Introduction

Improving knowledge about species’ demographic and evolutionary histories is increasingly important to landscape and spatial genetics. In particular, conservation measures can be strengthened by identifying patterns of allelic differentiation in spatially complex and dynamic environments (Storfer et al. 2010; Balkenhol et al. 2016). Spatial patterns in genetic diversity result from the interacting processes of migration, dispersal and reproduction (i.e., gene flow), and are highly influenced by the nature of the intervening landscape mosaic (Cushman et al. 2006, 2013). Heterogeneous environmental patterns of factors that limit movement affect the dispersal abilities of organisms and produce spatial patterns in genetic diversity and genetic differentiation (Cushman et al. 2012, 2013; Landguth et al. 2010, 2012).

Under spatially limited dispersal, population genetic theory predicts that differentiation would increase with increased geographic distance, creating isolation-by-distance (IBD) patterns (Wright 1943). In such situations, individuals living in close proximities to each other will present genetic spatial autocorrelation, that is, they will be more genetically similar than those living further apart, as a consequence of their genetic neighbourhood size (NS), an area in which gene flow is high relative to drift (Wright 1946; e.g., Kuhn et al. 2017). In heterogeneous environments, the effective distance between individuals as a function of the movement cost between them is usually most strongly related to genetic differentiation, in a process commonly termed isolation-by-resistance (IBR; e.g., Cushman et al. 2006; Shirk et al. 2017a).

To identify spatial patterns and modes of isolation, methods designed to detect barriers or clusters of sub-populations have been widely adopted in conservation genetics (Blair et al. 2012; Guillot et al. 2009; Schwartz and McKelvey 2008). However, these methods are only reliable when obvious barriers to gene flow are present, and the populations can be unequivocally identified as distinct (François and Durand 2010).

Spurious breaks and clusters can become more apparent in populations separated by IBD or IBR (Guillot et al. 2009; Schwartz and McKelvey 2008; François and Durand 2010; Cushman and Landguth 2010). This is of particular concern when populations or individuals are distributed over a continuous area, without obvious obstacles to movement (Guillot et al. 2009; Cushman et al. 2015), and inference of patterns is difficult without accounting explicitly for the spatial autocorrelation of allele frequencies (Jombart et al. 2008a; Wagner and Fortin 2012).

Methods that account for spatial autocorrelation in the distribution of genetic observations offer valuable tools to dissect patterns of genetic autocorrelation at multiple spatial scales (Jombart et al. 2009; Wagner and Fortin 2012). These methods often rely on a spatial weighting matrix (SWM), which represents a weighted connection network expressing the links between spatial units (Dray et al. 2006; Bauman et al. 2018a, 2018b). While SWMs can be purely mathematical objects to test for IBD for example, they have also been shown to be valuable tools to incorporate ecological knowledge or landscape hypotheses of impediment to movement to optimise the detection of spatial patterns (Dray et al. 2006; Bauman et al. 2018a; Benone et al. 2020). Moran’s eigenvector maps (MEM; Dray et al. 2006) is a spatial eigenvector-based method that generates spatial eigenfunctions proportional to Moran’sIcoefficient of autocorrelation by diagonalising a doubly-centred SWM (details in Dray et al. 2006; Bauman et al. 2018a). They are a powerful tool to optimally detect non-random spatial patterns ranging from simple linear gradients to complex irregular fine-scaled patterns (Dray et al. 2006). These spatial variables have proved to be accurate tools to study genetic or species composition patterns, when used in regression or constrained ordination methods (Legendre et al. 2015; Manel et al. 2010; Peres-Neto et al. 2006; Bauman et al 2018c), and have been increasingly applied in genetics studies (Manel et al. 2010; Galpern et al. 2014; Dalongeville et al. 2018; Breyne et al. 2014). These spatial methods are particularly suited to identify cryptic genetic patterns and can serve as a proxy for unmeasured landscape factors (Jombart et al. 2009; Wagner and Fortin 2016; Galpern et al. 2014).

In the context of correlative landscape genetics inferences, metrics of distance derived from Principal Component Analysis (PCA) eigenvectors have been recommended to detect significant landscape-gene relationships (Shirk et al 2017b). Their use, however, is contingent upon the identification of the number of axes and proportion of inertia that captures the spatial variance in the dataset (Shirk et al. 2017b). Concurrent to the adoption of PCA-based genetic distances in link-based landscape genetics analyses (Shirk et al. 2017b; Burgess and Garrick 2020; Savary et al. 2021), the use of ordination axes as response variables in node-based regression techniques using MEM has also been shown to successfully remove redundant genetic information, while capturing meaningful variation (Dalongeville et al. 2018; Forester et al. 2016; Breyne et al. 2014; Guerrero et al. 2018). However, in both methodological approaches, the selection of the retained PCA eigenvectors often appears arbitrary, with some exceptions (Forester et al. 2016).

We therefore suggest that assessing which ordination axes can identify significant spatial structures is essential to generating reliable landscape genetics conclusions. As species differ in their demographic traits (Shirk et al. 2017b; Hein et al. 2021) and in their genetic diversity (Landguth et al. 2012), we would expect patterns to be sensitive to the strength of the genetic signal embedded in the analysed loci (Shirk et al. 2017b; Landguth et al. 2012). Understanding how different PCA components can identify and describe spatial genetic patterns, and how a trade-off in the number of markers versus the number of samples influences such detectability (e.g. Hein et al. 2021; Landguth et al. 2012) is therefore crucial.

