Lynx data were collected by two domestic non-governmental organisations (Sect. S0 in the Supplement) using a 50-question face-to-face interview with key informants (i.e. hunters, game wardens, foresters, shepherds, livestock breeders, beekeepers, cafeteria or market owners) in randomly selected villages in the northern and eastern Albania (91 villages) and western the FYR of Macedonia (154 villages) (Sect. S0) (Ivanov et al., 2008). At least two people were randomly selected to be interviewed in each village by Ivanov et al. (2008). A grid cell of 10 km × 10 km for Albania and the FYR of Macedonia (henceforth “Macedonia”) was used based on the lynx population and lynx population density in 2001 of the publication of Arx et al. (2004) (Ivanov et al., 2008). The population density of the lynx was estimated to be between 0.65 and 1.09 in Albania and 2.06 in Macedonia in 2001 (see Sect. S0). The spatial coverage of this survey was approximately 13 600 km2 (i.e. 63 grid cells in Albania and 73 grid cells in Macedonia, Ivanov et al., 2008). The occurrence of the lynx and lynx prey (chamois, brown hare, roe deer) was based on the “relative number of positive answers” of interviewees on the species occurrences (Sect.  of the questionnaire was on presence and distribution of large mammal species in the last 5 years; Sect. S0), in a 10 km × 10 km grid cell. A probable occurrence (permanent occurrences in this study) was selected if there were more than 50 % affirmative answers (to questions, e.g. on hard facts like lynx tracks, stuffed lynx, prepared lynx pelts, lynx attacks on humans, lynx attacks on domestic animals, more than one lynx or female with cubs observed) of interviewees on the species occurrence in a grid cell of 10 km × 10 km (Ivanov et al., 2008). A possible occurrence (temporal occurrences in this study) resulted if there were less than 50 % of affirmative answers of interviewees on the species occurrence in a grid cell of 10 km × 10 km and no species occurrence if there were no affirmative answers (i.e. on hard facts like lynx tracks, stuffed lynx, prepared lynx pelts, lynx attacks on humans, lynx attacks on domestic animals, more than one lynx or female with cubs observed) of the interviewees on the species occurrences in a grid cell of 10 km × 10 km (Ivanov et al., 2008). See Sect. S0, for detailed information on lynx data collected between 2006 and 2007, as well as for data on lynx distribution and lynx data in 2001.

The Balkan Lynx Recovery Programme collected the lynx prey occurrence records consisting of species of brown hare, chamois and roe deer (Ivanov et al., 2008). Roe deer occurrences were located mostly in the same grid cell of 10 km × 10 km of the lynx occurrences (Ivanov et al., 2008). Brown hare and chamois had the widest and the smallest distribution, respectively. Chamois and brown hare records were used in this study to investigate any spatial effects of the smallest distribution of chamois and the widest distribution of brown hare in the occurrence (records) of the lynx in terms of neighbourhood scale of the best-performing model 1 (see Model selection for the lynx). In total, 87 % of records of chamois and 89 % of records of brown hare were located from approximately 2 to 23 km from the closest lynx occurrences. For more information on lynx prey occurrence data collected between 2006 and 2007, see Sect. S0.

We used 109 (39 permanent and 70 temporal) lynx occurrence records, 114 chamois occurrence records, 135 occurrence brown hare records in protected areas and public-owned land, in our study area. The lynx occurrence records (109) consisted of 37 lynx permanent occurrences records (25 in Macedonia and 12 in Albania) and 72 lynx temporal occurrences records (36 in Macedonia, 26 in Albania, 6 in Montenegro, and 4 in Kosovo). We geo-referenced lynx occurrence records from for the lynx in Kosovo and Montenegro from the maps of Arx et al. (2004), and lynx occurrence records from 2006 to 2007 in Albania and Macedonia from the maps of Ivanov et al. (2008) (Fig. 1). We also geo-referenced occurrence records of species of lynx prey of a resolution 10 km × 10 km for Albania and Macedonia from the maps of Ivanov et al. (2008), the Balkan Lynx compendium (IUCN/SSC Cat Specialist Group, 2011). We then obtained the coordinates of X and Y of the lynx occurrences and of the species of lynx prey (chamois and brown hare). We assigned a location for each species (lynx, chamois, brown hare) within a 1 km × 1 km grid cell study unit by spatially joining the layer of the species occurrence record and of the grid 1 km × 1 km using Spatial Join of the Analysis Tool in ArcGIS transferring the attribute of species occurrence record (X, Y) to the 1 km × 1 km grid (for each species i.e. lynx, chamois, brown hare).

