Landscape Ecol (2018) 33:879–893 https://doi.org/10.1007/s10980-018-0637-9 RESEARCH AR TIC L E Integrating animal movement with habitat suitability for estimating dynamic migratory connectivity . . . . Marielle L. van Toor Bart Kranstauber Scott H. Newman Diann J. Prosser . . . . John Y. Takekawa Georgios Technitis Robert Weibel Martin Wikelski Kamran Saﬁ Received: 31 March 2017 / Accepted: 23 March 2018 / Published online: 26 April 2018 This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2018 Abstract Objectives We introduce an approach that combines Context High-resolution animal movement data are movement-informed simulated trajectories with an becoming increasingly available, yet having a multi- environment-informed estimate of the trajectories’ tude of empirical trajectories alone does not allow us plausibility to derive connectivity. Using the example to easily predict animal movement. To answer of bar-headed geese we estimated migratory connec- ecological and evolutionary questions at a population tivity at a landscape level throughout the annual cycle level, quantitative estimates of a species’ potential to in their native range. link patches or populations are of importance. Methods We used tracking data of bar-headed geese to develop a multi-state movement model and to estimate temporally explicit habitat suitability within the species’ range. We simulated migratory move- Electronic supplementary material The online version of ments between range fragments, and calculated a this article (https://doi.org/10.1007/s10980-018-0637-9) con- measure we called route viability. The results are tains supplementary material, which is available to authorized users. M. L. van Toor (&) M. Wikelski K. Saﬁ S. H. Newman Department of Migration and Immuno-Ecology, Max Food and Agriculture Organization of the United Nations, Planck Institute for Ornithology, Am Obstberg 1, Regional Ofﬁce for Africa, 2 Gamel Abdul Nasser Road, 78315 Radolfzell, Germany Accra, Ghana e-mail: firstname.lastname@example.org D. J. Prosser M. L. van Toor M. Wikelski K. Saﬁ U.S. Geological Survey, Patuxent Wildlife Research Department of Biology, University of Konstanz, Center, Beltsville, MD 20705, USA Universita ¨tsstrasse 10, 78464 Konstanz, Germany J. Y. Takekawa Present Address: Suisun Resource Conservation District, 2544 Grizzly M. L. van Toor Island Road, Suisun City, CA 94585, USA Department of Biology and Environmental Science, Linnæus University, Barlastgatan 11, 39182 Kalmar, Sweden G. Technitis R. Weibel Department of Geography, University of Zurich, B. Kranstauber Winterthurerstrasse 190, 8057 Zu ¨ rich, Switzerland Department of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland 123 880 Landscape Ecol (2018) 33:879–893 compared to expectations derived from published there are limitations to their application (Calabrese literature. and Fagan 2004), as distance alone can be insufﬁcient Results Simulated migrations matched empirical to explain patch connectivity. Estimates of effective trajectories in key characteristics such as stopover distance between patches that incorporate barriers and duration. The viability of the simulated trajectories facilitations to animal movement can be used to was similar to that of the empirical trajectories. We improve predictions of connectivity. Algorithms like found that, overall, the migratory connectivity was least-cost paths (e.g., Ferreras 2001; Graham 2001) higher within the breeding than in wintering areas, and electrical circuit theory (McRae et al. 2008) can, corroborating previous ﬁndings for this species. in combination with spatially explicit predictors of Conclusions We show how empirical tracking data landscape resistance to movement, provide environ- and environmental information can be fused for mentally informed estimates of connectivity between meaningful predictions of animal movements through- patches (e.g. for population genetics Row et al. 2010). out the year and even outside the spatial range of the Often, however, the animal location data used to available data. Beyond predicting migratory connec- inform models used for predicting such resistance tivity, our framework will prove useful for modelling surfaces lack a behavioural context. Consequently, ecological processes facilitated by animal movement, these resistance surfaces might not be representative such as seed dispersal or disease ecology. of how animals move through the environment (Keeley et al. 2017). Keywords Anser indicus Bar-headed goose More recently, use of remote tracking technology Empirical random trajectory generator Migratory on wild animals has provided great insights into how, connectivity Movement model Stepping-stone when, and where animals move (Hussey et al. 2015; migration model Kays et al. 2015). Such data are not only a rich source of information about the movement and behaviour of individuals, but can also reveal actual connectivity between spatially separated areas in great detail. In Introduction combination with environmental information about the utilised habitat, movement data can provide Animal movements and migrations can provide func- detailed insight into habitat connectivity for the tional connectivity between areas that are separated in observed individuals (Almpanidou et al. 2014). Con- geographical space by transporting biomass, genes, nectivity estimates derived from observed movement, and less mobile organisms. This connectivity has as for example in fragmented landscapes, have been wider ecological implications for the species’ popu- shown to outperform predictions derived from resis- lation structure, and can also provide the dispersal tance surfaces (LaPoint et al. 2013). Yet to estimate opportunities for organisms like ﬂowering plants by connectivity the use of animal movement data is not moving pollen and seeds, or pathogens (Altizer et al. without constraints (Calabrese and Fagan 2004). 