A Model for Iberian Wolf (Canis lupus signatus, Cabrera 1907) Predation Risk Assessment on Cattle in the Central System (Spain)

Abstract

As a consequence of the exponential increase of the demographic and technological development of the human being, conflicts with the natural environment are accentuated. Pollution or the loss of biodiversity represent examples of problems that we must face to maintain the balance between the evolution of human beings and the conservation of nature. However, there are conflicts whose origin is not as modern as those mentioned, and we return to the Neolithic to find the origin of the conflict of man with the great predators. This condition has existed since then and at this point in history, is reaching very high levels of tension in developed countries, as a result of the depredation of livestock. Wolf is one of the species that generates more conflict and is currently suffering a slight demographic expansion. Although current laws mostly seek their recovery and conservation, the wolf is experiencing great difficulties due to the poor social perception it has. Faced with this situation, a model has been developed using geographic information systems which categorizes the areas according to their probability that the cattle could suffer a wolf attack. Based on natural and anthropogenic variables of the environment, the areas with a greater or lesser probability of attack were evaluated, with the objective of designing a prevention plan to reduce or eliminate the attacks. Since different authors demonstrate that population control measures on the species are not effective in reducing attacks on livestock, the solution to the conflict should be based on preventive measures. The use of the designed model will enable the competent authorities to apply these measures optimally, reducing expenses and allowing to anticipate future areas of conflict.

1. Introduction

The Iberian wolf (Canis lupus signatus, Cabrera 1907) is one of the 32 classified subspecies of wolves in the world comprising more than 2000 individuals [1], in addition to nine extinguished subspecies according to the catalogue of animal species extinguished by man. While C. lupus signatus can be framed within the brown wolves, present in Eurasia and in Western Europe [2], its endemicity to the Iberian Peninsula results in unique morphological and ethological characteristics [3].

The conservation of the Iberian wolf is subjected to controversy, since hundreds of attacks are reported every year by farmers [3]. Wolves are often dependent on landfills and livestock, as wild ungulates are disappearing in many areas of the Iberian Peninsula [4]. The opportunistic behaviour of the wolf, results in very different preying patterns depending on prey availability. It is well studied how wolves are able to adapt their prey preferences and hunting strategies to obtain the maximal energetic reward [5]. In this sense, domestic herds provide high concentrations of animals deprived of defensive instincts [6]. For instance, in central Portugal, which has human-influenced landscapes, domestic goats (62%), cows (20%), and sheep (13%) constitute the main diet of Iberian wolves [7]. In contrast, in north-eastern Portugal [8] and north-western Spain [4], wolves’ food preferences in a human–wildlife conflict-free environment were wild ungulates (Roe deer Capreolus capreolus), with the red deer Cervus elaphus being the most important prey species) and wild boar (Sus scrofa) having priority. In the Galician Region, wild ponies were the main food source [9].

Like many other big predators, wolf populations have been decimated by humans since the Neolithic [10]. In Spain, from 1817 to 1970, bounties were offered by local and regional administrations to capture and/or kill wolves, resulting in the near extinction of the species. For instance, estimations in 1970, report only 500 individuals split in three poorly interconnected regions: Cantabrian Cordillera, Sierra de Gata and Sierra Morena [11].

Pro-wolf social movements followed the systematic eradication of this emblematic species, resulting in several regulations and measures that helped the partial restoration of Iberian wolf populations [12]. Examples of such measures include legislation, and habitat models of wolf ecological suitability and distribution to identify optimal areas to reintroduce wolves or to apply conservation measures [13,14,15,16,17]. Such models include ecological (i.e., prey availability, diversity) and anthropogenic pressure-based variables (i.e., size and distance of human settlements) that are known to affect the distribution patterns and behavior of wolves [18,19,20,21,22,23]. These models are not designed, however, to prevent or relief the wolf conflict. As a matter of fact, the territories that present the greater wolf settling potential are those where the conflict with ranchers is more intense.

Cattle ranchers, who progressively adapted their practices to the absence of predators, are now again challenged with increasing numbers of wolves menacing their cattle. While different viewpoints on wolf conservation can be found among ranchers, the majority perceive wolf populations as a risk for their cattle and their business. Consequently, a social conflict is at stage between conservationists and cattle ranchers.

