Quantifying exchanges of Allis shads between river catchments by combining otolith microchemistry and abundance indices in a Bayesian model

Quantifying exchanges of Allis shads between river catchments by combining otolith microchemistry... Abstract Similar to many diadromous fish species, dramatic declines were observed for Allis shad, an anadromous Clupeidae, since the beginning of the 2000s. The knowledge of population and metapopulation dynamics is a key issue for the management of migratory species. Although homing behaviour is dominant in Allis shad, staying causes exchanges between populations of each river catchment. Currently, the management of Allis shad is applied at the population scale, without accounting for a potential metapopulation structure. Herein we propose a method to estimate the exchanges flux between rivers and a method to identify source and sink rivers. We used otolith microchemistry within a Bayesian model of reallocation coupled with abundance estimates of spawners per watershed. Results showed a metapopulation dynamic with several rivers acting as sources and other as sinks. However, the lack of precision and homogeneity in abundance data resulted in large credibility intervals, which calls for a better standardization in the acquisition of abundance data. Nevertheless, this method should provide an overview of the metapopulation dynamics of other anadromous species with management concerns. Introduction In the context of increased habitat fragmentation worldwide, the metapopulation concept is a promising and relevant tool to investigate population dynamics of wild species (Hanski, 1999). A metapopulation is basically defined as a set of isolated breeding habitats connected by dispersal (Hanski, 1998; Kritzer and Sale, 2004; Smith and Green, 2005). So far, the metapopulation paradigm has been assessed for various terrestrial species (Hanski and Thomas, 1994; Esler, 2000; Hanski and Ovaskainen, 2000; Inchausti and Weimerskirch, 2002; Smith and Green, 2005; Heard et al., 2013), demonstrating its relevance in conservation and management concerns (Southwell et al., 2016). The understanding of metapopulation structure is of great importance as it provides insight on the relevant management scale and priorities. Ignoring the metapopulation structure in management decisions is known to lead to depletion of local populations and eventually collapses (Hilborn et al., 2003; Kritzer and Sale, 2004; Neat et al., 2014). Most temperate anadromous species (i.e. species performing migrations between marine and freshwater habitats where they reproduce; McDowall, 2008) have undergone dramatic declines within the North Atlantic area during the last century, mostly caused by anthropogenic pressures and climate change (Groot, 2002; Limburg and Waldman, 2009; Aprahamian et al., 2010), raising key conservation issues. In this context, a better understanding of their population health is crucial to support management actions. Though the metapopulation concept has been widely applied to salmonids (Taylor, 1991; Quinn, 1993; King et al., 2001), many anadromous species are managed locally at the catchment scale, ignoring exchanges between catchments. This is the case of the European Allis shad (Alosa alosa), an anadromous Clupeidae which remains as juvenile in freshwater for few weeks before performing a seaward migration as YOY (i.e. Young Of the Year) and spends between 3 and 7 years long growth phase at sea (Lochet, 2006). Reproduction occurs in the higher middle watercourse of rivers in spring and summer (Baglinière et al., 2003). The distribution area of Allis shad has significantly decreased, from a historical range from Norway to Morocco in the middle of the 20th century, to a modern range from France to Portugal (Baglinière et al., 2003). Until the end of the 20th century, the Dordogne and Garonne populations (Figure 1) were considered as the most important in Europe (Elie and Baglinière, 2000; Castelnaud et al., 2001). However, at the beginning of the 2000s, the Dordogne and Garonne populations collapsed (Rougier et al., 2012). Despite a drastic fishing ban measure, these populations have not recovered yet. At the same time, from the mid-twentieth century, a decrease in the number of spawners was observed in the Minho River in Portugal (Mota et al., 2015). Water pollution, habitat loss, obstacles to migration (such as dams) and overfishing have been suggested as possible causes of shad population declines (Jonsson et al., 1999; Groot, 2002; Limburg and Waldman, 2009). Figure 1. View largeDownload slide Maps of Europe (left panel) and adult, juvenile Allis shad and water samples in France and Portugal (respectively the middle and right panel). Details of the Blavet-Scorff and Adour estuaries are presented in inset maps. Grey lines correspond to the rivers where samples were available. Symbols represent the kind of samples for each river. Filled circle: water samples; Filled diamond: adult samples; Asterisk: water and adult samples; Filled triangle: water and juvenile samples; Filled square: water, adult and juvenile samples. Figure 1. View largeDownload slide Maps of Europe (left panel) and adult, juvenile Allis shad and water samples in France and Portugal (respectively the middle and right panel). Details of the Blavet-Scorff and Adour estuaries are presented in inset maps. Grey lines correspond to the rivers where samples were available. Symbols represent the kind of samples for each river. Filled circle: water samples; Filled diamond: adult samples; Asterisk: water and adult samples; Filled triangle: water and juvenile samples; Filled square: water, adult and juvenile samples. To analyse the collapse and decline of populations, a deeper knowledge of population structure for the entire species is necessary to understand whether Allis shad forms discrete independent populations, or if populations have significant exchanges of individuals, resulting in a metapopulation (Kritzer and Sale, 2004). In this context, it is essential to understand whether shad populations display strict homing (i.e. all individuals of a generation return to their natal stream to reproduce; McDowall, 2008; Secor, 2015), which would induce no exchanges between populations, or if populations perform straying (i.e. individuals migrate to non-natal site to reproduce; Quinn, 1993; Keefer and Caudill, 2014; Secor, 2015), which would result in metapopulation dynamics. From the end of the 20th century, otolith microchemistry has been employed to examine fish migration, natal origin and population connectivity (Kennedy et al., 2002; Daverat et al., 2012; Rooker et al., 2016). Otoliths of teleost fishes are small calcareous concretions located in the inner ear which grow during the whole life of fishes by continuous accretion of inert elements (Campana, 1999; Söllner et al., 2003), some of them originating from the ambient water (Campana, 1999; Morais and Daverat, 2016). By coupling microchemistry and micro-increments analyses, they can be used to reconstruct the habitat use of the fish from birth (i.e. the core of the otolith) to death (i.e. the edge of the otolith) (Bath et al., 2000; Walther and Thorrold, 2006; Morais and Daverat, 2016). Because of technical advances, the otolith microchemistry approach currently appears to be one of the most relevant methods to elicit Allis shad natal origin (Tomas et al., 2005; Martin et al., 2015). In 2005, Tomas et al. examined the structure of Garonne—Dordogne populations using otolith microchemistry analysis and suggested that the Dordogne river acted as a source of spawners in the entire Garonne-Dordogne watershed. Then in 2014, technical and methodological progresses enabled the identification of natal origin of spawners from 15 rivers along the Atlantic coast (Martin et al., 2015). Martin et al. (2015) used a Bayesian model with otolith microchemistry datasets to reallocate individuals to their natal river. Authors found that most adults caught in a river were indeed born in this river or in the watershed. They also observed exchanges at short distance scale (20–100 km). Although Martin et al.’s (2015) results suggested a high level of natal homing, they were not able to estimate the “true” probabilities of homing and straying, i.e. the exchange fluxes between populations, as their analysis did not include estimates of population sizes throughout the range of Allis shad (Munch and Clarke, 2008; Martin et al., 2015). In this context, this study goes one step further from Martin et al. (2015). We combined Martin et al.’s (2015) Bayesian model with abundance indices of spawners to estimate exchange fluxes between donor (i.e. natal rivers) and recipient rivers (i.e. spawning ground rivers). By coupling these two models, we quantified flux between populations and consequently provide insights on whether (i) populations are strictly isolated and deserved to be managed independently, or whether (ii) populations are connected sub-populations, which need to be included in a large scale management of the metapopulation. Material and methods Sampling Update of datasets In this study, we used the microchemistry datasets previously analysed by Martin et al. (2015) in France and Portugal (Figure 1) and added additional adult, juvenile and water samples (Table 1). Table 1. Number of adult and juvenile Allis shad and water samples per river and year.     Grey cells indicate new samples compared with Martin et al. (2015). Further, we completed a Garonne baseline (with juveniles from the Garonne and Aveyron rivers). We also added adult samples from the Garonne and Dordogne rivers before the collapse that occurred in 2000s (Rougier et al., 2012). These new samples provided a comparison of the exchanges between the Garonne and Dordogne populations before and after this collapse. Unfortunately, only otoliths from these two rivers were available for this study before the collapse. The geographical extent of this sampling (around 2000 km from the Vire to Mondego rivers) was particularly adapted to investigate the metapopulation structure of Allis shad along the Atlantic coast. Among the 18 rivers sampled, some of them share common estuaries or are tributaries of larger rivers (Figure 1; Table 2). This feature could potentially impact the exchanges between rivers since adult Allis shad could display homing to estuaries or river tributaries, rather than the sampled rivers. Table 2. Distance matrix between rivers.     Distances (in km) between river terminuses were measured following the coast and exclude estuaries. Distances between rivers sharing common estuaries are null. Common estuaries are highlighted with grey cells. Water Eighteen rivers in France and Portugal were sampled to analyse water microchemistry (Figure 1). These rivers are considered to be major spawning catchments throughout the range of Allis shad (Aprahamian et al., 2003). For 17 of these rivers, samplings were performed during the reproduction period, near the spawning grounds (Table 1). At each site, Barium and Strontium in ratio to Calcium (Sr/Ca and Ba/Ca) were quantified, as well as the stable isotope ratio of Strontium (87Sr/86Sr). See Martin et al. (2015) for more details about the sampling design and protocol. Because bedrock geology varies extensively throughout this range, important differences in the water microchemistry were found between watersheds (Martin et al., 2015). The Aveyron river is a tributary of the Garonne river. It presents a different hydrology, especially in 87Sr/86Sr and Sr/Ca (Semhi et al., 2000), which could induce significant differences in the otolith composition of juveniles. Here, the isotopic ratio and elemental concentrations of water in the Aveyron river were retrieved from a previous study (Semhi et al., 2000) (Table 1). Juveniles and adults In their study, Martin et al. (2015) analysed juvenile Allis shad (n = 44), collected during the downstream migration in four French rivers (the Blavet, Vilaine, Loire and Dordogne rivers) and in the Minho river in Portugal (Table 1). Here, we analysed additional juveniles. Two juveniles from the Dordogne river and 5 from the Garonne river were collected in 2015. Eight juveniles from the Aveyron River, caught in 2001 were obtained in Tomas et al. (2005) collection. Therefore 59 juveniles were sampled between 2009 and 2015 in France and Portugal (Table 1). Adult Allis shad (n = 421) were analysed in Martin et al. (2015). They were sampled in 15 rivers from upstream spawning sites to tidal freshwater parts of the watercourse from 2001 to 2014 (Table 1) during the upstream spawning migration (Elie and Baglinière, 2000). Respectively 32 and 162 supplementary adult otoliths were analysed from the Dordogne (year 2001) and Garonne (years 2001, 2008, and 2014) rivers (Table 1). Note that the water baseline contains four rivers without adult fish samples (Aveyron, Charente, Oloron and Nive Rivers). The Adour E. is an estuary receiving several spawning tributaries (Figure 1). We aimed at reallocating adult samples from Adour estuary to any tributary of Adour watershed or a different river. Sample preparation and microchemistry analysis Sample preparation is detailed in Martin et al. (2015). Additional samples were analysed following the same protocol. Water samples were analysed to measure elemental concentrations using a solution-based-sensitive Inductively Coupled Plasma Mass Spectrometer (ICP-MS). The isotopic ratio (87Sr/86Sr) analysis was performed using a Nu-Plasma Multi-Collector Inductively Coupled Plasma Mass Spectrometer (MC-ICP-MS) following the protocol described by Martin et al. (2013). In order to target the portion of the otolith core corresponding to the larval stage and avoid the maternal effect on the core signature, Martin et al. (2015) performed two C-shaped ablation trajectories 40 µm away from the core. Such trajectory corresponds approximately to 2 weeks before day 20 according to Lochet et al. (2008). A first semi corona (i.e. half circle) was ablated by a laser to ICP-MS for elemental concentrations analysis and a second semi corona was ablated by a laser to MC-ICP-MS for isotopic ratio analysis. 