2011; Bauer and Hoye 2014). Identifying connectivity While the miniaturisation of tracking technologies networks and understanding the contribution of animal permits scientists to follow ever more individuals of movement to such networks is a prime motive in ever smaller species, the cost and effort associated ecology and is pivotal to our understanding of spatial with animal tracking limit sample size, as well as the structuring processes. spatial and temporal extent of the data that can be Establishing whether, how, and when animal collected. Thus, the number of individuals that scien- movement provides a functional connection in space, tists are realistically able to track will remain minus- however, is not easily achieved. Capture-mark-recap- cule compared to even the most conservative estimates ture techniques have revealed much about dispersal of the numbers of moving animals on this planet. The capabalities of individual animals, thereby providing a goal of an increasing number of studies is to utilise the history of observed connectivity between distant knowledge from few, well-studied individuals to patches. Estimates such as maximum observed dis- estimate the behaviour at a population level. However, persal distances can be used to infer connectivity such generalisations are not straightforward, mainly networks where movement has not been observed, yet because the movement behaviour of individuals and 123 Landscape Ecol (2018) 33:879–893 881 the observed variation may not be representative of the environmental context of movement behaviour into population (e.g., Austin et al. 2004). Individual deci- account, but also acknowledge the different movement sion-making is not only inﬂuenced by general species strategies expressed by a species (see e.g. Morales properties, but also by variation between individuals et al. 2004). One example of such a multi-state and their needs and the surrounding environmental movement behaviour with striking differences conditions (Nathan et al. 2008). Any kind of move- between states are the stepping-stone-like migrations ment behaviour is thus to some extent unique to the as performed by many migratory bird species that individual, and explicit in time, space, and its envi- predominantly use ﬂapping ﬂight for locomotion. ronmental conditions as well as its ecological context. Here, we refer to stepping-stone migrations as per- The literature published on models developed for formed by large waterbirds like ducks and geese capturing animal movement is extensive, and such covering large distances in fast and non-stop ﬂight and models have been shown to provide useful and using stopover locations for extended staging periods sensible estimates of the behaviour of observed as to replenish their fat reserves. Context-aware, multi- well as unobserved individuals (e.g., Morales et al. state approaches for simulating animal trajectories are 2004; Codling et al. 2008; Michelot et al. 2017;Pe ´ron uncommon. An additional difﬁculty for the simulation et al. 2017). Providing sensible hypotheses of the of stepping-stone migratory movements, is that routes that animals take might require the contextu- detailed knowledge about available stopover sites for staging migrants might be necessary. alisation of observed movement, and the understand- ing of how animals utilise environmental features for Here, we introduce a novel approach that allows for route decision-making. Consequently, movement inferring environmentally informed migratory trajec- models that incorporate resource-selection functions tories from a multi-state discrete movement model. (step-selection functions, e.g. Fortin et al. 2005; Using a conditional movement model speciﬁcally Thurfjell et al. 2014) are becoming increasingly designed for generating random trajectories from popular. Step-selection functions have been shown template empirical trajectories (Technitis et al. to yield functional estimates of how environmental 2016), we developed this approach with stepping- features inﬂuence an animal’s movement through the stone migrations and similar movement strategies in landscape (e.g., Richard and Armstrong 2010), and mind. We extend this movement model to represent have been used to estimate connectivity between the two major states of stepping-stone migrations, the patches (Squires et al. 2013). Such step-selection non-stop migratory ﬂights and the staging periods, functions, representing resource selection during using a stochastic switch informed by empirical actual movement, can be used to derive behaviour- estimates of typical duration of both behaviours. Our speciﬁc predictions for resistance of a landscape to multi-state movement model can simulate migratory movement. In combination with least-cost paths or trajectories that realisticically represent empirically- circuit theory, these context-aware resistance surfaces collected migratory movements by exclusively sam- provide the means to predict the movement of pling from empirical distribution functions. We individuals through the landscape (e.g., Zeller et al. develop a measure of route viability that integrates 2014, 2016). properties of the simulated trajectory and its environ- In many cases, animals use series of different mental context to assess the joint suitability of the movement strategies that change in response to the simulated migratory route and timing strategy. For surrounding environment, or in response to the stepping-stone migrations, we assume that the quality different needs an animal has for different behaviour of stopover sites between the breeding grounds and or life-history stages. Currently, however, even con- wintering areas predominantly determines how prefer- text-aware approaches used for predicting the move- able a certain route might be (Green et al. 2002; Drent ment of unstudied individuals often make the et al. 2007). While the migration simulation model assumption that animals follow a single, constant and the measure of route viability we introduce here decision rule. As shown by Zeller et al. (2016), these are tailored for our study system, the approach in decision rules are considered to be independent of the general is ﬂexible and could be applicable to many supply needs of the individual. We think that realistic other study systems and strategies. movement simulations should not only take the 123 882 Landscape Ecol (2018) 33:879–893 Speciﬁcally, we