Spatial model of livestock predation by jaguar and puma in Mexico: Conservation planning

Biological Conservation 159 (2013) 80–87

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Spatial model of livestock predation by jaguar and puma in Mexico: Conservation planning Martha M. Zarco-González a,b, Octavio Monroy-Vilchis a,b,⇑, Jorge Alaníz c a

Sierra Nanchititla Biological Station, Faculty of Sciences, Autonomous University of the State of Mexico, Mexico Instituto literario 100, Centro, Toluca, Estado de México, CP 5000, Mexico c Faculty of Sciences, Autonomous University of Baja California, Carretera Tijuana-Ensenada Km 106, 22800 Ensenda, BC, Mexico b

a r t i c l e

i n f o

Article history: Received 15 May 2012 Received in revised form 23 October 2012 Accepted 4 November 2012

Keywords: Livestock Predation Ecological niche model Puma Jaguar México

a b s t r a c t Predation on livestock is one of the main factors that cause the felids hunting, in particular for puma and jaguar this conflict with humans is severe. Most studies have assessed the predation impacts on livestock production; however there is a spatial pattern in attacks occurrence that is feasible to analyze from ecological niche modeling. The objective of this research was to generate a risk model of livestock predation by puma and jaguar in Mexico based on environmental and livestock management variables, which allows identification of zones of risk in order to define mitigation strategies at national level. We produced a geographic ensemble model of risk of predation from three algorithms for jaguar and five for puma. The variables most positively related with predation risk by jaguar were vegetative cover percentage, percentage of free grazing animals, and altitude, whereas arid vegetation has a negative influence on predation risk. In the case of puma the variables with highest contribution were livestock density, which negatively influences on the predation risk, in addition to forest and altitude, both with a positive relation. The ensemble models are an accurate approach to delineating the zones of predation risk by felids; however at a regional scale the environmental characteristics that favor predation may be different. It is recommended that researchers carry out studies for each biogeographic province that facilitate the identification of specific patterns and the definition of mitigation strategies most suitable for each one. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Populations of large carnivores are declining worldwide due to the loss or fragmentation of their habitat, and by direct hunting of the carnivores or their prey; currently, 17% of the species are threatened (IUCN, 2011). The hunting of felids takes place in response to their supposed predation on livestock (Holmern et al., 2007; Kissui, 2008; Gusset et al., 2009); this problem affects 75% of felid species worldwide, and in particular is severe for puma and jaguar (Inskip and Zimmermann, 2009). In previous studies, data on felids hunted in retaliation for predation have been reported, which range from seven pumas killed per year on average in a ranch in Sao Paulo to 150 pumas and jaguars in Alta Floresta, Brazil (Inskip and Zimmermann, 2009). Hence, it is evident that a fundamental topic in large cats’ conservation is the analysis of the conflicts with livestock holders. This issue has mainly been approached by describing the impact of predation on livestock production and identifying factors related with ⇑ Corresponding author at: Instituto literario 100, Centro, Toluca, Estado de México, CP 5000, Mexico. Tel.: +1 722 296 55 53. E-mail addresses: [email protected] (M.M. Zarco-González), [email protected], [email protected] (O. Monroy-Vilchis). 0006-3207/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.biocon.2012.11.007

the predation levels (Patterson et al., 2004; Kolowski and Holekamp, 2006; Azevedo and Murray, 2007; Van et al., 2007; Palmeira et al., 2008; Iftikhar et al., 2009). Other authors have observed differences in the environmental characteristics of sites with and without predation (Jackson et al., 1996), and this may be an indicator of conditions inherent to the sites that influence on the risk (Stahl et al., 2002). Among the proposed environmental variables that may be related with the frequency of attacks are proximity to forest zones (Mazzolli et al., 2002; Stahl et al., 2002; Azevedo and Murray, 2007; Palmeira et al., 2008), the vegetation type (Rosas-Rosas et al., 2010), altitude (Lui et al., 2006), topography (Stahl et al., 2002; Michalski et al., 2006; Kissling et al., 2009), density of livestock and wild prey (Treves et al., 2004; Bagchi and Mishra, 2006; Kolowski and Holekamp, 2006), distance to protected areas, human settlements, roads, and water sources (Lui et al., 2006; Van et al., 2007; Gusset et al., 2009; Rosas-Rosas et al., 2010). An approach that may be useful in decreasing the severity of the conflict is to anticipate its spatial location and to propose preventive actions in specific areas, optimizing economic and human resources. A commonly used tool to plan strategies of wildlife management, which relates ecological variables and spatial processes, are ecological niche models (Gibson et al., 2007; Zarco-González et al., 2012), the modeling provides estimates of occurrence

