Migratory connectivity of Swan Geese based on species' distribution models, feather stable isotope assignment and satellite tracking

Understanding connectivity between avian breeding and non‐breeding areas is essential to understand processes affecting threatened migrants throughout their annual cycle. We attempted to establish migratory connectivity and flyway structure of the IUCN vulnerable Swan Geese (Anser cygnoides) by combining citizen science species' distribution models (SDMs) and feather stable isotope analysis.


| INTRODUC TI ON
Migratory connectivity describes the movement of individuals between summer and winter home ranges, as well as use of intermediate stopover sites (Webster, Marra, Haig, Bensch, & Holmes, 2002).
Defining connectivity for migratory species is essential to differentiate discrete populations as a basis for comprehending their population dynamics and life-history strategies (Pekarsky et al., 2015;Rolshausen, Segelbacher, Hobson, & Schaefer, 2009). This need is more urgent for declining taxa. More than 30% of all vertebrates species are reported to be declining (Thompson, Klütsch, Manseau, & Wilson, 2019), rising to at least 40% among birds (McLaren et al., 2018). More than 40% of global avian species undertake annual migrations (Newton, 2007), during which they interact with a series of local environments and provide a variety of ecosystem services (e.g. Duarte, Laura, Willem, & Jordi, 2016;Tian et al., 2015).
However, with increasing pressure on migratory birds at multiple points along their annual flyway corridors, understanding connectivity is becoming more urgent in order to develop effective conservation strategies, especially for the most rapidly declining populations (Hobson & Wassenaar, 2019).
Multiple techniques have been employed to describe the geospatial movement of individual birds. The extensive application of passive extrinsic markers such as metal rings and neck collars has provided great historical insights into migration patterns, but is limited by extremely low reporting rates (Hobson, Norris, Kardynal, & Yohannes, 2019). Recent innovation has provided devices that can be mounted on birds that record time-stamped positions with great accuracy using the global positioning system facility, with data downloaded via the mobile telephone system, albeit with potential effects on tagged individuals (Bodey et al., 2018).
In contrast, intrinsic markers (such as the stable isotope ratios of body tissues) do not require device attachments but rely solely on features of the birds' physiology and ecology, as well as our ability to decode the information via the comparison of these features with known geophysical spatial isotopic patterns. As a result, intrinsic markers may be less subject to bias (e.g. towards easily accessible regions for trapping and marking of birds), as well as being relatively less costly to implement. The stable hydrogen isotope ratio ( 2 H: 1 H, hereafter depicted by δ 2 H) of avian tissue has become a popular intrinsic marker to infer bird movements Vander Zanden, Nelson, Wunder, Conkling, & Katzner, 2018). Natural variation in δ 2 H in precipitation (δ 2 H p ) can be characterized across space and time (López-Calderón, Van Wilgenburg, Roth, Flaspohler, & Hobson, 2019;Vander Zanden et al., 2018). Values of δ 2 H p reflect hydrogen taken up and incorporated into plant tissues and by their primary consumers, both of which will be assimilated into the organs of birds via their food. As a result, the specific isotopic value in any given feather (δ 2 H f ) reflects the amount-weighted, mean annual δ 2 H p at the natal or moult location (Fox et al., 2017). It is therefore possible to create assignment models by comparing δ 2 H f values and prevailing environmental values in amount-weighted, time-averaged δ 2 H p . Nevertheless, while δ 2 H-based methods are highly tractable and pragmatic, their assignments are generally coarse as large geographical regions share similar δ 2 H p values.