apply the conditional movement environmentally informed quantitative null hypothe- model on a pronounced long-distance migrant, the bar- ses for animal movement which can be utilised for headed goose (Anser indicus, Latham 1790). This estimating migratory connectivity based on limited species of waterbird occurs in Central Asia and is well observations (summarised in Fig. 1). known for its incredible performance of crossing the Himalayas during migration. The distribution range of bar-headed geese is characterised by four distinct Methods breeding areas which are mirrored by four distinct wintering areas south of the Himalayas. Previous Tracking data and movement model tracking studies have revealed that large parts of the respective populations migrate from their breeding Tracking data of bar-headed geese were available to us grounds in Mongolia, northern China and the Tibetan from a broader disease and migration ecology study Plateau over the Himalayas to their wintering grounds on the Indian subcontinent (e.g., Bishop et al. 1997; Takekawa et al. 2009; Guo-Gang et al. 2011; Hawkes et al. 2011; Prosser et al. 2011). But while the crossing of the Himalayas has been studied in great detail (Hawkes et al. 2011, 2013; Bishop et al. 2015), less is known about the connectivity between range frag- ments both within the wintering and breeding range (Takekawa et al. 2009). The bar-headed goose thus provides a suitable study species for our approach. We establish a model for bar-headed goose migrations from previously published tracking data, and simulate migrations of unobserved individuals between all fragments of the species’ distribution range. We assess the viability of these trajectories during several times of year using a segmented habitat suitability model to derive a dynamic migratory connectivity network. To assess whether this migratory connectivity network could serve as a quantitative null hypothesis for bar- headed goose migration, we test our predictions against two very simple hypotheses generated from previously published studies. Stable isotope analyses suggested that the connec- tivity within the breeding range of bar-headed geese is relatively high (Bridge et al. 2015), a notion that has been supported by tracking data as well (Cui et al. 2010). In the wintering range, however, relatively few movements have been observed (Kalra et al. 2011). Based on these ﬁndings (Cui et al. 2010; Kalra et al. Fig. 1 General concept for our approach of environmentally 2011; Bridge et al. 2015), we expect to ﬁnd a higher informing simulated stepping-stone migrations: (I) Empirical overall viability of trajectories between the fragments tracking data are (IIa) used to derive an informed eRTG to of the breeding range than within the wintering range. simulate conditional movement between sites of interest, and We further predict that on average, the temporal (IIb) combined with environmental correlates to derive predic- tions of relevant measurements of landscape permeability (here: variation in viability of simulated migratory routes suitability of stopover sites). (III) Finally, the simulated within the breeding grounds should be higher than conditional trajectories are evaluated based on characteristics within the wintering grounds. Overall, we would like of the trajectory and permeability using an informed measure of to introduce a new approach for deriving route viability 123 Landscape Ecol (2018) 33:879–893 883 implemented by the Food & Agriculture Organization within the realms of the empirical distributions of e.g. of the United Nations (FAO) and U.S. Geological step lengths and turning angles, the simulation fails Survey (USGS). In total, 91 individuals were captured rather than forcing the last step towards the during the years 2007–2009 in several locations: Lake destination. Qinghai in China (hereafter termed ‘‘Lake Qinghai’’), We extended this movement model by incorporat- Chilika Lake and Koonthankulum bird sanctuary in ing a stochastic switch between the two main states of India (hereafter termed ‘‘India’’), and Terkhiin bar-headed goose migration, non-stop migratory Tsagaan Lake, Mongolia (hereafter termed ‘‘West ﬂights (‘‘migratory state’’) and movements during Mongolia’’). All individuals were equipped with staging periods at stopover locations (‘‘stopover ARGOS-GPS tags which were programmed to record state’’). We classiﬁed the entire tracking data accord- the animals’ location every 2 h (ARGOS PTT-100; ing to the individuals’ movement behaviour to identify Microwave Telemetry, Columbia, Maryland, USA). these states prior to extracting the empirical distribu- Eighty of the deployed tags collected and transmitted tions functions for the eRTG. First, we clustered the data for 241 253 ðmean SDÞ days. In total, locations in the tracking data using an expectation- 169, 887 ﬁxes could be acquired over the course of maximisation binary clustering algorithm designed for the tracking period (Table 1 and Takekawa et al. 2009; annotating animal movement data (EMbC, Garriga Hawkes et al. 2011). Individuals that were tracked for et al. 2016). The EMbC divided the trajectories of bar- less than a complete year were excluded from the headed geese into four behavioural classes (slow speed subsequent analyses, which left a total of 66 individ- & low turning angles, slow speed & high tuning uals (Lake Qinghai: 20, India: 20, West Mongolia: 26). angles, high speed & low turning angles, and high We pooled data from all capture sites for the analyses. speed & high turning angles), which we then re- We used the recently developed the empirical classiﬁed into two behavioural classes, namely high- Random Trajectory Generator (eRTG, Technitis et al. speed movements (combining the two high speed 2016) to simulate the migrations of unobserved classes) and low-speed movements (combining the individuals of bar-headed geese. This movement two low speed classes). Within the high-speed model is conditional, i.e. simulates the movement behavioural cluster, the average speed between loca- between two end locations with a ﬁxed number of tions was 8:4 6:7 (mean ± SD) whereas the steps based on a dynamic drift