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probability of these processes in the study area. This technique has been applied to study the relations between environmental parameters and richness of species (Araújo and Williams, 2000; Ferrier et al., 2002; Scotts and Drielsma, 2003; Mac Nally and Fleishman, 2004), invasive potential of exotic species (Peterson, 2003; Goolsby, 2004), and species distributions (Bakkenes et al., 2002; Hugall et al., 2002; Araújo et al., 2004; Peterson et al., 2004; Skov and Svenning, 2004; Thomas et al., 2004; Thuiller et al., 2005; Rodríguez-Soto et al., 2011). By applying this methodology to the study of human-wildlife conflict, from the location and characterization of the sites where predation on livestock is present, it is possible to spatially predict the zones of predation risk, as well as to identify the variables that propitiate this interaction. This enables planning actions to manage livestock and predators in specific zones to minimize the conflicts, optimize livestock production, and reduce the hunting of wild felids. The objective of this study was to generate a risk model of livestock predation by puma and jaguar in Mexico based on environmental and livestock management variables. The model further allows identifying and prioritizing of zones of felid predation risk in order to develop mitigation strategies at national level.

2. Materials and methods 2.1. Study area Mexico is located in northern America, its territorial extension is 1,953,162 km2 (Fig. 1). Its extreme coordinates are: 14°320 2700 south, 32°430 0600 north; 86°420 3600 east and 118°270 2400 west (INEGI, 2011). Mexico possesses a varied topography, more than 65%

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of the country is above 1000 m above sea level and nearly 47% of the surface has slopes over 27% (UNAM, 1990; Mittermeier and Mittermeier, 1992). In conservation importance, Mexico hosts between 8% and 12% of the total of the species on the planet (Mittermeier and Mittermeier, 1992), including six feline species, of which puma (Puma concolor) and jaguar (Panthera onca) are the largest. The records of attacks on livestock by puma and jaguar in Mexico were collected in three ways: (1) databases of the Mexican government, Secretariat of Environment and Natural Resources (SEMARNAT), Pronatura (civil association) and technical reports (Núñez, 2007a); (2) review of scientific literature: theses (BuenoCabrera, 2004; Villordo-Galván, 2009), books (Brown and López, 2001; Rosas-Rosas and López-Soto, 2002; Caso, 2007; Cruz et al., 2007; Leyequién and Balvanera, 2007; Lira and Ramos-Fernández, 2007; Navarro et al., 2007; Núñez, 2007b), and papers (Rosas-Rosas et al., 2008; Chávez and Zarza, 2009; Zarco-González et al., 2012); (3) and field work in different states of the country (states of Mexico, Chihuahua, Yucatán, Campeche, Baja California and Guerrero). Approximately 78% of predation data were recorded at the site of attack with GPS devices and 22% were inferred using Google Earth and maps and descriptions presented in the original sources. A database of predation events was produced with the records specifying date, predator species, place of attack, and geographic coordinates (Fig. 1). Considering the reports of other studies in relation to the influence of the environmental factors on the predation risk (Stahl et al., 2002; Treves et al., 2004; Bagchi and Mishra, 2006; Kolowski and Holekamp, 2006; Lui et al., 2006; Michalski et al., 2006; Van et al., 2007; Gusset et al., 2009; Kissling et al., 2009; Rosas-Rosas et al., 2010), the variables used to characterize the sites of attack were grouped in three types: landscape, livestock management,

Fig. 1. Mexico location and records of predation by jaguar and puma.

