In this study, we developed a novel application of network analysis to the study of hybridization phenomena between sister species. Networks were constructed based on distinct genetic distances (RD and SAD), differently sensitive to time since divergence (respectively based on allele lengths or on shared alleles), allowing the comparison of the divergence degree at different time-scales.
The first important picture obtained on network built with Rozenfeld Distance (RD) is the straightforward recognition of two well-defined clusters of F. vesiculosus and F. spiralis (Figure 1). This confirms that reproductive isolation and genetic divergence is rather advanced between those two species, despite a significant amount of shared polymorphism. Thus this multi-locus phylogenetic distance may be used to assign individuals to their species of origin. This result also supports the existence of phylogenetic information from microsatellite loci  which is accurately delivered by RD.
The second important result is the occurrence of clusters of individuals exhibiting an intermediate position between both species and maintaining a connection between some F. vesiculosus populations and the F. spiralis cluster as revealed on the SAD network (Figures 2 and 3). This intermediate cluster is formed by tens of individuals, among which those pointed out as intermediate with the RD. In case of the shared polymorphism being mostly ancestral, one may expect to observe some connections anywhere in the distribution range including in allopatric zones, but these F. vesiculosus individuals of intermediate genotypes are only detected in the Northwest Iberia, located specifically at the edge of the locations where both species occur in sympatry. Interestingly, intermediate individuals, although much less numerous, also emerge in two other sympatric areas: Northeastern America and the English Channel, whereas no such individuals are observed in any of the allopatric zones, further supporting the hybridization hypothesis. The SAD distance integrates more recent history, therefore giving it more weight than the RD, which takes into account phylogenetic divergence [19, 38]. It is therefore likely to better reflect present day exchange of genes between the two species. Those intermediate individuals that did cluster with the main F. vesiculosus cluster with RD, with SAD do now connect closer to F. spiralis than to the other con-specifics. This is likely caused by these individuals sharing more alleles with F. spiralis than with the other F. vesiculosus (therefore the branching with SAD distance), but the alleles they do not share with F. spiralis exhibit a strong divergence with this last species and are typical from F. vesiculosus (therefore the clustering of those individuals with F. vesiculosus with RD). The occurrence of all those individuals in the sympatric zone supports these intermediate genotypes as the product of present day hybridization between anciently diverged lineages/species.
The four additional networks built including simulated synthetic hybrids from F1, as well as backcrosses with each of the mother species (Figure 3), confirm this scenario. Indeed, the synthetic hybrids are present at the interface of the two sister-species, although they tend to be more isolated than most of the natural putative hybrids. This isolation seems due to the F1 nature of synthetic hybrids, truly half F. spiralis/half F. vesiculosus, while naturally occurring hybrids may be the product of backcrosses. When the backcrosses are plugged into the network, all possible backcrosses do not lead to a convergence towards the initial topology based on real data only. The admixture of (F1 X F. spiralis) and (F1 X F. vesiculosus) in the same dataset show the most similar network topology to the original one, while backcrosses resulting from (F1 X F. spiralis) or (F1 X F. vesiculosus) plugged alone tend to cluster closer to their species of origin without fitting exactly the same position as the natural intermediates.
The use of network here provides specific advantages, mainly the ability to identify agents (nodes) connecting identified clusters through genetic distance (links). Hybridization indeed usually results in a reticulate tree that cannot be built with classical phylogenetic methods but can be easily grasped on a network. Moreover, the possibility to follow the evolution of network topology through a gradient of genetic distance threshold helps to visualize and understand the attachment preferences to one or the other of the species clusters.
The use of STRUCTURE also illustrates the clear separation between the two species and allows the identification of admixed individuals, although not systematically the same as the intermediate agents appearing on the networks. In order to test for the accuracy of each method in those doubtful cases, the discrepancies between results obtained with both methods can be considered in perspective with geographical locations and ecological conditions in which intermediate agents (network) do not appear as admixed individuals (STRUCTURE), or the other way round. Interestingly, intermediate agents unidentified by STRUCTURE as admixed individuals correspond to samples collected at the edge of the zone where the two species occur in sympatry, Northwest Iberia. On the contrary, the admixed individuals detected by STRUCTURE that do not appear as intermediate agents were collected in the allopatric zone, thereby rendering enigmatic the origin of such admixture.
