1 INTRODUCTION

At present, many populations of large mammals, including giant panda, Amur tiger, Amur leopard and brown bear are supported by release and rewilding projects (Goodrich and Miquelle, 2005; Miquelle et al., 2015; Tosi et al., 2015). Such projects need scientific support in setting release targets. In Sichuan, giant panda (Ailuropoda melanoleuca)—panda hereafter—feeds on 32 species of bamboo belonging to 7 genera, including staple food such as Bashania fangiana, Yushania brevipaniculata and Chimonobambusa szechuanensis (Yi and Jiang, 2010). The conservation history of the panda in China can be traced back to the 1970s. Then, the large-scale flowering and subsequent die-off of arrow bamboo (Fargesia nitida), the main food of panda, resulted in a large number of deaths (Hu, 2004). As a response, trials on breeding captive panda were undertaken dealing with, among others, the onset of estrus, mating, domestication, artificial insemination and cub nursing (Ding et al., 2019; Hama et al., 2009; Martin-Wintle et al., 2019). Lately, the number of captive-bred panda has been growing at a rate of about 9.3% per year (Xinhuanet, 2019). Moreover, the Giant Panda National Park established in 2017 (Zhao et al., 2019) is available for release. Despite the great effort, panda is still listed as vulnerable in the current Red List of Threatened Species (IUCN, 2019). The vulnerability is partly brought about by habitat fragmentation that hinders gene exchange and accelerates the decrease the genetic diversity within wild populations (Xiong, 2018). Currently, two thirds of the panda in Sichuan province live in small, unconnected habitat patches at a high risk of extinction (Information Office of the State Council, 2015). The level of inbreeding in wild panda is greater than expected for a solitary mammal (Hu et al., 2017). In order to optimize the number and genetic diversity of panda, two complementary strategies maybe implemented, namely release and rewilding of captive-bred panda into isolated habitat patches (Zhang and Wei, 2006) and establishment of dispersal corridors between such patches (Yin et al., 2010). Rewilding is an accepted rescue strategy for panda. Rewilding panda can preserve genetic diversity and improve the probability of survival in small isolated panda population (Dai et al., 2020). Previous studies have shown that trained and rewilded pandas gradually approximate that of wild pandas on habitat selection (Zhang et al., 2013) and gut microorganism (Jin et al., 2019), which can be taken as an indicator of guarantee of welfare in rewilding of panda. By effective planning and guidance of local government, the conflicts between pandas and locals are rare and endurable. Rewilding is also highly and socially accepted by the local due to it social, economic and ecological benefits (Ma et al., 2016). Recently, pilot cases of successful rewilding of panda have been reported (An, 2017; Wang, 2017; Yu, 2017), suggesting large-scale rewilding has become feasible. The establishment of corridors between two otherwise isolated habitat patches is a common conservation strategy as well and may mitigate inbreeding depression over long time scales (Buglione et al., 2020; Wang et al., 2014).

The panda is mainly found in the Sichuan, Shanxi and Gansu Provinces. In Sichuan, the occupied habitat covers about 25.800 km2. The additional potential or uninhabited habitat is estimated at about 9.100 km2. Both increased in extent at 11.8 and 6.3% respectively over the past decades (Sichuan Forestry Department, 2015). The number of panda in the wild reached 1864 animals, mostly (n = 1387; 74.4%) in Sichuan (Geng, 2015). The annual growth rate was 1.5% (Geng, 2015). The panda density is low (0.07 animals/km2), suggesting potential for population growth (Sichuan Forestry Department, 2015).

The “Captive Giant Panda Release Project” (Swaisgood et al., 2011) is expected to start shortly in Sichuan. However, a target density or target number of panda to be released has not been established. Our study aims at contributing to the Release Project by establishing the extent of the uninhabited, well connected panda habitat and the number of captive-bred panda that should be released annually to populate these habitats. The location and extent of potential habitat patches was estimate by a spatial maximum entropy model (MaxEnt), the uninhabited habitat by subtraction of the known occupied habitat. Then, we calculated Least Cost Paths (LCPs) between the habitat patches. The LCPs may function as dispersal corridors to avoid inbreeding. The number of panda to be released annually was assessed by the known home range (Hu et al., 1985) and net reproduction rate (Hou, 2000).