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and anthropogenic; topographic variables were altitude (USGS/ NASA, 2007) and slope. The vegetative associations of the National Forest Inventory were also included (SEMARNAP, 2001) and grouped into seven types: forest (conifers, oaks and riverside vegetation), dry forest, rainforests, arid vegetation, underwater vegetation, and agriculture. The percentage of tree cover was obtained from Global Land Cover Facility (De Fries et al., 2000). In relation to livestock management, layers of livestock density and percentage in free grazing were generated by interpolating the values of each municipality from the 2007 agricultural, livestock, and forest census (INEGI, 2009). Human perturbation, considering the human population density (Salvatore et al., 2005) and distance to paved roads (CONABIO, 2008), was included as an anthropogenic variable. Each of these layers was processed in a raster format, with a 1-km2 resolution; to unify them, pixels with no data and water sources were excluded. Although the information represented in each variable is different, the correlation between them was calculated using BioMapper4 (Hirzel, 2008). Variables retained in the models have a correlation of less than 0.5. For reducing the spatial correlation between records, they were filtered to obtain only one datum per pixel. The records thus obtained were randomly divided into two groups for each species: 75% to calibrate the prediction models and 25% to validate the models (Guisan and Zimmermann, 2000). It is assumed that this sample of the original data contains independent observations that can be used in a statistical test (Araújo et al., 2005). To obtain the different models of predation risk for each species, we used the software Open Modeller version 1.1.0 (http:// www.openmodeller.sf.net), including the algorithms: Artificial Neural Network (Gevrey et al., 2003; Pearson et al., 2004), Environmental Distance (Hirzel and Arlettaz, 2003), GARP (Genetic Algorithm for Rule-set Production; in both versions: single run and with best subsets, Stockwell and Peters, 1999) and SVM (Support Vector Machines; Cristianini and Scholkopf, 2002; Huang et al., 2002; Guo et al., 2005; Drake and Bossenbroek, 2009). We also used BioMapper4 (Hirzel, 2008) and Maximum Entropy Species Distribution Modeling v3.3.3e (Phillips et al., 2006), to obtain the algorithms of ENFA (Hirzel et al., 2002) and Maxent (Phillips et al., 2006), respectively, the latter also to get the influence of each variable in the predation risk. Once the models were obtained, their individual performance was evaluated from the area under the curve (AUC) ROC (Receiver Operating Characteristic, Hanley and McNeil, 1982). The AUC values between 0.5 and 0.7 are considered low (model with poor performance); between 0.7 and 0.9 are moderate; and >0.9 are high performance (Manel et al., 2001). We used the ROC module of the Idrisi Andes software (Clark Labs, 2006) in order to calculate this value. We obtained two evaluations for each model, one based on the calibration data (internal) and other with the validation data (external). Comparing the efficacy of different modeling methods we have noticed that in spite of some being more effective for prediction (Elith et al., 2006; Tsoar et al., 2007), none proved to be the best in all cases (Hernandez et al., 2008). To overcome this variability, a solution is to develop models using multiple algorithms that identify common areas of consistent prediction (Anderson et al., 2003; Araújo et al., 2006). The consensual area between predictions incorporates the uncertainties of modeling and produces more reliable estimations (Hartley et al., 2006). This methodology has been applied in the prediction of the distribution of species of plants (Marmion et al., 2009), invasive arthropod species (RouraPascual et al., 2008), reptiles (Domínguez-Vega et al., 2012) and carnivorous mammals (Rodríguez-Soto et al., 2011). Consensus approaches are particularly useful in cases where there are not adequate data to evaluate which model makes the most accurate predictions, as is the case with species invading new areas, project-

ing future distributions under environmental change scenarios, and in very data-poor regions (Hernandez et al., 2008). Because of uncertainties in individual models, an ensemble model of predation risk for each felid species was produced. In the ensemble model, we included the models with AUC values P0.75 in the internal evaluation. We used the weighted average, as it has been demonstrated that it has the highest predictive performance of all the consensus methods (Marmion et al., 2009), AUC value was also calculated to evaluate the ensemble model performance. To facilitate their interpretation, the original prediction values (0–100) were reclassified considering the mean probability value of the records used to calibrate the models, so that the zones with a prediction value greater than or equal to this mean were considered those with high risk and those with values lower were considered low risk (Liu et al., 2005).

