On the top eigenvalue of heavy-tailed random matrices

We study the statistics of the largest eigenvalue lambda_max of N x N random matrices with unit variance, but power-law distributed entries, P(M_{ij})~ |M_{ij}|^{-1-mu}. When mu > 4, lambda_max converges to 2 with Tracy-Widom fluctuations of order N^{-2/3}. When mu < 4, lambda_max is of order N^{2/mu-1/2} and is governed by Fr\'echet statistics. The marginal case mu=4 provides a new class of limiting distribution that we compute explicitely. We extend these results to sample covariance matrices, and show that extreme events may cause the largest eigenvalue to significantly exceed the Marcenko-Pastur edge. Connections with Directed Polymers are briefly discussed.Comment: 4 pages, 2 figure

Genetic Population Structure in the Antarctic Benthos: Insights from the Widespread Amphipod, Orchomenella franklini

Currently there is very limited understanding of genetic population structure in the Antarctic benthos. We conducted one of the first studies of microsatellite variation in an Antarctic benthic invertebrate, using the ubiquitous amphipod Orchomenella franklini (Walker, 1903). Seven microsatellite loci were used to assess genetic structure on three spatial scales: sites (100 s of metres), locations (1–10 kilometres) and regions (1000 s of kilometres) sampled in East Antarctica at Casey and Davis stations. Considerable genetic diversity was revealed, which varied between the two regions and also between polluted and unpolluted sites. Genetic differentiation among all populations was highly significant (FST = 0.086, RST = 0.139, p<0.001) consistent with the brooding mode of development in O. franklini. Hierarchical AMOVA revealed that the majority of the genetic subdivision occurred across the largest geographical scale, with Nem≈1 suggesting insufficient gene flow to prevent independent evolution of the two regions, i.e., Casey and Davis are effectively isolated. Isolation by distance was detected at smaller scales and indicates that gene flow in O. franklini occurs primarily through stepping-stone dispersal. Three of the microsatellite loci showed signs of selection, providing evidence that localised adaptation may occur within the Antarctic benthos. These results provide insights into processes of speciation in Antarctic brooders, and will help inform the design of spatial management initiatives recently endorsed for the Antarctic benthos

The Whereabouts of an Ancient Wanderer: Global Phylogeography of the Solitary Ascidian Styela plicata

Genetic tools have greatly aided in tracing the sources and colonization history of introduced species. However, recurrent introductions and repeated shuffling of populations may have blurred some of the genetic signals left by ancient introductions. Styela plicata is a solitary ascidian distributed worldwide. Although its origin remains unclear, this species is believed to have spread worldwide by travelling on ship's hulls. The goals of this study were to infer the genetic structure and global phylogeography of S. plicata and to look for present-day and historical genetic patterns. Two genetic markers were used: a fragment of the mitochondrial gene Cytochrome Oxidase subunit I (COI) and a fragment of the nuclear gene Adenine Nucleotide Transporter/ADP-ATP Translocase (ANT). A total of 368 individuals for COI and 315 for ANT were sequenced from 17 locations worldwide. The levels of gene diversity were moderate for COI to high for ANT. The Mediterranean populations showed the least diversity and allelic richness for both markers, while the Indian, Atlantic and Pacific Oceans had the highest gene and nucleotide diversities. Network and phylogenetic analyses with COI and ANT revealed two groups of alleles separated by 15 and 4 mutational steps, respectively. The existence of different lineages suggested an ancient population split. However, the geographic distributions of these groups did not show any consistent pattern, indicating different phylogeographic histories for each gene. Genetic divergence was significant for many population-pairs irrespective of the geographic distance among them. Stochastic introduction events are reflected in the uneven distribution of COI and ANT allele frequencies and groups among many populations. Our results confirmed that S. plicata has been present in all studied oceans for a long time, and that recurrent colonization events and occasional shuffling among populations have determined the actual genetic structure of this species

The Biodiversity of the Mediterranean Sea: Estimates, Patterns, and Threats

The Mediterranean Sea is a marine biodiversity hot spot. Here we combined an extensive literature analysis with expert opinions to update publicly available estimates of major taxa in this marine ecosystem and to revise and update several species lists. We also assessed overall spatial and temporal patterns of species diversity and identified major changes and threats. Our results listed approximately 17,000 marine species occurring in the Mediterranean Sea. However, our estimates of marine diversity are still incomplete as yet—undescribed species will be added in the future. Diversity for microbes is substantially underestimated, and the deep-sea areas and portions of the southern and eastern region are still poorly known. In addition, the invasion of alien species is a crucial factor that will continue to change the biodiversity of the Mediterranean, mainly in its eastern basin that can spread rapidly northwards and westwards due to the warming of the Mediterranean Sea. Spatial patterns showed a general decrease in biodiversity from northwestern to southeastern regions following a gradient of production, with some exceptions and caution due to gaps in our knowledge of the biota along the southern and eastern rims. Biodiversity was also generally higher in coastal areas and continental shelves, and decreases with depth. Temporal trends indicated that overexploitation and habitat loss have been the main human drivers of historical changes in biodiversity. At present, habitat loss and degradation, followed by fishing impacts, pollution, climate change, eutrophication, and the establishment of alien species are the most important threats and affect the greatest number of taxonomic groups. All these impacts are expected to grow in importance in the future, especially climate change and habitat degradation. The spatial identification of hot spots highlighted the ecological importance of most of the western Mediterranean shelves (and in particular, the Strait of Gibraltar and the adjacent Alboran Sea), western African coast, the Adriatic, and the Aegean Sea, which show high concentrations of endangered, threatened, or vulnerable species. The Levantine Basin, severely impacted by the invasion of species, is endangered as well