2 MATERIALS AND METHODS

2.1 Research Area

Our research area is the Sichuan Province (4.86 × 105 km2) in southwest China located between 26°03′–34°19′ N and 92°21′–108°12′ E (Fig. 1). The main landforms (Fig. 1) are the high plateau in the west (4000–4500 m), the central and a southern mountains (>4000 m) and the basin and hills (1000–3000 m) in the east (Shao et al., 2012).

Fig. 1.
figure 1

Location map of Sichuan Province, the occupied habitat of the panda and the main landforms depicted by the digital elevation model (DEM).

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Needle leaved forests dominate on the high plateau and broadleaved deciduous forests in the basin and on the hills. At forested mid-elevations (1500-3000 m) in the central and southern mountains, bamboo is common as understory in forest and forest openings. At the high plateau with its cold-temperate climate fewer bamboo species occur. The basin and hills as well as the lower elevations of the mountains are situated in a humid, subtropical monsoon climate. Above alpine elevations (>3200–3500 m) in the mountains, grass and shrub dominate. The highest elevations are seasonally snow-capped or even glaciated. Bashania fangiana, Yushania brevipaniculata and Chimonobambusa szechuanensis, as the staple food of pandas, are widely and mixed distributed in various habitats of pandas (Gao et al., 2014; Yi and Jiang, 2010).

Sichuan has nearly 87 million inhabitants. The eastern basin and hills have the highest population density. The mountains show a medium density, concentrated in urban settlements at valley bottoms. The western plateau is sparsely populated. The road network in Sichuan include 7500 km expressways with a large impact on giant panda (Zhou, 2002). Sichuan is covered by forest (40% ), grassland (25%), cultivated land (14%), residential land (4%), industry (2%), orchards (2%), water bodies (2%) and unused land (9%) (Wang and Deng, 2006). Opencast mines (2%) are widely distributed in the central mountains coinciding with panda habitat (Yang, 2009).

2.2 Research Data

The panda presence points (n = 1014) cover the period from 2011 to 2014 (Sichuan Forestry Department, 2015). We used the four fundamental environmental predictor categories (Table 1) relevant for habitat modeling of terrestrial macro-fauna, namely climate, terrain, vegetation and human impact (van Gils et al., 2014). We used the climate data from the CHELSA database (Karger et al., 2017) of 1979–2013. The Incoming Solar Radiation (ISR) values were calculated per 30 minutes and summed up per growing season. In Sichuan, spring lasts from Feb. 6 to Mar. 31, summer from Apr. 1 to Sep. 5, autumn from Sep. 6 to Oct. 10, and winter from Oct. 11 to Feb. 5 (Li et al., 2007). All spatial data preprocessing and calculations were done with standard operations in ArcGIS 10.2 and projected in UTM-WGS-1984. Where necessary we resampled to 30 arc-seconds.

Table 1. The environmental predictor variables used in modelling the panda release habitat (Column 1). The source of the variables is provided in column 2. The third column contains the value range of the contiguous variables or for categorical variables the types as found in the research area
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2.3 Panda Habitat Modeling

A maximum entropy method (MaxEnt) (Phillips et al., 2017) was selected from among Species Distribution Models (SDMs). Potential pitfalls that may affect the accuracy of the model are spatial autocorrelation of presence points and multicollinearity of predictor variables (Merckx et al., 2011). We minimized spatial autocorrelation by filtering all panda presence points with the SDM Toolbox v1.1c in ArcGIS 10.2. For the first step of the filtering, we used the natural break with a maximum distance of 25 km and a minimum of 5 km (Fekede et al., 2019). In the subsequent spatial rarefying, we set a minimum distance of 13 km between each pair of points. At 13 km, the probability that two points represent the same panda is close to zero (Luo et al., 2017).