Species exhibiting cryptic genetic patterns, resulting from low genetic diversity, low population densities and high dispersal ability, could particularly benefit from the dimensionality reduction of a PCA (Shirk et al. 2017b). One such species is the snow leopard (Panthera uncia), occurring in the mountains of Central Asia and subject to population declines across its range (McCarthy et al. 2017). Despite the well-established importance of genetic surveys for species conservation (Frankham 2005), information on the genetic diversity of snow leopard populations remains scarce (Weckworth 2021). With the exceptions represented by two broad-scale genetic analyses (Janecka et al. 2017; Korablev et al. 2021), genetics studies on snow leopard are usually limited in spatial extent and sample size (e.g., Janecka et al. 2008; Karmacharya et al. 2011; Aryal et al. 2014). The few studies that have described spatial genetic structure at a local spatial scale have inferred clusters of individuals coming from disconnected study areas (Shrestha and Kindlmann 2020; Zhang et al. 2019), possibly yielding spurious patterns due to sample biases (Schwartz and McKelvey 2008; Oyler-McCance et al. 2013).

Range-wide and landscape-specific connectivity information for this species remains limited (Riordan et al. 2016; Li et al. 2020; Shrestha and Kindlmann 2020), with little known regarding the relationships between snow leopard genetic diversity and landscape characteristics. Thus, in the context of existing and emerging threats to populations (McCarthy et al. 2017), it is important to assess the genetic status of local populations, and understand landscape features that impede connectivity, potentially causing isolation and resulting in decreased genetic diversity or inbreeding depression (Frankham 2005; Weckworth 2021).

With this study we aim to quantify the spatial genetic patterns in a snow leopard population from Gansu, China, comparing two different datasets, with different numbers of loci and alleles. We summarise genetic information using PCA, and use derived principal components, at several levels of retained variance, as dependent variables to test for spatial genetic structures. We also use spatially explicit diversity indices calculated on the extent of Wright’s neighbourhood size (Shirk and Cushman 2011, 2014), and assess how these indices varied in the different sampling sub-localities. This approach complements population genetic analyses, as it enables identification of discontinuities and rapid changes in diversity indices across space, which, in turn, can help to identify demographic hypotheses in relation to the observed spatial patterns of allele distributions (e.g., Ruiz-Gonzalez et al. 2015).

We aim to answer the following questions:

  1. (1)

    Are there significant spatial autocorrelation genetic patterns within a snow leopard population inhabiting an apparently continuous landscape, and how do these relate to local variability of genetic diversity indices?

  2. (2)

    In the case of an absence of detectable genetic spatial patterns, can the latter be due to the species dispersal capacity, the extent of allelic diversity, or the apparent homogeneity and continuity of the landscape?

  3. (3)

    In the presence of genetic spatial structures, to what extent does the structure detection depend on the number of loci/individuals, and the content of PCA variance used as response variable?

Methods

Study area

All study areas were in Gansu Province, China (Fig. 1), in which a total of seven surveys were conducted between 2014 and 2017 (Supplementary Fig. S1). Specifically, we surveyed the localities of Yanchiwan National Nature Reserve (YCW) in Subei Mongolian Autonomous County, and parts of the Qilianshan National Nature Reserve (QLS) in Sunan Yugur County. YCW, established in 1982 and upgraded at the National level in 2006, has a total area of ~13,600 km2, and elevations ranging from 2600 to 5483 m above sea level (a.s.l.), with wide valleys found from 3000 to 4200 m a.s.l. YCW is composed of alpine cold desert, alpine meadow grassland, wetland, and desert ecosystems. QLS was established in 1988, encompassing an area of 19,872 km2, and has elevations ranging between 2300 and 5564 m a.s.l. The landcover is composed mainly of large areas of shrubs and alpine grasslands. Forests are found at elevations from 2300 to 3000 m a.s.l., with spruce, aspen and birch trees being the dominant species. The two reserves are located at the intersection of two eco-regions, characterised by particular vegetation and abiotic environments. Specifically, YCW is in the Kunlun alpine desert arid region, in the plateau sub-cold zone, and QLS lies in the Qilian coniferous forest and steppe semi-arid region, in the plateau temperate zone (Wu et al. 2003). Efforts by the local and national government authorities to join these two reserves and create the Qilianshan National Park (50,200 km2) were initiated in 2018 (Atzeni et al. 2020).

Fig. 1: Map of study areas and genetic datasets used in this study.
figure 1

The upper figure shows sub-localities names and County-level administrative divisions. Lower figures represent the locations of the uniquely identified individuals, divided by macro-collection area (Yanchiwan, YCW; Qilianshan, QLS). Borders represent a portion of the newly established Qilianshan National Park (QLSNP).

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Sample collection

In YCW, we collected snow leopard faecal samples in the mountain ranges of Shule Nan Shan, Yema Nan Shan, Danghe Nan Shan (Fig. 1). In QLS, collection was conducted in the management areas of Qifeng, Longchanghe and Sidalong (Fig. 1). We surveyed a total extent of 4850 km2, with a maximum inter-site distance of ~400 km, considering the two outermost sampling sites. We conducted line transects to collect scats believed to belong to snow leopard, using 50 mL plastic centrifuge tubes containing ~30 mL of silica gel drying agent (Janecka et al. 2008). In the field, samples were stored in dark, dry, and cool conditions, and immediately stored at −20 °C upon arrival at laboratory facilities.