Preventive measures, such as the use of guard dogs, electric fences, or RAG boxes, among others, are proven to be highly effective when designed to fit the local circumstances [6,24,25,26]. In Spain, the adoption of such measures is frequently slowed by the reluctance of administrations and stockbreeders due to the high cost and the area extension that is potentially affected.

To find meaningful and longstanding solutions to the Iberian wolf conservation conflict, it is necessary to develop reliable models of wolf presence and attack probability in response to different factors. Such models are necessary to help decision makers to implement realistic and efficient measures to prevent, or at least, considerably reduce, wolf attacks on cattle.

The aim of this work is to implement an Iberian wolf attack risk assessment model that identifies the most relevant variables affecting the predatory behaviour of wolves on livestock as well as predicting the areas with higher vulnerability to wolf attacks. Our hypothesis is that we can predict the attack risk based on different wolf behaviour predictors. The development of an accurate risk assessment model will help in the process of measure application by both administrations and cattle ranchers.

2. Materials and Methods

2.1. Study Area and Data Gathering

The study was conducted in Avila, (Castilla y León, Spain). The province shows an increasing rate of Iberian wolf attacks on livestock according to official regional environmental authorities, with a high level of conflict due to the large number of records of Iberian wolf attacks on livestock.

GIS data were gathered from the National Topographic Base using a 1:200,000 scale (BTN200). Prior to statistical testing, the study area was selected using 10 × 10 km grids downloaded from the National Biodiversity Inventory (INB) provided by the Ministry of Agriculture, Fisheries, Food and Environment (MAPAMA in Spanish) (Figure 1). Grids were selected when at least one third of their surface was included within the administrative boundaries of Avila. We also analyze the grids where at least one wolf attack was reported by the environmental agents of Avila between 2016 and 2017.

2.2. Iberian Wolf Attack Risk Assessment Model

This paper will develop an accurate model to predict wolf attack risk according to different parameters. The model was created in four steps: (a) variable selection, (b) data extraction, (c) generalized linear model (glm), and (d) validation of the model.

The set of variables were chosen based on previous studies about wolf ecology and behaviour (Figure 2). Using QGIS, the mean values of these variables were extracted for each grid.

A glm is performed to explain how accurately “the distance of the attacks of wolves to the cattle ranch” related to the set of variables.

The predictions of the model are then compared with wolf attacks on livestock in the province of Avila suffered during the years 2016 and 2017 (official census of attacks ceded by the Junta de Castilla y León).

Finally, based on our predictions, we create a map that shows the risk attack probability. All statistical analyses were performed using Statgraphics software.

2.2.1. Stage 1. Analysis of the Variates to Be Considered

2.2.1.1. Anthropogenic Variables

A1. Distance to Buildings (meters)

Iberian wolves have evolved to avoid human contact [2]. Therefore, the presence of any building may have an influence of the foraging patterns of wolves and their behaviour, as showed by studies modelling wolf distribution [13]. To take this into account, the Euclidean distance to any human infrastructure was calculated using the National Topographic Base at a scale of 1:200,000 (BTN200) from the National Geographic Information Centre (CNIG in Spanish).

A2. Distance to Main Roads (meters)

Roads represent important items in the landscape configuration, which wolves are capable to identify and avoid, thus influencing their distribution [13]. According to the traffic intensity and width, roads were distinguished in two different categories: main roads and secondary roads. Main roads include highways, motorways, and national roads. The Euclidean distance is calculated from any point to the nearest main road.

A3. Distance to Secondary Roads (meters)

While the traffic on secondary roads is generally reduced, they can also affect the behaviour of wolves [14]. We considered all the autonomous roads that correspond to a large part of the road network in the study area as secondary roads. While they are thinner than main roads, they are more numerous and difficult to avoid for wolves. The Euclidean distance was calculated from secondary roads to any point in the study area.

A4. Road Density (m²)

According to several studies carried out in North America, road density is a major variable in the distribution of wolves [27]. We calculated overall road density (main roads and secondary roads) as the total road length in each of the 10 × 10 km grid divided by its total area [13]. Values for smaller resolutions were calculated using the Inverse Distance Weighting (IDW) interpolation.

A5. Population Density (inhabitants/km²)

The number of humans presents in a given region or area is a major factor that influences the foraging patterns of wolves [2]. We used municipalities’ census in 2017 from the National Statistics Institute (INE). We then used IDW interpolation to obtain the scores for each pixel on the map.

