Introduction
Reconstructing the evolutionary history of a species is a challenging exercise only partially eased by the growing size of genetic data available. However, larger amounts of data will indeed provide more precision but not more accuracy if the model(s) chosen to infer demographic parameters is distant from the true one. Species are dynamic entities whose geographic range has often changed in time trough range expansions, contractions and shifts (Arenas, Ray, Currat, & Excoffier, 2012; Excoffier, Foll, & Petit, 2009; Mona, Ray, Arenas, & Excoffier, 2014). This suggests that species are most likely organized in meta-populations (i.e. groups of demes or sub-populations exchanging migrants to some extent), even though the more vagile ones might be panmictic at a large scale (Corrigan et al., 2018; Karl et al., 2010). Neglecting the meta-population structure (i.e., performing demographic inferences under unstructured models) may lead to spurious inference of population size change (Chikhi, Sousa, Luisi, Goossens, & Beaumont, 2010; Maisano Delser et al., 2019, 2016; Olivier Mazet, Rodríguez, & Chikhi, 2015), which is particularly worrisome for species of conservation concern. Unfortunately, the link between the inferred temporal trajectory of Ne and the real demographic history of the meta-population remains largely under explored. However, the role of connectivity, particularly the number of migrants Nm exchanged each generation and the migration matrix, has been put forward as a key actor in shaping the gene genealogy of lineages sampled from a deme belonging to a meta-population (Chikhi et al., 2010; Mona et al., 2014; Ray, Currat, & Excoffier, 2003; Städler, Haubold, Merino, Stephan, & Pfaffelhuber, 2009).
Understanding the relations between meta-population structure, the inferred Ne variation under unstructured models, and species dispersal abilities, is crucial to correctly interpret the pattern of genetic variability and to establish conservation priorities. To search for general rules describing such relations, we followed an inductive approach investigating species: i) with large distribution (which in principle should guarantee an organization in meta-populations); ii) with different life history traits (LHT) related to dispersal; iii) of conservation concerns. In this spirit, we selected for our genomic study four shark species (Carcharhinus amblyrhynchos , Carcharhinus limbatus , Carcharhinus melanopterus, and Galeocerdo cuvier ) from New Caledonia. These species have a large and overlapping distribution in the Indo-Pacific (https://sharksrays.org/) and they differ for LHT features such as size (which is positively correlated with the capacity for long distance swimming and oceanic migration (Parsons, 1990)), residency pattern, and long-distance dispersal ability as measured by tagging data (Table S1). Moreover, the IUCN red list reported that Carcharhinus limbatusand Galeocerdo cuvier are Near Threatened (with a decreasing trend in the tiger shark), Carcharhinus melanopterus is vulnerable with decreasing trend, and Carcharhinus amblyrhynchosis Endangered with decreasing trend as well. We first compared several population genetics models by means of coalescent simulations coupled with an approximate Bayesian computation framework (Bertorelle, Benazzo, & Mona, 2010) to detect whether panmixia or a meta-population model best describe the genomic variation of each species. Then, we inferred the demographic parameters under the most likely model and applied the stairwayplot , which assumes a panmictic unstructured population (Liu & Fu, 2015), to detect theNe variation through time in each species. We finally run extensive coalescent simulations under the tested meta-population models with parameters compatible to those observed in real data. The simulated datasets were in turn analysed with the stairwayplot to: i) help interpreting the observed data in the four shark species; ii) providing general coalescent arguments relating the demographic history of a meta-population and the reconstructed variation in Ne through time by means of unstructured models.