3. Theory Machine learning methods are algorithms that are used to learn the mapping function or classification rules inductively, directly from the training data (Franklin, 2009). They include artificial neural networks, genetic algorithms, maximum entropy and support vector machines. These methods tend to perform well given complex classification problems, however, interpreting the modeled relationships between predictors and response is not always straightforward in some machine learning implementations. ANNs consist of many processing elements (artificial neurons) that are interconnected to form a network. ANNs are ‘‘trained’’ by repeatedly passing large numbers of known examples of the problem under consideration through the network. By repeatedly adjusting the connections between processing elements the difference between the network predictions and the known examples can be minimized (Pearson et al., 2004). Neural networks can identify non-linear responses to environmental variables, as well as incorporating multiple types of variables, including qualitative and quantitative. A disadvantage of this method is that it does not identify the relative contribution of the different variables (Gevrey et al., 2003). The details of the classifier developed using neural networks are not obvious or interpretable, it is considered a ‘‘black box’’ approach to classification, and so the main advantage of this method is that it sometimes achieves much higher classification accuracy than other methods in high-dimensional, complex classification problems (Franklin, 2009). The GARP software implements an ensemble method that generates a population of prediction rules based on several different types of models, and then uses a genetic algorithm to select among them and develop a final rule set to make predictions. Further, because the output from GARP is stochastic, it is typical to run the model multiple times, and then average a subset of the best models (Stockwell and Peters, 1999). GARP is not able to model responses to categorical predictors and tends to over predict the extent of species distributions, that is, to have higher commission errors (Franklin, 2009). In Maxent the multivariate distribution of suitable habitat conditions in environmental feature-space is estimated using the best approximation of an unknown distribution with maximum entropy (the most dispersed) subject to known constraints. The advantages of this method are that it can use both categorical and continuous data, as well as incorporate interactions between different variables (Phillips et al., 2006), additionally Maxent can work well with very small samples that have relatively widespread geographic distributions (Hernandez et al., 2008). SVM use a functional relationship known as a kernel to map data onto a new hyperspace in which complicated patterns can

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be more simply represented. Functionally, SVMs seek to find an optimal separating hyperplane with the maximal margin between the training points for presence and absence data in multidimensional space (Cristianini and Scholkopf, 2002; Huang et al., 2002; Guo et al., 2005; Drake and Bossenbroek, 2009). SVM are able to handle categorical and non-linear data and not make assumptions about the probability of data density (Guo et al., 2005). However, it is difficult to tell if it is possible to interpret its classification rules from these models in order to verify its ecological meaning or validity (in terms of the importance of predictors and the form of their relationship with the response; Franklin, 2009). Distance-based methods, like Environmental Distance and ENFA, have limitations, they work best when organisms are using optimal habitat, are well-sampled in environmental space, and when habitat variables are not dynamic (Franklin, 2009). Additionally, these methods are not well-suited for categorical predictors; they equally weight predictors, and assume linear relationships between environmental variables and habitat suitability. Environmental distance defines the suitability area in the environmental space of each species’ record. The geometric media or the distance of each record to rest of them are calculated, in this way, a high density of records in the environment space imply a high habitat suitability (Hirzel and Arlettaz, 2003). ENFA is based on a multivariate description of species occurrence locations. It estimates species niche more explicitly based on the magnitude of the difference between the species mean and the entire range of environmental conditions observed. This model estimates marginality and specialization (Hirzel et al., 2002). ENFA is prone to high commission error or low specificity in comparison with other methods (Franklin, 2009).

Table 2 AUC values of the models for jaguar. Algorithm

Maxenta GARP (with best subsets)a SVMa ENFA GARP (single run) ANN Maxent (open modeller) Environmental distance ENFA (open modeller) a

AUC External evaluation

Internal evaluation

0.799 0.784 0.767 0.728 0.728 0.725 0.704 0.626 0.500

0.919 0.792 0.837 0.743 0.714 0.730 0.669 0.923 0.520

Algorithms included in the ensemble model.