A6. Livestock Density (breeding cows/km²)

The abundance of domestic cattle may result in a greater number of wolves in a region, as they constitute an additional prey item, which is also, particularly vulnerable. In Ávila, the environmental service of the Junta de Castilla y León indicates that the 85% of the registered attacks were directed to calves. Therefore, livestock density was calculated based on the number of breeding cows in each municipality, which was downloaded from the open database of the Junta de Castilla y León. IDW interpolation was then applied to obtain the number of reproductive cows in each pixel.

2.2.1.2. Biophysical Variables

B1. Shannon Diversity Index

Wolves in general and the Iberian wolf in particular are known for their highly adaptive behaviour to different types of prey and environments [12].

The diversity of prey may offer a greater array of items to choose from with positive effects of the successful settlements of wolf packs [28]. We considered the diversity and evenness of prey available to wolves using the Shannon diversity index [29], computing the different CORINE Land Cover 2018 land uses included in each 10 × 10 km grid of the National Biodiversity Inventory (INB, MAPAMA). Shannon index was used to include the diversity of the landscape of the wolf home range, trying to differentiate natural from anthropogenic land uses. The values of this index increase when the number of species grows, but also when their relative abundance is even and then obtained the corresponding IDW interpolation for the chosen resolution.

B2. Species Richness (number for different species/km²)

Another way of categorising ecosystems is the number of species [30]. The overall number of plant and animal species referenced to the 10 × 10 km grid of the National Biodiversity Inventory (INB) was obtained from the Ministry of Agriculture, Fisheries, Food and Environment (MAPAMA). IDW was performed to obtain raster values at the chosen resolution. This variable is included in the model to differentiate those areas with high biodiversity from other areas that are poorer. In this way, the model can highlight how wolves would prefer richer or poorer ecosystems.

B3. Presence of Artiodactlys (artiodactyls/km²)

While wolves are generalist predators, in the absence of livestock, they more frequently prey on artiodactyls [3,31]. The species of artiodactyls present in the study area were selected using the 2016 National Biodiversity Inventory (MAPAMA, 2016). Among the present artiodactyls we found roe deer (Capreolus capreolus, Linnaeus 1758), wild boar (Sus scofra, Linnaeus 1758), Hispanic goat (Capra pirenaica victorieae, Schinz 1838) and red deer (Cervus elaphus, Linnaeus 1758). The presence or absence of artiodactyls on each grid was obtained using IDW interpolation at the grid resolution chosen.

B4. Distance to Hydrography (meters)

A major factor explaining the distribution of wolves is access to water [2]. Wolves travel great distances daily and thus require regular water uptakes [3]. The presence and distribution of water sources was obtained using the BTN200 database, and the Euclidean distance between these sources and each grid point was calculated.

C.1. Dependent Variable-Distance to Registered Attacks (number of attacks/km²)

The attacks on cattle in the years 2016 and 2017 reported by the Junta de Castilla y León were used as a dependent variable. Note, that these attacks are certified by the administrative authority prior to their inclusion in the register, providing their location and date. The register does not consider the output of the attack (simple bite, death of one or more animals are considered the same). The census does not specify either the type of livestock affected, but more than 80% of the attacks are on calves and in a small proportion, old or sick cows.

The Euclidean distance to the 2016 and 2017 attacks has been calculated, so that the final map shows by distances the probability of the different areas of the study to suffer attacks. A large distance to registered attacks means a low risk of attack.

2.2.2. Stage 2. Statistical Analysis

To test whether the set of variables chosen were able to accurately explain the attack risk, a glm was performed. The response variable is C1, and it is explained by all the other variables.

Having processed all the variables as described in Stage 1, it is necessary to take a series of samples, from which we will obtain data for each variable. This amount of sample must be large enough to be statistically significant for the total area of study. In this particular case, we have chosen to take the same amount of sample as from attacks, as has been done in other animal population modelling studies [32,33]. In this way, a layer of random points has been generated within the study area of 1770 points, which corresponds to the number of attacks recorded during the years 2016 and 2017, and which will be from where the data of the 11 variables will be taken.