Resolution of δ 2 H-based assignments can be improved by incorporating prior sources of information. These include ring-recovery data (Guillemain, Van Wilgenburg, Legagneux, & Hobson, 2014;Procházka, Van Wilgenburg, Neto, Yosef, & Hobson, 2013), genetic markers (Chabot, Hobson, Van Wilgenburg, McQuat, & Lougheed, 2012;Clegg, Kelly, Kimura, & Smith, 2003) and predictions from species' distribution models, SDMs (Fournier, Drake, & Tozer, 2017;Pekarsky et al., 2015). While it can be difficult to incorporate systematic genetic and ring-recovery data at a comprehensive scale, the extensive data collected by citizen scientists can be used to generate SDMs that provide excellent utility for refining isotopic assignments of migratory connectivity (Fournier, Sullivan, et al., 2017;Pekarsky et al., 2015). Citizen science enlists (often non-professional) observers to collect and/or process data, some of which extend over several decades (Bonney et al., 2009;Bonney, Phillips, Ballard, & Enck, 2015). For example, eBird (eBird, 2017) engages the global bird-watching community to collect more than 5000,000 bird observations every month, submitted to a central database. These data have been used in at least 90 peer-reviewed publications on various topics (Bonney et al., 2014). Despite data quality issues related to citizen science (Hunter, Alabri, & van Ingen, 2013;Kosmala, Wiggins, Swanson, & Simmons, 2016), observation records from these repositories can be effectively employed in presence-only species distribution modelling to generate valuable priors which, in our case, can be used to subsequently refine isotopic assignment of individuals to localities. This is essential for understanding the distribution range and population dynamics of migratory species, especially for those populations that are confined to fragmented and/or remote regions.  Dementiev & Gladkov, 1952). However, by the early 1990s, its breeding range was increasingly restricted to Mongolian steppe wetlands, in the west extending into neighbouring Tuva in the Russian Federation and in the east extending into Russian Chita and northeast China. Elsewhere in Russia, there remain a few breeding birds around Khanka Lake, another group around Lake Udyl and the coast at Schastye Bay and perhaps a few on Sakhalin Island (Fox & Leafloor, 2018;Kear, 2005;Poyarkov, Klenova, & Kholodova, 2010). Swan Goose wintering range also once traversed Korea, Japan and much of China, but in recent years, this has contracted to China and concentrated increasingly there at Poyang Lake in Jiangxi Province (Fox & Leafloor, 2018).
To date, there is limited information on the migration connectivity of this species. Initial tracking studies demonstrated that most marked geese from northeastern Mongolia followed more indirect and energetically costly autumn migration pathways than the expected direct flight to the winter quarters, which was potentially explained as the result of adverse landscape changes in east China affecting historical migratory behaviour (Batbayar et al., 2011). More recent tracking has confirmed connections between Swan Geese breeding in Far East Russia and disjunct wintering areas on the southeastern coast of China (Minjiang River Estuary, Fujian Province, C. Y. Choi, personal communication), the subject of prolonged speculation (Choi et al., 2016;Poyarkov, 2005;Poyarkov et al., 2010). These studies, however, were confined to restricted areas of the breeding grounds, and the recent rapid consolidation of the species at Poyang Lake makes it imperative to undertake a broader study of the movements of remaining Swan Geese.
In this study, we develop a framework for generating spatially explicit predictions of the breeding/moulting origins for Asian large-bodied waterbirds, by integrating SDMs, constructed from citizen science and systematic survey data, with stable isotope analysis of feathers from individual birds. We test this framework on Swan Geese caught on their winter quarters to trace their summer origins. Given that more than 95% of the total population seems now to occur at Poyang Lake (Fox & Leafloor, 2018) and the characteristic long-term pair bonds of the species, we made two predictions.
(1) That feathers from individuals captured at Poyang Lake would differ significantly in their δ 2 H f values reflecting the different δ 2 H f isoscape values representing the summer moult locations. (2) There would be no difference between sexes. Furthermore, the breeding range is thought to have become more fragmented in recent times (Poyarkov, 2005). Increased human population density and urbanization in eastern China (Batbayar et al., 2011), as well as severe loss of natural wetlands in northeastern China (Lu et al., 2016;Xu et al., 2019) have also likely affected the migratory routes followed by Swan Geese in recent years. We therefore also tested the prediction that wintering Swan Geese in China have altered their historical summering distribution range, using δ 2 H f measurements from museum specimens.