derived from a step- average speed for the low-speed behavioural cluster wise joint probability surface. One main advantage of was 0:3 1:0 (mean ± SD). As estimates of speed the eRTG is that the trajectories it simulates retain the and turning angle are highly dependent on the geometric characteristics of the empirical tracking sampling rate of the data, we removed those parts of data (step length, turning angle, as well as covariance the trajectories that exceeded the average sampling and auto-correlation of step length and turning angle), interval of 2 h. Subsequently, we used the low-speed as it relies entirely on empirical distribution functions. locations for the empirical distribution functions for Consequently, if a destination cannot be reached the stopover state of the two-state eRTG, and the Table 1 A summary of the catching sites and corresponding sample sizes Capture site Year of capture Sample size(individuals) First ﬁx Tracking days GPS ﬁxes Lake Qinghai 2007 13 Mar 25–31 303 ½207; 411 1; 670 ½682; 2; 565 2008 10 Mar 30–Apr 4 396 ½260; 845 2; 211 ½1; 341; 3; 573 India 2008 17 Dec 10–18 129 ½92; 401 2; 060 ½1; 578; 2; 714 2009 7 Jan 27 – Feb 06 134 ½53; 448 1; 321 ½1; 107; 3; 800 West Mongolia 2008 19 Jul 13–15 122 ½90; 190 537 ½366; 1; 312 2009 14 Jul 05–08 105 ½100; 128 421 ½330; 473 The number of tracking days and GPS ﬁxes are listed as a median per individual, with the 25 and 75% quantiles in square brackets. Eleven out of the total of 91 tags deployed did not transfer any data, and are not included in this table 123 884 Landscape Ecol (2018) 33:879–893 locations classiﬁed as high-speed for the empirical were calculated. By using cumulative distance and distribution functions for the migratory state of the duration as well as the empirically derived dm and max eRTG (see Figure S2). Finally, we derived the step Tm , our two-state eRTG was based on a binomial max lengths and turning angles from each coherent stretch experiment with two possible outcomes: switching to of data (i.e. only subsequent ﬁxes with a sampling rate the stopover state with a probability of p ,or ms of 2 hours). Following this, we calculated the changes resuming migration with a probability of 1 p . ms in step length and turning angle at a lag of one We deﬁned p , the transition probability to switch ms observation, as well as the covariance between from migratory state to stopover state, as contemporary observations of step length and turning P P t t ðdmÞ ðTmÞ i¼0 i¼0 angle. We derived the corresponding empirical distri- ð1Þ p ðtÞ¼ ms dm Tm max max bution functions for both movement states and prepared them for use in the eRTG functions. where dm and Tm represent the distance and duration Finally, we determined the duration of staging between two consecutive locations during a migratory periods, and the duration and cumulative distance of leg. At step t, the simulation of the migratory individual migratory legs from the tracking data. We movement can switch to the unconditional stopover ﬁrst identiﬁed seasonal migration events between state, corresponding to a correlated random walk, with breeding and wintering grounds (and vice versa) in the a probability of p ðtÞ. Likewise, the simulation can ms empirical trajectories using the behavioural annota- switch back from stopover state to migratory state with tion. We then determined migratory legs (sequential the probability p ðtÞ, which we deﬁned as as sm locations classiﬁed as migratory state) as well as ðTsÞ stopovers (sequential locations classiﬁed as stopover i¼0 ð2Þ p ðtÞ¼ sm state, with a duration [ 12h). We used two main Ts max proxies to characterise migratory legs, namely cumu- where Ts represents the duration between two con- lative migratory distance as well as duration, and one secutive locations during a stopover. This process is proxy to characterise staging periods, namely stopover then repeated until the simulation terminates because: duration. We calculated these proxies for all individ- either the trajectory reached its destination, or the step- uals and migrations, and determined the maximum wise joint probability surface did not allow for observed distance (dm ) and duration (Tm )ofa max max reaching the destination with the remaining number migratory leg. As we did not distinguish between of steps (resulting in a dead end or zero probability). extended staging (e.g. during moult, or after unsuc- cessful breeding attempts) from use of stopover Evaluating the plausibility of simulated migrations locations during migration, we calculated the 95% quantile of the observed stopover durations (Ts ) max We estimated the plausibility of each simulated rather than the maximum. trajectory, representing a unique migratory route, using a measure we called route viability U aimed to Simulating a bar-headed goose migration integrate the ecological context into the movement with the two-state eRTG simulations. We developed this measure speciﬁcally with the stepping-stone migratory strategy of bar- When simulating a conditional random trajectory headed geese or similar species in mind, and it is between two arbitrary locations a and z, the two-state deﬁned by the time spent in migratory mode, the time eRTG initially draws from the distribution functions spent at stopover sites, and the habitat suitability of the for the migratory state, producing a fast, directed respective utilised stopover sites. For this speciﬁc trajectory. To determine the time available for moving measure of route viability, we made two main from a to z, we assumed the mean empirical ﬂight assumptions: (1), it is desirable to reach the destina- speed derived for the migratory state, and calculated tions quickly, i.e. staging at a stopover site comes at the number of required steps accordingly. While the cost of delaying migration, and (2), the cost simulating the trajectory, after each step modelled by imposed by delaying migration is inversely-propor- the eRTG, the cumulative distance of the trajectory as tional to the quality of the stopover site, i.e. the use of well as the duration since the start of the migratory leg 123 Landscape Ecol (2018) 33:879–893 885 M;a;z superior