Afterwards, the data of each variable (in raster format) are extracted for each sampling point, obtaining a layer, through which the statistical analysis will be performed. The glm was used to predict the number of attacks in response to the set of variables chosen [34].

2.2.3. Stage 3. Analysis of Significant Variables

Understanding the influence of the variables in the attacks of Iberian wolf on the cattle, it possible to calculate a model created from the selected variables. In this way, a raster map will be obtained, which represents the expected distances according to the model to the wolf attacks. This map, therefore, represents the probability that according to the model created, the different locations of the study area have to suffer wolf attacks in their livestock. This allows us to compare if the the model adjusts to the registered attacks of 2016 and 2017 and therefore, if the model would be able to anticipate the attacks of wolf, in areas where, it is thought that sooner or later it will recolonize again. In addition, there is a statistical data, which indicates the level of confidence of the model: the determination coefficient (R²). This coefficient determines the quality of the model to replicate results and the proportion of variation in results that can be explained by this model, which applied to the model created would be the proportion of the attacks that the model would be able to predict.

If you have data from actual wolf attack records, you can calculate the risk. The formula that defines risk is [35,36]:

$$\mathrm{Risk}=\mathrm{Probability}+\mathrm{Frequency}$$

The probability is calculated as described in the previous section, for the calculation of the frequency, being calculated for each grid by means of the expression:

$$\mathrm{F}=\frac{1}{\mathrm{number} \mathrm{of} \mathrm{years} \mathrm{of} \mathrm{record}} \ast {\sum }^{ }\mathrm{number} \mathrm{of} \mathrm{attacks} \mathrm{recorded} \mathrm{per} \mathrm{grid}$$

In this way, a risk map will be obtained for the study area.

3. Results and Discussion

3.1. Stage 1. Analysis of the Variables to Be Considered

The aim of processing the variables is to obtain a map of each one of them, in which the values are represented in each pixel of the map. As a summary,

Table 1. Summary of the basic statistics obtained in the processing of each variable.

Variable	Number of Cells with Data	Maximum Value	Minimum Value	Sum	Arithmetic Average	Standard Deviation
A1 (meters)	26,885,600	12,146.43	0	32,521,068,737.80	1209.61	1669.11
A2 (meters)	26,885,600	66927.13	0	348,723,596,948	12,970.65	16,353.62
A3 (meters)	26,885,600	11,790.78	0	24,061,785,943.20	894.99	1410.98
A4 (m2)	15,203,200	0.063	0	184,186.13	0.01	0.01
A5 (inhabitants/km2)	15,360,000	58,147	14	25,162,221,679	1638	3093
A6 (breeding cows/km2)	15,203,200	4114	0	6,232,913,316.60	409	412.59
B1	15,360,000	3.68	0.05	31,737,914.15	2.06	0.69
B2 (number for different species/km2)	15,360,000	253	61	2,116,696,272	138	26.50
B3 (artiodactyls/km2)	15,203,200	1	0	12,348,351	0.8	0.25
B4 (meters)	26,885,600	8604.72	0	18,021,992,738.70	670.32	976.15
C1 (number of attacks/km2)	26,885,600	12,146.43	0	32,521,068,737,80	1209.61	1669.11

shows the basic statistics obtained in the processing of each variable.

3.2. Stage 2. Statistical Analysis

In this stage, the variables are compared, adjusting them to a generalized linear model. Once the first adjustment has been made, the variables that have no influence on the statistical model are observed. This is determined according to its coefficient “p” (if it is greater than 0.05, the variable has no influence) and according to the limits of the expected values of each variable.

The model presented considers 7 compared variables, influential variables in wolf attacks on livestock. It was necessary to discard A1, which was the Euclidean distance to the population centers. As observed in the results, the distances were very homogeneous in almost all the territory, and it is for this reason that the model has not considered them influential. The same is true for the secondary roads, A3. The Euclidean distances to them were similar throughout the territory and, in addition, the wolf’s capacity to adapt probably gave it the loss of fear of crossing small roads, as shown by the numerous road traffic accidents suffered on Madrid’s mountain roads. The presence of artiodactyls, B3, has also been discarded. It was also to be expected after seeing the results, since its presence was confirmed in all the territory except in the northern area, where there are no wolves. In other words, there can be no attacks.

With the estimated error calculated, you can see how the model relates the variables with the distance to the attacks by observing the sign taken by the estimated error. We proceed to analyze them one by one and show in

Table 2. Estimated regression model results.