| ME THODS
We analysed δ 2 H values for feathers collected from breeding and wintering grounds (Figure 1). Because feather keratin is metabolically inert after formation, feathers sampled in the summer should reflect isotopic environments occupied during post-breeding feather growth (Scordato et al., 2019). Probable origins of wintering birds were determined by (1) construction of season-specific SDMs representing the prior probability of Swan Goose occurrence; (2) construction of a spatially explicit δ 2 H f isoscape for F I G U R E 1 Moulting occurrence observations (black dots) and feather sampling locations (red dots) of the Swan Goose Anser cygnoides reported in this study. The extent of the breeding range is derived from BirdLife International and Handbook of the Birds of the World (2018) which are marked in yellow Swan Goose based on a derived relationship between measured δ 2 H f and δ 2 H p primarily from the International Atomic Agency (IAEA) Global Network of Isotopes in Precipitation (GNIP); and (3) application of a Bayesian assignment algorithm to depict spatially explicit probability of origin surfaces for Swan Geese based on their δ 2 H f values.

| Telemetry and feather sample collection
Ninety-six feathers of birds from 12 summering (July) and five wintering sites (November to February) were obtained between 2010 and 2017 (Table 1). On the moulting areas, we rounded up flightless geese using boats, gently pushed them into corrals and nets on land. Secondary median wing coverts from captured adults were plucked (feather base intact) and stored in separate paper envelopes. Wing coverts were chosen as they are regrown with (Kear, 2005) or after (Ashton, 2012) primaries and secondaries, reducing the risk of impairing flight due to sampling flight feathers.
Wintering geese were caught using static mist nets or by pursuit in boats with strong lamps to catch geese with hand nets at roost sites (see Aharon-Rotman et al., 2017 for full details). Four wintering geese (Table S1; Sample ID: #1, #33, #36, #42) were fitted with GPS/GSM loggers before releasing to identify their subsequent moulting locations. Feather specimens from two museums were also included in analyses (Table 1). Feather bases were removed for sex identification based on DNA analysis (Dawson, Dos Remedios, & Horsburgh, 2016), while feather vane material was used for δ 2 H analysis. Based on this, the δ 2 H f in feathers grown during the previous summer provided information on (1) the approximate latitude of natal origin in the case of one-year-old birds or (2) approximate previous post-breeding moult location in the case of older birds (Hobson, Wassenaar, & Bayne, 2004

| Species distribution modelling
Species' distribution models are widely used to predict the probability of occurrence for species across the landscape based on the relationship estimated between species' observation records and their corresponding environmental characteristics (Elith et al., 2011;Hijmans, 2012). There is now a plethora of methods for modelling species' distributions, among which maximum entropy (MaxEnt) models are commonly used (Radosavljevic & Anderson, 2014) because they generate robust results using sparse, irregularly sampled data with minor locational errors (Elith et al., 2006;Kramer-Schadt et al., 2013). Moreover, MaxEnt has the advantage of using presence-only data, avoiding the need for confirmed absence records (Elith et al., 2006), making it especially suitable for rare species and/ or those with a fragmented range.

| Spatial filtering of occurrence data and correction for sampling bias
We defined the flightless moult period as 16 June to 16 September (Batbayar et al., 2011). A probability surface for Swan Goose moulting areas was generated based on presence records during this period (Table S2) from three main sources: (1) sampling locations of feather collections; (2) moulting locations described elsewhere; and (3) records downloaded from the eBird and GBIF citizen sciences databases (https://ebird.org/home; https://www.gbif.org/).
We chose Maxent version 3.3.3k (Phillips, Anderson, & Schapire, 2006) for species distribution modelling for two main reasons. Firstly, we are constrained to use a presence-only modelling approach because the majority of our records (68.69%, Table S2) were collected with unknown sampling effort. Hence, it is impossible to incorporate covariates that account for heterogeneity in detectability, effort and reporting (duration spent searching for birds, start time, distance travelled, etc.) when constructing SDMs (Johnston et al., 2019). Secondly, Maxent is documented to outperform other presence-only modelling approaches (Ruan et al., 2018;Townsend Peterson, Papeş, & Eaton, 2007). A fundamental assumption in Maxent is that the entire area of interest has been systematically sampled. However, most data sources (e.g. from museums and citizen science programmes) exhibit strong spatial bias in survey effort (Stolar & Nielsen, 2015), as some sites are more likely to be surveyed than others (Ruizgutierrez & Zipkin, 2011). This can severely impact model quality ) by over-representation of certain environmental features of more accessible and extensively surveyed areas.
To overcome such sampling bias, the entire dataset was spatially filtered and a bias grid was generated to modify the random selection of background points using tools from the SDM toolbox (Brown, 2014) Table S2) and bias grid were utilized in Maxent as the occurrence data and bias file, respectively.