stopover sites can counterbalance the delay. \U \1. Using this metric, we assessed simu- a;z a;z Our argument for these assumptions is that during lated trajectories in a way that is biologically mean- spring migration, the arrival at the breeding grounds ingful for bar-headed geese. In the next section, we needs to be well-timed with the phenology of their detail how we calculated the route viability U for each major food resources (Bauer et al. 2008). Further- simulated migration. more, the quality of stopover sites has been shown to be of crucial importance for other species of geese A migratory connectivity network for bar-headed with similar migratory strategies (Green et al. 2002; geese Drent et al. 2007). Each simulated multi-state trajectory between two We simulated migrations of bar-headed geese within arbitrary locations a and z can be characterised by a the native range of the species which naturally occurs total migration duration s , which consists of the total a;z in Central Asia (68–107 N , 9–52 E). According to ﬂight time s and the total staging time at stopover M;a;z BirdLife International and NatureServe (2013), both sites s . The total ﬂight time s is the sum of the S;a;z M;a;z the breeding and wintering range are separated into time spent ﬂying during each migratory leg l, and is four distinct range fragments (see also Figure S1), with thus s ¼ t ðlÞ, with t ðlÞ corresponding to M;a;z M M minimum distances between range fragments ranging l¼0 the time spent ﬂying during migratory leg l. Similarly, from 79 km to 2884 km. For this study, we investi- the total staging time s consists of the staging times S;a;z gated how well, in terms of an environmentally at all visited stopover sites, corresponding to informed measure of route viability and the number s ¼ t ðkÞ, where t ðkÞ amounts to the stag- S;a;z S S of stopovers required to reach a range fragment, these k¼0 ing time at stopover site k. For our metric of route range fragments can be connected by simulated viability, we will consider the time spent staging at migrations of bar-headed geese. stopover locations s as a delay compared to the To choose start- and endpoints for the simulated S;a;z time spent in ﬂight. This delay is, however, mediated migrations, we sampled ten random locations from by the beneﬁt b an individual gains at the stopover site each of the range fragments indicated in the distribu- from replenishing its fat reserves. We deﬁne this tion data provided by BirdLife International and beneﬁt gained by staying at stopover site k, b(k), as NatureServe (2013). We simulated 1000 trajectories proportional to the time spent at site k, t ðkÞ, and the for all pairs of range fragments (100 trajectories per habitat suitability of site k, S(k). This habitat suitability location pair) and counted the number of successes S should range between [0, 1], which allows our (trajectories reach the destination) and failures (tra- measure of route viability to range between [0, 1] as jectories terminate in a dead end). We proceeded to well. We further assume the effects of several calculate the viability of simulated routes in the sequential stopovers to be cumulative, and thus deﬁne following way: Initially, we determined the total the total beneﬁt of a migratory trajectory between duration of the trajectory between locations a and z, locations a and z with n stopovers as s , the number of stopover sites used, n , as well as a;z a;z B ¼ SðkÞ t ðkÞ. Finally, we deﬁne the route the time spent at each stopover site, t ðkÞ, for each of a;z S S k¼0 viability U of any trajectory between a and z as: the total n stopovers (corresponding to the number a;z a;z of steps multiplied with the location interval of 2 h). s s M;a;z M;a;z U ¼ ¼ a;z ð3Þ We determined the habitat suitability of stopover s þ s B s B M;a;z S;a;z a;z a;z a;z locations S(k) using habitat suitability landscapes for Thus, the viability of a trajectory with no stopovers bar-headed geese during ﬁve periods of the year (see and a trajectory with stopovers of the highest possible Figure S3): winter/early spring (mid-November–Fe- quality (SðkÞ¼ 1) will be equal, and is deﬁned solely bruary), mid-spring (mid March–mid April), late by the time the individual spent in migratory state spring/summer (mid April–mid August), early autumn (U ¼ 1). For trajectories with stopovers in less than a;z (mid August–mid September), and late autumn (mid optimal sites, however, the viability of trajectories is September–mid November). We identiﬁed these peri- relative to both the staging duration and quality of ods using a segmentation by habitat use (van Toor stopover sites, and should take values of et al. 2016, for details see Section A in the Electronic 123 886 Landscape Ecol (2018) 33:879–893 Supplementary Material (ESM)). The segmentation- trajectories connecting two range fragments. We by-habitat-use procedure uses animal location data calculated this average by using non-parametric and associated environmental information to identify bootstrapping on the median route viability U avg: time periods for which habitat use is consistent. (using 1000 replicates), and also computed the corre- Habitat suitability models derived for these time sponding 95% conﬁdence intervals (CI) of the median periods should thus reﬂect differences in habitat use route viability U . We did this for each of the ﬁve avg: by bar-headed geese throughout the year. We used time periods represented in the suitability landscapes, time series of remotely sensed environmental infor- and also computed an overall migratory connectivity mation and Random Forest models (Breiman 2001)to by averaging all ﬁve habitat suitability values for each derive habitat suitability models corresponding to stopover site prior to calculating U. these ﬁve time periods, and predicted the correspond- We wanted to compare migratory connectivity ing habitat suitability landscapes (Section A in the within the breeding range and migratory connectivity ESM). Following the prediction of habitat suitability in the wintering range to test our ﬁrst hypothesis landscapes for winter/early spring, mid-spring, late stating that migratory connectivity