87Sr/86Sr, Sr/Ca, and Ba/Ca were chosen because of their incorporation in otoliths according to ambient water chemistry, their temporal stability and their discriminatory power allowing the characterization of the natal origin of adults (Kennedy et al., 2000; Walther and Thorrold, 2006). Bayesian hierarchical model of reallocation Using baseline datasets (i.e. juveniles and water) and otolith microchemistry of adults with unknown origins, the Bayesian hierarchical model provided estimates of natal stream origins for each spawner, and an average vector of probabilities of origins for each river of capture. These probabilities were then multiplied with estimates of abundance of spawners per river to provide estimates of fluxes between rivers. Construction of the Bayesian model In the following subsection, f and j correspond respectively to the adult and juvenile stages. Natal rivers were denoted by n and are included in [1 kb], with kb the number of rivers where water samples were available, so that this range corresponds to the number of rivers of the water baseline. Brackets {} denote vectors and braces [] represent matrices. The otolith composition could be seen as the result of the integration of the water elements and a partitioning due to three interfaces, the gills, the cellular transport, and the crystallization in the otolith (Campana, 1999; Bath et al., 2000). As some authors found a linear relation between water and otolith concentrations in Ba and Sr (Walther and Thorrold, 2008; Martin et al., 2013), a linear regression was performed between the water concentrations in Ba and Sr in the rivers where juveniles were sampled and the otolith concentrations of juveniles. All rivers where water and juvenile datasets were available were pooled to build a single regression per element. The regressions were significant for Sr/Ca (F = 1269; df = 3; p-value = 4.9e-05) and Ba/Ca (F = 18.06; df = 3; p-value = 0.024) with a high degree of positive correlation between the water and the otolith concentrations (respectively R2 = 0.99 and 0.86 for Sr/Ca and Ba/Ca). Therefore, because the Sr/Ca and Ba/Ca ratios in the otolith are deposited in proportion to their ratios in water, a linear relationship was assumed between water and otolith composition in the Bayesian model. Such a linear regression was not required for the isotopic ratio 87Sr/86Sr since it is not partitioned (Blum et al., 2000; Kennedy et al., 2002; Pouilly et al., 2014). The otolith (both adult and juvenile) and water composition matrices (individuals or rivers in row, elemental concentration and isotopic ratio in columns) centring and scaling consists in first, subtracting a statistic (generally the column mean) to each column, and then dividing by a second statistic (generally the column standard deviation) to each column. Adult and juveniles signatures were centred and scaled with respect to similar statistics (mean signatures and standard deviations of adult otoliths) so that they remain comparable. Water elemental concentrations matrix was centred and scaled with respect to its mean over rivers and standard deviation over rivers. We centred both water and otolith isotopic ratios with respect to mean isotopic ratio in adult otoliths and to scale with respect to standard deviations in these otoliths, so that signatures remained comparable (since there is no partition in isotopic ratio). This transformation was performed to decrease the correlation between regression parameters and to provide a single scale of variations among the elements and the isotopic ratio. The otolith composition of an adult f was considered to follow a multinormal distribution (MN). The expectation {Ō(r)} (i.e. the average composition of the otolith) was defined by a linear relation linking the water composition of a river r with the partitioning coefficients a and b:   ({Oto(f)}|N(f) =r)∼MN({a}. {Water(r)}+ {b},[Σ]), (1) where Oto(f) and Water(r) correspond respectively to the otolith composition of an adult f and the water composition of a river r. N(f) represents the natal river of the adult f and [∑] is the variance and co-variance matrix. It was assumed that the partitioning coefficients for the isotopic ratio are b = 0 and a = 1 because no partitioning occurs between the water and the otolith compartments. For the elemental composition, partitioning coefficients follow wide uniform distributions (a∼Unif(0,2) b∼Unif(−3,3)). An uninformative prior was chosen for [∑]:   [∑]∼Wishart([I],ne) (2) with [I] the identity matrix (dimension 3 × 3) and ne the degree of freedom (number of elements +1). Wishart is a multivariate distribution often used as a prior of the inverse of a variance–covariance matrix. For the juveniles, the natal river is already known, so their otolith compositions are described by the following relation:   {Oto(j)}∼MN({a} .{Water(N(j))}+{b},[∑]) (3) with N(j) the natal river, and thus the catch river, of the juvenile j. Finally, a categorical distribution was proposed to reallocate the adults Allis shad to their natal river, for a fish caught in river c(f) and during period p(f):   N(f)∼Categorical({θc(f),p(f))}). (4) We introduced a period p (before 2008, after 2008) effect in the probabilities of origin to account for a possible modification of the dynamics after the collapse of the population from the Garonne River (Rougier et al., 2012). Recruitment started to collapse in 2000s till to 2005. Spawner abundances were fairly stable till 2005. So adult individuals collected after 2008 were clearly collected after the collapse. We do not have any individuals collected from 2002 to 2007. Individuals collected in 2001 were sampled before or at the beginning of the collapse, that is why we chose to consider to split the dataset in two periods. For each catch river c and period p, the vector {θc,p} denotes the probabilities that a fish caught in c during p was indeed born in each of the kb river of the water baseline. Those vectors follow a Dirichlet distribution:   {θc(f),y(f)}∼Dirichlet(αc,p*{γ1:kb}) (5) with γ1 =… = γ kb = 1/kb and kb = 18 (i.e. the number of rivers in the water baseline). Parameter α in a Dirichlet distribution is called a concentration parameter. In their study, Martin et al. (2015) did not introduced a concentration parameter but assumed that it would have been useful, considering that all potential natal rivers were not sampled throughout the range of Allis shad. Here we decided to introduce this parameter. It is a crucial parameter since it directly governs the number of clusters in the resulting reallocation: with a large α, individuals tends to be reallocated in many natal rivers, each river having few individuals, whereas a small α tends to reallocate individuals in a limited number of natal rivers (Neubauer et al., 2013). Theoretically, a prior can be built to introduce a priori information on the number of sources, however information is not available in our situation. Consequently, we chose to follow Dorazio, (2009) and Neubauer et al. (2013) who proposed a generic prior for α that can be used in a large number of situations, and more specifically in our situation, a gamma distribution that mimics an uninformative prior on the number of sources:   αc,p∼Gammasc,p,rc,p (6) with sc,p and rc,p the shape and rate of a gamma distribution that minimizes the sum DKL:   DKL=-lognc,p-1kb×∑k=1kblogrc,psc,pS1kb,kΓsc,p⋅∫0∞uk+sc,p-1exp-rc,pΓuΓu+kbdu. (7)nc,p are the number of fishes caught in river c and period p in the sample, Γ denotes the gamma function and S1 the unsigned Stirling number of first kind. The Bayesian hierarchical model provides a probabilistic estimate of the natal river of adults. The transfer of information between the juvenile baseline and the otolith microchemistry of adults is performed by means of the variance–covariance matrix [∑] and the regression parameters a and b. Bayesian posterior distribution using Monte Carlo Markov Chain sampling Computations were performed with R software (R Development Core Team, R.3.1.1, 2014). The Monte Carlo Markov Chain (MCMC) method was used to draw simulations from Bayesian posterior distributions with the rjags package providing an interface from R Just Another Gibbs Sampling (Plummer, 2003) library. Three MCMC chains were run in parallel with 20 000 iterations after a burn-in period of 10 000 iterations. The monitoring was performed on a, b, [∑], α, Ō(r), N(f) and {θ}. More specifically, N(f) informs on fish reallocation while {θ} informs on the exchange probabilities between rivers. Convergence diagnosis The convergence was tested for all posterior samplings using the Gelman and Rubin (1992) convergence diagnosis with the Coda library. The convergence of a parameter is checked if the potential reduction factor (prf) is below the threshold of 1.05 (Brooks and Gelman, 1998). Additionally, we checked the convergence for the categorical variable of reallocation N(f) of each adult, using a percentage of agreement between MCMC chains at the end of the iterative process (i.e. number of concordant iteration relatively to the total number of iteration). In case of convergence, one can consider that parameter estimates are meaningful. Reallocation process At the end of the iterative process, each fish has been reallocated in one or more sources. The frequency of reallocation of a fish f in a source k was defined as the number of iterations of the MCMC in which fish f was indeed reallocated in source k divided by the total number of iterations of the MCMC and represents a probability of reallocation of f in k. This frequency was calculated for each fish and source so that each fish has a vector Ff containing the kb probabilities of reallocation (one per river of the water baseline). With a matrix containing the Ff of each fish in rows and natal river in columns, we computed the correlation between each pairs of columns (using Spearman correlation test, threshold 0.05). A strong and positive correlation indicates a “confusion” between the corresponding rivers during the reallocation process while a strong and negative correlation indicates that the rivers are well discriminated. Fluxes between donor and recipient rivers Abundance estimates were available in several rivers in France from Non-Governmental Organizations (transmitted and updated by P. Jatteau, personal observation). Abundance estimates are presented in Table 3. Data for several watersheds are missing because reports do not discriminate A. alosa and Alosa fallax (in the Charente and Vilaine rivers) or because of a lack of reliable monitoring. The abundances of adult Allis shad in the Minho river in 2009, 2010, and 2011 were retrieved from Mota et al. (2015). For the Garonne and Dordogne rivers, the abundance estimates were derived from a “bull” (i.e. the sound made by spawning shads) counting following the method of Carry and Borie, (2013). For the other rivers, the abundance estimates were obtained by a video counting system on fishways usually located downstream the spawning grounds, but some fishes may remain downstream of the barrier and therefore not be counted by the device (which is the case of Loire river, P. Jatteau, pers. obs.). Table 3. Surface of watersheds (km2) and abundance indices of adult Allis shad per sampling year.     