| Environmental variables
Twenty-four raster layers ( Goose in the field (e.g. land cover vs. elevation), finally five variables (Table S3) were retained for further modelling. All grids were clipped to match the distribution range of the Swan Goose, with a resampling resolution of 1 km.

| Stable isotope analysis
Feather samples were cleaned with 2:1 chloroform-methanol solution and dried at room temperature in a fume hood. Distal sub-

| Statistical analyses
We tested for differences in δ 2 H f from the same location, but from different years at Poyang Lake and Chenyao Lake (

| Identifying goose origins
An appropriate rescaling relationship between δ 2 H f and δ 2 H p is a prerequisite for stable isotope-derived geographical assignments (Vander Zanden et al., 2018). The calibration set used to determine the relationship between δ 2 H f and δ 2 H p comprised a set of 50 feathers from 12 moulting locations. We regressed the δ 2 H f against mean annual growing season δ 2 H p at the site of sampling locations and further used this relationship to convert a GIS-based model of δ 2 H p across the study area into a spatially explicit raster depicting mean expected δ 2 H f values (Bowen, Wassenaar, & Hobson, 2005).
Due to sources of variance inherited from the regression model, δ 2 H f values expected from any given pixels are best characterized as a distribution of potential values rather than a single value; hence, we reported the origins of a given bird as a normal density function (Hope et al., 2016;Pekarsky et al., 2015): where f (y| , ) is the probability that any given cell on the isoscape represents a potential origin for an individual with δ 2 H f value of y, with an expected mean (μ) of δ 2 H f and expected standard deviation (σ) based on the rescaling equation. The σ value was estimated using the standard deviation of the residuals from the regression equation, given that this accounts for the deviation of the δ 2 H f from the expected geographical pattern, which is present in the ambient water, thus representing the variance in the predicted value within the calibrated isoscape.
We incorporated the SDM as prior information for the stable isotope assignment using Bayes' rule: where f (b|y) is the posterior probability a given pixel on the raster rep- To depict the likely origins of each population, we assigned each individual separately and converted the raster to a binary surface using a 2:1 odds ratio (Fox et al., 2017;Procházka et al., 2013), where isoscape cells in the upper 66.7% of probabilities were considered as likely (1) and, otherwise, unlikely (0) origins. Assignments to each cell throughout the distribution range were generated in this way, which were subsequently "stacked" together for all individuals in the wintering samples to depict potential moulting origins for each wintering group. Each cell value represented the sum of these individual-level binary grids, summed and then normalized by dividing by the number of geese in each group, thus obtaining the posterior probability surface of origin for the group. Digital file manipulation and assignment to origin analyses were conducted using multiple R packages including "raSter" (Hijmans et al., 2015) and "MaptoolS" (Bivand & Lewin-Koh, 2015).

| Assignment verification via satellite tracking
30 km for at least 21 days (Kölzsch et al., 2019) were identified as moulting. The central location of the data points during moulting period was considered as the moulting point and was plotted on the origin prediction map of corresponding capture group along with the tracking routes of each individual to verify the prediction power of the Bayesian models.

| Differences in feather stable isotopes
There was a significant difference between the two sets of samples  Figure 2), while all the samples from Chenyao Lake were treated as one group. Kruskal-Wallis tests suggested marginally significant differences between the six testing groups ( 2 5 = 11.2, p = .0048), while none of the pairwise sex groups exhibited significant difference according to the P values after Bonferroni correction (Table S4).