We argue that the lynx may be anywhere in a 10  × 10 km cell; however, the lynx is also thought to perceive forests up to 1 km apart as connected (Kramer-Schadt et al., 2005). Thus we chose to undertake the study using a spatial resolution of 1 km2.

We used pseudo-absences to use our species distribution models. We selected pseudo-absences following three criterion concerning the total number of pseudo-absences, the number of locations of pseudo-absences from a given cell of 1 km2, and the location of pseudo-absences in forest areas (Sect. S1 in the Supplement).

We developed species distribution models based on the permanent occurrences data. The models were based on information-theoretic methods, which focus on the search for a parsimonious model as the primary philosophy of statistical inference (Burnham and Anderson, 2002; Johnson and Omland, 2004). We identified a set of a priori hypotheses on the estimated probability of the lynx occurrence that describe the natural conditions and resources required for refuge, food and breeding of the lynx based on knowledge on ecology and biology that exists for the Balkan lynx and Eurasian lynx (Table 1). We split the variables for species distribution modelling into two categories, namely “natural” and “human”, e.g. a “two dimensional” habitat model that was developed for the brown bear in Spain (see Naves et al., 2003). The “natural” hypothesis has environmental variables that are related with food abundance of the lynx and forest connectivity. The “human disturbance” hypothesis assumed that human activities (e.g. land-use activities and roads) affect (lynx) mortality (Naves et al., 2003). Natural factors consisted of layers such as forest cover, elevation and the terrain ruggedness index (derived from slope of terrain), coniferous forests, broadleaved forests mixed forests, pastures, bare rocks and transitional shrub land-woodland composing model 1. The human variables comprised layers such as agricultural land, urban land, burnt land, Euclidean distance to road (i.e. proximity to roads), Euclidean distance to human settlements, and village density composing model 2 (see Sect. S2 for details). The layers depicting land cover, forest cover, roads and villages were transformed into a set of neighbourhood variables (calculating the mean value of the original variable within a specified neighbourhood radius around the target cell) from 1 to 15 grid cells (corresponding to a radii of 1, 2, 3, 4, 5, 10, 15 km) and resulted in a total of 84 neighbourhood variables for potential use in the lynx models. The neighbourhood variables helped obtain information about the scale at which the lynx perceived the landscape and at which (natural) resources needed to be available. For details on neighbourhood variables see Sect. S3. The range of neighbourhood values (i.e. 1, 2, 3, 4, 5, 10, 15 km) corresponded roughly to the known variation in home-range size of the lynx (Bojovič, 1978; Balkan Lynx Strategy Group, 2008). We removed all variables that were highly correlated (Pearson correlation test; r > 0.7) and variables that did not show statistically significant differences between occurrence and pseudo-absence locations of the lynx (Kruskal–Wallis test; p > 0.05) (Sect. S4). We calculated the spatial autocorrelation of the dependent variable and for further details on spatial autocorrelation see Sect. S5.

We used generalised linear models (GLM) with logit-link to relate occurrence and pseudo-absence data to sets of explanatory variables to predict the probability of occurrence of the lynx in the study area. GLMs are an extension of classic linear regression models (McCullagh and Nelder, 1989). We used binomial error structure (logistic regression) to account for the lynx data structure. A logistic regression model predicts the probability of the occurrence of the lynx (e.g. for food and or refuge) at a given location within the study area. An estimated high probability of occurrence of the lynx would indicate suitable habitat of the lynx (suitable habitat is above the threshold value of the probability of occurrence of the lynx that is estimated by the species distribution modelling; see Model selection for the lynx and Model evaluation). All GLM (and resource selection probability function (RSPF) models that calculate species habitat selection are shown in Model evaluation) were fitted within the program R 2.9.0 (R Development Core Team, 2009).

