Connectivity modelling informs metapopulation structure and conservation priorities for a reef‐building species

In coastal marine systems, biogenic reef‐building species have great importance for conservation as they provide habitat for a wide range of species, promoting biodiversity, ecosystem functioning and services. Biogenic reef persistence and recovery from perturbations depend on recolonization by new recruits. Characterizing larval dispersal among distant reefs is key to understanding how connectivity shapes metapopulation structure and determines network coherence; all of which are of critical importance for effective conservation.


| INTRODUC TI ON
Our oceans and coastal seas are fundamentally changing. Increased concentrations of atmospheric greenhouse gases are raising sea surface temperatures and changing ocean circulation patterns (Shin & Alexander, 2020;van Gennip et al., 2017), while the introduction of artificial barriers is further altering pathways to dispersal, contributing to large-scale loss and fragmentation of marine habitats (Bishop et al., 2017;Firth et al., 2016). Increasingly, conservation efforts like Marine Protected Areas (MPAs) are considered necessary to counteract the negative effects of environmental change and anthropogenic activities on marine life (Bunn et al., 2000;Treml et al., 2008).
However, our understanding of how habitat loss and fragmentation disrupt the connectivity corridors among MPAs, that are fundamental to the maintenance and persistence of existing biodiversity and marine communities, remains largely unexplored.
In marine systems, the production and dispersal of planktonic early life-history stages is a key determinant of spatial organization of species across local and seascape scales (James et al., 2019).
Ensuring connectivity is argued to be one solution to biodiversity loss and a key tenet of sustainable ecological networks (Gonzalez et al., 2017). The dispersive larval stage is particularly important as it contributes to local population persistence through self-recruitment (Cowen & Sponaugle, 2009;Paris et al., 2007;Pineda et al., 2010) and resilience to disturbance via re-colonization (Burgess et al., 2014).
Studying this dispersive stage provides a means to understand population connectivity, defined as the exchange of individuals among distinct populations (Cowen & Sponaugle, 2009). This exchange of individuals is fundamental to the structural connectedness of a network of otherwise isolated populations (sensu, a metapopulation), and is considered critical to our understanding of metapopulation structure and dynamics Jones et al., 2007).
Networks of marine populations that are constrained by natural topography, such as coastline configuration, can be more or less linearly connected, imparting higher importance to some sites over others (Kininmonth et al., 2010;Urban & Keitt, 2001;Watson et al., 2011). Understanding connectivity in such networks helps to identify key populations that contribute more than others to overall network functioning and coherence (Bodin & Saura, 2010;Urban et al., 2009), and in the setting of conservation priorities (Hastings & Botsford, 2006). The notion of network coherence in particular refers to the deviation from consensus, or how robust the network structure is in the presence of stochastic disturbances (Patterson & Bamieh, 2014). There are several tools available for estimating marine connectivity, and describe the structure of metapopulation networks. Physical tags such as radio or satellite trackers can be used to directly measure connectivity (Le Bris et al., 2013), but these are not feasible for small organisms such as larvae or plant propagules.