| Species' distribution models
Some spatial bias was detected in the moulting observations for the Swan Goose. Within the summering range, sampling intensity was highest in eastern Mongolia the adjacent Daurian area located along the boundary of China, Russia and Mongolia, while the potential moulting areas in western Mongolia and eastern Kazakhstan were less sampled ( Figure S1). Although SDM without spatial bias correction could accurately predict the test presence locations as demonstrated by their high area under the curve (AUC) of the receiver operating characteristic curve (ROC) values ( Figure S2), this is largely because they predicted a higher presence in the more densely sampled eastern Mongolia and adjacent Daurian region. This spatial bias in observations was translated into environmental bias by providing the bias grid as an "environmental covariate" to Maxent when constructing the moulting SDMs.
By generating a separate assignment map for each independent capture group, Swan Geese wintering in Poyang Lake were predicted to originate mainly from the Kherlen River, which derives from eastern Mongolia before emptying into Hulun Lake in China. Adjacent areas of eastern Mongolia, Hulun Lake and northern East Ujimqin Island and the Ussuri River region were also inferred as potential hotspots of high probability for the summer provenances for geese sampled in the 1960 and 1970s. However, geese sampled at the beginning of the 21st century (from Fujian Province, Figure 5c) show no such linkages with Far East Russia and seem to exhibit a transition state of summering origins between historical and modern patterns.

| Comparing telemetry tracks and stable isotope predictions
Among the four tracked geese, one from Poyang Lake and another from Chenyao Lake (#36 and #42, respectively; Table S1) migrated to western Mongolia for the subsequent breeding season (Figure 4b,d), both moulting in the northeastern corner of Uvs Lake, the largest saline lake in Mongolia. Two other Poyang Lake marked geese went to Inner Mongolia, China (Figure 4b,c) but one moulted in Hulun Lake (#1 ; Table S1) while another stopped in East Ujimqin Banner (#33; Table S1). The final moulting destinations for all these four geese showed a high coincidence with the regions predicted by our assignment model. Nevertheless, because numbers of tracked individuals were few, there was no evidence of moulting provenance for those hotspots located in central Mongolia (Figure 4b

| D ISCUSS I ON
Using a Bayesian framework to combine SDMs derived from citizen science observations with δ 2 H assignments to produce high-resolution estimates of the origins of Swan Geese, we provided evidence to support the known contraction in range of the species on their Russian and Mongolian breeding areas (Batbayar et al., 2011;Goroshko, 2001). This is the first case study in Asia to successfully define the migratory origin of the wintering Anatidae based on a species-specific rescaling relationship between δ 2 H f and δ 2 H p , confirmed by satellite telemetry.
The integration of SDMs greatly improved the accuracy of stable hydrogen isotope assignments for Swan Geese. To demonstrate the improvement, we depicted the probable origin surface of all the wintering geese caught in China. Model uncertainty exacerbates the natural lack of resolution in stable isotope-based assignment (Figure 5b), for which the probable origin of birds extended over a vast area from Western Mongolia as far north as southern Baikal Lake region and east to the lower reaches of the Amur River, with F I G U R E 3 (a) Relationship between δ 2 H in precipitation (δ 2 H p ) and δ 2 H of feather samples (δ 2 H f ) for Swan Geese Anser cygnoides of known provenance, and (b) relationship between δ 2 H f and longitude of sampling locations. Shadow area represents for the confidence interval, and significant correlation was indicated at the top-left corner based on Pearson's analysis (p = 2.3e −7 and p = .00032, respectively) for each panel low resolution. Conditioning isotope assignments on the moult-specific SDM greatly enhanced geographical assignment (Figure 5a), which confined the final predicted areas of origin to adjacent areas distributed between eastern Mongolia, China and the Chita region of Russia as well as central and western parts of Mongolia. Given that we suspect that the current breeding/moulting distribution range of the Swan Goose is severely fragmented compared to that in the recent past, we thus conclude that the prediction power of the Bayesian approach had benefitted by integrating the moult-specific SDM.
Combining SDMs and δ 2 H f data, we predicted the potential moulting origins for 46 geese sampled on their Chinese winter quarters, including the currently most important wintering location, Poyang Lake in Jiangxi Province, as well as museum specimens wintering along the coast from the 1960s and 1970s. Our results confirmed the absence of sex effect on δ 2 H f values among the tested groups, but revealed differences in moulting provenance of Swan Geese between feathers sampled from contemporary and historically derived geese despite the potential limitations associated with the relatively small sample size among the latter. We contend that while the improvement of the sample size would provide more confidence in the precision of the geospatial assignment of historical individuals, in all likelihood the historical summering range extended further to the north and east than that of the current population.