should be higher spring/summer, early autumn, and late autumn, we within the breeding range. To do so, we differentiated annotated all stopover state locations of the simulated between route viability among breeding range frag- trajectories with the corresponding habitat suitability. ments (U ), among the wintering areas breeding We then calculated the beneﬁt b gained by using a (U ), and between breeding and wintering range wintering stopover location k using the mean suitability for each fragments (U ). We computed the median and 95% mixed of the stopover locations, S(k), and the duration spent CIs of route viability with non-parametric bootstrap- at stopover locations, s ðkÞ. ping with 1000 replicates, using the average habitat To calculate the route viability U , we also a;z suitability of all ﬁve suitability landscapes for all required an estimate for duration of migration if a trajectories within the breeding range, all trajectories simulation were exclusively using the migratory state in the wintering range, and all trajectories connecting s , without the utilisation of stopover sites. We M;a;z breeding range fragments with wintering range used a simple linear model to predict ﬂight time as a fragments. function of geographic distance which we trained on To test our second hypothesis, stating that variation the empirical data derived from the migratory legs (see in migratory connectivity throughout the year should Section B in the ESM for details). By basing the linear be higher in the breeding range than in the wintering model on the empirical migratory legs rather than range, we calculated the standard deviation of route mean ﬂight speed, the estimate for s retains the viability for the ﬁve suitability landscapes in the inherent tortuosity of waterbird migrations. For each breeding range and in the wintering range. We did this simulated trajectory, we then calculated the geo- by again differentiating trajectories in the wintering graphic distance between its start- and endpoint, and range, trajectories in the breeding range, and trajec- predicted the expected ﬂight time s . Finally, we M;a;z tories connecting breeding range fragments with calculated route viability U for all trajectories using wintering range fragments. We computed route via- a;z Eq. 3, repeating the process for each of the ﬁve bility U for each of the ﬁve suitability landscapes for suitability landscapes derived from the segmentation all trajectories, and pooled the corresponding values by habitat use. This resulted in ﬁve different values of for U , U , U , midspring late winter=early spring late spring=summer U for every simulated trajectory, corresponding to a;z U , and U for the wintering range, early autumn late autumn winter/early spring, mid-spring, late spring/summer, for the breeding range, and for trajectories connecting early autumn, and late autumn, respectively. breeding range fragments with wintering range frag- ments separately. We then used a non-parametric Calculating migratory connectivity as average route bootstrapping (1,000 replicates) on the standard devi- viability ation over the ﬁve time periods, and determined the corresponding 95% CIs on the standard deviation. We calculated migratory connectivity between range fragments as the average route viability U of all avg: 123 Landscape Ecol (2018) 33:879–893 887 Calculating route viability for empirical migrations Migratory connectivity network informed by route viability Following the above described procedure, we anno- tated the stopover locations of empirical migrations We separated the simulated trajectories into move- with the habitat suitability of the corresponding time ments within the breeding range, movements within period, and calculated the route viability for these the wintering range, and movements resembling migratory trajectories in the same way as described seasonal migrations between the breeding and winter- above. We then used non-parametric bootstrapping on ing range. Here, we found that viability of trajectories the median route viability for all empirical migrations was highest within the breeding range (95% CIs for (U ), only spring migrations (U ) and median U : ½0:0676; 0:0684; 95%-quantiles of emp:;total emp:;spring breeding only autumn migrations (U ), and computed median U : ½0:1469; 0:1546), and lowest within emp:;autumn breeding 95% CIs for the median of U , U , and the wintering range (95% CIs for median emp:;total emp:;spring U . U : ½0:0590; 0:0596; 95%-quantile of median wintering emp:;autumn U : ½0:1090; 0:1147), predicting that move- wintering ments between range fragments should occur more Results often within the breeding than in the wintering areas. The median route viability for migrations between Route viability of empirical and simulated breeding and wintering range fragments was interme- migrations diate (95% CIs for median U : ½0:0618; 0:0622; mixed 95%-quantile of median U : ½0:1224; 0:1296). mixed The simulations resulted in a total of 30,730 simulated These patterns are reﬂected in the simpliﬁed network trajectories, of which 8945 trajectories connected of average migratory connectivity U (Fig. 3). We avg: breeding range fragments (simulation success rate: also identiﬁed the single trajectory with the maximum 74:5%), 5393 trajectories connected wintering range route viability between range fragments rather than the fragments (simulation success rate: 44:9%), and the median (Figure S5). This network of maximum remaining 16,392 trajectories connected breeding and migratory connectivity shows that migrations that wintering range fragments (simulation success rate: connect the breeding and wintering ranges have the 51:2%; see Figure S4). While all these trajectories highest route viability. Finally, the number of stopover were successful in connecting origin and destination locations of movements was proportional to the (i.e. did not result in a dead end), they differed geographic distance between range fragments profoundly in their route viability U , which (Figure S6). simulated ranged between 0.014 and 0.59. We found that simulated migrations had a higher route viability for Temporal variability