In total, we fitted 11 GLM candidate models for the lynx comprising the two categories of variables (candidate models are in Sect. S6 and the results of best models are in Sects. S7, S8). We selected the most parsimonious model from 11 candidate models using the corrected Akaike information criterion (AICc) for small samples (Johnson and Omland, 2004). The uncertainty was assessed using AIC weights (e.g. Fernández et al., 2006). AIC weights represented the relative likelihood of a model. AIC weights was taken as the approximate probability that each model is the best model out of the set of all proposed models (Anderson et al., 2000). We also calculated the difference of corrected Akaike information criterion ΔAICc between competing candidate models (in Sect. S7). We mapped out predictions of probability of lynx occurrences for the most parsimonious model to identify the high probability values of lynx occurrences (most suitable habitat) and the low probability values of lynx occurrences (marginal and non-suitable habitat). We calculated the average value of estimated probability values of the lynx occurrences from 0.50 (e.g. Naves et al., 2003) to 1.00 to select a threshold (e.g. Liu et al., 2005). An estimated probability value above the threshold value, e.g. of 0.5 would be a suitable habitat. Marginal habitat and non-suitable habitats had values below or equal to this threshold value, e.g. of 0.5 for the lynx. The layers of model 1 and of model 2 were used as the biodiversity layer and cost layer, respectively, in Zonation to identify conservation areas for the lynx.

We evaluated our models using three methods. First, all models were evaluated by calculating the area under the receiver operating characteristic curve (AUC). The value of AUC is from 0 to 1. A model with a value of AUC ≥ 70 % performs well and a model with a high value of AUC ≥ 90 % indicates outstanding discrimination between estimated high probability values of lynx occurrences (occurrences) and estimated low probability values of lynx occurrences (pseudo-absences in this study) (Hosmer and Lemeshow, 2000). We also calculated the predictive accuracy of the most parsimonious (from all candidate models) model using the deviance explained in percentage (D2). We used cross-validation for logistic regression with a binary dependent variable because we had only one data set to check if there was over-fitting in the fitted models (e.g. Fernández et al., 2003; Kanagaraj et al., 2011). Our data set was divided into 10 parts (folds) where nine folds were used for fitting the model and the tenth fold was used for testing the model. This was repeated 10 times so that each fold was used for model testing. We considered the value of predicted probability (i.e. “cross-validation estimate of accuracy”) which was calculated as an average value of probability after testing the model 10 times. A predicted probability value is from 0 to 1 (for details see DAAG package in R Development Core Team, 2009). Second, we calculated the resource selection probability function (RSPF) (Johnson et al., 2004; Lele et al., 2013; Thurfjell et al., 2014) for 11 (GLM) candidate models. RSPF shows the probability that an available natural resource unit, e.g. chamois prey, is selected (Thurfjell et al., 2014) by the lynx when encountered. We assessed the model fit (logistic regression with 39 permanent occurrences and 39 pseudo-absences) for 11 RSPF candidate models using Hosmer–Lemeshow test for goodness of fit by calculating the log-likelihood, the Bayesian information criteria (BIC), and the chi-squared test statistic (χ2) (Hosmer and Lemeshow, 2000). We calculated the p value for 11 RSPF candidate models to assess the statistical significance of 11 RSPF candidate models (see, e.g. Johnson et al., 2004). We ran the best RSPF model (out of 11 RSPF candidate models) with 10 permanent occurrences and 10 randomly selected pseudo-absences i.e. we removed (at random) 25 % of 39 permanent occurrences of the lynx. We calculated the Spearman correlation coefficient between the best RSPF model with 10 permanent occurrences and 10 randomly selected pseudo-absences and the best RSPF model with 39 permanent occurrences and 39 randomly selected pseudo-absences (i.e. no permanent occurrences removed). We removed (at random) 51 % of 39 permanent occurrences and of 39 pseudo-absences of the lynx. We ran the best RSPF model with 20 permanent occurrences and 20 randomly selected pseudo-absences of the lynx. The Spearman correlation coefficient was then calculated between this RSPF model with 20 permanent occurrences and 20 randomly selected pseudo-absences of the lynx and the best RSPF model with 39 permanent occurrences and 39 randomly selected pseudo-absences of the lynx. A high value of Spearman correlation coefficient shows a strong prediction by the best RSPF candidate model (e.g. Johnson et al., 2004).