| Multiple moulting origins among Poyang Lake wintering geese
Two groups of Swan Geese sampled in the same year but in subsequent seasons at Poyang Lake exhibited significantly different δ 2 H f values, demonstrating multiple moulting origins for geese sampled there. Batbayar et al. (2011) showed that telemetry tracked geese from eastern Mongolia mainly migrated to Poyang Lake in winter, while those from central and eastern Mongolia were likely to appear F I G U R E 4 Probable origins of wintering Swan Goose Anser cygnoides sampled in Poyang Lake in March 2015 (a, n = 18), Poyang Lake in December 2015 (b, n = 16), total Poyang Lake (c, n = 34) combining (a) and (b), and Chenyao Lake in 2015 (d, n = 6) based on Bayesian stable hydrogen isotope assignment. Tracking routes of Swan Geese which were also included in the stable hydrogen analysis are presented by different coloured lines (red -#36; green -#33; sea green -#1; magenta -#42) and crosses within circles indicate their moulting sites in the subsequent year. The defined polygons (shown by the coloured areas) represent the summer distribution range as defined by, and retrieved from, BirdLife International and Handbook of the Birds of the World (2018). Major rivers and lakes within were marked in royal blue. Legend values represent the number of birds potentially originating from each raster cell. Binary assignment surfaces were created by applying a 2:1 odds ratio at Shengjin Lake, Anhui Province (Fox & Leafloor, 2018). The loss of submerged macrophytes in Anhui Lakes  has reduced the carrying capacity for tuber-consuming birds, altering the distribution and abundance of the Vallisneria tuber-feeding avian guild. This has notably affected the Swan Goose, which is perhaps more specialized in this respect than other species (Chen, Zhang, Cao, De Boer, & Fox, 2019;Fox et al., 2011). At Shengjin Lake, wintering Swan Goose numbers decreased more than 10-fold between 2003and 2008. The wintering range continues to contract (Cao, Zhang, Barter, & Lei, 2010;Zhang et al., 2011), concentrating at Poyang Lake, where more than 95% of the world population currently occurs (Fox & Leafloor, 2018). It is therefore not surprising that Poyang Lake supports wintering Swan Geese of increasingly diverse breeding provenance. These include birds from known important summering areas, distributed between China and Mongolia (Ganbold et al., 2017;Goroshko, 2004;Songtao, Xinhai, & Gerilechaoketu, 2014), the southeastern Transbaikalia region in Russia (Goroshko, 2001;Goroshko, Cornely, & Bouffard, 2008), and in western/central Mongolia and northeast China (Tian, Jia, Tao, & Li, 2010).

| Changes in moulting distribution in northeast China
The distinctive differences in the predicted geographical origins between historical and modern feather samples potentially indicate a change in distribution of summering Swan Geese despite the relatively small sample size available from museum specimens.
The Swan Goose formerly bred in the Tuva republic, the Nanweng River wetlands in Heilongjiang Province, and the Ergun wetlands in Inner Mongolia in the central and western parts of its former range (Poyarkov, 2005). In addition, the species has almost completely disappeared in summer from the Amur-Heilong River Basin, the Ussuri River and Khanka Lake as well as throughout Far East Russia, so our data from museum samples from Fujian Province suggesting links with that area may reflect the transient state at that time. This reflects documented major environmental change in the area: for example, Swan Geese were common at Lake Kizi (Lower Amur region) in the 1930s, but the site was abandoned by geese in the 1950-1960s as a result of extensive timber cutting operations along the lake shore (Poyarkov, 2005). Cultivation and agricultural intensification forced F I G U R E 5 Probable moult origins of wintering Swan Goose Anser cygnoides inferred from feather δ 2 H f values with (a) or without (b) incorporating species' distribution models for inland (all except those from museums, Table 1) and coastal individuals (corresponding to geese from Fujian Province (c) and Shanghai City (d)). The defined polygons (shown by coloured areas) represent the summer distribution range as defined by, and retrieved from, BirdLife International and Handbook of the Birds of the World (2018). Major rivers and lakes within this range are marked in royal blue. Legend values represent the number (a and b, n > 2) or the probability (c and d, n = 2) of birds potentially originating from each raster cell. Binary assignment surfaces were created by applying a 2:1 odds ratio Swan Geese to leave the Lefu River basin (Ilistaya River) during the same period (Poyarkov, 2005). Currently, the Amur-Korean-SE China Swan Goose migratory population is isolated, consisting of a few hundred individuals (Fox & Leafloor, 2018;Rozenfeld, Shpak, & Paramonov, 2014). Northeastern China formerly supported 26.5% of natural wetlands in China (Lu et al., 2016), but since 1970 has suffered extensive habitat loss and degradation from wetland reclamation, human activity, agricultural intensification and climate change (Huang et al., 2010;Lu et al., 2016;Zhang et al., 2018). The serious continuous loss of natural wetlands in northeast China, which used to be extremely important breeding/moulting habitats for waterfowl, is particularly severe in Heilongjiang Province, which used to support abundant Swan Geese (Li, 1996), but where the species is now rare (Fox & Leafloor, 2018).