Alternatively, indirect measures such as molecular tools can be used to infer gene flow and migration rates (Gaggiotti et al., 2004;Liggins et al., 2013), or coupled biological and hydrodynamic (biophysical) models can be used to predict dispersal of particles (North et al., 2009;van Sebille et al., 2018). Recently, biophysical models have been used extensively to estimate connectivity in fish and benthic invertebrate populations, and test hypotheses related to the effects of pelagic larval duration Treml et al., 2012), dispersal distance (Cowen et al., 2006;Shanks et al., 2003), or larval swimming behaviour (James et al., 2019) on propagule dispersal by ocean currents (Knights et al., 2006;Nicolle et al., 2017).
In coastal marine systems, animal ecosystem engineers like corals, bivalves and polychaetes constitute important biogenic reef habitats for conservation and have long been recognized for the ecosystem services that they provide (Beck et al., 2011;Dubois et al., 2006;Lemasson et al., 2017). The biodiversity associated with biogenic reef habitats is often higher than the surrounding environment and can vary with the evolution and ecological status of these habitats (Dubois et al., 2002;Jones et al., 2018). Despite their important role in ecosystem structure and functioning, biogenic reef habitats are considered among the most threatened globally (Beck et al., 2011;Chaverra et al., 2019) and their effective protection requires an in-depth understanding of their population dynamics, connectivity and ecology (Knights et al., 2014;Piet et al., 2015).
In Europe, the polychaete Sabellaria alveolata (L.) is an important intertidal reef-builder along the Atlantic coast of Europe, extending from Ireland to Mauritania (Curd et al., 2020). The French coast supports the largest reefs in Europe; extending >100 ha and >1.5 m height in Mont-Saint-Michel Bay, (Noernberg et al., 2010). S. alveolata has a biphasic life cycle with sessile adults, and a planktonic dispersive larval phase (Dubois et al., 2007;Wilson, 1970). While spawning can occur throughout the year, two main peaks are typically observed; in late spring (around May) and late summer (around September) (Curd et al., 2021;Dubois et al., 2007). This species can be locally common but may undergo localized extirpation following natural and anthropogenic perturbations (Dubois et al., 2002(Dubois et al., , 2006Firth et al., 2015Firth et al., , 2021bPlicanti et al., 2016) Despite the importance of conservation and protection afforded to S. alveolata by European legislation, the reefs are classed as datadeficient habitats in many regions (e.g., Bertocci et al., 2017;Firth et al., 2021a), and the number of recorded observations of this species remains limited (Curd et al., 2020). The status monitoring is lacking over the entire distribution and there is little known about how discrete reefs might function and persist as a regional entity through connectivity. Given that current alterations in environmental K E Y W O R D S betweenness centrality, graph theory, habitat fragmentation, hydrodynamic modelling, larval dispersal, network analysis, resilience conditions and anthropogenic stressors pose threats to S. alveolata (Firth et al., 2021b;Plicanti et al., 2016), a better understanding of the distribution and, importantly, connectivity of this species is needed. Such information will shed light on metapopulation (i.e., network of interconnected populations) functioning and resilience to disturbance, and will pinpoint areas for conservation prioritization. Here, we used a biophysical transport model to simulate largescale dispersal of larval S. alveolata on the Atlantic coast of France.
We synthesized multi-year larval dispersal events into a structural network to: (1) describe connectedness across the reefs network, (2) test the resilience of the network to perturbation, allowing the stability of the regional S. alveolata metapopulation and its potential for fragmentation to be assessed, and (3) identify populations of local and regional importance to network structure and coherence. The outcome of integrated dispersal modelling and network analysis will provide a baseline framework for the effective regional management of this important habitat.