We then applied the best RSPF model in the Step-Selection Function (SSF) using Geospatial Modelling Environment (GME) (www.spatialecology.com/gme/). The SSF is normally used with telemetry data of species involving randomly walking of animal (see, e.g. Proulx et al., 2013). The SSF links consecutive 39 lynx locations that are called (used) steps (Thurfjell et al., 2014). We made three assumptions for the SSF. Firstly, we assumed that our lynx data were as accurate as the telemetry data of species for our data modelling (e.g. Johnson et al., 2008). Secondly, we assumed no seasonal variation for collected lynx data in year 2006. We expected five “available” random steps for each of the lynx's steps used (e.g. lynx canadensis in Thurfjell et al., 2014). For each used and random steps, we calculated the step length and turning angles using non-linear functions (for details, see Beyer, 2015). Thirdly, we assumed an exponential function to calculate the lynx step length with a different single rate parameter and we assumed wrapped Cauchy function (see Beyer, 2015) to calculate lynx turning angles. We simulated our SSF model 30 times. We calculated the number of lynx steps predicted by each SSF model simulation. We then overlapped the predicted lynx steps by each SSF model simulation with predicted probability of occurrence of the lynx (above the threshold of estimated probability of occurrence of the lynx; see Model fitting) by our best GLM model. We selected the SSF model simulation with the highest number of lynx steps overlapped with predicted probability of occurrence of the lynx (above the threshold of the estimated probability of occurrence of the lynx) to calculate the mean of step length of the lynx. We compared the step length mean (in km) of the selected SSF model simulation with the range (radius in km) of neighbourhood variables of our best GLM models. We also overlapped the predicted lynx steps by the selected SSF model simulation with the prioritised conservation areas of 10 and 20 % by Zonation. Third, we randomly removed 1, 2, 4, 8, and 16 permanent occurrences and replaced the same number of removed permanent occurrences (1, 2, 4, 8, and 16) with randomly selected locations (no presence) from 136 cells of 10 km × 10 km of the lynx survey of Ivanov et al. (2008) and we ran the best GLM model. We did the same for combined permanent and temporal lynx occurrences (see Sect. S9 in the Supplement).

Finally, we collected information on evidence for lynx presence (photos) in the study area. We used Google Earth, ArcGIS and information about the locations evidence of lynx presence gathered in the study area to overlap with the predicted probability of occurrence of the lynx (see Evaluation of GLM models). This information was collected in National Park Rugova in 2015, western Kosovo, in Munella Mountain in 2014, in Thethi National Park, and in Thira in 2015, northern Albania, in Pelister National Park in 2013, and in Mavrovo National Park in 2015, Macedonia (Balkan Lynx Recovery Programme, 2014). In Albania, all lynx photos in 2014 were taken by camera traps that were placed from 1 to 2 km from each other covering an area of 400 km2 (Balkan Lynx Recovery Programme, 2014).

The conservation planning software package “Zonation” (Moilanen et al., 2012) was used to identify well-connected habitat in the landscape suitable for lynx conservation (see Sect. S10 for the Zonation configuration settings used). Although Zonation is designed for prioritising areas with multiple species, it is also appropriate to use with a single species. Here, we utilise features of Zonation which allow us explore locations for extending existing conservation areas while accounting for connectivity (of the lynx habitat). The main output of Zonation is a landscape prioritisation in the form of a raster map where each raster cell is ranked in terms of its importance in providing lynx habitat. Thus, Zonation can be used to identify locations in the landscape that should be protected to ensure the conservation of the lynx. Using Zonation we examined the extent to which existing protected areas in the four countries overlapped the most important areas for lynx conservation as predicted by Zonation. We then undertook a separate Zonation analysis to examine how these protected areas should be expanded to maximise conservation benefits to the lynx.

We used the species distribution model derived from natural factors as the primary input for Zonation. The core-area variant of the Zonation algorithm was used (Moilanen et al., 2005), which minimizes biological loss by iteratively picking a cell i, for removal that has the smallest biological loss, δ until all cells have been removed. For a single species, the biological loss is determined by δi=QiSci. The function Qi(S) identifies the proportion of the remaining distribution of lynx habitat located in cell i, out of in the remaining cells to be prioritised, S. When a part of the distribution of the species is removed by Zonation, the proportion located in each remaining cell is raised, which results in Zonation attempting to maintain core areas of lynx habitat until the process of cell removal was finished. Ci is the cost associated cell i (Moilanen, 2007). We used the species distribution model derived from human factors to generate the cost layer. This was chosen as all the factors in this model were thought to be detrimental to the lynx, and we inverted the layer so that areas with low values of the estimated probability of the lynx occurrence (marginal and non-suitable habitat; see Model selection for the lynx and Model evaluation) had a high cost, and areas with high values of estimated probability of the lynx occurrence (suitable habitat) had a low cost of lynx conservation. (This means that suitable habitats are less expensive to maintain, manage, and conserve the lynx habitat located in natural and semi-natural forests compared to non-suitable habitats located in agricultural areas for the lynx. We assume the land conversion from non-preferred agricultural land to preferred forested land would be associated with a high cost for the conservation of the lynx).