		Error
Parameter	Estimation	Standard Erorr	Lower 95% Confidence Interval	Upper 95% Confidence Interval	Variance Inflation Factor
CONSTANT	14,215.70	827.23	12,594.40	15,837.10
A2	0.29	0.02	0.24	0.33	1.21
A4	−51,236.00	18,889.40	−88,258.70	−14,213.40	1.27
A5	−0.28	0.05	−0.38	−0.18	1.10
A6	−3.22	0.35	−3.89	−2.54	1.13
B1	−7386.30	227.66	−7832.51	−6940.09	1.53
B2	55.25	6.72	42.06	68.43	1.83
B4	0.45	0.13	0.19	0.70	1.02
R2= 49.64%

In the case of this model, the results were as follows: R² = 49.64%. R² (adjusted by l.g.) = 49.43%. Standard error of the estimate = 5422.43. Mean absolute error = 4173.14. Durbin-Watson Statistic = 2.14. The R² statistic indicates that the model, thus adjusted, explains 49.64% of the variability of distance to wolf attacks. The adjusted R² statistic, which is more appropriate for comparing models with different number of independent variables, is 49.43%. The standard error of the estimate shows that the standard deviation of the residuals is 5422.43. This value can be used to construct prediction limits for new observations. The mean absolute error (MAE) of 4173.14 is the average value of the residuals. The Durbin-Watson (DW) statistic test determined that here is no significant correlation.

the results of the estimated regression model (Table 2).

3.3. Discussion on the Results of the Variables

3.3.1. Anthropogenic Variables

A1. Distance to Buildings

The shortest distances are found in the largest population centre, in the city of Ávila. Otherwise, the distribution of the buildings is quite homogeneous in the study area. These are relatively small buildings, but numerous and evenly distributed. In the southwest extreme, on the other hand, there is an absence of buildings. This area is known for its number of crops, where the cultivation of tobacco is remarkable [37]. Therefore, the area appears with almost no buildings, which does not mean that it is absent of human activity, because it is an important cultivation area in the region. A larger number of buildings can be seen to the north of these growing areas than in the rest of the study area, but they are also smaller. Generally speaking, the distances are medium-sized in the south extreme and south-west extreme, small in the north and central zone, and large in the south-west extreme and north-west extreme. However, the point that we should consider here is that wolves adapted to human existence can reach out to the villages with less housing. Transmitter-equipped Iberian wolves were detected within 200 m of dwellings [38]. In addition, it is reported that wolves can enter the residential garden and attack domestic animals, especially in winter [39].

A2. Distance to Main Roads

In the study area there are few sections of motorways or highways, however, the national roads that connect Ávila to the provinces of Cáceres, Madrid, Toledo, Valladolid, Segovia, and Salamanca, replace them in several ways. They are the roads that connect provinces and therefore those that will condense most of the transport related to goods. The speed of transit is somewhat lower than on motorways and the difficulty of overtaking greater, however the intensity of traffic can be very high. For this reason, it is possible to see a clear differentiation between the areas according to their distance to the main roads. As there are only five of them, the distances are small only where the roads pass, and quite large where they do not pass. The influence will not be homogeneous in the whole territory, but, probably, quite accentuated in the areas where these main roads are located.

The parameter estimated for the variable is positive, so the model interprets that the greater the distance to main roads, the greater the distance to attacks. In other words, the greater the distance to main roads is, the lower the probability of being attacked by wolf. This supports the finding that wolves avoid the close vicinity of villages and roads, as well as general proximity to major roads [40]. However, a study of wolf roadkill in the Castilla y León Region revealed that the deaths occurred in high traffic areas and were not affected by high traffic density [41]. Of course, these deaths increase during the wolf’s breeding time.

A3. Distance to Secondary Roads

Only regional roads have been considered as secondary roads, as motorways, dual highways and national roads have been considered as main roads. These roads are widely distributed in the study area. This typology of roads is in charge of the union between the most important roads. They do not have high heavy traffic intensity, but they are the connection roads for the residents, so the traffic will be quite continuous. The distribution of this variable is similar to the A1 variable. They are homogeneously distributed in the study area, except for the south-west area. It can therefore be considered that their influence will be homogeneous throughout the territory and that it will not be excessively determining.