| ME THODS
Here, we combined hydrodynamic modelling and graph theory to assess regional connectivity and to identify local zones that were either key to maintaining network coherence or were at high risk of becoming isolated, therefore constituting protection priorities. The general approach was to use a hydrodynamic ocean model with a transport module to simulate dispersal of larval S. alveolata on the French Atlantic and Western English Channel (hereafter Atlantic and Channel) coasts (Figure 1a, inset c). This region represents the core of S. alveolata distribution and supports the largest known reefs.
Moreover, this region encompasses the only reefs that are regularly monitored, therefore providing the necessary baseline information on reef status and occupancy to support a study such as ours.
Understanding connectivity among these reefs and their resilience will be of critical importance for extending our understanding of this species, particularly in regions that are data poor. Network analysis was then used to integrate seasonal and annual dispersal events among coastal zones with reefs. We selected two network metrics to characterize the network structure, and two operations to evaluate changes in the network, e.g., the fragmentation potential. We further compared scenarios of reef loss, whose selection criterion could be used as effective conservative strategies.

| The hydrodynamic ocean model
The hydrodynamic conditions on the Atlantic and Channel coasts were simulated using the fully validated ocean model MARS3D (Model for Application at Regional Scale; https://mars3d.ifrem er.fr/docs/docum entat ion.html) (Lazure et al., 2009;Lazure & Dumas, 2008) with the configuration MANGA2500. The model domain extends between 41°N and 55°N latitude and 5°E to 16°W longitude. The regular numerical grid has a 2.5 km horizontal resolution and 40 sigma vertical layers. Open boundaries and initial conditions were provided by the larger-scale model Mercator with a resolution of 0.0833°. Hourly atmospheric forcing was provided by the Meteo-France ARPEGE HR model with a 0.1° spatial resolution.
River discharge values, including Garonne, Vilaine and Loire rivers, were obtained from time series at daily frequencies provided by the French freshwater office database (http://www.hydro.eaufr ance.fr).
Oceanic circulation over the Atlantic shelf is predominantly poleward, and follows the shelf topography with an average speed of 3 cm s −1 (Le Boyer et al., 2013). Atlantic coastal circulation is driven by tides, dynamic winds and density currents from river outflows (Koutsikopoulos & Le Cann, 1996), while the Channel circulation is dominated by strong tidal currents (Salomon & Breton, 1993).
Where the Atlantic and Channel meet, the water circulation forms a biogeographic border between the temperate and cold-temperate provinces ( Figure 1a) (Spalding et al., 2007). Here, the Ushant Sea, at the western tip of the French coast, is characterized by strong thermal fronts, particularly during spring-summer, acting as a barrier to dispersal (Kelly-Gerreyn et al., 2006).
In addition to simulating oceanographic conditions along the northeast Atlantic shelf, MARS3D has previously been coupled with a pelagic ecosystem model, ECO-MARS3D, developed and validated against historical data (Ménesguen et al., 2019), and was also used to investigate the dispersal of fish and benthic invertebrate larvae coupled with a Lagrangian (Ayata et al., 2010;Huret et al., 2010) and an Eulerian transport model (Ayata et al., 2009).