Table 3 AUC values of the models for puma. Algorithm

Maxenta Environmental distancea ENFAa GARP (with best subsets)a GARP (single run)a ANN SVM Maxent (open modeller) ENFA (open modeller) a

AUC External evaluation

Internal evaluation

0.944 0.875 0.866 0.817 0.767 0.720 0.617 0.503 0.500

0.934 0.961 0.828 0.802 0.790 0.730 0.591 0.505 0.510

Algorithms included in the ensemble model.

Table 4 Importance of variables in the models generated with Maxent for each felid species (only the most important are shown).

4. Results We obtained 241 records of felid attacks on livestock in Mexico, and after data reduction we retained 222 records; 152 predation events by jaguar and 70 by puma. The retained records are from 1990 to 2010, and are distributed in 19 states (Table 1). For jaguar, three algorithms were considered suitable according to the internal evaluation: Maxent, GARP-with best subsets and SVM (Table 2). For puma five algorithms were considered: Maxent, Environmental distance, ENFA, GARP-with best subsets and GARPsingle run (Table 3). For both species the algorithm with the best performance was Maxent. According to ENFA, for data from jaguars, we obtained a global marginality value of 0.793, which indicates that the observed conditions in the sites of attack are different from the average environmental conditions and the range in which predation occurs is very restricted in relation to the global characteristics. Maxent indicates that the variables with highest contribution to the model are tree cover percentage, percentage of animals in free grazing areas, and altitude. These variables are positively related with the risk

Table 1 Number of data obtained of each source and year of collect. Source

Number of data

Year of collect

Secretariat of Environment and Natural Resources (SEMARNAT) Pronatura (civil association) and technical reports Theses Books Papers Field work

80

2009–2010

10

2000–2007

13 36 26 76

2000–2006 1991–2006 1998–2004 2006–2010

Variable

Altitude Forest Arid vegetation Cover percentage Livestock density Percentage of free gazing livestock

Maxent (contribution percentage) Jaguar

Puma

10.3 3.7 8.5 47 4.5 12.1

12.3 34.1 0.5 6.7 35.2 6.6

of attack by jaguar, whereas arid vegetation has a negative correlation with predation risk (Table 4). In the case of puma, ENFA indicated a marginality global value of 1.157, these results imply that the characteristics of predation sites by puma are very specific, even higher than those of jaguar, and the general variation in these characteristics is low. Maxent showed that the variables with highest contribution were livestock density, which negatively influences on the predation risk by puma, in addition to forest and altitude, both with a positive relation (Table 4). The ensemble model for jaguar had an AUC value of 0.8. The zones of highest predation risk by this species (probability > 64) are in the western Sierra Madre Occidental, at the border with Sonorense province, the Costa del Pacífico, western and center of Cuenca del Balsas, eastern Sierra Madre del Sur, eastern Soconusco, the northern and southern limits of Altos de Chiapas and Golfo de México, mainly northern and limits with Sierra Madre del Sur, Yucatán, Petén and southern Sierra Madre Oriental (Fig. 2). The ensemble model for puma presented an AUC value of 0.9. In this case the risk zones (probability > 69) are concentrated on southern California, western and central Sierra Madre Occidental,

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Fig. 2. Ensemble model of risk predation by jaguar in Mexico. (1) Sierra Madre Occidental, (2) Sonorense, (3) Costa del Pacífico, (4) Cuenca del Balsas, (5) Sierra Madre del Sur, (6) Soconusco, (7) Altos de Chiapas, (8) Golfo de México, (9) Yucatán, (10) Petén y, (11) Sierra Madre Oriental.