Overview of genetic methods

The approaches used to generate snow leopard consensus genotypes are detailed in Supplementary Appendix 1 and summarised here. After DNA extraction, we identified carnivore species using methods described in Bai et al. (2018). We conducted individual identification using eleven snow leopard-specific microsatellite loci (Janecka et al. 2008, 2017), and employed the Quality Index criterion (QI; Miquel et al. 2006) to increase the reliability of the consensus genotypes. We clustered the profiles using allelematch (Galpern et al. 2012) to find unique multi-locus genotypes (hereafter GEN11). We then subset samples whose consensus was reached immediately after the first three replicates, identified unique individuals as before, and selected unique multi-locus genotypes to amplify further sixteen microsatellite loci (Janecka et al. 2017), totalling 27 loci (hereafter GEN27). This approach thus yielded two sets of samples, one composed of more individuals genotyped at a number of loci typically employed in non-invasive population genetics studies (GEN11), and the other composed of a higher-quality-DNA restricted pool of individuals (GEN27), allowing a more extensive genotyping and improving the trade-off between genetic profile reliability and investment of economic resources.

Summary statistics of genetic diversity

For both datasets, the number of alleles (AN) and effective number of alleles (AE) were summarised using GenAlEx 6.51b2 (Peakall and Smouse 2006, 2012). The software INEst 2 (Chybicki and Burczyk 2009) was used to calculate observed (HO) and unbiased expected (HE) heterozygosity, adjusted estimates of observed (HO) and expected (HE) heterozygosity, and inbreeding coefficient (FIS = 1 − (HO/HE)), accounting for the probabilistic presence of null alleles, dependent on a probabilistic genotyping failure rate. A full ‘nfb’ model, consisting in the probabilistic estimation of inbreeding coefficient (f), null alleles (n) and genotyping failures (b), was run for both datasets using 1,000,000 total cycles and 100,000 burn-in cycles. Global Hardy–Weinberg equilibrium was calculated using an exact test in GENEPOP (Rousset 2008) with 10,000 dememorizations, 100 batches and 10,000 iterations per batch, whilst per-locus exact tests were estimated using the R package pegas (Paradis 2010), with 10,000 Monte Carlo permutations.

Genetic profile ordination

An ordination in reduced space was implemented using PCA (Pearson 1901) on both datasets to summarize the overall variability among individuals in uncorrelated synthetic axes. Allele frequencies were centred and scaled (Jombart et al. 2009) using the function scaleGen in adegenet (Jombart 2008b), and missing allelic information was replaced with mean values (Jombart 2017). Initially, eigenvalues were converted to percentages of total variation, and then used to create four PCA objects for each of the GEN11 and GEN27 datasets, retaining the number of axes explaining ~25, 50, 75, and 100% of the total genetic inertia (hereafter PCA_25, PCA_50, PCA_75 and PCA_100). The significance of PCA axes was tested using the broken stick model (Jackson 1993) (functions bstick in the vegan package (Oksanen et al. 2019) and PCAsignificance in BiodiversityR (Kindt and Coe 2005)).

Spatially explicit indices of genetic diversity based on Wright’s genetic neighbourhoods

To explore the range of spatial autocorrelation in the snow leopard genetic profiles, we tested the relationships between genetic datasets, Euclidean and resistance distances through the spatially explicit approach implemented in spatial Genetic Diversity (sGD, Shirk and Cushman 2011, 2014), an approach that overcomes bias due to Wahlund’s effect (Wahlund 1928) occurring when indices are inferred at an extent greater than local population structure, and which addresses the non-transitive continuous structure of the snow leopard population (Shirk and Cushman 2011, 2014; Cushman et al. 2015).

The resistance surface in this analysis adopted the best model for this study area from Atzeni et al. (2020), which used a model selection approach based on the MaxEnt algorithm (Phillips et al. 2006), and found that grassland extent, landscape aggregation and fine-scale topographic position index were the main predictors of snow leopard detection in this landscape.

The habitat suitability surface from Atzeni et al. (2020) was converted to a resistance layer through a negative exponential transformation (Mateo-Sánchez et al. 2015; Wan et al. 2019), to assign higher resistance to movement only to low suitability pixels, in the form of

$$R = 100^{\left( { - 1 x HS} \right)},$$

where HS represents habitat suitability scores.

The resistance surface was rescaled from 1 to 20 in spatialEco (Evans 2020), and the original cell size (90 m) was increased to 200 m to reduce the computational time (Supplementary Fig. S2), but was of fine-enough resolution to avoid losing important landscape characteristics, thereby having a negligible overall effect on pairwise cost-distances (Cushman and Landguth 2010). Pairwise Euclidean and resistance distances were calculated through the distmat function in sGD (Shirk and Cushman 2011).

sGD calculates effective population size (NE) at different radii, adopting the Burrow’s method based on linkage disequilibrium implemented in NeEstimator (Do et al. 2014). NE represents an important parameter in genetics, as it reflects the rate at which populations lose genetic diversity as a function of selection and genetic drift (Charlesworth 2009; Shirk and Cushman 2014), and it is closely related to the risk of extinction, especially in small populations (Neel et al. 2013).

