fit different combinations of linear and quadratic terms of the six covariates described earlier to each of the 10 replicate calibration data subsets (Table 2). We tested quadratic terms because exploratory graphic analysis revealed that presences occurred in a narrow range of these covariates, and a polynomial function can capture such ‘optimal’ conditions (Elith & Graham, 2009; Václavík, Kupfer & Meentemeyer, 2012). However, the number of independent observations was limited, so we compared just four alternative models. Our first model (mdl1) contained linear terms for all six variables. The second (mdl2) excluded factors associated with seasonal variability, because research in other carnivores suggests that environmental variability may be less important influence on occurrence than it is on population dynamics (Franklin, 2010). The third model (mdl3) added quadratic terms for forest cover and precipitation, because these have been suggested as the most important for creating ‘optimal’ conditions for Andean bears (Cuesta, Peralvo & Manen, 2003). Our final model (mdl4) was the most reduced and included just linear terms for forest cover, precipitation and two other climatic variables, which have been proposed by experts to be the most important variables driving Andean bear occurrence (Cuesta et al., 2000). The ‘best’ model was considered to be the one that both converged and had the lowest corrected Akaike information criterion (AICc) in most replicates (Burnham & Anderson, 2004). Table 2. Statistical support (AICc values), AUC and accuracy index (S obs /S exp ) for four models of Andean bear occupancy, fit with MaxLike to 10 replicate data subsets mdl1a mdl2b mdl3c mdl4d Replicate AICc AUC S obs /S exp AICc AUC S obs /S exp AICc AUC S obs /S exp AICc AUC S obs /S exp 1 726 0.773 0.964 720 0.776 0.927 * 0.810 0.942 * * * 2 732 0.706 0.788 727 0.718 0.800 * 0.777 0.924 * * * 3 727 0.704 0.980 723 0.705 0.988 * 0.729 0.918 * * * 4 729 0.694 0.843 724 0.694 0.835 * 0.699 0.830 732 0.664 0.872 5 * 0.660 * 727 0.722 3.503 718 0.748 0.754 * 0.709 0.713 6 * 0.568 * 718 0.577 6.788 * 0.686 0.843 * 0.642 0.652 7 * * * * * * * * * * * * 8 730 0.714 1.310 725 0.701 1.287 * * * * 0.748 0.752 9 730 0.754 1.063 724 0.743 1.141 * * * * * * 10 * * * 738 0.716 0.904 * * * 736 0.591 5.610 The best model was then used to predict expected values of Ψ for each replicate, which were then evaluated with the corresponding evaluation subset replicate. To examine the predictive accuracy of the replicates for the best model, we compared the observed (S obs ) and expected sensitivity (S exp ) (Vaughan & Omerod, 2005; see Supporting Information Appendix S1). For any given occurrence probability Ψ between 0 and 1, S obs at Ψ is equal to the true positive rate. In the case of MaxLike, S exp is simply 1 − Ψ; for example, at an occurrence probability of 0.1, expected sensitivity is 0.9. Values of S obs /S exp near one indicate a good fit, whereas values over or under 1 suggest overfitting or underestimation, respectively (Vaughan & Omerod, 2005). We next used replicates with the best predictive accuracy (0.8 < S obs /S exp < 1.2; Table 2) to estimate median occurrence probability and its median absolute deviation for each pixel in the study region (Fielding & Bell, 1997; Russell & Taylor, 2005), and build spatial predictions of Ψ. We calculated the total area of occurrence by summing occurrence probabilities across the study area and multiplying the result by cell size (Vaughan & Omerod, 2005). For comparison, we also applied the common technique of fixing an arbitrary threshold (Ψ > 0.5) to calculate the total number of pixels with high occurrence probability (Liu et al., 2005).