of migratory connectivity late spring and summer than for autumn (Fig. 2). The range of route viability for simulated migra- We found that the spatial patterns of migratory tions was comparable to that of the empirical migra- connectivity varied across the ﬁve habitat suitability tions (U : 0.01–0.38). Overall, we found that landscapes representing ﬁve periods of consistent emp:;total route viability of empirical migrations was higher for habitat suitability (Fig. 4; see also Figure S3 for details spring migrations (U : [0.0614; 0.1070]; 95% on the temporal correspondence of the time periods). emp:;spring For the suitability landscapes derived for winter/early CIs on the median) than for autumn migrations (U : [0.0270; 0.0514]; 95% CIs on the spring, mid spring, and late spring/summer, the emp:;autumn estimated connectivity predicted that bar-headed median). This was caused both by differences in the goose migrations are most likely to occur between habitat suitability of utilised stopover locations and by the wintering and breeding range, and within the differences in migration duration between spring and breeding range. For early autumn, connectivity pat- autumn migrations. We found that bar-headed geese terns predicted that movement is most likely between on average stayed longer at stopover locations during breeding and wintering areas. For late autumn, we autumn than during spring migrations (spring: 6:8 observed connectivity within the wintering range of 14:2 days, autumn: 11:8 12:2 days; mean ± SD). 123 888 Landscape Ecol (2018) 33:879–893 Fig. 2 The route viability U of empirical and simulated late autumn). The black bars show the 95% CIs for the migrations. Here we show U for spring and autumn migrations, respective medians, and the grey dots and violin plots show the as well as the U for the simulated trajectories across all ﬁve observed (empirical trajectories) and route viability densities suitability landscapes (Seg. 1: winter/early spring, Seg. 2: mid- (simulated trajectories) spring, Seg. 3: late spring/summer, Seg. 4: early autumn, Seg. 5: the species. We calculated the 95% CIs for the overall were able to successfully develop a model that migratory connectivity values for each time period simulates the migratory movements of bar-headed (Fig. 2), which predicted the highest median route geese. Our extension of the eRTG with a stochastic viability for the periods from winter/early spring (mid- switch between a migratory state and a stopover state November–February) as well as from late spring/sum- was sufﬁcient to capture the overall migratory strategy mer (mid April–mid August). We also compared the of this species. With this model for bar-headed goose standard deviation of route viability across suitability migrations, we inferred the migrations of unobserved landscapes and found the highest variation for the individuals between all fragments of the species’ breeding range (95% CIs for s.d. of U : distribution range, and used an environmentally- breeding informed measure of route viability to derive average [0.0124; 0.0133]) and the lowest variation for the wintering range (95% CIs for s.d. of estimates of migratory connectivity between range fragments. We put this simpliﬁed predictive network U : ½0:0041; 0:0046). Again, the trajectories wintering of migratory connectivity to a simple test using between breeding and wintering range fragments predictions derived from the literature. Indeed, we showed intermediate values (95% CIs for s.d. of found that the average route viability, as an indicator U : ½0:0084; 0:0089). mixed of migratory connectivity, was higher within the species’ breeding range (U ) than in the winter- breeding ing areas (U ), conﬁrming the expectations from Discussion and conclusions wintering the literature (Cui et al. 2010; Kalra et al. 2011; Using tracking data of bar-headed geese and the Bridge et al. 2015). While bar-headed geese are empirical Random Trajectory Generator (eRTG), we thought to be philopatric to their breeding grounds 123 Landscape Ecol (2018) 33:879–893 889 Fig. 3 The median route viability U between range fragments show the native breeding area of the species. Green polygons of bar-headed geese. We summarised U for all pairwise range show the native wintering range. Long edges are curved for sake fragment trajectories using the median route viability. The of visibility thickness of edges represents the sample size. Blue polygons 123 890 Landscape Ecol (2018) 33:879–893 Fig. 4 Temporal dynamics of the route viability U. Here we median route viability U that is higher than 75% of the route show the predicted movements for each of the ﬁve suitability viability for the complete network. The respective time periods landscapes separately. The visible edges of the network have a associated to these networks is displayed in Figure S3 (Takekawa et al. 2009), the post-breeding period breeding areas north of the Himalayas than in the seems to be a time of great individual variability and subtropical wintering areas. extensive movements (Cui et al. 2010). This ﬂexibil- Simulating trajectories with multiple movement ity in long-distance movements has also been states and an element of randomness can be useful to observed for other Anatidae species (e.g., Gehrold infer the movements of unobserved individuals. Here, et al. 2014), and due to the temporary ﬂightlessness we simulated migratory trajectories under the assump- during moult the choice of suitable moulting sites is tion that the movements of the tracked individuals are critical to many waterfowl species. As the average similar to those of other individuals. While this limits route viability within the breeding range and during the informative value of an estimate of migratory the summer months is high, unsuccessful breeders and connectivity, through repeated simulations it may be individuals in the post-breeding period may not be not possible to explore the routes of unobserved individ- limited by sufﬁciently suitable stopover locations uals according to the movement behaviour observed in when moving between breeding range fragments. empirical data on the same temporal scale. Indeed, Furthermore, our