Surfaces were estimated from headwater to terminus (i.e. estuaries were excluded from these measures). Grey cells correspond to data matching with samplings of adult otoliths. Note that exchange fluxes were estimated only for the second period (i.e. after 2008). Since several rivers are unsampled (Table 3) and because our abundance indices are uncertain (differences between monitoring devices), a method to generate likely abundances was required. Focusing on the second period (after 2008), we plotted the observed abundances (log10 scale) as a function of the river catchment (log10 scale), defined as the river surface from headwater to terminus, so that estuaries were excluded from these measures. We chose to exclude the first period because few adults were sampled before 2008, except in the Gironde populations. Two groups were separated: large catchments (i.e. the Loire, Garonne and Dordogne rivers) with high abundances and small catchments with lower recruitments (Figure 2). Consequently, log10 abundances for small catchments were drawn from a uniform distribution between 0 and 4 while log10 abundances for large catchments were drawn from a uniform distribution between 3 and 5. Mondego, Charente, Vilaine, Minho, and Adour rivers display intermediate catchment surface areas, however no abundance data were available for this range. Therefore, we simulated log10 abundances in a large uniform distribution from 0 to 5. Figure 2. View largeDownload slide Relation between the log10 abundance of adults Allis shad and the log10 surface (km2) per watershed. Surfaces were estimated from headwater to terminus (i.e. estuaries were excluded from these measures). Rivers are ordered by surface. Black boxes indicate the limits of groups where rivers are included. Three groups are defined based on the surfaces and the abundances of spawners. Each circle corresponds to a sampling year. Figure 2. View largeDownload slide Relation between the log10 abundance of adults Allis shad and the log10 surface (km2) per watershed. Surfaces were estimated from headwater to terminus (i.e. estuaries were excluded from these measures). Rivers are ordered by surface. Black boxes indicate the limits of groups where rivers are included. Three groups are defined based on the surfaces and the abundances of spawners. Each circle corresponds to a sampling year. Those simulated abundances were multiplied with the probabilities of origin {θ} corresponding to the outputs of the Bayesian model to estimate fluxes between donor and recipient rivers. This approach allowed the quantification of flux directions and intensities. A donor river produces spawners (homing and straying fishes) and a recipient river received spawners (homing and straying fishes). Homing occurs when the donor is also the recipient river. A closed river only exhibits homing and is thus not connected to other rivers. We defined a source as a river which produced more individuals than received whereas a sink river received spawners but produced only few individuals. Since, we did not describe the internal dynamics (e.g. subpopulations growth rate) in each river, our “sinks” and “sources” were not totally consistent with the standard definition relative to the metapopulation concept (Pulliam, 1988; Kritzer and Sale, 2004; Figueira and Crowder, 2006), though still referring to subpopulations that exchange individuals to other subpopulations. We computed four indicators with the aim of defining source and sink rivers. First, we defined an indicator I1r which measures the production of spawners per river relatively to the whole metapopulation production:   I1r=Br,h+Br,s∑r(Br,h+Br,s) (8) with Br,h the number of produced adults which displayed natal homing and Br,s the number of produced adults which displayed straying towards another river. This indicator allows the identification of the most productive rivers within the metapopulation, and thus could trend towards prioritization of restoration and conservation efforts. Second, we provided an indicator I2r indicating the proportion of straying adults received by a river:   I2r=Rr,sRr,h+Rr,s (9) with Rr,h the number of entering adults which displayed natal homing and Rr,s the number of entering adults which displayed straying from another river (i.e. fish not borne in river r). This second indicator identifies rivers which received predominantly straying adults during the spawning period. Then, a third indicator I3r corresponds to the proportion of straying adults produced by a river relatively to the total number of adults produced in this river:   I3r=Br,sBr,h+Br,s (10) This indicator is a measure of the non-fidelity of adult shads to their natal stream. Then, the balance between production and reception of adults was calculated using the indicator I4r:   I4r=Br,h+Br,sRr,h+Rr,s+Br,h+Br,s (11) A balance > 0.5 indicates that the river produced more fish than it received. This balance allows the identification of sources (i.e. rivers which produced more spawners than they received) and sinks (i.e. rivers which received more spawners than it produced) across the distribution range. All these indicators vary between 0 and 1 and provide information on the production capacity (I1r), attraction of strayers (I2r), non-fidelity of spawners (I3r) and source/sink rivers (I4r). Because Allis shad does not spawn in estuaries, fishes sampled in the Adour estuary could potentially have chosen the Adour or a tributary to reproduce. Therefore, the Adour estuary was excluded from the calculation of these source/sink indicators. Results Model convergence Considering the large number of parameters (n = 387), we checked the convergence according to the Gelman and Rubin diagnosis. We found that all parameters fulfilled the convergence criteria except one concentration parameter (α Blavet, second period) presenting prf = 1.06, which is above our threshold of 1.05. Additionally, we checked the convergence for the categorical variable of reallocation of each adult and concluded that 100% of fish satisfied to the convergence criteria, with >90% of agreement between chains. Probabilities of reallocation Flux between rivers Probabilities that a fish caught in a river was born in each of the potential natal rivers for each period were given by vectors {θ}. For Aulne, Blavet, Vilaine, Dordogne, Nivelle, and Minho rivers, the maximum probabilities of reallocation indicated high probabilities of return to the natal rivers (Figure 3). Exchanges between donor and recipient rivers occurred mostly at the watershed scale (i.e. between rivers sharing the same estuary) (Figure 3), a case observed for the Blavet (i.e. the donor river) and the Scorff (i.e. the recipient river). High probabilities of origin were found for rivers within the same watershed such as Adour, Saison and Oloron rivers in France, and in Portugal where the Minho river exchanges individuals with Lima and Mondego rivers. High probability of origin was found between the Garonne river (recipient river) and its neighbour river Dordogne (donor river) during the first and second periods (Figure 3). Low probabilities of origin were found between the Garonne river (recipient river) and the Aveyron and Adour rivers, respectively during the first and second periods. Figure 3. View largeDownload slide Probabilities of natal origins for each period and capture river. Rivers where adults were sampled are presented in row and natal rivers in columns. The horizontal bar corresponds to the probabilities. Circles are the 95% credibility intervals. Solid circles indicate large credibility intervals whereas empty circle correspond to short credibility intervals. Dark and grey cells represent respectively a homing at river scale and a homing at watershed scale. Concentration parameters are indicated for each period and capture river. Figure 3. View largeDownload slide Probabilities of natal origins for each period and capture river. Rivers where adults were sampled are presented in row and natal rivers in columns. The horizontal bar corresponds to the probabilities. Circles are the 95% credibility intervals. Solid circles indicate large credibility intervals whereas empty circle correspond to short credibility intervals. Dark and grey cells represent respectively a homing at river scale and a homing at watershed scale. Concentration parameters are indicated for each period and capture river. Wide credibility intervals of Dirichlet distributions combined to large αc,p (i.e. large number of potential natal rivers) were found in Adour R., Saison, Lima, and Mondego rivers. However, for other rivers such as the Minho, Garonne, Dordogne and Vire rivers, low credibility intervals and low αc,p were estimated. This confirmed that individuals caught in the same river displayed similar otolith signatures so that they are reallocated to a limited number of natal rivers. It was especially the case for rivers in which a great number of shads were collected (e.g. the Minho, Dordogne or Garonne rivers presented low αc,p). Confusions between reallocation rivers The analysis of the correlation matrix showed that confusions exist during the reallocation (Figure 4). This was especially true for the rivers of the Adour watershed (Adour, Oloron, Nive, and Saison). Vire river tended to be confused with Blavet river, the Charente with Saison river, the Garonne with Adour river and the Loire with Aveyron river. This last confusion may explain why Loire samples presented high probabilities of origin in the Aveyron river (Figure 3). Figure 4. View largeDownload slide Confusion matrix between reallocation rivers. A positive correlation indicates a confusion while a negative correlation indicates a good discrimination between rivers. The colours (or shades of grey) and sizes of the circles indicate the intensity and direction of the correlations. Only significant correlations (p-value < 0.05) are presented in colour. Figure 4. View largeDownload slide Confusion matrix between reallocation rivers. A positive correlation indicates a confusion while a negative correlation indicates a good discrimination between rivers. The colours (or shades of grey) and sizes of the circles indicate the intensity and direction of the correlations. Only significant correlations (p-value < 0.05) are presented in colour. Recipient, donor, and closed rivers Contributions The multiplication of the vectors {θ} with simulated abundances provided an insight on the contribution of the different rivers to the total number of spawners in the area. Despite large credibility intervals, it showed that the Dordogne river has the highest contribution (Figure 5a). Garonne river also had an important contribution though mainly due to Aveyron spawning grounds which might be partly confused with Loire river (in this analysis we pooled the Garonne and Aveyron rivers because we focused on the second period). Though less important than Dordogne river, the contribution of Blavet, Vilaine, Adour and Minho rivers was significant (Figure 5a). Figure 5. View largeDownload slide Four indicators of exchange for the rivers which are both recipient and donor rivers. The first indicator (a) represents the contribution of the river to the total production of spawners in the metapopulation, the second indicator (b) represents the proportion of strayers among adults entering a river to reproduce, the third indicator (c) represents the proportion of strayers produced in the river while the last indicator (d) represents the balance between production and production + reception. Each boxplot represent the first quantile (25%), the median (50%) and the last quantile (75%) of the distribution. The segments are the 95% credibility intervals. The horizontal line indicates 0.5 and allows the identification of sources and sinks. Garonne was merged with Aveyron in these plots. Because some rivers were not recipient and/or donor rivers, it was not possible to carry out the analysis for those rivers (Adour estuary and Nive and Charente rivers). Figure 5. View largeDownload slide Four indicators of exchange for the rivers which are both recipient and donor rivers. The first indicator (a) represents the contribution of the river to the total production of spawners in the metapopulation, the second indicator (b) represents the proportion of strayers among adults entering a river to reproduce, the third indicator (c) represents the proportion of strayers produced in the river while the last indicator (d) represents the balance between production and production + reception. Each boxplot represent the first quantile (25%), the median (50%) and the last quantile (75%) of the distribution. The segments are the 95% credibility intervals. The horizontal line indicates 0.5 and allows the identification of sources and sinks. Garonne was merged with Aveyron in these plots. Because some rivers were not recipient and/or