In their simulations, Shirk and Cushman (2014) noted that when the extent of breeding approaches 2σ (the circular radius defining the outer extent of Wright’s neighbourhood, NS), the ratio between NE:NS approaches unity. We selected this criterion to define NS in our two datasets, based on alleles with at least 10% frequency (Shirk and Cushman 2014). Breaks of 25 km were used for the Euclidean distance scenario (hereafter referred to as geo scenario), and 100,000 cost unit breaks for the resistance distance scenario (referred to as res scenario), equivalent to roughly 20 km of dispersal in optimal habitat.

We expected to observe discrepancies between the two datasets related to sample size, especially involving the resistance scenarios. Thus, as the datasets differ only in the number of loci, given that the dispersal capacity of the species is constant across the datasets, we relied on the GEN11 dataset (more individuals) for the definition of the neighbourhood sizes, constraining GEN27 to those thresholds to allow full comparability, as the same neighbourhood size must be used to compare between analyses. We predicted missing values in the calculation of indices using the package missForest (Stekhoven 2013), to allow a complete representation of all indices on the study area for the two datasets. The random forests machine learning algorithm was run for maximum 10 iterations of 1000 forests each.

Spatial analysis with Moran’s eigenvector maps

The spatial structures of snow leopard genotypes were analysed using Moran’s Eigenvectors Maps (MEM) (Dray et al. 2006). MEM are flexible and powerful eigenvector-based methods that generate a spectral decomposition of a set of spatial coordinates allowing to model multi-scale spatial structures. MEM are generated from a spatial weighting matrix (SWM), consisting of the Hadamard product of a connectivity and a weighting matrix that define which objects are connected and how connections are weighted, for example as a decreasing function of distance (Dray et al. 2006; Bauman et al. 2018a, b).

Two key steps in MEM are the selection of a SWM among a set of candidate matrices (Bauman et al. 2018a), and the definition of a subset of spatial eigenvectors to be further used as spatial predictors within the selected SWM (Bauman et al. 2018b). We optimised these selections on the basis of six SWMs built from two contrasted graph-based connection schemes (minimum spanning tree (MST) and Delaunay triangulation (DEL)), and one distance-based SWM, connecting all neighbours within a distance inferior to the smallest distance maintaining all sites connected (i.e., the longest edge of the MST graph (ND_max.edge.mst)). To weight connections along the edges of these SWMs, we tested a linear function and a concave-up function with an exponent of 0.25, yielding a total of six SWM candidates. The two weighting functions were calculated both from the Euclidean and the resistance distances, totalling two sets of six SWMs (SWMgeo and SWMres, respectively). To find the most supported topologies, we used built-in syntax of the function listw.candidates in adespatial (Dray et al. 2020) to generate SWMgeo candidates, and created ad-hoc code to create SWMres candidates. These were then fed into the function listw.select of the same package to find the most supported SWM and subset of spatial predictors within it. The presence of spatial structures in the genetic profiles was tested on the whole set of MEM associated with positive autocorrelation structures for each SWM separately, using 9999 permutations and adjusted p values for multiple tests (Bauman et al. 2018a). If a SWM captured significant spatial patterns in the genetic data, we performed a spatial eigenvector selection using the forward selection procedure with double stopping criterion (Blanchet et al. 2008). The SWM and subset of spatial eigenvectors (MEMgeo and MEMres, for Euclidean and landscape resistance scenarios, respectively) yielding the highest adjusted R2 were selected, an approach shown to produce the highest accuracy and power (Bauman et al. 2018a, b).

We assessed significance of each redundancy analysis (RDA, Wollenberg 1977) axis through the marginal method (Legendre et al. 2011) implemented in the function anova.cca in vegan, using 999 permutations. We ran the same RDAs as above using the pcaiv function in ade4 (Dray and Dufour 2007), to display the fitted scores on the constrained RDA axes. All analyses were performed in the R statistical environment (R Core Team 2021; R code provided as Supplementary Appendix 3).

Results

Species identification, genotyping, and clustering

A total of 475 faecal samples were collected, of which 230 were identified as snow leopards. In the interest of space, we provide full details in Supplementary Appendix 1.

Summary statistics of genetic diversity

Both datasets confirmed low allelic diversity of the population (AN = 4.364 and 4.259; AE = 2.627 and 2.536 for GEN11 and GEN27, respectively). The population was consistent with HWE assumptions (p values = 0.124 and 0.937 for GEN11 and GEN27, respectively), showing only one locus deviating from HWE expectations in both datasets (PUN132). Snow leopards in Gansu were characterised by a low inbreeding coefficient (FIS equal to 0.033 and 0.011 in GEN11 and GEN27, respectively) and by intermediate values of heterozygosity in both datasets. Corrected estimates of these indices, accounting for inbreeding coefficients and null alleles, were consistent with empirical observations, due to the extremely low average rates of null alleles in both datasets (Supplementary Tables S1 and S2).

Non-spatial methods - ordination

In the two datasets (GEN11 and GEN27), the amounts of variance explained by the PCAs (25, 50, 75 and 100%) were approximately achieved by 3, 7, 13, 37 axes and 3, 8, 15, 33 axes, respectively. No significant axes were found by the broken stick models in GEN27, while the first three were identified in GEN11 (Supplementary Fig. S3). There was a clinal degree of overlap along the first three principal components in both datasets, considering genotype location (YCW and QLS), that became more marked when the number of loci was reduced (GEN11) (Fig. 2). The clinal pattern of genetic diversity was well represented by the first PC axis in both datasets, suggesting a contact zone in the area of Shule Nan Shan (Fig. 3). The subsequent two principal components highlighted finer scale differences, especially in the localities of Shule Nan Shan and Qifeng, with the two extremes of the sampled area progressively more differentiated as the inertia of the axes was reduced. Colorplots of the first three PCA axes however did not clearly identify clines or structures (Supplementary Fig. S4).