A4. Road Density

The highest densities accumulate in the surroundings of the city of Ávila and the lowest in the northern area. The high density of roads in the south-south-west area stands out, because the number of secondary roads in that area, as seen above, is limited. This will happen because two important national roads cross that area and will accumulate many kilometres of road. Heterogeneity is observed in the value of the variable for the study area, so there can be expected, as in the main roads, high influence in the bordering areas to high values of the variables and little or none in the areas with low values.

The parameter estimated for the variable is negative, so the model interprets that the lower the density of roads, the greater the distance to the attacks. In other words, territories with lower road density are less likely to suffer wolf attacks. Qualitatively speaking, it expresses the same as the A2 variable. It seems clear that the more roads, either in terms of density (A4) or distance (A2), the greater the probability that livestock will be affected by the wolf. This may have an obvious explanation. The pasture areas where cattle are extensively farmed often have numerous roads around them. Cattle breeders are looking for grazing areas well connected by roads to facilitate their care work. For this reason, there will be more cattle in areas with many roads and, therefore, more attacks. In previous studies of wolf population modelling, this variable also had the same type of influence [13].

A5. Population Density

We find a high density of inhabitants in the vicinity of the city of Ávila and towards Madrid (East). The rest of the study area has constant low population values between 203 and 3000. On the southern slope of Gredos there are several municipalities with higher values than the rest of the territories, with over 5000 inhabitants in some areas.

This variable is interpreted as inversely dependent on the distance to the attacks. In other words, the lower the population density, the greater the distance to the attacks and the lower the probability of attack. It is also noteworthy that, as happens in the previous variables, the greater the human activity, the greater the probability of suffering attacks. In this case, the greater the density of inhabitants, the greater the probability of suffering attacks. This may be because in the most inhabited areas are usually the most degraded and therefore the wolf cannot optimally develop their hunting, either by the absence of potential prey or by the absence of ecosystems suitable for their survival.

A6. Livestock Density

There are three areas with high livestock intensity in the study area: the east-center of the study area, the southeast extreme in the vicinity of Toledo and the east extreme, between Segovia and Madrid. There are areas with more or less intensity, but in practically all the territory there are cows extensively farmed. Therefore, the wolf has, regardless of its location, always cattle in its environment that can be attacked.

The parameter estimated for the variable is negative. For this reason, the lower the livestock intensity, the greater the distance to the attacks. In other words, as expected, the greater the livestock intensity, the greater the probability that it will be preyed on by the wolf. For instance, in north-central Portugal, where the most suitable habitats for wolves have already been identified, optimal habitat is characterized by lower human presence and higher animal density [41].

3.3.2. Biophysical Variables

B1. Shannon Diversity Index

The most important thing to bear in mind when observing this variable is that the maximum value that the index can take for the ecosystem typology of the study area is 5 [42]. It is observed that the ecosystems in the north of the study area are much less diverse than the rest and it is very remarkable that in the vicinity of the city of Ávila, there is an area with a very low diversity. This is probably due to the continuous overexploitation of pastures by livestock for many years, as this area, which has been visited during the study, stands out for the intensity of livestock that can be seen with the naked eye. The continuous browsing and the absence of scrub make the existence impossible due to the lack of an adequate ecosystem for numerous species. In the southwest extreme, the highest values of diversity can be observed, associated with the presence of protected areas. This is due to the fact that this area is largely one of the areas with the highest rainfall in the Gredos mountain system, which makes possible the existence of species that cannot inhabit other places [43]. Along this mountainous system, we find medium–high diversity data. There is heterogeneity in the variable, and we will see later if this influences wolf attacks on livestock.

The statistical coefficient is negative. This implies that the lower the Shannon index, the lower the probability of suffering wolf attacks, meaning that most attacks occur in places with high Shannon indexes. In order to interpret it, it is necessary to think again about where the cattle graze. In the case of the study area, cattle graze in almost all non-mountainous areas [44]. The areas with the lowest Shannon indexes correspond to cultivated, used, or abandoned areas. In other words, cows do not graze in places with the lowest Shannon indexes and therefore cannot be attacked by wolves in these places. The areas where these cattle graze tend to be areas with average Shannon indexes in the study area analyzed.