donor rivers, it was not possible to carry out the analysis for those rivers (Adour estuary and Nive and Charente rivers). Sink and source rivers Vire, Scorff, Loire, Garonne, Saison, and Mondego rivers received a high proportion of spawners with relatively low credibility intervals (Figure 5b). However, the contribution of those rivers (except the Garonne/Aveyron river) to the total production of spawners was small (Figure 5a) and most of them (except the Loire river, but with a high credibility interval) generated a high proportion of strayers (Figure 5c). Interestingly, the balance for the Loire river was inferior to 0.5 (Figure 5d), suggesting that this river may act as a sink though this statement should be moderated because of the confusion between the Loire and Aveyron rivers (Figure 4). On the other hand, the Aulne, Blavet, Vilaine, Dordogne, Nivelle, and Minho rivers appeared to be sources. They received a limited proportion of strayers (Figure 5b) and produced strayers (Figure 5c) leading to a balance > 0.5 with relatively small credibility intervals (Figure 5d). Dordogne river was found as a major source, with the strongest contribution to the total production of spawners, making this river the main source throughout the distribution range (Figure 5d). The large credibility intervals around the median balance for the other rivers (Vire, Scorff, Adour, Saison, Lima, and Mondego rivers) impaired our ability to assess their functioning. Garonne river received a high proportion of strayers (99.9%) (Figure 5b), which means that low homing occurred in this river as found by Martin et al. (2015). The homing in Garonne river during the second period was very small (Figures 3, 5b, and c), and probably very small during the first period given the small probability of reallocation θ (Figure 3). We cannot conclude for the first period because flux calculation was assessed for the second period. Despite a large credibility interval, the Garonne river showed a non-null contribution to the total number of spawners. The only contribution of the Garonne river was found for spawners born in Aveyron that migrated to the Loire river but the confusion between Aveyron and Loire rivers may ever lower the contribution of the Garonne river (Figure 4). Discussion In the context of global decline of Allis shad populations through its entire distribution range, the understanding of the whole population dynamics is an important concern to understand whether this species is distributed in isolated populations or has significant exchanges between subpopulations (Kritzer and Sale, 2004). The identification of the most relevant management scale (i.e. the population scale in case of isolated populations, or the metapopulation in case of connected subpopulations) is crucial for Allis shad, as populations are currently managed independently across the distribution range, ignoring a potential metapopulation functioning. Building on Martin et al. (2015), this study aimed at estimating exchanges between the different populations and at achieving an estimation of exchange and homing rates. Model and data weakness Limitation through a fixed number of natal river: the exclusivity assumption Although we combined water and juvenile baselines to elicit natal origin of adults, the source water baseline permitted reallocation to certain rivers. This represents a strong limitation since the confidence in the reallocation is based on the quality of the spatial coverage of water samplings. Indeed, among adults, some of them could be, in reality, borne in a river that we did not considered in our water baseline. In this case, the baseline would constrained the reallocation in the most chemically similar river of the baseline, and thus lead to miss-classification of adults. The present analysis would thus greatly gain from expanding the spatial coverage of the water baseline, at least in large catchments where important spawning sites were ignored. An interesting way to circumvent the exclusivity assumption could be the use of Infinite Mixture Models (IMM) as suggesting by numerous authors over the past decade (Munch and Clarke, 2008; White et al., 2008; Neubauer et al., 2013). Though, Neubauer et al. (2013) showed that the DPM (i.e. Dirichlet Process Model which are a particular case of IMM that use Dirichlet distribution for probabilities of reallocation) was a particularly relevant tool to reallocate some individuals in groups out of the baseline, they had problems of convergence especially with large datasets of individuals. Herein, we preferred using a Bayesian model of reallocation that introduces a concentration parameter α. This parameter mimics the number of sources to be estimated (Dorazio, 2009; Neubauer et al., 2013). It could be viewed as an alternative to DPM since a non-informative prior was chosen. However, we assumed that contrary to DPM, the reallocations were constrained in rivers of the water baseline. Is the concentration parameter (α) a good way to circumvent the exclusivity assumption? As mentioned earlier, the concentration parameter is a key parameter in a Gaussian mixture model (Escobar and West, 1995; Rasmussen, 2000; Dorazio, 2009). This parameter directly governs the number of sources in the sample, i.e. in our situation the number of donor rivers re-associated with each receiver river. More importantly, it governs the balance between the number of groups and the influence of the water baseline: with a small value, the algorithm produces a small number of groups even if some individuals are “far” from the water baseline, while with a high value, the algorithm favours the proximity of individuals with the water baseline even if it produces many groups. Following Dorazio, (2009) and Neubauer et al. (2013), we used an uninformative prior for this parameter. Estimated values were very small in most rivers (Figure 3) and this has several consequences. First, this means that in most rivers, adult shad display similar signatures so that few groups of individuals are created. However, with such low values, the algorithm tends to favour a limited number of group compared with the proximity between fish and otolith signatures. This can increase the confusions between donor rivers with very similar water signatures and may explain why most receiver rivers were dominated by a single donor river. Larger credibility intervals around this concentration parameter for Lima, Adour and Mondego rivers resulted in a higher number of associated donor rivers and/or to an increase of credibility intervals around the reallocation probabilities. Those larger credibility intervals resulted both from a limited number of samples in those rivers and to a higher variability of adults signatures. Interpretations of straying between more distant rivers, as for instance between the Mondego and Scorff rivers (1580 km distant, Table 2), may be biased by large credibility intervals and a low number of adults and baseline samples. The confusion of reallocation between rivers may also limit ecological interpretation. Confusions of reallocation and limited discrimination among river signatures Confusions of reallocation were pointed out between connected rivers within the same watershed (e.g. the Adour, Nive, Saison, and Oloron rivers) and also between distant rivers (e.g. the Loire and Aveyron rivers), reducing our ability to interpret exchanges between catchments. As explained previously, confusions were partly due to the concentration parameter, which means that some rivers were not discriminated. We suggest improving water and juvenile baselines and adult fish numbers would likely provide better a discrimination among rivers. Besides, ultra-trace elements in addition to 87Sr/86Sr and Sr/Ca and Ba/Ca ratios have the potential to increase the discrimination between sources, provided such addition is meaningful and wise regarding discrimination power (Mercier et al., 2011). Ultra-trace elements sometimes under the Limit Of Detection (LOD), are often excluded of the studies because they are not always measurable. Higgins et al. (2013) and De Pontual et al. (2000) suggested that data below the LOD could contribute meaningfully to the discrimination between sites, using the presence/absence information to discriminate sites with overlapping signatures. Therefore, we suggest improving discrimination between sources (and thus limiting the confusion between reallocation rivers) using geospatially meaningful additional ultra-trace elements to be treated in a mix of quantitative and qualitative data. An overview of the metapopulation dynamics A first step towards the spatial and temporal dynamic of the metapopulation Herein, we developed a method allowing the estimation of flux between basins. We identified sources and sinks, river contributions and homing rates. However, because of missing otolith datasets before 2008, we excluded the first period of the analysis. Consequently, we cannot draw conclusions about the temporal dynamic of exchanges between watersheds. Though, the introduction of a temporal dynamic within this study would have been particularly valuable, especially to understand temporal trends of homing in large catchments such as the Garonne and Dordogne populations. Focusing on the second period, we analysed spatial exchanges by multiplying probabilities of origin with abundance indices. For numerous indicators and rivers, large credibility intervals were found and resulted from the product of two estimates with large credibility intervals. Probabilities were uncertain because of low number of adult and baseline samples and low discrimination between rivers, whereas large credibility intervals of abundance indices were due to incomplete and various monitoring of shads populations. Future samplings would likely improve our statements about the metapopulation dynamics, reducing credibility intervals. Despite these limitations, this study proposed a simple method which provided an overview of the metapopulation dynamics. We especially found that Allis shad populations are relatively connected, at least at the watershed scale, a result which differed from the current view that supposed strong natal homing in this species (Tomas et al., 2005; Alexandrino et al., 2006; Jolly et al., 2012; Martin et al., 2015). Identifications of sources and sinks: implication for management Despite large credibility intervals, our results suggested that some rivers were sinks and did not contribute significantly to the total number of spawners in the metapopulation. Such a result could indicate that spawning grounds are of poor quality or hardly accessible, or that juvenile survival is low, a hypothesis that deserves interest, at least for Garonne river case. Most spawners entering the Garonne river were born in the Dordogne river confirming previous results of Tomas et al. (2005), and to a minor extent from the Adour river. This tended to show that, what was thought to be the largest population in the Western Europe was in fact mainly due to the attraction of a large number of strayers from the Dordogne and Adour rivers. As explained by Schtickzelle and Quinn, (2007), the question of metapopulation dynamics in anadromous fish is not well studied. Nevertheless, the metapopulation dynamic is of interest to management through the prioritization of watershed conservation, restoration and fisheries regulation. Using a simple method, we estimated fluxes and found that the Allis shad metapopulation probably satisfy to the source-sink metapopulation concept. If confirmed by further studies, such functioning may support management prioritizing actions in the most productive rivers and if possible, restoration (e.g. spawning habitat, connectivity) on sinks. Despite an incomplete sampling scheme, our study provided an overview of the metapopulation functioning and we think that this method could be applied to other anadromous species with conservation concerns, especially when water and otolith samples are readily accessible. Acknowledgements We are also grateful to fishermen P. Boisneau and D. Macé for adult samples from Loire and Vilaine Rivers respectively. Additionally, we thank E. Rivot, E. Reveillac and M. Nevoux for fruitful discussions. Finally, we are grateful to the Editor D. Secor and reviewers, including K. Limburg, for their relevant remarks and advice that largely improved the quality of this work. Funding This study was funded by IRSTEA (Institut national de Recherche en Sciences et Technologies pour l’Environnement et l’Agriculture) and was included in the Shad’eau programme co-funded by Agence de l’Eau Adour Garonne and Nouvelle Aquitaine Region. 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Quantifying exchanges of Allis shads between river catchments by combining otolith microchemistry and abundance indices in a Bayesian model