The boundary quality penalty (BQP) function of Zonation was used in our analysis to incorporate spatial aggregation into the areas prioritised for the lynx for conservation. When using the BQP, Eq. () is replaced by a more complex equation to determine the cell removal rule (for details see Moilanen, 2007). This allowed the habitat value of each cell to be adjusted based on proportion of the cells containing habitat within a specified neighbourhood around a given focal cell. The BQP is characterised by an effect radius and a response curve. The effect radius specifies the size of the neighbourhood used in calculating the BQP. For the lynx we used an effect radius determined by the radius of the neighbourhood variable used in the best fitting model 1; this value was 4 km2( corresponding to 50.2 km2). The response curve specifies how the local quality of a focal cell changes when different proportions of areas with high probability of lynx occurrences are lost from within the effect radius, and it is related to the sensitivity of the lynx to fragmentation of its habitat (Moilanen and Wintle, 2007; Gordon et al., 2009). The BQP curve used for this analysis is given in the Supplement (Sect. S10). The Zonation analysis was done using maps with the same 1 km2 resolution as used in the species distribution modelling.

Finally, Zonation was run in both “constrained” and “unconstrained” mode. In the unconstrained mode, the algorithm can pick cells purely based on Eq. (). In the constrained model we included the current protected areas using Zonation's mask function (Moilanen et al., 2012). This forced the raster cells in the protected areas to have the highest rankings to determine areas to extend the current set of protected areas.

The best RSPF model (selected model) was model 1 at the range of approximately 50 km2. This model fully agreed with the best GLM models in terms of sign of coefficients and of variables. RSPF model 1 is statistically significant (p value of 0.026) with a negative value of log-likelihood of 93.3, with a value of χ2 of 17.3 and the lowest value of AIC of 196.6 from 11 RSPF models. The neighbourhood scale of this RSPF model 1 has a radius of 4 km, implying that the natural resources and prey are available and encountered by the lynx at the range of approximately 50 km2, the lynx selects these natural resources, e.g. for food (Table 3). The Spearman correlation coefficient between the best RSPF model (no permanent presence removed) and the best RSPF model, removing 25 % of the permanent occurrences, was 0.93. The Spearman correlation coefficient between the best RSPF model (no permanent presence removed) and the best RSPF model, removing 51 % of the permanent occurrences, was also 0.93, indicating strong prediction by the best RSPF model (see Model evaluation). We simulated SSF with the selected RSPF model (model 1). We selected SSF model simulation with 222 predicted lynx steps as the best SSF model simulation. We overlapped 222 predicted lynx steps by the best SSF model simulation with predicted probability of occurrence of lynx with H>0.65 (threshold) of best GLM model (model 1 in Table 2). The selected SSF simulation had the highest number of steps of 36 % and a mean step length of 3.3 km for 222 predicted lynx steps by 30 SSF model simulations. The mean step length of 3.3 km corresponds closely to the radius of 4 km of our neighbourhood variables (at range of approximately 50 km2) for our best GLM models (Table 2). We mapped out the predicted probability of occurrence of the lynx (H > 0.65) by the best RSPF model and predicted probability of occurrence of lynx with H > 0.65 by our best GLM model. We found that maps of the best RSPF model and best GLM model were very alike (Fig. S9 in the Supplement). Predicted probability of occurrence of lynx with H > 0.65 by best RSPF model and predicted probability of occurrence of lynx with H > 0.65 by our best GLM model resulted in 11.9 and 11.8 % of the entire study area, respectively. This indicates GLM model adequately predicted the probability of occurrences of the lynx.