| Transport module
We used a Eulerian approach to simulate larval dispersal by tracking concentration of suspended particles. Specifically, we used the transport module of the ocean model MARS3D, which was run online with an adaptative time step of ~135 s. Larval dispersal was calculated by solving an advection-diffusion equation, spatially centred using an Arakawa G-grid. Given the regional scale of the study and variability in diffusion terms along the coast, here, we ignored horizontal diffusion, thus focusing on the strength of advection in defining dispersal patterns (Largier, 2003). When the water depth was <1 m, particles were advected in 2-D. Concentrations of particles remained conservative over the model domain, with no behaviour implemented at the top, bottom and coastal boundaries. The offshore boundary was absorbing particles, but because of the spatial extent of the model, no particle ever reached that boundary. Since the present study focuses on the large-scale dispersal patterns and not on estimating absolute numbers of larval exchanges, the choice was made to consider particles as passive with no mortality rate included. Passive larval transport for a species-specific planktonic larval duration (PLD), for example, was found to be the dominant driver of gene flow (Padrón et al., 2018). Simulating dispersal of S. alveolata larvae in the western English Channel, Ayata et al. (2009) found that the number of settled larvae was inversely proportional to mortality rate (tested values ranged from 0 to 0.36 day −1 ), but the dispersal patterns and settlement dynamics were not altered. Nevertheless, we acknowledge the potential overestimation of connectivity levels by transport models, especially when mortality or vertical behaviour of larvae is not included (Manel et al., 2019;Paris et al., 2007).
Setting the mortality coefficient to zero in transport models has the advantage of preserving potential, yet rare, dispersal events, while later back-calculating dispersal probabilities that include mortality can lead to exploring the more likely dispersal connections and pathways (Treml et al., 2008). Similar simplifications were considered in other studies on larval dispersal when the focus was on large-scale patterns (Álvarez-Noriega et al., 2020;Andrello et al., 2013) or on rare dispersal events (Treml et al., 2008).
Model outputs from the ocean and transport model, containing particles concentrations over the MARS3D model domain, were saved as netCDF files. The netCDF files were further analysed with the R software as follows. A 30 km × 30 km horizontal grid was overlaid onto the MARS3D model grid to aggregate coastline ocean model cells into larger regional 'zones' covering the entire French Atlantic and Channel coastline (without a priori knowledge about reef occurrence and status within each zone) ( Figure 1a, inset d). One zone grouped in average 21 MARS3D model cells of 2.5 km × 2.5 km. The choice to aggregate model cells into larger zones was made in the attempt to get an overview of the broad-scale connectivity potential over the entire coast, as seen in other studies (Boschetti et al., 2020;Boulanger et al., 2020;Holstein et al., 2014). Our choice was based on the knowledge that large-scale oceanographic processes constrain small-scale processes, and thus are those that affect whether larvae are supplied near settlement sites (Pineda, 2000). We found the size of the coastal zones in our simulations to be representative of the dispersal kernel of S. alveolata larvae, which should be larger than the mean dispersal distance (Palumbi, 2003). In our simulations, larvae were transported over more than two adjacent zones at a time with no apparent overestimation in local retention, which could be indicative of too large zones (see Figure S1 in Appendix S1). Of the 60 zones covering the French F I G U R E 1 Study area located on the western coast of Europe (a, inset c). Coloured segments delineate distinct regional zones on the French Atlantic and Channel coastline considered to simulate hydrodynamic connectivity (a). The zones were delineated using a 30 km grid in which ocean model cells adjacent to coastline (indicated with coloured points in inset d) were pooled by individual zones. Among all the zones delineated along the coastline, only those containing S. alveolata reefs (numbered from 1 in the north to 31 in the south) were retained to analyse connectivity (b). Reef quality in each zone was characterized by Curd et al. (2020) using a semi-quantitative score (i.e., 0.25; 0.5; 0.75 or 1, as shown by bullet sizes). Arrows symbolize general ocean circulation patterns in the Bay of Biscay and the English Channel (after Ayata et al., 2010, based on Salomon & Breton, 1993, and Koutsikopoulos & Le Cann, 1996 Atlantic and Channel coastline, only 31 contain recorded observations of S. alveolata reefs, and were considered ecologically relevant for the connectivity simulations ( Figure 1b). Our choice of grid size reflects the best consensus we found between computational resources and the spatial scale and frequency of recorded observations of the species.
Even with increased computational efforts due to higher-resolution modelling, a delineation of smaller zones would not have been feasible for our study for the simple reason that we lack the information on reef status and occupation in smaller grid cells. In the most comprehensive S. alveolata database (Curd et al., 2020), all known historical and contemporary records of the species presence and qualitative abundance were also polled into cells of 50 km (see figure at https://www.seanoe. org/data/00610/ 72164/) to provide an overview over the entire distribution domain of this species.
Simulations were initialized with particle concentrations of 10 6 m −2 in the bottom layer of the model, assuming that homogenous densities of larvae are released from the seabed. Similar larval concentrations were estimated to be released by reefs in the Channel (Ayata et al., 2009), however, since we used relative connectivity rates throughout this study the effect of initial particle concentra- This assured a better representation of large-scale advection processes over the study area (Largier, 2003), however, without making any inference on settlement dynamics where smaller-scale processes and larval behaviour prevail (Pineda et al., 2010).

| Hydrodynamic connectivity
At the end of each simulation, particle concentrations (labelled by the release or source zone) in each of the 31 geographic zones containing reefs were used to estimate connectivity patterns through three matrices as follows: (1) a connectivity matrix C, whose elements c ij represent the relative concentration of particles released in zone i found at the end of simulation in zone j; the diagonal, formed by the elements c ii , represents the relative concentration of particles released in zone i found at the end of simulation in the same zone i, referred to as local retention; (2) an adjacent matrix A, derived from the connectivity matrix C based on a threshold (see Section on Network metrics and operations, link thresholding, for details), whose elements a ij have values of 0 if c ij < threshold, or 1 if c ij ≥ threshold, corresponding to absence (0) or presence (1)  to be mentioned that throughout the paper we are referring to larval dispersal, defined as the spread of larvae from a source area to a settlement site (considering only the start and end location), contrary to larval transport, which is longer than dispersal and follow the movement of larvae with ocean currents . Therefore, we found the linear geographic distance to be representative in our case for larval dispersal estimates. This choice is also in line with the Eulerian transport used to estimate dispersal.