Three main methods are used and validated to reduce multicollinearity of predictor variables in spatial modeling, namely, the Principal Component Analysis (PCA) (Farrell et al., 2019; Fekede et al., 2019), the Stepwise Backward Elimination (SBE) (van Gils et al., 2014) and the correlation coefficient elimination (D’Elia et al., 2015). The latter method has been found less optimal (Drake et al., 2006) and has not been considered. The other two have been used in parallel in this paper. Since the number of climate variables is much higher than other variables, we used PCA (SPSS 22.0) to select major climatic predictors (Fekede et al., 2019). We used eigenvalues larger than 1.0 and the scree plot criterion or ‘broken stick’ stopping rule for PCA in item level factoring (Bernstein, 1988). The climate predictors with factor loading ≥0.95 were used for subsequent analysis (Landau and Everitt, 2004). Then, we used PCA for the second time to obtain orthogonal principal component (PC) predictors to reduce multicollinearity (Huang et al., 2018). We used the component score as the coefficient of each standardized predictors to combine the selected climatic predictors and the remaining continuous predictors (human impact, elevation, slope angle, ISR, distance to river). This process uses a series of orthogonal transformations to re-orient a set of new, uncorrelated variables. The formula for deriving principal components (PCi) is as follows:

$$P{{C}_{i}} = {{V}_{{{{i}_{1}}}}}{{X}_{{{{i}_{1}}}}} + {{V}_{{{{i}_{2}}}}}{{X}_{2}} + \ldots + {{V}_{{{{i}_{j}}}}}{{X}_{{{{i}_{j}}}}} + \ldots + {{V}_{{{{i}_{m}}}}}{{X}_{{{{i}_{m}}}}},$$
(1)

Vij is the coefficient corresponding to the standardized original variable Xij.

The coefficients’ matrix V consists of the eigenvectors from the covariance matrix of the standardized original variables and is obtained by the principal component analysis in SPSS 22.0. The eigenvalue of covariance matrix shows the ability of principal components to synthetically reflect variable X1, X2, …, Xm. The larger the eigenvalue, the higher the ability of reflecting the original variables. The standardization of variables is achieved by z-score normalization, which is subtraction from the average value and divide the result by the standard deviation (Levi and Rasmussen, 2014).

Finally, we performed Variance Inflation Factor (VIF) analysis on the PCs. A VIF larger than 10 indicates high multicollinearity (Duque-Lazo et al., 2016). The uncorrelated predictor variables and the filtered points served as the data input in MaxEnt. A limitation of PCA is that it is optimized for quantitative data (Vaughan and Ormerod, 2005). Therefore, the categorical variables, soil type and land cover, were fed directly into MaxEnt. The PCs, soil type, land cover and the presence points were used to build and validate the spatial models based on 10 bootstrap replicates. We tested the regularization multiplier (β) between 1 to 5 to determine the optimal value. For the remaining parameters, we kept the default settings. For visualization, the Jenks natural break was used to classify the model output (Liu et al., 2019). Smoothing for map visualization followed (van Gils et al., 2014). The output was labeled SDM-1.

The process of evaluating or assessing a model is often referred to as “validation” (Minasny et al., 2017). The key component of model training and validation procedures is the criterion which evaluates the model performance. We use threshold dependent and threshold independent criteria. The area under the ROC curve (AUC) is a threshold independent criterion based on plotting the true positives against the false positive fractions for a range of thresholds in prediction probability (Rushton et al. 2004). Currently, the AUC is considered the best criterion for assessing model success for presence/absence data (Austin 2017). AUC is often used as the single criterion for assessment of model performance (Manel and Ormerod 2010; McPherson et al. 2004; Thuiller et al. 2003). As threshold dependent validation measure, we used confusion matrix-based measures including the Kappa test (Liu et al., 2010), correctly classified instances (CCI) (Fielding and Bell, 1997), the normalised mutual information statistic (NMI) (Forbes, 1995), the odds ratio (Fielding and Bell, 1997) and the true skill statistic (TSS) (Allouche et al., 2010). The Kappa statistic and TSS normalise the overall accuracy by the accuracy that might have occurred by chance alone. The percentage of CCI is the rate of correctly classified cells. NMI quantifies the information included in the model predictions compared to that included in the observations. The odds ratio is the ratio of correctly assigned cased to the incorrectly assigned cases. An optimal odds ratio may reach positive infinity, whereas all other criteria are optimal at their maximum, one. Our model has been assessed by all criteria mentioned. Further we compared the average, min, max, median output of the 10 bootstrap replicates with each other. After applying the same visualization process as for the SDM-1, we visually assessed the similarity of the high probability areas of the four outputs. To further validate our model, the coincident area of SDM-1 and the occupied habitat (Sichuan Forestry Department, 2015) was calculated. As additional assessment/validation, we built an alternative model (SDM-2) with the same input data using a posteriori stepwise backward elimination of predictor variables (van Gils et al., 2014) instead of a priori variable selection by PCA (Fig. 2).