Fig. 3. Ensemble model of risk predation by puma in Mexico. (1) California, (2) Sierra Madre Occidental, (3) Sierra Madre Oriental, (4) Eje Volcánico Transmexicano, (5) Cuenca del Balsas, (6) Sierra Madre del Sur, (7) Soconusco y, (8) Altos de Chiapas.

northern Sierra Madre Oriental, the southern limit of the Eje Volcánico Transmexicano, the center of Cuenca del Balsas, Sierra Madre del Sur, Soconusco and the center of Altos de Chiapas (Fig. 3).

5. Discussion The conflict of livestock predation by the two large cats of Mexico has negatively impacted on the populations of both jaguar and puma. In the north of the country, the illegal hunting of jaguar is perhaps the main threat for its conservation (Rosas-Rosas et al., 2008). However, in the case of puma the severity of the conflict has not been assessed, but it is known that in some areas predation on livestock is the most frequent reason for their hunting by hu-

mans (Zarco-González et al., 2012). Despite this situation, systematic data on the topic are scarce, and most of the published studies are focused on jaguar (Rosas-Rosas et al., 2008, 2010; Chávez and Zarza, 2009; Villordo-Galván, 2009). Fewer studies have been carried out on puma (Bueno-Cabrera, 2004; Zarco-González et al., 2012). As a consequence, there are no data where livestock predation occurs, and much less on the impact on livestock production or on the felids conservation, so the present risk model shows a spatial panorama of the predation problem in Mexico. One of the most recent actions to address this issue was carried out in 2009 by the National Livestock Confederation and the Secretariat of Agriculture, Livestock, Rural Development, Fishing and Alimentation (SAGARPA). They established a program providing livestock insurance for death due to predators. The general objec-

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tive of the fund is to protect the patrimony of Mexican livestock holders and the operative continuity of their production units. This program is intended to address at a regional level the problem of predation, however, the compensation to affected livestock holders has not been done efficiently. In this sense, the accurate identification of the risk zones will enable the directing of financial and human resources to the zones most vulnerable to predation. Most of the studies in Mexico have analyzed the impact on felid predation on bovines (Rosas-Rosas et al., 2008, 2010; Chávez and Zarza, 2009; Villordo-Galván, 2009), the interest in this livestock is related to the higher economic value in relation to the smaller domestic species (SAGARPA, 2006). Additionally, the reports of attacks on small livestock are less frequent. These conditions have favored that the most data on predation are related to jaguar, as that jaguars more frequently consume large domestic prey (bovines, Hoogesteijn, 2001). Hence, the impact of predation by puma is probably underestimated and eventually so would be the risk area predicted in this study. To overcome these limitations is necessary to evaluate with greater precision the cases of attacks by puma, particularly on sheep and goats. On the other hand, considering the priority areas for jaguar conservation proposed by RodríguezSoto et al. (2011), it is observed that they coincide with the zones of highest predation risk, in this sense it is necessary to invest resources on the application of strategies to reduce the human-jaguar conflict. According to the specialization values for both species is clear that the attributes of the zones with attacks are particular, even different from those that characterize the general species habitat. Chávez and Zarza (2009) found that vegetation was the variable that best explains the jaguar’s potential distribution in Yucatan Peninsula, conversely, the human-jaguar conflict model generated in the same study shows that the most of predation events takes place around human settlements. This reaffirms the fact that sites in which the attacks on livestock occur have particular characteristics that make their inclusion into a predictive model feasible. Maxent indicates that the percentage of cover and the presence of arid vegetation are positively and negatively related, respectively, with predation risk by jaguar. In particular, tree cover influences on the success probability of attack by jaguar, which is a stalk-and-ambush predator; on the contrary, scarce cover, a characteristic of arid vegetation, explains the negative relation with the risk. The zones with highest predation risk by jaguar are those with a tree cover percentage over 70%. In a study carried out at local level, it is also mentioned that the predation sites by jaguar are characterized by having dense vegetation (Rosas-Rosas et al., 2010), particularly oaks, thorny shrubs, xeric bushes and mesquites. However, Michalski et al. (2006) suggest that a tendency exists in the spatial variation in predation events, such that most events occur in ranches embedded in large forested zones. This must be taken cautiously, as it has been observed that in these zones frequency of attacks is negatively related to the abundance of wild prey (Stahl et al., 2002; Polisar et al., 2003; Woodroffe et al., 2005; Kolowski and Holekamp, 2006). Maxent also indicates that the percentage of free-grazing livestock is related with the risk, being higher when this variable is above 20%. The lack of shelter for livestock is a situation that in many studies has been considered the main cause of predation by felids (Jackson et al., 1996; Mazzolli et al., 2002; Wang and Macdonald, 2006; Van et al., 2007; Inskip and Zimmermann, 2009). The spatial exposition of livestock to predators, lack of vigilance as well as a deficient sanitary and feeding management favor a higher incidence of diseases that weakens the animals. Likewise, the birth of offspring in sites of risk and the lack of forage in dry season are both factors that propitiate predation. The zones identified with the highest predation risk by jaguar and where the percentage of free-grazing animals is the highest