| Graphical representation of network connectivity
Graph theory (sensu Barabási, 2016) was used to explore patterns of connectivity in the network of reefs, identify zones with reefs of importance to network coherence, and indicate zones of concern or conservation priority. A 'graph' is the visual representation of a network of nodes connected by links, with each link l ij connecting two nodes n i and n j (Barabási, 2016;Urban & Keitt, 2001). In addition to direct links, there can be multiple ways to go from a node i to a node j (called 'paths'), passing by other nodes. The length of a path from n i to n j can be measured by the number of links connecting the two nodes or the sum of their weights. Here, the nodes represent the coastal zones and were defined geographically using the spatial centroid of each zone (1-31; Figure 1b). Each node was weighted by a semi-quantitative score attributed to each zone, which was defined on expert knowl-

| Network metrics and operations
While there is a variety of metrics used in network analysis ( namely, link thresholding and node deletion (Urban & Keitt, 2001).
Link thresholding explores how the sequential constraining of links above a predetermined threshold alters the scale of connectivity and structure of the network (Treml et al., 2008). The threshold can be ecologically interpreted as the minimum relative flux of larvae required to effectively connect two distant sub-populations, and can be used to rescale connectivity (Cowen et al., 2006;Samsing et al., 2019;Treml et al., 2012). Below the threshold, larval flux is considered marginal, and the two sub-populations disconnected.
As the threshold increases, the network gets fragmented into disconnected subgraphs (or components). It should be kept in mind that while this exercise will not reveal the exact levels of connectivity, it will allow a dynamic exploration of connectivity patterns and network coherence in absence of meaningful biological information. First, the network was built using the connectivity matrix C for linkage weights. Links were deleted from the network by iteratively increasing the threshold from zero (or no threshold applied in this case), which maintains all zones connected as a single component across all simulated spawning events, up to 7%, which results in each zone becoming an isolated or disconnected component ( Figure S2). 1. Random deletion: nodes were randomly selected for each deletion event. For each sequential deletion (N = 30), a bootstrap approach was used to test for the effect of selecting a different node for deletion at each step. For each step, 125 permutations (a total of 30 × 125 = 3750 simulations) were run allowing mean metric estimates to be generated; 2. Low betweenness centrality: nodes were deleted starting with the smallest values in betweenness centrality metric BC i (Freeman, 1977). BC i measures the proportion of shortest paths p between any two nodes that pass through a focal node i. The shortest or fastest path p jk between two nodes j and k, here is the shortest distance (sum of linkages weight defined by the geographic linear distance in km, as in matrix D). The shortest path p jk was found using the Dijkstra's shortest path first algorithm in the directed and weighted graph (West, 1996). It is important to note that BC metric does not consider the number of direct paths, or links, of a node i in the graph, which represents the number of connections, nor the local retention c ii , which represents a loop in the graph; Saved model outputs (netCDF files) from the ocean and transport model underwent post-processing in R, version 3.5.0 (R Core Team, 2020), specifically the particle concentrations in the coastal zones were extracted at the end of each run and connectivity matrices calculated. All network calculations and statistical analyses were undertaken using the igraph package (Csardi & Nepusz, 2006). Zone mapping was performed using ArcGIS version 10.6.1 (ESRI).