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Abstract

Abstract Similar to many diadromous fish species, dramatic declines were observed for Allis shad, an anadromous Clupeidae, since the beginning of the 2000s. The knowledge of population and metapopulation dynamics is a key issue for the management of migratory species. Although homing behaviour is dominant in Allis shad, staying causes exchanges between populations of each river catchment. Currently, the management of Allis shad is applied at the population scale, without accounting for a potential metapopulation structure. Herein we propose a method to estimate the exchanges flux between rivers and a method to identify source and sink rivers. We used otolith microchemistry within a Bayesian model of reallocation coupled with abundance estimates of spawners per watershed. Results showed a metapopulation dynamic with several rivers acting as sources and other as sinks. However, the lack of precision and homogeneity in abundance data resulted in large credibility intervals, which calls for a better standardization in the acquisition of abundance data. Nevertheless, this method should provide an overview of the metapopulation dynamics of other anadromous species with management concerns. Introduction In the context of increased habitat fragmentation worldwide, the metapopulation concept is a promising and relevant tool to investigate population dynamics of wild species (Hanski, 1999). A metapopulation is basically defined as a set of isolated breeding habitats connected by dispersal (Hanski, 1998; Kritzer and Sale, 2004; Smith and Green, 2005). So far, the metapopulation paradigm has been assessed for various terrestrial species (Hanski and Thomas, 1994; Esler, 2000; Hanski and Ovaskainen, 2000; Inchausti and Weimerskirch, 2002; Smith and Green, 2005; Heard et al., 2013), demonstrating its relevance in conservation and management concerns (Southwell et al., 2016). The understanding of metapopulation structure is of great importance as it provides insight on the relevant management scale and priorities. Ignoring the metapopulation structure in management decisions is known to lead to depletion of local populations and eventually collapses (Hilborn et al., 2003; Kritzer and Sale, 2004; Neat et al., 2014). Most temperate anadromous species (i.e. species performing migrations between marine and freshwater habitats where they reproduce; McDowall, 2008) have undergone dramatic declines within the North Atlantic area during the last century, mostly caused by anthropogenic pressures and climate change (Groot, 2002; Limburg and Waldman, 2009; Aprahamian et al., 2010), raising key conservation issues. In this context, a better understanding of their population health is crucial to support management actions. Though the metapopulation concept has been widely applied to salmonids (Taylor, 1991; Quinn, 1993; King et al., 2001), many anadromous species are managed locally at the catchment scale, ignoring exchanges between catchments. This is the case of the European Allis shad (Alosa alosa), an anadromous Clupeidae which remains as juvenile in freshwater for few weeks before performing a seaward migration as YOY (i.e. Young Of the Year) and spends between 3 and 7 years long growth phase at sea (Lochet, 2006). Reproduction occurs in the higher middle watercourse of rivers in spring and summer (Baglinière et al., 2003). The distribution area of Allis shad has significantly decreased, from a historical range from Norway to Morocco in the middle of the 20th century, to a modern range from France to Portugal (Baglinière et al., 2003). Until the end of the 20th century, the Dordogne and Garonne populations (Figure 1) were considered as the most important in Europe (Elie and Baglinière, 2000; Castelnaud et al., 2001). However, at the beginning of the 2000s, the Dordogne and Garonne populations collapsed (Rougier et al., 2012). Despite a drastic fishing ban measure, these populations have not recovered yet. At the same time, from the mid-twentieth century, a decrease in the number of spawners was observed in the Minho River in Portugal (Mota et al., 2015). Water pollution, habitat loss, obstacles to migration (such as dams) and overfishing have been suggested as possible causes of shad population declines (Jonsson et al., 1999; Groot, 2002; Limburg and Waldman, 2009). Figure 1. View largeDownload slide Maps of Europe (left panel) and adult, juvenile Allis shad and water samples in France and Portugal (respectively the middle and right panel). Details of the Blavet-Scorff and Adour estuaries are presented in inset maps. Grey lines correspond to the rivers where samples were available. Symbols represent the kind of samples for each river. Filled circle: water samples; Filled diamond: adult samples; Asterisk: water and adult samples; Filled triangle: water and juvenile samples; Filled square: water, adult and juvenile samples. Figure 1. View largeDownload slide Maps of Europe (left panel) and adult, juvenile Allis shad and water samples in France and Portugal (respectively the middle and right panel). Details of the Blavet-Scorff and Adour estuaries are presented in inset maps. Grey lines correspond to the rivers where samples were available. Symbols represent the kind of samples for each river. Filled circle: water samples; Filled diamond: adult samples; Asterisk: water and adult samples; Filled triangle: water and juvenile samples; Filled square: water, adult and juvenile samples. To analyse the collapse and decline of populations, a deeper knowledge of population structure for the entire species is necessary to understand whether Allis shad forms discrete independent populations, or if populations have significant exchanges of individuals, resulting in a metapopulation (Kritzer and Sale, 2004). In this context, it is essential to understand whether shad populations display strict homing (i.e. all individuals of a generation return to their natal stream to reproduce; McDowall, 2008; Secor, 2015), which would induce no exchanges between populations, or if populations perform straying (i.e. individuals migrate to non-natal site to reproduce; Quinn, 1993; Keefer and Caudill, 2014; Secor, 2015), which would result in metapopulation dynamics. From the end of the 20th century, otolith microchemistry has been employed to examine fish migration, natal origin and population connectivity (Kennedy et al., 2002; Daverat et al., 2012; Rooker et al., 2016). Otoliths of teleost fishes are small calcareous concretions located in the inner ear which grow during the whole life of fishes by continuous accretion of inert elements (Campana, 1999; Söllner et al., 2003), some of them originating from the ambient water (Campana, 1999; Morais and Daverat, 2016). By coupling microchemistry and micro-increments analyses, they can be used to reconstruct the habitat use of the fish from birth (i.e. the core of the otolith) to death (i.e. the edge of the otolith) (Bath et al., 2000; Walther and Thorrold, 2006; Morais and Daverat, 2016). Because of technical advances, the otolith microchemistry approach currently appears to be one of the most relevant methods to elicit Allis shad natal origin (Tomas et al., 2005; Martin et al., 2015). In 2005, Tomas et al. examined the structure of Garonne—Dordogne populations using otolith microchemistry analysis and suggested that the Dordogne river acted as a source of spawners in the entire Garonne-Dordogne watershed. Then in 2014, technical and methodological progresses enabled the identification of natal origin of spawners from 15 rivers along the Atlantic coast (Martin et al., 2015). Martin et al. (2015) used a Bayesian model with otolith microchemistry datasets to reallocate individuals to their natal river. Authors found that most adults caught in a river were indeed born in this river or in the watershed. They also observed exchanges at short distance scale (20–100 km). Although Martin et al.’s (2015) results suggested a high level of natal homing, they were not able to estimate the “true” probabilities of homing and straying, i.e. the exchange fluxes between populations, as their analysis did not include estimates of population sizes throughout the range of Allis shad (Munch and Clarke, 2008; Martin et al., 2015). In this context, this study goes one step further from Martin et al. (2015). We combined Martin et al.’s (2015) Bayesian model with abundance indices of spawners to estimate exchange fluxes between donor (i.e. natal rivers) and recipient rivers (i.e. spawning ground rivers). By coupling these two models, we quantified flux between populations and consequently provide insights on whether (i) populations are strictly isolated and deserved to be managed independently, or whether (ii) populations are connected sub-populations, which need to be included in a large scale management of the metapopulation. Material and methods Sampling Update of datasets In this study, we used the microchemistry datasets previously analysed by Martin et al. (2015) in France and Portugal (Figure 1) and added additional adult, juvenile and water samples (Table 1). Table 1. Number of adult and juvenile Allis shad and water samples per river and year.     Grey cells indicate new samples compared with Martin et al. (2015). Further, we completed a Garonne baseline (with juveniles from the Garonne and Aveyron rivers). We also added adult samples from the Garonne and Dordogne rivers before the collapse that occurred in 2000s (Rougier et al., 2012). These new samples provided a comparison of the exchanges between the Garonne and Dordogne populations before and after this collapse. Unfortunately, only otoliths from these two rivers were available for this study before the collapse. The geographical extent of this sampling (around 2000 km from the Vire to Mondego rivers) was particularly adapted to investigate the metapopulation structure of Allis shad along the Atlantic coast. Among the 18 rivers sampled, some of them share common estuaries or are tributaries of larger rivers (Figure 1; Table 2). This feature could potentially impact the exchanges between rivers since adult Allis shad could display homing to estuaries or river tributaries, rather than the sampled rivers. Table 2. Distance matrix between rivers.     Distances (in km) between river terminuses were measured following the coast and exclude estuaries. Distances between rivers sharing common estuaries are null. Common estuaries are highlighted with grey cells. Water Eighteen rivers in France and Portugal were sampled to analyse water microchemistry (Figure 1). These rivers are considered to be major spawning catchments throughout the range of Allis shad (Aprahamian et al., 2003). For 17 of these rivers, samplings were performed during the reproduction period, near the spawning grounds (Table 1). At each site, Barium and Strontium in ratio to Calcium (Sr/Ca and Ba/Ca) were quantified, as well as the stable isotope ratio of Strontium (87Sr/86Sr). See Martin et al. (2015) for more details about the sampling design and protocol. Because bedrock geology varies extensively throughout this range, important differences in the water microchemistry were found between watersheds (Martin et al., 2015). The Aveyron river is a tributary of the Garonne river. It presents a different hydrology, especially in 87Sr/86Sr and Sr/Ca (Semhi et al., 2000), which could induce significant differences in the otolith composition of juveniles. Here, the isotopic ratio and elemental concentrations of water in the Aveyron river were retrieved from a previous study (Semhi et al., 2000) (Table 1). Juveniles and adults In their study, Martin et al. (2015) analysed juvenile Allis shad (n = 44), collected during the downstream migration in four French rivers (the Blavet, Vilaine, Loire and Dordogne rivers) and in the Minho river in Portugal (Table 1). Here, we analysed additional juveniles. Two juveniles from the Dordogne river and 5 from the Garonne river were collected in 2015. Eight juveniles from the Aveyron River, caught in 2001 were obtained in Tomas et al. (2005) collection. Therefore 59 juveniles were sampled between 2009 and 2015 in France and Portugal (Table 1). Adult Allis shad (n = 421) were analysed in Martin et al. (2015). They were sampled in 15 rivers from upstream spawning sites to tidal freshwater parts of the watercourse from 2001 to 2014 (Table 1) during the upstream spawning migration (Elie and Baglinière, 2000). Respectively 32 and 162 supplementary adult otoliths were analysed from the Dordogne (year 2001) and Garonne (years 2001, 2008, and 2014) rivers (Table 1). Note that the water baseline contains four rivers without adult fish samples (Aveyron, Charente, Oloron and Nive Rivers). The Adour E. is an estuary receiving several spawning tributaries (Figure 1). We aimed at reallocating adult samples from Adour estuary to any tributary of Adour watershed or a different river. Sample preparation and microchemistry analysis Sample preparation is detailed in Martin et al. (2015). Additional samples were analysed following the same protocol. Water samples were analysed to measure elemental concentrations using a solution-based-sensitive Inductively Coupled Plasma Mass Spectrometer (ICP-MS). The isotopic ratio (87Sr/86Sr) analysis was performed using a Nu-Plasma Multi-Collector Inductively Coupled Plasma Mass Spectrometer (MC-ICP-MS) following the protocol described by Martin et al. (2013). In order to target the portion of the otolith core corresponding to the larval stage and avoid the maternal effect on the core signature, Martin et al. (2015) performed two C-shaped ablation trajectories 40 µm away from the core. Such trajectory corresponds approximately to 2 weeks before day 20 according to Lochet et al. (2008). A first semi corona (i.e. half circle) was ablated by a laser to ICP-MS for elemental concentrations analysis and a second semi corona was ablated by a laser to MC-ICP-MS for isotopic ratio analysis. 