Finally, we found that predicted lynx steps by SSF model increased from 36 % in areas with high probability of lynx occurrence (H > 0.65) to 50 % in areas with low probability of lynx occurrence (H > 0.50 to H < 0.65), estimated by our best GLM model (Fig. 2c). We overlapped 222 predicted steps by the selected SSF simulation with prioritised conservation areas of 10 and 20 % by Zonation. We found approximately 20 and 56 % of all steps inside of prioritised conservation areas of 10 and 20 % by Zonation, respectively (Fig. 3). We also simulated SSF model with RSPF model 2 including agricultural land at the range of 314 km2. Then, we overlapped 195 lynx steps predicted by the SSF model (with RSPF model 2) simulation with predicted probability of occurrences of the lynx with H > 0.50 (threshold of estimated probability of occurrences of the lynx) for the GLM model 2 (see Table 2). We found that 89 % of all steps predicted by this SSF model (with RSPF model of anthropological factors) simulation were associated with no agricultural land.

The change of AICc was below 2 (ΔAICc <2) between models of the best GLM model (model 1 in Table 2) with 1, 2 randomly removed permanent occurrences and the best GLM model (no permanent occurrences removed). Models with randomly removed 4, 8, and 16 permanent occurrences had a change of AICc above 2 (ΔAICc > 2) compared to our best GLM model (see Model evaluation). Results are shown in Sect. S9.

All evidence of the lynx overlaps with areas with high probability of lynx occurrences of H > 0.65 and with areas with low probability of lynx occurrences (marginal habitat) of H > 0.50 and H < 0.65 in Fig. 2 and in Sect. S11. Four pieces of evidence numbered (1), (2), (5) and (6) were inside of protected areas, and numbers (3) and (4) were in the surrounding protected areas. Evidence piece (3) was 12 km, and evidence pieces (4) was a 5 km (straight line) far from the closest protected area boundary (see Fig. 2b).

We mapped out the estimated probability of occurrence of the lynx in the model 1 and model 2 (Table 2; Fig. 2). The cut-off value in the estimated probability of occurrence of the lynx (predicted habitat suitability, H) in the model 1 was H > 0.65 and in model 2 H > 0.50. This cut-off enabled us to distinguish areas with high probability of lynx occurrence (e.g. for model 1 H > 0.65) from areas with low probability of lynx occurrence (e.g. for model 1 H < 0.65) (see, e.g. Naves et al., 2003). Areas with high probability of lynx occurrence (suitable habitat) tended to occur in forested areas and areas with high elevation, while areas with low probability of lynx occurrence (marginal and non-suitable habitat) was concentrated in low land and non-forested land (i.e. agricultural land; the expansion of agricultural land may decrease the areas of areas with estimated high probability of lynx occurrence of the lynx in the study area). Patches with estimated high probability of lynx occurrence were fragmented and divided by areas of estimated low probability of lynx occurrence.

The areas with estimated high probability of lynx occurrence was spatially distributed over all four countries in the study area. Two large areas with estimated high probability of lynx occurrence, one spanning Montenegro, Kosovo, and Albania, the other spanning Albania, Kosovo, and the FYR of Macedonia is a key finding of this analysis (indicated by the zoomed-in maps in (a) and (b) in Fig. 2). The areas with estimated high probability of lynx occurrence outside protected areas were identified within Albania, which may ensure the connection of two multi-border areas of Albania, Montenegro, and Kosovo in the north and Albania, Macedonia, and Kosovo in centre of the study area, respectively. Areas with estimated high probability of lynx occurrence were also identified in the cross-border between Macedonia and Greece.

The areas with probability of the lynx occurrence (H > 0.65) predicted by the model 1 and model 2, respectively, overlapped (i.e. map (c) and map (d) in Fig.2). The model 1 and model 2 showed insignificant value of correlation (Spearman correlation; r= 0.013). Areas of overlap in both models indicated the presence of forested elevated land (model 1) as well as less agricultural land (model 2). These areas tended to occur predominantly in Macedonia and Albania and in western Kosovo.

The areas with estimated high probability of lynx occurrence for the lynx were identified in protected areas that had forested elevated areas and species of lynx prey (model 1) and have little or no agriculture land (model 2). This indicated that protected areas were well-located for lynx conservation. The areas with estimated probability values from H > 0.50 to H < 0.65 in protected areas can still be beneficial for the lynx (e.g. the photos of lynx were collected in Pelister National Park; (6) in Map (b) in Fig. 2 in 2013 (Balkan Lynx Recovery Programme, 2014).