| Link thresholding
The number of components in the network predictably increased  Figures 2, 3 and S3).
Comparison of linkage probabilities over all simulated spawning events between two thresholds confirms that at a threshold of 0.01% all zones are strongly connected into one compact network with medium to high probability. At a threshold of 0.5%, the network became fragmented into four components with low linkage probability among them (Figure 3 and S3). The absolute numbers of dispersing larvae and settlers are dependent on the production levels of local reefs, unknown for most S. alveolata reefs. Nevertheless, assessing relative connectivity potential (regardless of local spawning potential, as here we assumed homogeneous release of larvae) holds meaningful biological interpretation as these results strongly concur with the genetic structure of S. alveolata reefs. Nunes et al. (2021) showed that reefs along the Bay of Biscay and the English Channel were well connected within each region, but only little exchange seems to occur between the two regions. Hence, the genetic structure reflects a cut-off connectivity threshold resting between 0.01% and 0.5% for all PLDs tested of 3w, 4w or 6w. It should be noted that the threshold range found here meaningful remains descriptive for generic simulations of potential connectivity without larval behaviour, mortality or settlement rates. An attempt in applying a mortality rate of 0.09 day −1 to dispersing larvae, as used by Ayata et al. (2009), would imply a daily exponential decrease in particle concentrations, resulting by the end of simulations to a remaining fraction of 0.15, 0.08 and 0.02 of the initial concentrations after 3w, 4w and 6w dispersal, respectively. In this case, the same fraction would reflect in a lower threshold inducing network fragmentation. Nevertheless, higher accumulated mortality over longer PLD would result in leveraging the differences in connectivity patterns resulted from various PLD by removing the longer and rare dispersal events.

| Node deletion
Among all scenarios, sequential deletion of zones starting with the high betweenness centrality (highBC) had the biggest impact on network fragmentation (Figures 4 and S4), hence those zones have the greatest influence on network structure and coherence.
Taking the example of 4w PLD, which is a common PLD for this species (Dubois et al., 2007), the network fragmented into two disconnected components after just 5 node deletions. Deleting 10 (33%) nodes fragmented the original network into four components, with the largest component connecting ~1/3rd of all nodes.
Sequential deletion of nodes based on reef size (smallest to largest reefs and vice versa) or random deletion of nodes were comparable ( Figure 4). The same fragmentation patterns were obvious when 3w and 6w PLDs were tested, with slight variations in the magnitude of fragmentation ( Figure S4). Nevertheless, by far, the nodes with highBC stand out as a meaningful criterion that needs to be considered in maintaining a connected network. Using a different threshold might shift the timing of fragmentation (equivalent here to the number of nodes deleted), but highBC would remain the most meaningful criterion among those (scenarios) tested here. The network retained its greatest coherence (i.e., as a single component) when sequentially deleting the lowBC nodes first (Figures 4 and S4). Because lowBC nodes are peripheral, their deletion did not fragment the network into disconnected components but rather gradually decreased the size of the largest component ( Figure 4b). On the other hand, selecting the zones with the largest reefs for protection, which in general are considered the best source of larvae due to larger reproductive output, is not key in maintaining this network connected; nor is protecting the smallest reefs, assuming those are at risk of extension. Indeed, adding more biological aspects to simulations, such as accurate estimations of reproductive output (or number of larvae released), mortality or settlement success rates, would increase the realism of simulations, but we remain confident that our key findings will not be altered.

| DISCUSS ION
We used a biophysical model to simulate relative larval dispersal and assess connectivity potential among S. alveolata reefs along the French Atlantic and the Western English Channel coastline.
Our results revealed a network of highly intra-connected reef F I G U R E 2 Change in network metrics number of components (Nbc; panels a, d, g) and relative size of the largest component (Size; panels b, e, h), under different connectivity thresholds (%). Data are pooled across all simulated spawning events with a pelagic larval duration of 3 (first row, panels a, b, c), 4 (second row, panels d, e, f) and 6 weeks (third row, panels g, h, j), and boxplots display median, 25% and 75% quantiles, and outliers. (c, f, j) Estimated mean change in network metrics (Nbc: Dashed blue line, Size: Solid orange line) are shown as a function of connectivity threshold values increasing from 0.01% (which implies that all zones are connected as a single component) to 0.5% (which implies that the network is fragmented into four components); mean values represent a subset of data highlighted with the blue (in panels a, d, g) and orange (in panels b, e, h) rectangles clusters linked through sporadic dispersal events. With limited biological features of the study species, link thresholding, an approach that in reality might reflect a reduction in the reproductive output (fecundity/patch size/quality), identified coastline locations most at risk of isolation from the wider network. On the other hand, reefs with high betweenness centrality were extremely important to network coherence and therefore should be the focus of conservation and/or protective measures to ensure metapopulation stability.