Fig. 2: Scatterplot of the first three principal component (PC) axes in the two genetic datasets.
figure 2

GEN27 = 34 individuals typed at 27 loci; GEN11 = 49 individuals typed at 11 loci.

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Fig. 3: Principal Component Analysis (PCA) patterns.
figure 3

Principal component (PC) scores relative to the first three PCA axes in the two datasets. GEN27 = 34 individuals typed at 27 loci; GEN11 = 49 individuals typed at 11 loci.

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Spatially explicit neighbourhood-based diversity indices

The threshold at which the ratio NE:NS approached unity based on Euclidean distances was 100 km in both datasets. In the resistance distance scenario, a threshold of 400,000 cost units was identified in GEN11, and 1.2 million cost units in GEN27 loci (Supplementary Fig. S5). Since the use of a single threshold was needed to explicitly compare results between the two analyses, we constrained this threshold in GEN27 to be the same as GEN11, similar to the threshold identified in the Euclidean distance scenario, amounting a distance of 80 km-equivalent circa.

All the estimated average neighbourhood-based indices remained similar within the two datasets across scenarios (Table 1). In GEN11 (Fig. 4), both scenarios showed higher average number of alleles per locus and higher NE in the centre of the sample distribution, with progressively lower values at the periphery. Patterns of FIS differed slightly between the scenarios. For Euclidean distance (GEN11geo), both edges of the study area presented the lowest values. Considering distances based on movement cost (GEN11res), only the easternmost locality displayed the lowest values, while the central localities presented FIS values slightly higher than the westernmost edge (Fig. 4). Higher values of heterozygosity (HO) were observed in the QLS portion of the study area in both scenarios. Spatially explicit indices for the GEN27 dataset (Fig. 5) were mostly concordant with those described above, especially with regard to number of alleles and NE (lower at either edge). Heterozygosity patterns in GEN27 were also higher in the QLS region, and FIS estimates were generally lower on the eastern portion of the study area, compared to the central part (Fig. 5).

Table 1 Spatially explicit indices of genetic diversity calculated at the neighbourhood radius for which the ratio between effective population size (NE) and neighbourhood size (NS) approached 1 (100 km in geo scenario, 400,000 cost-units in res scenario; see main text).
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Fig. 4: Indices of genetic diversity calculated on GEN11 dataset at the neighbourhood radius identified by the Ne:Ns ratio in the Euclidean distance (geo) and resistance distance (res) scenarios.
figure 4

An number of alleles, Ho Observed heterozygosity, Fis inbreeding coefficient, Ne effective population size.

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Fig. 5: Indices of genetic diversity calculated on GEN27 dataset at the neighbourhood radius identified by the Ne:Ns ratio in the Euclidean distance (geo) and resistance distance (res) scenarios.
figure 5

An number of alleles, Ho Observed heterozygosity, Fis inbreeding coefficient, Ne effective population size.

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Spatial analysis - spatial weighting matrices and canonical ordination

Significant genetic spatial patterns were systematically present for both distance and resistance scenarios at all PCA inertia fractions in GEN27, and only at PCA_25 in GEN11 (Table 2; Supplementary Table S3). Usually, GEN27 sets were described by a distance-based network with a sole exception relative to PCA_75 in SWMgeo, while a graph-based connection scheme was always selected by PCA_25 in GEN11 (Table 2). The two scenarios possessed approximately the same explanatory power, with slightly higher values for SWMres in GEN27 and SWMgeo in GEN11 (Table 2). Spatial genetic structures identified in both modes of isolation were generally weak. The proportion of genetic diversity explained by eigenvectors was remarkably low when considering the full genetic variance of GEN27, and remained relatively low even when the content of PCA inertia was reduced in both datasets (Table 2). All the sets retrieved no more than four significant eigenvectors (Supplementary Table S4). Significant RDA axes were always three for PCA variance equal to, or above 50%, and no more than two for the PCA_25 fractions in both GEN27 and GEN11 (Supplementary Table S5).

Table 2 Most supported Spatial Weighting Matrices (SWM) and significant spatial functions retained (N. var) in each topology for each level of PCA inertia in the two sets.
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Major spatial patterns of snow leopard genetic diversity in Gansu

We only describe results relative to the full content of information (PCA_100) in the GEN27 dataset, as the patterns were concordant across all PCA inertia fractions (Supplementary Appendix 2, Supplementary Figs. A2.1–A2.3).

The main spatial pattern based on both RDAres and RDAgeo was a major division between the geographic locality of YCW and that of QLS. We observed admixed allelic patterns in the area of Shule Nan Shan (Fig. 6). The first axis in both RDAs found some degree of differentiation in the westernmost portion of Danghe Nan Shan mountain.

Fig. 6: Redundancy analysis (RDA) patterns.
figure 6

Significant axes for the landscape resistance scenario (RDAres) and Euclidean distance scenario (RDAgeo), in the set at 27 loci (GEN27), PCA variance equal to 100%.