87Sr/86Sr, Sr/Ca, and Ba/Ca were chosen because of their incorporation in otoliths according to ambient water chemistry, their temporal stability and their discriminatory power allowing the characterization of the natal origin of adults (Kennedy et al., 2000; Walther and Thorrold, 2006). Bayesian hierarchical model of reallocation Using baseline datasets (i.e. juveniles and water) and otolith microchemistry of adults with unknown origins, the Bayesian hierarchical model provided estimates of natal stream origins for each spawner, and an average vector of probabilities of origins for each river of capture. These probabilities were then multiplied with estimates of abundance of spawners per river to provide estimates of fluxes between rivers. Construction of the Bayesian model In the following subsection, f and j correspond respectively to the adult and juvenile stages. Natal rivers were denoted by n and are included in [1 kb], with kb the number of rivers where water samples were available, so that this range corresponds to the number of rivers of the water baseline. Brackets {} denote vectors and braces [] represent matrices. The otolith composition could be seen as the result of the integration of the water elements and a partitioning due to three interfaces, the gills, the cellular transport, and the crystallization in the otolith (Campana, 1999; Bath et al., 2000). As some authors found a linear relation between water and otolith concentrations in Ba and Sr (Walther and Thorrold, 2008; Martin et al., 2013), a linear regression was performed between the water concentrations in Ba and Sr in the rivers where juveniles were sampled and the otolith concentrations of juveniles. All rivers where water and juvenile datasets were available were pooled to build a single regression per element. The regressions were significant for Sr/Ca (F = 1269; df = 3; p-value = 4.9e-05) and Ba/Ca (F = 18.06; df = 3; p-value = 0.024) with a high degree of positive correlation between the water and the otolith concentrations (respectively R2 = 0.99 and 0.86 for Sr/Ca and Ba/Ca). Therefore, because the Sr/Ca and Ba/Ca ratios in the otolith are deposited in proportion to their ratios in water, a linear relationship was assumed between water and otolith composition in the Bayesian model. Such a linear regression was not required for the isotopic ratio 87Sr/86Sr since it is not partitioned (Blum et al., 2000; Kennedy et al., 2002; Pouilly et al., 2014). The otolith (both adult and juvenile) and water composition matrices (individuals or rivers in row, elemental concentration and isotopic ratio in columns) centring and scaling consists in first, subtracting a statistic (generally the column mean) to each column, and then dividing by a second statistic (generally the column standard deviation) to each column. Adult and juveniles signatures were centred and scaled with respect to similar statistics (mean signatures and standard deviations of adult otoliths) so that they remain comparable. Water elemental concentrations matrix was centred and scaled with respect to its mean over rivers and standard deviation over rivers. We centred both water and otolith isotopic ratios with respect to mean isotopic ratio in adult otoliths and to scale with respect to standard deviations in these otoliths, so that signatures remained comparable (since there is no partition in isotopic ratio). This transformation was performed to decrease the correlation between regression parameters and to provide a single scale of variations among the elements and the isotopic ratio. The otolith composition of an adult f was considered to follow a multinormal distribution (MN). The expectation {Ō(r)} (i.e. the average composition of the otolith) was defined by a linear relation linking the water composition of a river r with the partitioning coefficients a and b:   ({Oto(f)}|N(f) =r)∼MN({a}. {Water(r)}+ {b},[Σ]), (1) where Oto(f) and Water(r) correspond respectively to the otolith composition of an adult f and the water composition of a river r. N(f) represents the natal river of the adult f and [∑] is the variance and co-variance matrix. It was assumed that the partitioning coefficients for the isotopic ratio are b = 0 and a = 1 because no partitioning occurs between the water and the otolith compartments. For the elemental composition, partitioning coefficients follow wide uniform distributions (a∼Unif(0,2) b∼Unif(−3,3)). An uninformative prior was chosen for [∑]:   [∑]∼Wishart([I],ne) (2) with [I] the identity matrix (dimension 3 × 3) and ne the degree of freedom (number of elements +1). Wishart is a multivariate distribution often used as a prior of the inverse of a variance–covariance matrix. For the juveniles, the natal river is already known, so their otolith compositions are described by the following relation:   {Oto(j)}∼MN({a} .{Water(N(j))}+{b},[∑]) (3) with N(j) the natal river, and thus the catch river, of the juvenile j. Finally, a categorical distribution was proposed to reallocate the adults Allis shad to their natal river, for a fish caught in river c(f) and during period p(f):   N(f)∼Categorical({θc(f),p(f))}). (4) We introduced a period p (before 2008, after 2008) effect in the probabilities of origin to account for a possible modification of the dynamics after the collapse of the population from the Garonne River (Rougier et al., 2012). Recruitment started to collapse in 2000s till to 2005. Spawner abundances were fairly stable till 2005. So adult individuals collected after 2008 were clearly collected after the collapse. We do not have any individuals collected from 2002 to 2007. Individuals collected in 2001 were sampled before or at the beginning of the collapse, that is why we chose to consider to split the dataset in two periods. For each catch river c and period p, the vector {θc,p} denotes the probabilities that a fish caught in c during p was indeed born in each of the kb river of the water baseline. Those vectors follow a Dirichlet distribution:   {θc(f),y(f)}∼Dirichlet(αc,p*{γ1:kb}) (5) with γ1 =… = γ kb = 1/kb and kb = 18 (i.e. the number of rivers in the water baseline). Parameter α in a Dirichlet distribution is called a concentration parameter. In their study, Martin et al. (2015) did not introduced a concentration parameter but assumed that it would have been useful, considering that all potential natal rivers were not sampled throughout the range of Allis shad. Here we decided to introduce this parameter. It is a crucial parameter since it directly governs the number of clusters in the resulting reallocation: with a large α, individuals tends to be reallocated in many natal rivers, each river having few individuals, whereas a small α tends to reallocate individuals in a limited number of natal rivers (Neubauer et al., 2013). Theoretically, a prior can be built to introduce a priori information on the number of sources, however information is not available in our situation. Consequently, we chose to follow Dorazio, (2009) and Neubauer et al. (2013) who proposed a generic prior for α that can be used in a large number of situations, and more specifically in our situation, a gamma distribution that mimics an uninformative prior on the number of sources:   αc,p∼Gammasc,p,rc,p (6) with sc,p and rc,p the shape and rate of a gamma distribution that minimizes the sum DKL:   DKL=-lognc,p-1kb×∑k=1kblogrc,psc,pS1kb,kΓsc,p⋅∫0∞uk+sc,p-1exp-rc,pΓuΓu+kbdu. (7)nc,p are the number of fishes caught in river c and period p in the sample, Γ denotes the gamma function and S1 the unsigned Stirling number of first kind. The Bayesian hierarchical model provides a probabilistic estimate of the natal river of adults. The transfer of information between the juvenile baseline and the otolith microchemistry of adults is performed by means of the variance–covariance matrix [∑] and the regression parameters a and b. Bayesian posterior distribution using Monte Carlo Markov Chain sampling Computations were performed with R software (R Development Core Team, R.3.1.1, 2014). The Monte Carlo Markov Chain (MCMC) method was used to draw simulations from Bayesian posterior distributions with the rjags package providing an interface from R Just Another Gibbs Sampling (Plummer, 2003) library. Three MCMC chains were run in parallel with 20 000 iterations after a burn-in period of 10 000 iterations. The monitoring was performed on a, b, [∑], α, Ō(r), N(f) and {θ}. More specifically, N(f) informs on fish reallocation while {θ} informs on the exchange probabilities between rivers. Convergence diagnosis The convergence was tested for all posterior samplings using the Gelman and Rubin (1992) convergence diagnosis with the Coda library. The convergence of a parameter is checked if the potential reduction factor (prf) is below the threshold of 1.05 (Brooks and Gelman, 1998). Additionally, we checked the convergence for the categorical variable of reallocation N(f) of each adult, using a percentage of agreement between MCMC chains at the end of the iterative process (i.e. number of concordant iteration relatively to the total number of iteration). In case of convergence, one can consider that parameter estimates are meaningful. Reallocation process At the end of the iterative process, each fish has been reallocated in one or more sources. The frequency of reallocation of a fish f in a source k was defined as the number of iterations of the MCMC in which fish f was indeed reallocated in source k divided by the total number of iterations of the MCMC and represents a probability of reallocation of f in k. This frequency was calculated for each fish and source so that each fish has a vector Ff containing the kb probabilities of reallocation (one per river of the water baseline). With a matrix containing the Ff of each fish in rows and natal river in columns, we computed the correlation between each pairs of columns (using Spearman correlation test, threshold 0.05). A strong and positive correlation indicates a “confusion” between the corresponding rivers during the reallocation process while a strong and negative correlation indicates that the rivers are well discriminated. Fluxes between donor and recipient rivers Abundance estimates were available in several rivers in France from Non-Governmental Organizations (transmitted and updated by P. Jatteau, personal observation). Abundance estimates are presented in Table 3. Data for several watersheds are missing because reports do not discriminate A. alosa and Alosa fallax (in the Charente and Vilaine rivers) or because of a lack of reliable monitoring. The abundances of adult Allis shad in the Minho river in 2009, 2010, and 2011 were retrieved from Mota et al. (2015). For the Garonne and Dordogne rivers, the abundance estimates were derived from a “bull” (i.e. the sound made by spawning shads) counting following the method of Carry and Borie, (2013). For the other rivers, the abundance estimates were obtained by a video counting system on fishways usually located downstream the spawning grounds, but some fishes may remain downstream of the barrier and therefore not be counted by the device (which is the case of Loire river, P. Jatteau, pers. obs.). Table 3. Surface of watersheds (km2) and abundance indices of adult Allis shad per sampling year.     