results conﬁrmed that the temporal average route viability corroborated previous studies variability of migratory connectivity was higher in the on the within-range movements for bar-headed geese 123 Landscape Ecol (2018) 33:879–893 891 even without additional ﬁltering. Consequently, in but also when the environment provides the conditions combination with relevant environmental and ecolog- that allow an individual to move from a to z. In our ical information, the simulation of unobserved migra- study, estimates of migratory connectivity were tions using a model like our two-state eRTG may affected by changes in the predicted habitat suitability provide a sensible and quantitative null hypothesis for of stopover locations, whereas in other cases, changes the migrations of bar-headed geese or species with in vegetation density throughout the year or the similar strategies. While we determined the route temporary freezing of waterbodies can be imagined viability using only the habitat suitability of the to change connectivity between distant sites. Using stopover locations and measures of migratory dura- time series of environmental information in combina- tion, other correlates such as wind support or altitude tion with an approach that segments a species utilisa- proﬁle may easily be incorporated for the migratory tion of the environment for moving, as shown here, state. Similarly, the transition probabilities that medi- could help with the identiﬁcation of temporal patterns ate the switch between movement modes may be of landscape connectivity. Accounting for such tem- extended to include environmental conditions. In poral changes in connectivity could also help to better general, our stochastic switch performed reasonably understand how for example, diseases can spread well in replicating the movement behaviour observed through through a metapopulation (such as white-nose from recorded tracks. We used simple functions to syndrome, Blehert et al. 2009; Turner et al. 2011,or Inﬂuenza A viruses in birds, Gaidet et al. 2010; determine transition probabilities due to the long ﬁx interval (2 h) and the amount of missed ﬁxes in the Newman et al. 2012). data. If a larger sample size were available, the Overall, models that incorporate a species’ move- functions we used (see Eqs. 1, 2) could be replaced by ment behaviour and its utilisation of the environment a probability distribution function that more ade- can provide sensible estimates for landscape connec- quately represents the decision-making of bar-headed tivity. This approach possibly provides the basis for a geese. Alternatively, algorithms such as state-space wider range of applications, for example the estima- models could be integrated to simulate animal move- tion of seed or pathogen dispersal on a population ment with a more complex conﬁguration of movement level. Our approach provides a starting point for states (Morales et al. 2004; Patterson et al. 2008). complementing tracking efforts with ecologically With a few modiﬁcations speciﬁc to the species of relevant estimates of a species’ potential to migrate interest, the approach described in this study could be through a landscape and act as a link between patches, adapted for other scenarios of animal movement. One populations, and ecosystems. important application for our approach could be to Acknowledgements Open access funding provided by Max support capture-mark-recapture data, especially when Planck Society. This work was made possible by the efforts of tracking data for multiple individuals are hard to the many cooperating scientists in China, India, and Mongolia acquire. Simulations from a multi-state movement who assisted the Wildlife Health and Ecology Program at the model informed by the movements of a few represen- Food and Agriculture Organization of the United Nations (FAO) and US Geological Survey (USGS) in the collection of the tative individuals could be used to infer alternative tracking data with ecological ﬁndings provided in other reports routes connecting the re-sightings of individually and papers. We are indebted to Markus Rampp and Karin Gross marked animals. A corresponding relevant measure at the Computation Center of the Max Planck Society for their of route viability could then be used to explore support with the computational facilities. We would like to thank Todd Lookingbill and one anonymous reviewer for their alternative strategies from an ecologically informed valuable comments. The use of trade, product, or ﬁrm names in perspective. In such a study, it could also be of interest this publication is for descriptive purposes only and does not to use Bayesian approaches to approximate ideal imply endorsement by the U.S. Government or the FAO. The routes using the environmental context. views expressed in this publication are those of the author(s) and do not necessarily reﬂect the views or policies of the FAO. This Furthermore, our results highlight the importance study re-analysed several datasets from FAO and USGS of integrating temporal changes in habitat use of published studies; Institutional Animal Care and Use moving animals into measures of landscape connec- Committee details are available in the original publications. tivity. Zeigler and Fagan (2014) argue that the MLvT was supported by the International Max Planck Research School for Organismal Biology and the European Union’s ecological function of landscape connectivity through animal movement is not only determined by where, 123 892 Landscape Ecol (2018) 33:879–893 Horizon 2020 research and innovation programme under Grant Anser indicus during breeding and post-breeding periods at Agreement No. 727922 (Delta-Flu). Qinghai Lake, China. J Ornithol 152:83–92 Drent RH, Eichhorn G, Flagstad A, Graaf AJ, Litvin KE, Stahl J Open Access This article is distributed under the terms of the (2007) Migratory connectivity in Arctic geese: spring Creative Commons Attribution 4.0 International License (http:// stopovers are the weak links in meeting targets for breed- creativecommons.org/licenses/by/4.0/), which permits unre- ing. 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