Role of evolutionary and ecological factors in the reproductive success and the spatial genetic structure of the temperate gorgonian Paramuricea clavata

15 páginas, 4 figuras, 4 tablas.Dispersal and mating features strongly influence the evolutionary dynamics and the spatial genetic structure (SGS) of marine populations. For the first time in a marine invertebrate, we examined individual reproductive success, by conducting larval paternity assignments after a natural spawning event, combined with a small-scale SGS analysis within a population of the gorgonian Paramuricea clavata. Thirty four percent of the larvae were sired by male colonies surrounding the brooding female colonies, revealing that the bulk of the mating was accomplished by males from outside the studied area. Male success increased with male height and decreased with increasing male to female distance. The parentage analyses, with a strong level of self-recruitment (25%), unveiled the occurrence of a complex family structure at a small spatial scale, consistent with the limited larval dispersal of this species. However, no evidence of small scale SGS was revealed despite this family structure. Furthermore, temporal genetic structure was not observed, which appears to be related to the rather large effective population size. The low level of inbreeding found suggests a pattern of random mating in this species, which disagrees with expectations that limited larval dispersal should lead to biparental inbreeding. Surface brooding and investment in sexual reproduction in P. clavata contribute to multiple paternity (on average 6.4 fathers were assigned per brood), which enhance genetic diversity of the brood. Several factors may have contributed to the lack of biparental inbreeding in our study such as (i) the lack of sperm limitation at a small scale, (ii) multiple paternity, and (iii) the large effective population size. Thus, our results indicate that limited larval dispersal and complex family structure do not necessarily lead to biparental inbreeding and SGS. In the framework of conservation purposes, our results suggested that colony size, proximity among colonies and the population size should be taken into consideration for restoration projects.This research was partly supported by the MCI project CGL2010-18466 and CoCoNet (FP7 Grant Agreement: 287844). R. C. is part of the Marine-Biogeochemistry and Global-Change-Research group from Generalitat de Catalunya.Peer reviewe

Morphological, physiological and genetic variability of the ophiuroid <i>Amphipholis squamata</i> from the lagoon system of Oliveri-Tindari (Sicily)

Amphipholis squamata is considered to be the only echinoderm distributed worldwide, excepted in polar regions. This vast distribution area contrasts with a low dispersal potential due to the lack of a pelagic larval stage and an aggregative spatial distribution. Previous works have shown strong inter- and intra-population variability among adult individuals for both phenotype and genotype, although the species seems to be anatomically uniform. The aim of this work was to understand these individual variations at three different levels: (a) the morphological differences characterized by the colour of arms and disc; (b) the physiological variations estimated by luminous capabilities and (c) the genetic variations as revealed by RAPDs. Four populations were sampled in the system of Oliveri-Tindari in Sicily which consists of several lagoons completely isolated from the open sea and from each other for various periods. This system constitutes a suitable model for studying differentiation between closely neighbouring demes. Our results confirm that each colour variety possesses its own luminous capabilities; they also indicate that colour varieties are genetically differentiated

Phylogeography of the red coral (Corallium rubrum): inferences on the evolutionary history of a temperate gorgonian

15 pages, 4 figures, 4 tablesThe red coral Corallium rubrum (Cnidaria, Octocorallia) is an exploited, long-lived sessile species from the Mediterranean Sea and the adjacent coastline in the Atlantic Ocean. Surveys of genetic variation using microsatellites have shown that populations of C. rubrum are characterized by strong differentiation at the local scale but a study of the phylogeography of this species was still lacking. Here, we used seven polymorphic microsatellite loci, together with sequence data from an intron of the elongation factor 1 (EF1) gene, to investigate the genetic structure of C. rubrum across its geographical range in the western Mediterranean Sea and in the Adriatic Sea. The EF1 sequences were also used to analyse the consequences of demographic fluctuations linked with past environmental change. Clustering analysis with microsatellite loci highlighted three to seven genetic groups with the distinction of North African and Adriatic populations; this distinction appeared significant with AMOVA and differentiation tests. Microsatellite and EF1 data extended the isolation by distance pattern previously observed for this species at the western Mediterranean scale. EF1 sequences confirmed the genetic differentiation observed between most samples with microsatellites. A statistical parsimony network of EF1 haplotypes provided no evidence of high sequence divergence among regions, suggesting no long-term isolation. Selective neutrality tests on microsatellites and EF1 were not significant but should be interpreted with caution in the case of EF1 because of the low sample sizes for this locus. Our results suggest that recent Quaternary environmental fluctuations had a limited impact on the genetic structure of C. rubrumThis work was funded by the French ANR (National Research Agency) in the Medchange program (www.medchange.org). This was also part of the EPIC project in the European Union Network of Excellence Marine Genomics. Some samples were obtained through the GBIRM project in the European Union Network of Excellence MARBEF. J.-B.L’s PhD was funded by the Région Provence Alpes Côte d’AzurPeer reviewe