Fig. 2.
figure 2

Flow chart of the procedure used for prediction and assessing the release habitat and the required annual number of released captive-bred panda SBE = Stepwise Backward Elimination.

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Finally, the uninhabited habitat patches were obtained by subtraction of the occupied habitat from the predicted habitat minus the buffered (0.5 km) opencast mines (Sichuan Forestry Department, 2015).

2.4 Dispersal Corridor Analysis

The connectivity of the habitat patches by dispersal corridors was calculated by the LCP approach (Fig. 2). LCP analysis estimates efficient movement routes and costs between pairs of habitat patches based on the suitability of the intervening matrix. LCP analysis is used for many terrestrial mammals, including brown bear (Peters et al., 2015) and cougar (LaRue and Nielsen, 2008). First, we built the cost surface. The cost value of each cell in the grid is based on the mobility of panda in different environments. Vegetation type, elevation and slope-angle raster maps (Table 1: Fig. 2) were used to create the cost surface (Ziółkowska et al., 2012). Elevations between 2000–3000 m, slope-angles from 18–27° and evergreen needle-leaved forest were assigned the lowest cost value (1—lowest resistance, easy to traverse). Raster cells with elevations below 1000 m or above 4000 m, a slope-angle larger than 50°, urban cover and bare cover were assigned the highest cost value (9—highest resistance, hard to traverse). The intermediate cost values are shown in supplementary information Table S.2. The rating of the three cost factors was added to create a cost surface (LaRue and Nielsen, 2008). LCPs were constructed between each pair of neighbouring habitat patches based on the cost surface (Rayfield et al., 2010). The LCPs were calculated with the Linkage Mapper V 2.0.0 in ArcGIS. The calculated paths were ranked into three classes (high, medium, and low) according to their accumulated costs by means of a K-means algorithm (Hashmi et al., 2017). The uninhabited habitat was divided into potential release regions by size (small/large), location (peripheral to/contiguous with occupied habitat), clustering (scattered/clustered) and connectivity (high/low quality LCP) of habitat patches. Finally, we summated the occupied habitat and the well-connected, uninhabited habitat as maximum available habitat (Fig. 2).

The panda is a solitary animal with a home range of 3.9–6.2 km2 showing a negligible overlap (Hu et al., 1985). The number of panda that maybe released was calculated by dividing the extent of the uninhabited, well-connected habitat by the home range. We adopted the average generation period of 12.16 years and the net reproduction rate of 1.0573 (Hou, 2000). The number of panda that could be released annually in the second or fourth generations was calculated with the following formula:

$$\begin{array} {c} \text{Annual}\,\,\text{release}\,\,\text{number} \\ =\frac{{{a}^{n}}\times 1387\,\,(\text{Current}\,\,\text{number}\,\,\text{of}\,\,\text{wild}\,\,\text{panda}}{\sum\limits_{i=1}^{n}{{{a}^{i}}}}. \\ \end{array}$$
(2)

Where: a = net reproduction rate and n = target period (year).

3 RESULTS

Hundred fifty-two (152) panda presence points remained after filtering. The PCA for climatic variables delivered four PCs together accounting for 97.2% of the total variance (Table 2). After PCA, the minimum temperature in April (hereinafter called tmin4, 44.1% contribution), the maximum temperature in June (hereinafter called tmax6, 36.2% contribution) and the temperature seasonality (hereinafter called bio4, 19.7% contribution) were kept for spatial modeling.

Table 2. The four Principal Components (PC) of the climatic variables, Eigenvalues of each PC and their variance and the cumulative variance of all climatic variables (n = 67)
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Using the component score coefficient (Supplementary Information Table S.3) as a combination of weights, we obtained eight PCs for the three selected climate variables and the other continuous variables. These eight PCs explained more than 90% of the variance and were uncorrelated (VIF 1.0-1.9). The eight PCs plus the categorical variables (soil and land cover) were entered in MaxEnt as environmental layers. With the increase of β, the predicted habitat area is also increasing. The optimal regularization multiplier for our habitat model is β = 1. The validation criteria of the SDM-1 and the SDM-2 were nearly identical demonstrating a robust panda habitat model (Table 3).