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The second RDAres axis also highlighted the broad geographical division, suggesting clines in the areas of Shule and Qifeng, and from Shule to Yema/Danghe. In contrast, the second RDAgeo clustered individuals from Yema and Danghe Nan Shan, revealed a north-south gradient in Shule Nan Shan, and clearly distinguished Qifeng from the other localities in QLS.

The third RDAres and third RDAgeo axes both differentiated snow leopards at either edge of the sampling area. Overall, they both described clinal patterns within QLS (RDAres) or between QLS and YCW (RDAgeo). Shule Nan Shan was a linkage area in which genetic patterns peculiar to Danghe, Yema and Qifeng admixed (Fig. 6).

Clinal patterns in YCW were evident in the colorplot of the first three significant RDA axes (GEN27 PCA_100; Supplementary Appendix 2, Supplementary Figs. A2.5 and A2.6). While RDAres would suggest a weak, but more marked structuring in YCW, RDAgeo tended to describe this area as a continuum, with individuals at the western edge of Danghe Nan Shan always more differentiated. Both scenarios suggested a weak transition zone extending from Danghe Nan Shan to Qifeng and differentiating the cline between Longchanghe and Sidalong through augmented colour contrast (Supplementary Appendix 2, Supplementary Figs. A2.5 and A2.6).

Discussion

Spatially heterogeneous genetic diversity indices

Genetic variation tends to be clinal and to vary locally when individuals are distributed over continuous areas (Chambers 1995). These variations also depend on differential patterns of landscape connectivity and habitat availability that create genetic structuring (Shirk and Cushman 2011, 2014; Jackson and Fahrig 2016). The relationships between higher genetic variation and habitat amount have been well documented in population genetics (Frankham 1996; Jackson and Fahrig 2016) and landscape genetics (Hearn et al. 2019; Macdonald et al. 2018; Bothwell et al. 2017). Availability of habitat resources and landscape continuity increase the amount of gene flow, the effective population size, and overall genetic diversity (Frankham 1996; Shirk and Cushman 2014; Bruggeman et al. 2010). Therefore, local variations in NE in heterogeneous landscapes are driven by local population sizes, which in turn are dependent on habitat amount and connectivity (Shirk and Cushman 2014; Jackson and Fahrig 2016; Frankham 1996).

In line with these assumptions, we observed higher NE and allelic richness in the central localities of Shule and Qifeng (Figs. 4 and 5), two areas found to harbour extensive suitable snow leopard habitats (Atzeni et al. 2020), and to be characterised by higher densities of individuals compared to the other localities analysed in this study (Wang Jun, unpublished data; Alexander et al. 2016).

When populations are genetically structured, there is a theoretical expectation for a decrease in NS and NE from the centre to the edge of a distribution (Shirk and Cushman 2014). However, the lower values in Longchanghe and Sidalong may also be influenced by the lower number of genotyped individuals. Since the distribution of snow leopards is continuous (Atzeni et al. 2020), the current status of knowledge does not allow us to determine whether the estimated NE and allelic number patterns reflect true demographic processes or are the effect of the sampling scheme employed in this study. However, consistent with Shirk and Cushman (2014), the lower NE and allele numbers in Yema and Danghe correspond with lower snow leopard abundance in these sub-areas, compared to the two core central areas (Wang Jun, personal observation), a pattern driven by landscape and habitat characteristics (Atzeni et al. 2020).

We found higher levels of inbreeding in the two core areas, compared to the periphery (Figs. 4 and 5). In simulation scenarios and in empirical datasets, Shirk and Cushman (2011, 2014) postulated that lower NS and NE at the edges of a species distribution can drive unrelated individuals to travel larger distances to mate (see also Shirk et al. 2020), resulting in an increase in heterozygosity and decrease in inbreeding coefficient. Furthermore, lower populations in peripheral areas might also drive populations inwards, causing the apparent increase in FIS in the core areas (Shirk and Cushman 2014).

Recently, Shirk et al. (2020) explored the effects of gene flow from unsampled demes on the genetic composition and spatial variation of indices of the contiguous population of interest. They suggested that admixture penetrating from unsampled individuals would produce more divergence compared to less admixed individuals near the core of the sampling area. In our context, this phenomenon likely resulted in higher FIS values at the centre of the sample distribution, and in lower values especially at the eastern edge, confirming evidence of genetic influence from snow leopard in the remaining portion of the Qilian mountains, and likely accounting for most of the observed genetic patterns seen in this study.

The theoretical expectation for these FIS patterns may also be supported by kin structure and philopatric behaviour, a trait that has been recently observed in snow leopards (Johansson et al. 2021), and postulated to create structuring at regional level (Korablev et al. 2021). As higher kin structure is associated with connected habitats and increased gene flow (Dharmarajan et al. 2014), it is possible that areas outside the central localities represent sink habitats, characterised by lower availability of resources and composed mostly of individuals dispersing from sampled and unsampled core localities, presenting low family structure and more genetic divergence.

Spatial structures of snow leopard genetic diversity in Gansu

The clinal pattern of differentiation (Figs. 2 and 3) did not support the existence of groupings in these areas, contradicting recent suggestions (Zhang et al. 2019). Examination of PCA axes (Supplementary Fig. S4) indicated the high dispersal capacity of these animals (McCarthy et al. 2005; Johansson et al. 2018), implying a limited role of the landscape in creating strong localised patterns of allele frequencies (Table 2).