B2. Species Richness

Species richness is an approximate measure of the diversity of an ecosystem [38]. It does not measure diversity; it is only a summation of the number of plants and animals present in each grid in this case. On the way to Madrid (East) there is an area with a high wealth, promoted by the orography that connects Ávila to Madrid. This causes different ecosystems to be created according to orientation and altitude, and, for this reason, the number of species observed is greater [45]. The same happens in the southwestern slope of Gredos, where the Shannon diversity index already showed us quite diverse ecosystems, the high richness observed corroborates what was predicted before. In the central area and the northern slope of the Gredos Mountain system there is a limited richness, promoted by the lack of heterogeneity of the orography. In addition, these areas are very anthropized by recent extensive cultivation and extensive grazing for years [46].

The statistical coefficient is positive, which is interpreted as the greater the species richness, the greater the distance to the attacks and, therefore, the lower the probability of attack. In other words, attacks occur more in the least rich places. This can be interpreted in two different ways. Either the wolf, in not very rich places only has option to prey on cattle or that either the cattle is always established in the most anthropized places and less rich [47]. That is why the attacks occur more there.

B3. Presence of Artiodactlys

The species of artiodactyls that have been analyzed for this variable correspond to the natural prey that the Iberian wolf prefers [12]: roe deer (Capreolus capreolus, Linnaeus 1758), wild boar (Sus scofra, Linnaeus 1758), Hispanic goat (Capra pirenaica victorieae, Schinz 1838) and red deer (Cervus elaphus, Linnaeus 1758). The data were downloaded from the 2016 National Biodiversity Inventory.

Except for the northern region of the study area, where the absence of scrub and forest precludes the existence of artiodactyls [48], it can be concluded that the wolf has, in principle, theoretical prey throughout the study area. However, it should not be forgotten that depending on the size and experience of the herds, they are capable of killing different species of artiodactyls [2]. Thus, a small and inexperienced herd would not try to hunt a wild boar, for example, since it involves too much risk and energy expenditure [49].

B4. Distance to Hydrography

The distances to the water cores in the study area are short. There is some difference between the northern and southern areas, having the latter smaller distances to the water cores than the former. It was to be expected, as there are more watercourses in the south than in the north. The western zone, together with the north, are the ones in which the distances to the water courses are greater, because the quantity of these is smaller.

The parameter estimated for the variable is positive. It is therefore interpreted that the greater the distances to hydrology, the greater the distance to the attacks, the less probability of suffering them. The further away we are from a water core, the lower the probability of suffering attacks. The majority of attacks therefore occur in places close to water cores. As in the previous variable, there are two possible explanations. Either most of the cattle are established around water cores, or it represents the proximity to these watercourses an incentive for the wolf to attack livestock.

3.3.3. C.1. Dependent Variable-Distance to Registered Attacks

We distinguish a priori two areas where the smallest distances are accumulated, that is to say, two areas where wolves tend to attack livestock more frequently. The central-east area, southeast of the city of Ávila, the vicinity of the municipalities of Tornadizos, Santa Cruz and Herradón de Pinares and the central-southwest area, in the municipalities of San Martín de la Vega del Alberche and San Martín del Pimpollar. The absence of attacks in the north is also noted, due to the absence of medium-high vegetation, making it impossible for wolves to live in the area and not facilitating their movements [3].

It is also important to point out that although small distances to the south of the Gredos mountain range can be seen, they occur only because a single attack was suffered in 2016, caused by a lone wolf (Junta de Castilla y León, Junta of Castile andLeón, Spain, 2017). The breeding in the south of this system has not been confirmed, so there is no population of wolves, for now, in the provinces of Cáceres or Toledo. On the other hand, the sporadic predation of wolves on mountain goats in the Gredos mountain range has been confirmed. As far as we can see, when the density of wolves increases, they will move across the mountains towards the south in search of new territories to recolonise.