Areas prioritised by Zonation (unconstrained solution) were concentrated in the centre and north of the study area with the majority of the top 20 % solution occurring in the cross border areas of Montenegro–Albania–Kosovo, Albania–Macedonia, as well as in Macedonia and Montenegro.

Constraining the Zonation solution with the current protected areas forced all protected areas to be in the top 20 % solution (and most in the top 10 %) (Fig. 3c). The constrained (Fig. 3c) and unconstrained solutions (Fig. 3d) were similar. This indicated again that the existing protected areas occurred in high priority locations for lynx conservation. The major differences between constrained and unconstrained solutions were a reduction in some of high priority areas in Albania, Macedonia, and between Albania and Macedonia border areas.

In the constrained solution, high priority rankings have been assigned to new areas outside the current protected areas in western Macedonia, the north and east of Albania as well as in northern and western Montenegro, (Fig. 3c). These new areas within the top 20 % landscape prioritisation connected the two protected areas situated in the Albania–Montenegro–Kosovo cross-border area (Fig. 3a) and the Albania–Macedonia–Kosovo cross-border area (Fig. 3b). Prioritised areas in Macedonia and Albania tended to be fragmented.

The number of steps predicted by SSF in top 10 % Zonation solution was larger for Macedonia compared to Albania, with Kosovo having a small share and no share for Montenegro (Fig. 4, light grey components of columns). The top 20 % solution increased the difference between Macedonia and three other countries (Albania, Montenegro, and Kosovo), with Macedonia having the largest share of 68.2 % (Fig. 4).

This study showed lynx conservation areas and predicted lynx steps by SSF were spread between Albania and Macedonia (Figs. 3 and 4). This indicates that these countries have similar responsibilities for the conservation of the lynx populations and habitat. Albania and Macedonia currently have the largest lynx populations and both countries share the largest part of predicted steps of lynx by SSP in the top 10 % of the landscape prioritised for lynx conservation (Fig. 4). Because of the existing lynx populations in Albania and Macedonia, both countries will be required to make all efforts to maintain these populations. Albania and Macedonia can collaborate to ensure a single long-term conservation plan of their cross-border areas, for example, to collaborate on preparing a species conservation plan. In addition, the results of our species distribution modelling and landscape prioritisation indicate that both countries may need to address the following factors: (i) the conserving of existing areas with high probability of lynx occurrence through forest conservation measures such as incentive programs to reduce the forested areas for forest harvesting and firewood (e.g. firewood is still important source for heating in rural areas in Albania; Laze, 2014); such an incentive program may compensate local people for the switching from wood harvesting to forest conservation (i.e. from resource to biodiversity forest ecosystem service); (ii) well-managed hunting activities such as limiting or halting chamois, brown hare and roe deer hunting at fixed times of the year; (iii) sustainable planning for the use of agriculture and pasture land; (iv) the collecting of constant seasonal and yearly lynx data using the advance monitoring system (radio-telemetry); (v) expansion of protected areas and the addition of new protected areas in locations such as the cross-border areas but also inside of Albania, Macedonia, Kosovo, and Montenegro (Fig. 3). This last point could help the lynx disperse from the north to the centre of the study area. This is because any lynx individual matters for the existing small population of the lynx. (Data collection on Carpathian lynx occurrence in the north of the study area (primarily Montenegro) can be useful to identify any potential overlapped areas of the distribution between Carpathian lynx and the lynx; yet, this is not our study objective).

Our results suggest that conservation efforts in the countries of our study could be oriented towards increasing the size of existed protected areas and their surrounding-buffer areas. This, however, will require a closer inter-country collaboration because the most promising areas for lynx conservation extend over the country borders. The expansion of protected areas must be associated with the conservation of forests, the reduction of human disturbance in the prioritised areas as well as with the connectivity of habitat patches for the lynx in their cross-border areas. This is because the lynx prefers larger areas of undisturbed forests, moves a great deal within its home-range (Balkan Lynx Strategy Group, 2008) to satisfy its needs for refuge, food and breeding as well as it is sensitive to anthropogenic land changes. We highlight here the relevance of large-area for the production of the lynx quoting as follows:

Although isolation is of great importance in the production of new species, on the whole I am inclined to believe that largeness of area is still more important, especially for the production of species which shall prove capable of enduring for a long period, and of spreading widely (Darwin, 2011).