However, RDA with MEM revealed that snow leopard genetic diversity was significantly spatially structured, albeit weakly (Table 2). Overall, the main division was between Yema and Danghe in YCW, and the entire QLS portion, with clinal patterns emerging at finer spatial scale, describing an extensive contact zone in Shule Nan Shan (Fig. 6; Supplementary Appendix 2). The differentiation of samples at either edge of the study area suggests the need for additional survey efforts along the whole Qilian mountains, and west of YCW in the Altun mountains.

The evidence generated by MEM analyses complements the patterns observed in spatial variation of diversity indices from sGD analysis (Figs. 4 and 5). Admixture in the core areas stresses the importance of these two structurally connected localities for overall landscape connectivity, especially at a transition zone between eco-regions (Wu et al. 2003). Shule and Qifeng, due to their favourable habitat characteristics, contained more individuals and received migrants from peripheral areas, creating a hotspot of genetic diversity in the northwestern portion of the Qilian mountains.

The spatial variability of patterns is indicative of non-isotropic clinal structures. Where gene flow is reduced by the effect of the landscape matrix, local densities decrease as a result of diminished functional connectivity (Kaszta et al. 2019, 2020). For example, Ruiz-Gonzalez et al. (2015) explored the spatial genetic structure of pine and stone martens in northern Spain. Their findings revealed complex clinal structures, with steeper differentiation corresponding to the boundaries of the identified clusters, likely driven by high landscape heterogeneity and fragmentation affecting gene flow. In our context, although our findings do not support the existence of discrete population units, we postulate that lower landscape connectivity in YCW might produce more differentiation over short distances, leading to the main genetic division observed in the data (Fig. 6; Supplementary Appendix 2). This results in an area of more rapid changes within a continuous genetic gradient (Fig. 6; Supplementary Appendix 2).

Strength and significance of patterns

Although significantly structured, spatial patterns were found to be relatively weak. This low spatial signal in the snow leopard genetic profiles may be attributable first to a combination of the inherent low genetic diversity and the high dispersal capacity of this species, and secondarily to limited sample sizes. Recently, Hein et al. (2021) demonstrated that demographic histories are among the most influential factors determining the strength of adjusted R2 in MEM-based genetic analyses. The authors also illustrated that low sample sizes (in this paper represented by the number of nodes in the topologies) generally diminish the strength of the spatial signals. Our observations imply that, for the extent analysed in this study, neither geographical distance alone nor the landscape matrix are sufficiently strong constraints to drive the emergence of strong, localised spatial genetic patterns (Cushman et al. 2013), given snow leopards’ ecology (Fig. 6; Supplementary Appendix 2).

Dispersal capacity of the species and the permeability of the landscapes are key parameters driving the signal-to-noise ratio in landscape genetics (Cushman et al. 2013; Shirk et al. 2017b, 2020). In this study, we explored the effect of the landscape matrix through an exponential transformation of a habitat model (Wan et al. 2019; Supplementary Fig. S2). Although this is a common practice in study of dispersal and/or landscape genetics (Zeller et al. 2018), additional work to optimise landscape resistance based on genetic differentiation (e.g., Shirk et al. 2010; Castillo et al. 2014; Shirk et al. 2017a) is necessary to improve the reliability of inferences regarding landscape effects on genetic diversity and genetic structure, given that habitat relationships often correlate poorly with patterns of genetic diversity and genetic differentiation (e.g., Wasserman et al. 2010).

Much emphasis has been previously given to the utility of resistance distances to weight the edges of SWMs (Bauman et al. 2018a; Galpern et al. 2014). We found that using either distance type produced comparable values of adjusted R2 for each of the PCA inertia fractions in the two datasets (Table 2), which could either suggest that other influential factors may determine the strength of spatial genetic structures (Hein et al. 2021; Shirk et al. 2017b), or that the response variables studied here are weakly structured at the range of spatial scales detectable by our sampling design. Further work will be necessary to gain better insight into the benefits of incorporating alternative landscape hypotheses in SWMs (Wagner and Fortin 2016).

Differences between datasets

Contrasting results were obtained from the different datasets in their ability to identify spatial structures and to describe finer scale genetic variation (consistent with Landguth et al. 2012). Hein et al. (2021), argued that the strength of the spatial structure is not affected by decreasing number of loci, and contrasted their observations to previous landscape genetics findings which demonstrated that correlations between genetic and ecological distances are sensitive to the number of loci and the level of polymorphism (Landguth et al. 2012; Oyler-McCance et al. 2013). These divergent conclusions might be resolved given that they are based on different analytical approaches and different questions: one seeking to ascertain whether there is significant genetic structure (and resulting spatial autocorrelation patterns), while the other attempting to find a landscape scenario creating those patterns. Our results partly agree with Hein et al. (2021)’s observations, and partly with those of Landguth et al. (2012) (e.g., stronger relationships in the dataset with more loci), but emphasise the importance of analysing the proportion of the allelic information which captures the spatial variation (e.g., Shirk et al. 2017b). In fact, even datasets with limited genetic resolution can describe significant spatial genetic variation (Hein et al. 2021), particularly when PCA analysis was used to retain meaningful portions of genetic variance while reducing the effect of random variation unrelated to spatial genetic structure (e.g., Shirk et al. 2017b; Table 2).