| Connectivity shapes metapopulation structure
Quantifying connectivity across seascapes, and specifically understanding how larval dispersal determines the strength and spatial structure of connectivity, is fundamental to understanding metapopulation structure (Treml et al., 2008). Our results suggest that the S. alveolata reefs along the Atlantic and English Channel coastlines of France resemble a 'small-world' network type (Watts & Strogatz, 1998) characterized by high connectivity among neighbouring zones over relatively short, linear steps. Similar network structures have been observed in coastal marine systems, including the Great Barrier Reef (Kininmonth et al., 2010) and the Southern California Bight (Watson et al., 2011), but also in other biological systems such as infectious diseases spread (Watts & Strogatz, 1998). Coastal marine populations are generally linked in a non-random fashion through larval dispersal with connectivity patterns constrained by coastline topography and oceanographic currents (Banks et al., 2007). When analysing the structure of networks, in addition to dispersal distances, connectivity strength is a key variable to be considered, varying from strong, permanent connections to weak, sporadic dispersal events among populations.
Removing the weakest links in our simulated network on the French coast through link thresholding identified two distinct levels of connectivity: (1) highly interconnected reefs forming local clusters that were robust to link thresholding, and (2) weakly-linked regional clusters more sensitive to thresholding (and hence to reduction in larval transport) that can fragment the network into a number of isolated components. Even though our modelling assumptions may possibly have overestimated connectivity strength by not considering F I G U R E 3 Network map showing the probability of a link between any two zones applying a connectivity threshold of 0.01% (a) and 0.5% (b). Probability is estimated as the presence frequency of a connection between two zones across all simulated spawning events with a pelagic larval duration of 4 weeks. The network is considered fragmented when the probability exceeds the arbitrarily set connectivity threshold (e.g., right map indicates 4 components: (1) zones 1-11; (2) zone 12; (3) zones 13-29; and (4) zones 30 and 31) mortality or settlement rates (Manel et al., 2019;Paris et al., 2007),  (Nunes et al., 2021), supporting our interpretation that the southern populations in the Bay of Biscay could be more isolated.
It should be kept in mind that genetic differentiations among S.
alveolata populations represent the realized connectivity (i.e., individuals successfully arrive in a new area and take part in reproduction), while hydrodynamic connectivity as simulated in our study represents the potential connectivity (i.e., individuals arrive in a new area but no further inference on their outcome is made) (Padrón et al., 2018).

F I G U R E 4
Change in network metrics number of components (a) and relative size of the largest component (b), following sequential node deletion. Five node deletion scenarios were tested: (1) random deletion-Random; (1) sequential deletion of low to high betweenness centrality-lowBC; (3) sequential deletion of high to low betweenness centrality-highBC; (4) sequential deletion of the smallest to the largest reef-smallReef; and (5) sequential deletion of the largest to smallest reef-largeReef. For all node deletion tests, a total of 30 deletions were performed for each simulation and metrics recalculated after each deletion. An iterative approach was undertaken for the random deletion scenario and replicated (bootstrap without replacement) 125 times. Metrics were calculated on all simulated events with a pelagic larval duration of 4 weeks based on a connectivity threshold of 0.01%. The lines represent the average values of the two metrics for the simulated spawning events (Apr-Sep, 2012-2016 (Trakhtenbrot et al., 2005), such long-distance dispersal events may be too low to influence population dynamics (Burgess et al., 2014). To capture these rare dispersal events as identified by gene flow, it is thought necessary to use multigenerational modelling that integrates stepping-stone dispersal (Jahnke et al., 2018).