Surfaces were estimated from headwater to terminus (i.e. estuaries were excluded from these measures). Grey cells correspond to data matching with samplings of adult otoliths. Note that exchange fluxes were estimated only for the second period (i.e. after 2008). Since several rivers are unsampled (Table 3) and because our abundance indices are uncertain (differences between monitoring devices), a method to generate likely abundances was required. Focusing on the second period (after 2008), we plotted the observed abundances (log10 scale) as a function of the river catchment (log10 scale), defined as the river surface from headwater to terminus, so that estuaries were excluded from these measures. We chose to exclude the first period because few adults were sampled before 2008, except in the Gironde populations. Two groups were separated: large catchments (i.e. the Loire, Garonne and Dordogne rivers) with high abundances and small catchments with lower recruitments (Figure 2). Consequently, log10 abundances for small catchments were drawn from a uniform distribution between 0 and 4 while log10 abundances for large catchments were drawn from a uniform distribution between 3 and 5. Mondego, Charente, Vilaine, Minho, and Adour rivers display intermediate catchment surface areas, however no abundance data were available for this range. Therefore, we simulated log10 abundances in a large uniform distribution from 0 to 5. Figure 2. View largeDownload slide Relation between the log10 abundance of adults Allis shad and the log10 surface (km2) per watershed. Surfaces were estimated from headwater to terminus (i.e. estuaries were excluded from these measures). Rivers are ordered by surface. Black boxes indicate the limits of groups where rivers are included. Three groups are defined based on the surfaces and the abundances of spawners. Each circle corresponds to a sampling year. Figure 2. View largeDownload slide Relation between the log10 abundance of adults Allis shad and the log10 surface (km2) per watershed. Surfaces were estimated from headwater to terminus (i.e. estuaries were excluded from these measures). Rivers are ordered by surface. Black boxes indicate the limits of groups where rivers are included. Three groups are defined based on the surfaces and the abundances of spawners. Each circle corresponds to a sampling year. Those simulated abundances were multiplied with the probabilities of origin {θ} corresponding to the outputs of the Bayesian model to estimate fluxes between donor and recipient rivers. This approach allowed the quantification of flux directions and intensities. A donor river produces spawners (homing and straying fishes) and a recipient river received spawners (homing and straying fishes). Homing occurs when the donor is also the recipient river. A closed river only exhibits homing and is thus not connected to other rivers. We defined a source as a river which produced more individuals than received whereas a sink river received spawners but produced only few individuals. Since, we did not describe the internal dynamics (e.g. subpopulations growth rate) in each river, our “sinks” and “sources” were not totally consistent with the standard definition relative to the metapopulation concept (Pulliam, 1988; Kritzer and Sale, 2004; Figueira and Crowder, 2006), though still referring to subpopulations that exchange individuals to other subpopulations. We computed four indicators with the aim of defining source and sink rivers. First, we defined an indicator I1r which measures the production of spawners per river relatively to the whole metapopulation production:   I1r=Br,h+Br,s∑r(Br,h+Br,s) (8) with Br,h the number of produced adults which displayed natal homing and Br,s the number of produced adults which displayed straying towards another river. This indicator allows the identification of the most productive rivers within the metapopulation, and thus could trend towards prioritization of restoration and conservation efforts. Second, we provided an indicator I2r indicating the proportion of straying adults received by a river:   I2r=Rr,sRr,h+Rr,s (9) with Rr,h the number of entering adults which displayed natal homing and Rr,s the number of entering adults which displayed straying from another river (i.e. fish not borne in river r). This second indicator identifies rivers which received predominantly straying adults during the spawning period. Then, a third indicator I3r corresponds to the proportion of straying adults produced by a river relatively to the total number of adults produced in this river:   I3r=Br,sBr,h+Br,s (10) This indicator is a measure of the non-fidelity of adult shads to their natal stream. Then, the balance between production and reception of adults was calculated using the indicator I4r:   I4r=Br,h+Br,sRr,h+Rr,s+Br,h+Br,s (11) A balance > 0.5 indicates that the river produced more fish than it received. This balance allows the identification of sources (i.e. rivers which produced more spawners than they received) and sinks (i.e. rivers which received more spawners than it produced) across the distribution range. All these indicators vary between 0 and 1 and provide information on the production capacity (I1r), attraction of strayers (I2r), non-fidelity of spawners (I3r) and source/sink rivers (I4r). Because Allis shad does not spawn in estuaries, fishes sampled in the Adour estuary could potentially have chosen the Adour or a tributary to reproduce. Therefore, the Adour estuary was excluded from the calculation of these source/sink indicators. Results Model convergence Considering the large number of parameters (n = 387), we checked the convergence according to the Gelman and Rubin diagnosis. We found that all parameters fulfilled the convergence criteria except one concentration parameter (α Blavet, second period) presenting prf = 1.06, which is above our threshold of 1.05. Additionally, we checked the convergence for the categorical variable of reallocation of each adult and concluded that 100% of fish satisfied to the convergence criteria, with >90% of agreement between chains. Probabilities of reallocation Flux between rivers Probabilities that a fish caught in a river was born in each of the potential natal rivers for each period were given by vectors {θ}. For Aulne, Blavet, Vilaine, Dordogne, Nivelle, and Minho rivers, the maximum probabilities of reallocation indicated high probabilities of return to the natal rivers (Figure 3). Exchanges between donor and recipient rivers occurred mostly at the watershed scale (i.e. between rivers sharing the same estuary) (Figure 3), a case observed for the Blavet (i.e. the donor river) and the Scorff (i.e. the recipient river). High probabilities of origin were found for rivers within the same watershed such as Adour, Saison and Oloron rivers in France, and in Portugal where the Minho river exchanges individuals with Lima and Mondego rivers. High probability of origin was found between the Garonne river (recipient river) and its neighbour river Dordogne (donor river) during the first and second periods (Figure 3). Low probabilities of origin were found between the Garonne river (recipient river) and the Aveyron and Adour rivers, respectively during the first and second periods. Figure 3. View largeDownload slide Probabilities of natal origins for each period and capture river. Rivers where adults were sampled are presented in row and natal rivers in columns. The horizontal bar corresponds to the probabilities. Circles are the 95% credibility intervals. Solid circles indicate large credibility intervals whereas empty circle correspond to short credibility intervals. Dark and grey cells represent respectively a homing at river scale and a homing at watershed scale. Concentration parameters are indicated for each period and capture river. Figure 3. View largeDownload slide Probabilities of natal origins for each period and capture river. Rivers where adults were sampled are presented in row and natal rivers in columns. The horizontal bar corresponds to the probabilities. Circles are the 95% credibility intervals. Solid circles indicate large credibility intervals whereas empty circle correspond to short credibility intervals. Dark and grey cells represent respectively a homing at river scale and a homing at watershed scale. Concentration parameters are indicated for each period and capture river. Wide credibility intervals of Dirichlet distributions combined to large αc,p (i.e. large number of potential natal rivers) were found in Adour R., Saison, Lima, and Mondego rivers. However, for other rivers such as the Minho, Garonne, Dordogne and Vire rivers, low credibility intervals and low αc,p were estimated. This confirmed that individuals caught in the same river displayed similar otolith signatures so that they are reallocated to a limited number of natal rivers. It was especially the case for rivers in which a great number of shads were collected (e.g. the Minho, Dordogne or Garonne rivers presented low αc,p). Confusions between reallocation rivers The analysis of the correlation matrix showed that confusions exist during the reallocation (Figure 4). This was especially true for the rivers of the Adour watershed (Adour, Oloron, Nive, and Saison). Vire river tended to be confused with Blavet river, the Charente with Saison river, the Garonne with Adour river and the Loire with Aveyron river. This last confusion may explain why Loire samples presented high probabilities of origin in the Aveyron river (Figure 3). Figure 4. View largeDownload slide Confusion matrix between reallocation rivers. A positive correlation indicates a confusion while a negative correlation indicates a good discrimination between rivers. The colours (or shades of grey) and sizes of the circles indicate the intensity and direction of the correlations. Only significant correlations (p-value < 0.05) are presented in colour. Figure 4. View largeDownload slide Confusion matrix between reallocation rivers. A positive correlation indicates a confusion while a negative correlation indicates a good discrimination between rivers. The colours (or shades of grey) and sizes of the circles indicate the intensity and direction of the correlations. Only significant correlations (p-value < 0.05) are presented in colour. Recipient, donor, and closed rivers Contributions The multiplication of the vectors {θ} with simulated abundances provided an insight on the contribution of the different rivers to the total number of spawners in the area. Despite large credibility intervals, it showed that the Dordogne river has the highest contribution (Figure 5a). Garonne river also had an important contribution though mainly due to Aveyron spawning grounds which might be partly confused with Loire river (in this analysis we pooled the Garonne and Aveyron rivers because we focused on the second period). Though less important than Dordogne river, the contribution of Blavet, Vilaine, Adour and Minho rivers was significant (Figure 5a). Figure 5. View largeDownload slide Four indicators of exchange for the rivers which are both recipient and donor rivers. The first indicator (a) represents the contribution of the river to the total production of spawners in the metapopulation, the second indicator (b) represents the proportion of strayers among adults entering a river to reproduce, the third indicator (c) represents the proportion of strayers produced in the river while the last indicator (d) represents the balance between production and production + reception. Each boxplot represent the first quantile (25%), the median (50%) and the last quantile (75%) of the distribution. The segments are the 95% credibility intervals. The horizontal line indicates 0.5 and allows the identification of sources and sinks. Garonne was merged with Aveyron in these plots. Because some rivers were not recipient and/or donor rivers, it was not possible to carry out the analysis for those rivers (Adour estuary and Nive and Charente rivers). Figure 5. View largeDownload slide Four indicators of exchange for the rivers which are both recipient and donor rivers. The first indicator (a) represents the contribution of the river to the total production of spawners in the metapopulation, the second indicator (b) represents the proportion of strayers among adults entering a river to reproduce, the third indicator (c) represents the proportion of strayers produced in the river while the last indicator (d) represents the balance between production and production + reception. Each boxplot represent the first quantile (25%), the median (50%) and the last quantile (75%) of the distribution. The segments are the 95% credibility intervals. The horizontal line indicates 0.5 and allows the identification of sources and sinks. Garonne was merged with Aveyron in these plots. Because some rivers were not recipient and/or donor rivers, it was not possible to carry out the analysis for those rivers (Adour