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at national level correspond to península de Yucatán, the states of Sonora, Durango, San Luis Potosí, Nuevo León and Tamaulipas, the central part of the Costa del Pacífico, Veracruz and Tabasco (INEGI, 2009). Península de Yucatán holds one of the most important jaguar populations, in this region the population of cattle reaches 898,393 animals, of which more than 60% are in free-grazing production system (Chávez and Zarza, 2009). Tamaulipas, Durango and San Luis Potosí belong to the arid and semi-arid productive region, characterized by deteriorated rangelands, whereas the Golfo de México and the Peninsula de Yucatán are comprised in the tropical humid region that provides 33% of the national beef production; however the reproductive parameters are low due to the lack of management (SAGARPA, 2006). Particularly, in Veracruz most of the operations are characterized by resorting to free grazing (Vilaboa and Díaz, 2009). Altitude explained about 10% of model variation, and there are two ranges (from 0 to 300 and from 2700 to 3000 m above sea level) in which the risk of attack by jaguar increases; the first related to the cases that took place in the Costa del Pacífico, the Golfo de México and the Península de Yucatán; and the second, to the Cuenca del Balsas and Sierra Madre Oriental, where it has been registered the presence of jaguar at higher altitudes that its typical distribution (Monroy-Vilchis et al., 2008). Maxent indicates that the predation risk by puma increases from 25% of forest vegetation (conifer forest, oaks and riverside vegetation), the use of this vegetation by puma, in particular pine-oak forest, was previously reported in central Mexico (Monroy-Vilchis et al., 2009). These results differ from Polisar et al. (2003), who mention that in Venezuelan llanos predation by puma seems to be less limited by the proximity of forest in comparison with jaguar; however, in Brazil, Palmeira et al. (2008) found that 50% of the pastures with predation events by puma were close to forest. As for altitude, from 2300 m above sea level the risk of attack by puma is considered high. The relation of sites of attack by puma with this variable is evident in the model, in which the zones with the highest risk virtually are present in all Mexican sierras, which are the areas with highest altitude in the country. It is also possible that the predation risk in these zones is determined by the proximity to cliffs, as it has been observed related to it in regional level studies (Bueno-Cabrera, 2004; Zarco-González et al., 2012). In a similar way, in a study performed in Patagonia, Kissling et al. (2009) found that at paddock level, topography had a notable effect on the risk of attacks by puma. There is an important negative relation between livestock density and predation risk by puma, even with a contribution percentage higher than before mentioned variables. The highest values of livestock density are present in central Mexico, mainly in the States of Mexico, Hidalgo, Puebla and Querétaro. The management of livestock in this zone, which is one of the most important in livestock production at national level (INEGI, 2008), is different to the rest of the country, farms in this region are intensive, many of them dedicated to fattening and export cattle (SAGARPA, 2006). These farms generally use fences and are away from forested areas, which reduce the risk of predation by puma. In comparing the variables that determine the risk of predation for each species of felid, it is clear the puma prey more frequently in mountain environments. The puma has a less elusive behavior, so it often hunts near human settlements, unlike the jaguar which usually hunts animals that are grazing freely in preserved environments with a high percentage of forest cover. These conditions occur mainly in the Southeast zone of the country, and reflect the primarily neotropical distribution of the jaguar. It is noteworthy that the use of algorithms for ecological niche modeling to identifying zones of predation risk is an innovative approach to this topic. The AUC of the models obtained by the differ-