| Conservation management in a network of reefs
Simulations of network fragmentation help identify populations that significantly contribute to network coherence, either as central connectivity hubs or as pivotal stepping-stones between major network components (Barabási, 2016;Estrada & Bodin, 2008;Samsing et al., 2019). Our scenarios simulating sequential loss of reefs indicated that losing reefs in the zones with highest betweenness centrality (BC) resulted in a critical fragmentation of the network by removing as few as 5 nodes (considering a PLD of 4 weeks).
Importantly, these areas located south of the Loire estuary that we identified as high BC zones, thus channelling many shortest connectivity paths between any other two reefs in the network, seemed to have been stable over the past decade, as they are colonized by some of the largest reef structures in Europe (Curd et al., 2020).
Furthermore, these reefs are characterized by the highest genetic diversity among Atlantic S. alveolata reefs-another indication of large populations (Nunes et al., 2021), and are likely to contribute to wider metapopulation persistence acting as an important source of larvae to other reefs. Habitat suitability for S. alveolata is, however, predicted to significantly decline under future climate change scenarios (Curd et al., 2021), thus conservation efforts will be of critical importance to minimize local stressors and consolidate the resilience of these key connectivity hubs against anthropogenic-and climatedriven changes.
Stepping-stone reefs are, on the other hand, key for connecting distant populations otherwise disconnected, and represent disproportionately important linking pathways among discrete network components (Boulanger et al., 2020). For instance, network analysis identified the Bay of Douarnenez population at the most north-western tip of the French Atlantic coast as pivotal in connecting Atlantic and Channel populations and maintaining S. alveolata metapopulation coherence across the French western coast. However, the stepping-stone reefs identified in Bay of Douarnenez are hydrodynamically remote from major reef clusters and hence may be more at risk of becoming isolated from external larval supply. Effective protection of such important isolated reefs will rely on local conservation initiatives to minimize local stressors (e.g., trampling, Plicanti et al., 2016), but it also requires an in-depth understanding of larval exchange and local to regional hydrodynamics, so that networks can function in a way that sustains a combination of local reefs as well as connectivity paths among more distant reefs (Botsford et al., 2001;Cowen et al., 2007;Jones et al., 2007). As it can identify local zones that are critical to network coherence, betweenness centrality proves a relevant criterion to prevent network fragmentation in an effort to maintaining connectivity and biodiversity (Andrello et al., 2013;Estrada & Bodin, 2008;Holstein et al., 2014). Conversely, betweenness centrality proves just as relevant to induce network fragmentation, when spread of invasive species or parasites needs to be contained (Kölzsch & Blasius, 2011;Samsing et al., 2019). Either way, when network connectivity is at stake, betweenness centrality should therefore be considered by managers and decision makers in conservation and spatial planning.

| Adopting network analysis in conservation practice
Here, using a species of ecological and conservation importance, we have shown how combining hydrodynamic modelling and network analysis can be used to assess metapopulation structure and inform conservation management. In the first instance, the results represent an important yet previously overlooked first step in describing connectivity pathways among discrete populations of this protected species. This analysis can be relatively easily achieved using similar open-source modelling tools (van Sebille et al., 2018), established graph (network) packages (e.g., igraph), and bio-physical data describing the species and region of interest.
Second, using basic network metrics and analyses, we identified reefs that are key to metapopulation functioning as contributing to larval/recruitment pool and network coherence. The combination of larval dispersal modelling and network analysis can therefore be used to identify reefs for protection, monitoring or management interventions that are critical for network coherence, and to maintain large-scale connectivity. We argue that this approach alone is invaluable for describing connectivity pathways and network functioning with limited biological information. Further developments to integrate this connectivity modelling within a framework that also accounts for other population processes, such as recruitment timing and local population abundance, survivorship and fecundity, are nevertheless essential to further resolve different aspects of network structure as well as long-term metapopulation dynamics and persistence.

ACK N OWLED G EM ENTS
This work is part of the REEHAB (REEf HABitat) project (www.

CO N FLI C T O F I NTE R E S T
The authors declare no competing interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
All input data and R code for data analysis are available on GitHub at https://github.com/cld32 1/conne ct_MARS3D.

PEER R E V I E W
The peer review history for this article is available at https://publo ns.com/publo n/10.1111/ddi.13596.