Table 3. The validation criteria of the SDM-1 and the SDM-2
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The overlay pattern of average, min, max, median output of the 10 bootstrap replicates was sufficiently similar (Fig. 3). The standard deviation of the ROC curve (Fig. 4) is small and even. The habitat predicted by the SDM-1 and the SDM-2 is largely the same, further validating our panda habitat model. In addition, our predicted habitat covered 90.5% of the surveyed occupied habitat which may be considered as an independent validation of our model accuracy.

Fig. 3.
figure 3

The average, minimum, maximum and median output of the 10 bootstrap replicates of the SDM-1. In the upper left corner, the box shows the location of the habitat in Sichuan, and the black box shows the enlarged area, which is the main content of this figure.

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Fig. 4.
figure 4

Receiver operating characteristic (ROC) curve of SDM-1 in red. The blue area is the SD, and the black line the random prediction.

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Soil and vegetation (land cover) types contribute together 78.5% to the SDM-1 habitat model and the PCs 21.5%. PC1, PC3 and PC7 are the top contributors among the PCs. The PC1 (8.4%) is related to the ambient temperature and elevation, the PC3 (3.3%) and PC7 (4.2%) represented temperature seasonality and human impact respectively (Supplementary Information Table S.4). The remaining PCs are not considered because of their small contribution. SDM-2 using the SBE method showed that the minimum temperature in June (hereinafter called tmin6, 27% contribution), mean diurnal temperature range (hereinafter called bio2, 25.8% contribution), soil (23.7% contribution) and vegetation (23.5% contribution) were the main predictor variables. Moreover, the probability of panda occurrence is high when the mean diurnal temperature range is small (5.5–6.5°C); the larger the temperature range, the lower the occurrence probability. Further, moderate minimum June temperatures (13–18°C) seem suitable for panda. Spodosols, entisols, broadleaved evergreen forest and, needle-leaved evergreen forests are predictors for panda presence.

The predicted habitat covers a belt from south to north in the middle of the central mountain range in Sichuan (Fig. 5). Habitat patches with medium connectivity occur mainly in the north (Aba), central (Aba), northeast (Bazhong and Dazhou) and the south (Liangshan) of Sichuan, and a small patch in the southeast (Luzhou). The predicted habitat of SDM-1 covers 18.342 km2.

Fig. 5.
figure 5

Predicted panda habitat by the SDM-1 in the Sichuan Province. In the upper left corner, the box shows the location of the habitat in Sichuan, and the black box shows the enlarged area, which is the main content of this figure.

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The 18.342 km2 predicted habitat leaves 18.155 km2 after removing the unusable open cast mining areas. The habitat in the Minshan mountains consist of two patches 15 km apart. The predicted habitat the Qionglai and Daxiangling mountains are connected. The predicted habitat patches in the Xiaoxiangling and Liangshan mountains are situated more than 15 km from other patches. The LCP analysis delivered 231 dispersal corridors (Fig. 6). The uninhabited habitat was subdivided into 7 potential release regions (A–G) (Table 4). The well-connected, uninhabited habitat is approximately 6.900 km2. Finally, the occupied and well-connected, uninhabited habitat together is about 25.000 km2. The occupied and well-connected habitat in Sichuan may ultimately accommodate 4040–6423 individuals. To achieve such numbers, annually 45–89 captive-bred individuals should be released over 25 years. Alternatively, full rewilding would take 50 years at an annual release of 10–20 captive-bred panda.

Fig. 6.
figure 6

The current occupied and the uninhabited panda habitat in the Sichuan Province with their medium and high-connectivity LCP dispersal corridors. Black box (A, B, D and F))) = peripheral, small release habitat patches. Green box (C, E and G))) = central large release habitat patches.

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Table 4. The predicted uninhabited habitat patches grouped into A-G regions from north to south (Fig. 6) with their pertinent release features and size in km2
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4 DISCUSSION

Our finding on the β parameter of MaxEnt is consistent with the characteristics of overfitting (Merckx et al., 2011). This implies that the default setting (β = 1) of MaxEnt is also correct in our research setting.