Ordination axes as response variables in RDA and partial RDA are increasingly applied in spatial genetics studies (e.g. Dalongeville et al. 2018; Guerrero et al. 2018; Breyne et al. 2014). This is because ordination methods can distil the meaningful genetic variation in each dataset, avoiding the inclusion of unnecessary axes capturing mostly noise (Patterson et al. 2006; Shirk et al. 2017b). In link-based analyses, Shirk et al. (2017b) recommended that under the most challenging conditions for detection of landscape genetics patterns (i.e., low sample size and high dispersal ability), including additional PCA axes would improve the accuracy of inferences regarding the processes driving genetic diversity. However, this appears to be related to the variability of allelic information contained in a given dataset, in which case adding further variance does not improve accuracy (Shirk et al. 2017b). These observations seem also to apply to other analytical frameworks, as in this study. Our results highlight the importance of other explorations of the utility and the behaviour of MEM in analysing landscape variation in genetic patterns. The circumstances in which detection of patterns will be enabled or inhibited, at varying number of ordination axes (e.g. Landguth et al. 2012; Forester et al. 2016), needs to be carefully inspected across a wide array of possible factors, represented by demographic histories, number of markers, genetic variability, sample sizes (i.e., nodes in the network), and possibly alternative landscape resistance hypotheses (e.g., Landguth et al. 2012; Cushman et al. 2013).

Implications for snow leopard research and conservation

The connection between the number of genetic markers, the genetic signal and their power to describe significant patterns has practical implications in studies of spatial genetic diversity. Theoretically, a small subset of loci can suffice to identify either spatial structures (Hein et al. 2021) or the generating landscape processes in link-based analyses (e.g., Short-Bull et al. 2011; Landguth et al. 2012). Given the slow progress of snow leopard genetic research (Weckworth 2021), to date no studies, besides this one, have produced a comprehensive description of local allelic diversity to guide further genetic surveys. As it is not possible to ascertain in advance the quality of samples, the number of reliable profiles, and the degree of polymorphism, studies limited in extent should proceed iteratively, ascertaining first whether the loci chosen for individual identification are enough to capture meaningful and significant spatial variation. This of course depends on the exploration of the variance expressed by ordination axes which is representative of the whole information contained in the datasets (Forester et al. 2016; Shirk et al. 2017b).

If patterns are undetectable, then evaluating the interplay between the number of markers and PCA variance, together with the adoption of the spatial methods applied in this study, will help researchers clarify whether there is in fact no spatial genetic pattern, or if the lack of detected structure may be related to insufficient data, be it sample size (Hein et al. 2021), number of markers (Landguth et al. 2012; Oyler-McCance et al. 2013), genetic variation, or their interaction (Landguth et al. 2012). Landscape genetics inferences regarding the landscape process that have generated spatial genetic patterns are highly susceptible to the interaction between sample size, number of markers and allelic richness (Landguth et al. 2012; Oyler-McCance et al. 2013). Ongoing work is revealing that analyses of few loci produce less ecologically accurate inferences for snow leopard genetic structure (Atzeni et al. submitted), which has a larger effect than that of sample size of genotyped individuals (Atzeni et al. submitted; Landguth et al. 2012). Future directions in landscape and spatial genetics might fruitfully evaluate relationships between the strength of a spatial signal and the accuracy of landscape genetics inferences, ideally using a simulation approach that controls the pattern-process relationships (e.g., Landguth and Cushman 2010; Landguth et al. 2012). These observations are generalisable to other highly vagile species for which cryptic genetic patterns are expected.

Conclusions

This study described the presence of weak spatial genetic structure in a snow leopard population from Gansu, China, revealing a principal geographical division between adjacent mountain ranges coupled with a cline of differentiation coincident with two admixture localities which were distinctive in their higher effective population size and allelic diversity.

Overall, spatially explicit indices of diversity, together with evidence generated through our MEM-based approach, emphasised the key importance of two core areas in providing potential snow leopard population strongholds and source for dispersal in the northwestern portion of the Qilian landscape.

Our analytical framework combined the detection of genetic structures with the assessment of the spatial variation of genetic diversity parameters. This gave us increased power to describe cryptic patterns of genetic diversity. Our approach represents a particularly effective strategy to gain insights into the localised differentiation in continuously distributed populations, providing a means to explain the nature of inferred spatial structures through demographic patterns. This enables hypothesis testing regarding the manner in which the landscape facilitates or impedes gene flow, which is essential for tailored conservation strategies.

This study also fills an important knowledge gap in snow leopard research, providing genetic baseline data for continuously distributed individuals in an under-studied landscape, at a relatively high number of microsatellite loci. The results will guide the design of future surveys to expand spatial genetics inferences to larger extents, and guide future large-scale correlative landscape genetics studies to quantify the effect of landscape structure on snow leopard gene flow across its range. As research and conservation efforts for snow leopard become more restricted to ‘high-quality’ patches (Johansson et al. 2016), it is increasingly vital to understand genetic structure and the landscape, management and other factors that might affect the species’ survival. Finally, this study raises important methodological questions regarding the applicability of PCA axes and spatial eigenvector-based methods such as MEM in landscape genetics, which we hope will inspire further work to improve our understanding of gene-environment relationships.

Data archiving

Genotypes and geographic coordinates of snow leopard individuals in the two datasets cannot currently made available due to restrictions and directives from the competent authorities of the Popular Republic of China.

The corresponding author is willing to consider any reasonable request for data sharing and to gather the necessary permissions to do so.

R code relative to the calculation of cost distance-weighted Spatial Weighting Matrices (SWMs), is provided as appendix material to this manuscript.