estuary and Nive and Charente rivers). Sink and source rivers Vire, Scorff, Loire, Garonne, Saison, and Mondego rivers received a high proportion of spawners with relatively low credibility intervals (Figure 5b). However, the contribution of those rivers (except the Garonne/Aveyron river) to the total production of spawners was small (Figure 5a) and most of them (except the Loire river, but with a high credibility interval) generated a high proportion of strayers (Figure 5c). Interestingly, the balance for the Loire river was inferior to 0.5 (Figure 5d), suggesting that this river may act as a sink though this statement should be moderated because of the confusion between the Loire and Aveyron rivers (Figure 4). On the other hand, the Aulne, Blavet, Vilaine, Dordogne, Nivelle, and Minho rivers appeared to be sources. They received a limited proportion of strayers (Figure 5b) and produced strayers (Figure 5c) leading to a balance > 0.5 with relatively small credibility intervals (Figure 5d). Dordogne river was found as a major source, with the strongest contribution to the total production of spawners, making this river the main source throughout the distribution range (Figure 5d). The large credibility intervals around the median balance for the other rivers (Vire, Scorff, Adour, Saison, Lima, and Mondego rivers) impaired our ability to assess their functioning. Garonne river received a high proportion of strayers (99.9%) (Figure 5b), which means that low homing occurred in this river as found by Martin et al. (2015). The homing in Garonne river during the second period was very small (Figures 3, 5b, and c), and probably very small during the first period given the small probability of reallocation θ (Figure 3). We cannot conclude for the first period because flux calculation was assessed for the second period. Despite a large credibility interval, the Garonne river showed a non-null contribution to the total number of spawners. The only contribution of the Garonne river was found for spawners born in Aveyron that migrated to the Loire river but the confusion between Aveyron and Loire rivers may ever lower the contribution of the Garonne river (Figure 4). Discussion In the context of global decline of Allis shad populations through its entire distribution range, the understanding of the whole population dynamics is an important concern to understand whether this species is distributed in isolated populations or has significant exchanges between subpopulations (Kritzer and Sale, 2004). The identification of the most relevant management scale (i.e. the population scale in case of isolated populations, or the metapopulation in case of connected subpopulations) is crucial for Allis shad, as populations are currently managed independently across the distribution range, ignoring a potential metapopulation functioning. Building on Martin et al. (2015), this study aimed at estimating exchanges between the different populations and at achieving an estimation of exchange and homing rates. Model and data weakness Limitation through a fixed number of natal river: the exclusivity assumption Although we combined water and juvenile baselines to elicit natal origin of adults, the source water baseline permitted reallocation to certain rivers. This represents a strong limitation since the confidence in the reallocation is based on the quality of the spatial coverage of water samplings. Indeed, among adults, some of them could be, in reality, borne in a river that we did not considered in our water baseline. In this case, the baseline would constrained the reallocation in the most chemically similar river of the baseline, and thus lead to miss-classification of adults. The present analysis would thus greatly gain from expanding the spatial coverage of the water baseline, at least in large catchments where important spawning sites were ignored. An interesting way to circumvent the exclusivity assumption could be the use of Infinite Mixture Models (IMM) as suggesting by numerous authors over the past decade (Munch and Clarke, 2008; White et al., 2008; Neubauer et al., 2013). Though, Neubauer et al. (2013) showed that the DPM (i.e. Dirichlet Process Model which are a particular case of IMM that use Dirichlet distribution for probabilities of reallocation) was a particularly relevant tool to reallocate some individuals in groups out of the baseline, they had problems of convergence especially with large datasets of individuals. Herein, we preferred using a Bayesian model of reallocation that introduces a concentration parameter α. This parameter mimics the number of sources to be estimated (Dorazio, 2009; Neubauer et al., 2013). It could be viewed as an alternative to DPM since a non-informative prior was chosen. However, we assumed that contrary to DPM, the reallocations were constrained in rivers of the water baseline. Is the concentration parameter (α) a good way to circumvent the exclusivity assumption? As mentioned earlier, the concentration parameter is a key parameter in a Gaussian mixture model (Escobar and West, 1995; Rasmussen, 2000; Dorazio, 2009). This parameter directly governs the number of sources in the sample, i.e. in our situation the number of donor rivers re-associated with each receiver river. More importantly, it governs the balance between the number of groups and the influence of the water baseline: with a small value, the algorithm produces a small number of groups even if some individuals are “far” from the water baseline, while with a high value, the algorithm favours the proximity of individuals with the water baseline even if it produces many groups. Following Dorazio, (2009) and Neubauer et al. (2013), we used an uninformative prior for this parameter. Estimated values were very small in most rivers (Figure 3) and this has several consequences. First, this means that in most rivers, adult shad display similar signatures so that few groups of individuals are created. However, with such low values, the algorithm tends to favour a limited number of group compared with the proximity between fish and otolith signatures. This can increase the confusions between donor rivers with very similar water signatures and may explain why most receiver rivers were dominated by a single donor river. Larger credibility intervals around this concentration parameter for Lima, Adour and Mondego rivers resulted in a higher number of associated donor rivers and/or to an increase of credibility intervals around the reallocation probabilities. Those larger credibility intervals resulted both from a limited number of samples in those rivers and to a higher variability of adults signatures. Interpretations of straying between more distant rivers, as for instance between the Mondego and Scorff rivers (1580 km distant, Table 2), may be biased by large credibility intervals and a low number of adults and baseline samples. The confusion of reallocation between rivers may also limit ecological interpretation. Confusions of reallocation and limited discrimination among river signatures Confusions of reallocation were pointed out between connected rivers within the same watershed (e.g. the Adour, Nive, Saison, and Oloron rivers) and also between distant rivers (e.g. the Loire and Aveyron rivers), reducing our ability to interpret exchanges between catchments. As explained previously, confusions were partly due to the concentration parameter, which means that some rivers were not discriminated. We suggest improving water and juvenile baselines and adult fish numbers would likely provide better a discrimination among rivers. Besides, ultra-trace elements in addition to 87Sr/86Sr and Sr/Ca and Ba/Ca ratios have the potential to increase the discrimination between sources, provided such addition is meaningful and wise regarding discrimination power (Mercier et al., 2011). Ultra-trace elements sometimes under the Limit Of Detection (LOD), are often excluded of the studies because they are not always measurable. Higgins et al. (2013) and De Pontual et al. (2000) suggested that data below the LOD could contribute meaningfully to the discrimination between sites, using the presence/absence information to discriminate sites with overlapping signatures. Therefore, we suggest improving discrimination between sources (and thus limiting the confusion between reallocation rivers) using geospatially meaningful additional ultra-trace elements to be treated in a mix of quantitative and qualitative data. An overview of the metapopulation dynamics A first step towards the spatial and temporal dynamic of the metapopulation Herein, we developed a method allowing the estimation of flux between basins. We identified sources and sinks, river contributions and homing rates. However, because of missing otolith datasets before 2008, we excluded the first period of the analysis. Consequently, we cannot draw conclusions about the temporal dynamic of exchanges between watersheds. Though, the introduction of a temporal dynamic within this study would have been particularly valuable, especially to understand temporal trends of homing in large catchments such as the Garonne and Dordogne populations. Focusing on the second period, we analysed spatial exchanges by multiplying probabilities of origin with abundance indices. For numerous indicators and rivers, large credibility intervals were found and resulted from the product of two estimates with large credibility intervals. Probabilities were uncertain because of low number of adult and baseline samples and low discrimination between rivers, whereas large credibility intervals of abundance indices were due to incomplete and various monitoring of shads populations. Future samplings would likely improve our statements about the metapopulation dynamics, reducing credibility intervals. Despite these limitations, this study proposed a simple method which provided an overview of the metapopulation dynamics. We especially found that Allis shad populations are relatively connected, at least at the watershed scale, a result which differed from the current view that supposed strong natal homing in this species (Tomas et al., 2005; Alexandrino et al., 2006; Jolly et al., 2012; Martin et al., 2015). Identifications of sources and sinks: implication for management Despite large credibility intervals, our results suggested that some rivers were sinks and did not contribute significantly to the total number of spawners in the metapopulation. Such a result could indicate that spawning grounds are of poor quality or hardly accessible, or that juvenile survival is low, a hypothesis that deserves interest, at least for Garonne river case. Most spawners entering the Garonne river were born in the Dordogne river confirming previous results of Tomas et al. (2005), and to a minor extent from the Adour river. This tended to show that, what was thought to be the largest population in the Western Europe was in fact mainly due to the attraction of a large number of strayers from the Dordogne and Adour rivers. As explained by Schtickzelle and Quinn, (2007), the question of metapopulation dynamics in anadromous fish is not well studied. Nevertheless, the metapopulation dynamic is of interest to management through the prioritization of watershed conservation, restoration and fisheries regulation. Using a simple method, we estimated fluxes and found that the Allis shad metapopulation probably satisfy to the source-sink metapopulation concept. If confirmed by further studies, such functioning may support management prioritizing actions in the most productive rivers and if possible, restoration (e.g. spawning habitat, connectivity) on sinks. Despite an incomplete sampling scheme, our study provided an overview of the metapopulation functioning and we think that this method could be applied to other anadromous species with conservation concerns, especially when water and otolith samples are readily accessible. Acknowledgements We are also grateful to fishermen P. Boisneau and D. Macé for adult samples from Loire and Vilaine Rivers respectively. Additionally, we thank E. Rivot, E. Reveillac and M. Nevoux for fruitful discussions. Finally, we are grateful to the Editor D. Secor and reviewers, including K. Limburg, for their relevant remarks and advice that largely improved the quality of this work. Funding This study was funded by IRSTEA (Institut national de Recherche en Sciences et Technologies pour l’Environnement et l’Agriculture) and was included in the Shad’eau programme co-funded by Agence de l’Eau Adour Garonne and Nouvelle Aquitaine Region. 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ICES Journal of Marine ScienceOxford University Press

Published: Jan 1, 2018

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