3.4. Stage 3. Analysis of Influential Variables

In this last stage, the model calculated in previous sections is applied, obtaining a final probability map, which represents the probability of the different areas to suffer wolf attacks, through distances. The formula obtained is as follows:

C1.Distance tothe attacks = 14,215.7 + (0.289015 *A2.Dist.main roads) – (51,236.0 *A4.Roads Dens.) – (0.284699 *A5.Population Dens.) – (3.21817 *A6.Livestock Int.) – (7386.3 *B1. Shannon Index) + (55.2475 *B2.Richness) + (0.447891 *B4.Dist. hydrography)

And by its application the following final map is obtained (Figure 3):

The distances between −22.686 and 3.214 have been taken as high probability values, the values between 3.214 and 10.137 have been taken as medium probability values and the values between 10.137 and 24.359 have been taken as low probability values. This classification has been made based on the usual areas of championship of the Iberian wolf [12] and in the ranges that better adapted the final data for its visualization.

It can be seen how the model optimally assesses the areas most likely to be attacked. In northern areas, the risk of attacks is low, due to the absence of significant predator densities, while areas where predator and livestock match are more likely to be attacked. It is also warned that the anthropization of the territories has a significant influence, since the bordering areas of large villages the probability is maximum. Therefore, it can be concluded that the extreme anthropization of the territories derives in the decrease of potential wild prey for the wolf [4] and in an increase of domestic prey. Consequently, there are more attacks on livestock [50].

Risk of Wolf Attacks

Performing the operations described in the methodology, we obtain the attack risk map for the study area (Figure 4). The results have been softened and concretized with regard to the previous probability map, so that it will adjust better to the reality of the attacks.

With this result, a prevention plan can be developed, in which dissuasive measures such as the use of mastiffs, enclosures, electric fences or the implementation of RAG (radio activated guard) can be implemented in places at risk of attacks, in order to reduce or eliminate their incidence on the livestock economy, as shown in different studies [6,24,51]. Depending on the level of risk of the area to be treated, more or less complex measures will be implemented. Thus, in high-risk places, more effective measures should be implemented, which usually require a greater effort in time and money, such as the RAG [26]. Meanwhile, in areas with medium or low risk, positive results will be achieved with the use of guard mastiffs, of autochthonous breeds, such as the Spanish Mastiff or the Leonese, that have good guarding skills for both sheep and cattle [52], if the number of individuals used is adequate [20]. With this categorization, it is possible to discard livestock areas in which the probabilities of attack are very low in order to exclude them from the preventive plan and save economic resources.

The information obtained is very useful in reconciling the presence of wolves in the area and livestock activity, and therefore very useful for the conservation of the species, since long-term conservation is not possible without a social conscience to protect it [53].

The current social tension is very high and breeders demand population controls of the canine, which on certain occasions have been carried out under the protection of the European Union [54], with the idea that attacks on livestock will be reduced, but the reality is that these population controls increase the depredation of wolves on livestock, due to the social restructuring that is incumbent [55,56,57]. For this reason, the results provided are relevant, generating immediate results so that the livestock sector relaxes its position and tension, but at the same time, be compatible with the conservation of the great predator of the Iberian Peninsula [58]. Prevention, as mentioned above, fulfils both requirements and the methodology designed optimizes its application to make the administration less reluctant to implement [25]. In addition, it can be applied to all the territories where the species lives or where it is likely to settle in the near future, as is the case of the southernmost regions of the Iberian Peninsula (regions such as Extremadura, with the aim of developing a prevention plan, before the first attacks on livestock occur, avoiding the tension of livestock farmers and favoring the social perception of the animal for conservation).

4. Conclusions

The calculated risk for the study area shows a central strip across the study area, where the risk is highest. At the northern and southern extremes, the risk is minimal. The areas of Tornadizos de Ávila and San Martín de la Vega del Alberche, and San Martín del Pimpollar (central areas of the study area) are the ones that register the most attacks and where the calculated risk is high.

The probability calculated through the fit to a linear model responds to 50% of the registered attacks and should be taken into account as a limitation of its application in new territories. It has proved to be useful for the discrimination of areas with very low probability, but not so much for specifying the areas with the highest probability. The best way to avoid losses for the farmer and to ensure that wolf populations continue growing or stabilising is to use preventive measures. In order to reduce the wolf–human conflict, it is necessary to take measures on both sides as minimizing wildlife deaths is a top priority for wolf management.

The main and most important conclusion that has been reached during the development of the work is that facing the conflict we are dealing with, there are numerous physical planning tools to minimize it. In the wolf–human conflict, the roles must be fairly well defined. Scientists must demonstrate how conflict should be reduced. The political conjuncture should play a role in how partnerships between government institutions and people will be, and most importantly, in providing finance.