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ent algorithms were generally acceptable; the greatest accuracy that was obtained by Maxent has been mentioned in other studies, which shown that it produces good results with species of wide distribution and few records (Hernandez et al., 2008). In this case, AUC value from Maxent for puma model was even higher than the ensemble model, which has been observed in other studies (Marmion et al., 2009). However, some authors have mentioned that the evaluation of a model basically depends on the study objectives and its usefulness, more than only on statistical results (Guisan and Zimmermann, 2000). One of the disadvantages of Maxent is that the prediction area is generally smaller contrasted to the results from other algorithms. Considering the approach of this study and the intended application for the risk map, it is not convenient to use a model that may predict a reduced area; in this case it is better to incorporate uncertainty or disagreement areas between algorithms in order to prevent underestimating the potential risk area, which was achieved through the ensemble model. The ensemble models are accurate approaching of the zones of predation risk by felids; however at a regional scale the environmental characteristics that favor predation may be different. Then it is recommended to carry out studies for each biogeographic province that facilitate the identification of specific patterns and the definition of mitigation strategies more suitable for each of them. 6. Conclusion We generated ensemble risk models of livestock predation by puma and jaguar in Mexico from ecological niche models, identifying the zones of risk and the environmental and livestock management variables that contributed to this risk. However, although the initial results are potentially useful, the characteristics of specific areas are very variable, fine-tuned models could be produced by applying them to regional scales. Acknowledgments We thank to Mexican people for funding this study through PROMEP (Project 103/10/0942), CONACYT (Project 101254), and with a scholarship to MMZG (212618). Fernando Cortés give us some records. Two reviews anonymous strengthen the manuscript. Luis Cejudo helps us with the translation of the text and C. Gienger review the english version. References Anderson, R.P., Lew, D., Peterson, A.T., 2003. Evaluating predictive models of species’ distributions: criteria for selecting optimal models. Ecol. Model. 162, 211–232. Araújo, M.B., Cabeza, M., Thuiller, W., Hannah, L., Williams, P.H., 2004. Would climate change drive species out of reserves? An assessment of existing reserveselection methods. Global Change Biol. 10, 1618–1626. Araújo, M.B., Williams, P.H., 2000. Selecting areas for species persistence using occurrence data. Biol. Conserv. 96, 331–345. Araújo, M.B., Pearson, R.G., Thuiller, W., Erhard, M., 2005. Validation of speciesclimate impact models under climate change. Global Change Biol. 11, 1504– 1513. Araújo, M.B., Thuiller, W., Pearson, R.G., 2006. Climate warming and the decline of amphibians and reptiles in Europe. J. Biogeog. 33, 1712–1728. Azevedo, F., Murray, D., 2007. Evaluation of potential factors predisposing livestock to predation by jaguars. J. Wildl. Manage. 71, 2379–2386. Bagchi, S., Mishra, C., 2006. Living with large carnivores: predation on livestock by the snow leopard (Uncia uncia). J. Zool. 268, 217–224. Bakkenes, M., Alkemad, J.R.M., Ihle, F., Leemans, R., Latour, J.B., 2002. Assessing effects of forecasted climate change on the diversity and distribution of European higher plants for 2050. Global Change Biol. 8, 390–407. Brown, D.E., López, C.A., 2001. Borderland Jaguars. The University of Utah Press, Salt Lake City, USA. Bueno-Cabrera, A., 2004. Impacto del puma (Puma concolor) en ranchos ganaderos del área natural protegida ‘‘Cañón de Santa Elena’’, Chihuahua. Tesis de Maestría. Instituto de Ecología, A.C. Xalapa, Veracruz, México. Caso, A., 2007. Situación del jaguar en el estado de Tamaulipas. In: Ceballos, G., Chávez, C., List, R., Zarza, H. (Eds.), Conservación y manejo del jaguar en México:

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