The two methods used in this study to reduce multicollinearity have their own advantages and disadvantages. The contribution of the environmental predictor variables were traceable with the stepwise backward elimination (SBE) method. However, the SBE may ignore a unique contribution of an omitted variable that could result in a substantial loss of explanatory power (Carnes and Slade, 1988; James and McCulloch, 1990). However, more recent research did not find such loss, neither within a contiguous research area (Gils et al. 2014) nor in testing the transferability of the model to a disjunctive area (Duque-Lazo et al. 2016). As for the PCA method, the first PC (PC1) contained the most of the data variability of the original variable. The succeeding component (PC2) had the highest variance possible under the constraint that it is orthogonal to the preceding component (Huang et al., 2018). The 8 PCs used in this study can explain more than 90% of the original variables, but it cannot determine the response of the original variables in the model. In this study, SDM-1 and SDM-2 are mutually verified, and the similarity of the results shows that both methods are effective. How these two methods should be selected in a different context requires further research.

The dominant contribution of the two categorical predictor variables vegetation and soil (78.5%) in the SDM-1 over and above climate and elevation comes not as a surprise. A similar finding was reported and explained in a bear distribution study in a mountainous environment (Gils et al. 2014). Therefore, spatial distribution models exclusively based on extrapolated climatic variables (WorldClim) should be interpreted carefully. More so as the current panda study used climatic data (CHELSA) extrapolated explicitly for the particulars of mountainous environments.

The human impact variables (roads, population density, scenic spot, opencast mines) used in this study contributed very little to the predicted habitat. This may be due to the fact that the remaining wild panda live in extensive forested areas without human settlement or isolated farms. Therefore, we did not include three human impact variables in the LCP calculation. However, opencast mines are known to have a substantial, negative local impact (Qi, 2009), as also suggested by the absence of panda records within a radius of 0.5 km of the mines (Sichuan Forestry Department, 2015).

The low contribution of the human population density variable on the model output may result from using global databases on population density and urban land cover in the absence of accessible, comprehensive provincial data. Such global databases imply out of necessity broad generalization. We suggest carrying out a provincial remote sensing study, including rural settlements, rural roads and agrarian land cover/use changes and rerun the habitat model with the more detailed data.

Our release target for pandas is based on the assumption that there is no significant change in habitat over the next 25–50 year. As the future climate change in Sichuan is predicted mainly concentrated at the highest elevations region (3800–4500 m) which is above the panda habitat (Lu et al., 2015), we exclude the influence of climate change on the habitat over the next 25–50 year.

Bamboo is the staple food of panda, and it’s sufficient supply is the premise that the giant pandas can fully occupy the maximum available habitat in the future. Some studies presented a pessimistic view on the impact of climate change on the extent and species of bamboo (Li et al., 2015). However, but the study used bamboo data from 2003 and only considered climate variables. The most recent data showed an increase of 61.49% of the bamboo covered area in Sichuan Province since 2003 (Information Office of the State Council, 2015). This substantial increase in bamboo over the past decade or so may be due to efforts to restore the panda habitat, including planting bamboo. Therefore, we speculate that bamboo resources can support the expansion and reintroduction of panda habitat.

The potential release targets as provide by our study will neither be limited by birth rate and high mortality of the captive-bred panda population (Li et al., 2017), nor by the number of young captive-bred pandas (Zhao, Zhang et al. 2017). Most female panda will reach the reproductive age (5–25 years) over the next ten years. Moreover, most captive-bred panda give birth to twins every second year (Hou, 2000). The limitation to reach the release target is likely to be the capability of pre-release training of panda.

5 CONCLUSIONS

Our study simulated the habitat of panda in Sichuan Province, and found that there were 6898 km2 of habitat patches with good connectivity in addition to the occupied habitat. To fully exploit the available well-connected habitat, 45–89/10–20 captive-bred individuals should be released every year for 25/50 years. Through this example, we construct a two-step PCA method to restrict multicollinearity among a large number of predictor variables. Overall, we have constructed a refined method to predict mammal habitats and release targets, and demonstrated its feasibility with multiple validation. The methods (MaxEnt; LCP), variables (vegetation/land cover, soil, climate, human impact) and parameters (home range; reproductive rate) used in our approach are applicable to many solitary terrestrial mammals and may provide insights helpful in setting feasible release targets.