| Lack of sex-linked provenance and moulting strategy
Lack of a sex effect on the δ 2 H f values of wintering geese and the significant negative relationship between δ 2 H f and longitude of sampling locations suggest similar provenance and moulting strategy for both genders. This is hardly surprising for a monogamous species that pairs for life (BirdLife International, 2019;Kear, 2005) in contrast to many seasonally monogamous duck species where females undertake brooding rearing and parental care alone (Salomonsen, 1968).

Non-breeders undertake moult migration to large open-water bod-
ies with adequate food resources (Batbayar et al., 2011), while breeders remain together with goslings until fledging (Poyarkov, 2005) and moult in the vicinity of their nesting site (Salomonsen, 1968).

However, even in favourable breeding seasons, non-breeding Swan
Goose aggregations in the Daurian region still constitute c.70% of the world population (Goroshko, 2004). Lifetime pair-bond duration and extended parental care are typical of goose species (Ely, Wilson, & Talbot, 2017), enabling Swan Geese to maintain social bonds with conspecific and even family groups (Robertson & Cooke, 1999). It is therefore not surprising to find local fine-scale genetic structure among birds sampled on the breeding grounds (Q. Zhu, I. Damba, Q.

| The value of combining telemetry and isotope approaches
The contribution from using stable isotope methods to interpret migratory connectivity is now well documented (Fournier, Drake, et al., 2017;Symes & Woodborne, 2010;Van Wilgenburg & Hobson, 2011) and verified by our study. Thanks to the predictable natural variation in δ 2 H p , we see the potential of using δ 2 H f as a means of compensating for the lack of long-term research and monitoring and especially traditional capture-mark-recapture approaches to determine levels of migratory connectivity in waterbirds in East Asia. There are likely to be further advantages in analysing for multiple elements to further improve the prediction resolution and accuracy of moulting provenance based on feather stable isotopes as demonstrated elsewhere (Fox et al., 2017;Pekarsky et al., 2015).
Although the application of telemetry devices to waterbirds has proved invaluable for describing individual migration patterns, given the general patterns of lifetime site fidelity in these species, the broader application of this technique to determining migratory connectivity within and between population remains limited.
Nevertheless, we see advantages in the complementary use of telemetry and stable isotopes in this context. Firstly, stable isotope analyses could identify potentially high-connectivity areas based on feather samples from unmarked birds. Sites believed to be key nodes in the connectivity matrix can then be investigated further by enhanced telemetry tracking to enlighten us about breeding provenance, habitat use and migration strategies to fully characterize migratory movements. Secondly, for species with a fragmented breeding range, applying tracking devices on more individuals to estimate the probability of their migration to each distinct breeding patch would generate an improved set of priors to apply within a Bayesian framework to greatly improve on current knowledge.

ACK N OWLED G EM ENTS
We would like to thank Kunpeng Yi, Xianghuang Li, Shujuan Fan and Hongbin Li, Sonia Rozenfeld and Olga V. Shpak for conducting fieldwork. We appreciate the help from Xiaoping Chen and

DATA AVA I L A B I L I T Y S TAT E M E N T
All the relevant data necessary for this study are included in the Supporting Information.