When analyzing the accuracy of both methods with synthetic hybrids and backcrosses, STRUCTURE shows high reliability in detecting F1 hybrids (100%), whereas only 71% of those are emphasized by an intermediate position on network. The detection of mixed individuals with STRUCTURE logically decreases to 92% for backcrosses with F. spiralis and to 64% for backcrosses with F. vesiculosus. This difference between the two species can be explained by the lower genetic diversity of F_spi, likely due to its reproductive mode, as illustrated by their GDS (see Figure A6 in additional file 7), resulting in an easier detection of the insertion of new alleles in the genetic pool. On the opposite, network analysis, by relying on shared links, shows backcrosses with F_spi having a stronger assimilation to its species of origin than backcrosses with F_ves. The integration of backcross events into the species gene pool seems to be rapid and renders them hard to identify. As a synthesis, both approaches appear as complementary, as STRUCTURE may perform slightly better in the systematic detection of admixed individuals, an advantage however balanced by a lower amount of misleading detection of hybrids (i.e. type I errors) obtained with network analysis. Besides, network analysis allows further screening of links and connections among geographic areas to describe patterns of spatial connectivity.
At the within species scale, finally, network analysis revealed two main genetically distinct clusters across the distributional range of both sister species F. spiralis and F. vesiculosus, (a) a Southern cluster in South Portugal, Morocco, Azores and Canary Islands, and (b) and a Northern cluster in North America, North Sea and Channel (see Figures A2 B and A4 B in additional files 2 and 4). These two regions are common to both species indicating a similar evolutionary history. Indeed, oscillations of climate during the past thousands of years have caused repeated geographic distributional shifts and extinction/recolonization events often experienced by many marine taxa. During the Last Glacial Maximum (LGM, 23-18 ka) in Europe, permafrost extended south at 47° N , leaving temperate species to shift their distribution to potential refugia. Marine species, including intertidal taxa, are also thought to have been displaced to small refugia in the North around the British Isles, Norway or in the Brittany region and more Southerly from the Iberian Peninsula to Mauritania . As the ice melted, species ranges were able to expand back to previous latitudes [42, 43]. On the North American Coast, the LGM may have covered by ice the complete hard substrate available there  and have caused the extinction of rocky shore species in this region. North American rocky shores are thought to have later been recolonized by European populations . For species in the genus Fucus, glacial refugia have been inferred along the Brittany area for F. serratus  or along Northwest Iberia for F. ceranoides  and F. vesiculosus along the American coast shows a genetic signature of a recent recolonization from Europe . In F. spiralis and F. vesiculosus, clustering on our networks is consistent with the presence of two refuge areas in Europe, possibly a Northern refuge (possibly along the Brittany or North Iberian region) and a southern one (possibly located along the southern Iberian Peninsula and/or North Africa). These inferences are thus consistent with a recent mitochondrial phylogeography of these two species for F. spiralis but are contradictory for F. vesiculosus, as the mitochondrial genome of F. vesiculosus supports a single refugial zone . Organelle genomes, with smaller effective population size than nuclear ones, are however more prone to being highly affected by introgressive sweeps, and indeed introgression and massive expansion of F. vesiculosus organelles into other Fucus species has been documented [32, 46]. Isolation into distinct glacial refugia would have been followed by a post-glacial expansion during which the Northern and Southern populations might have converged in a contact region along Northwest Iberia (Northern Portugal/Northwestern Spain) where despite hybridization genetic differentiation is still maintained nowadays (see Figures A2 B and A4 B in additional files 2 and 4) and which now also extends into the Brittany region [29, 30, 32], although in regions not included in our sampling. In the southern region, F. spiralis occurs only on the open coast whereas F. vesiculosus is present only in isolated sheltered areas such as estuaries and coastal lagoons . Consequently, along the broad areas of sympatry of their Northern distribution, the two sister species can hybridize [33, 34, 49], whereas in Southern Europe, their distribution is allopatric and hybridization is highly unlikely due to the limited dispersal capability of their gametes .
A more complex pattern appears on the networks in Northwest Iberia area (Figure 2). The Northwest Iberian close connection to the Northern cluster (North Sea and Channel) indicates a recent secondary expansion either from North Iberia into the Northern region or vice versa, having kept restricted gene flow with the southern clusters.
Another interesting point is the fact that hybrids are mostly localized in the Southern limit of the sympatric zone, where it contacts the allopatric zone ranging from Southern Portugal-Northwestern Africa and Atlantic islands. Hybridization may be favored by unknown factors in this area, such as the rate of hybrid fertility that may change between geographical locations, possibly being higher in Northwest Iberia area as suggest by Billard et al. . Also, reinforcement may be weak due to the recent gene flow from an allopatric zone where it would be lacking, whereas in the middle of the sympatric zone such mechanism would already have developed to maintain species integrity. This is further supported by the peculiar position and clustering of the individuals from the extreme edge of the sympatric zone in Mindelo, where more than half intermediate individuals were detected on the network, and which is the only sympatric population of F. spiralis clustering with the allopatric ones with Structure (k = 3; see Figure A7 in additional file 8). These results are in agreement with a recent multi-gene phylogeny of these species that reveals that in Northwest Iberia F. spiralis from southern origins become extremely introgressed .