Biogeography revisited with network theory: retracing the history of hydrothermal vent communities.

Defining biogeographic provinces to understand the history and evolution of communities associated with a given kind of ecosystem is challenging and usually requires a priori assumptions to be made. We applied network theory, a holistic and exploratory method, to the most complete database of faunal distribution available on oceanic hydrothermal vents, environments which support fragmented and unstable ecosystems, to infer the processes driving their worldwide biogeography. Besides the identification of robust provinces, the network topology allowed us to identify preferential pathways that had hitherto been overlooked. These pathways are consistent with the previously proposed hypothesis of a role of plate tectonics in the biogeographical history of hydrothermal vent communities. A possible ancestral position of the Western Pacific is also suggested for the first time. Finally, this work provides an innovative example of the potential of network tools to unravel the biogeographic history of faunal assemblages and to supply comprehensive information for the conservation and management of biodiversity.

Network analysis identifies weak and strong links in a metapopulation system.

The identification of key populations shaping the structure and connectivity of metapopulation systems is a major challenge in population ecology. The use of molecular markers in the theoretical framework of population genetics has allowed great advances in this field, but the prime question of quantifying the role of each population in the system remains unresolved. Furthermore, the use and interpretation of classical methods are still bounded by the need for a priori information and underlying assumptions that are seldom respected in natural systems. Network theory was applied to map the genetic structure in a metapopulation system by using microsatellite data from populations of a threatened seagrass, Posidonia oceanica, across its whole geographical range. The network approach, free from a priori assumptions and from the usual underlying hypotheses required for the interpretation of classical analyses, allows both the straightforward characterization of hierarchical population structure and the detection of populations acting as hubs critical for relaying gene flow or sustaining the metapopulation system. This development opens perspectives in ecology and evolution in general, particularly in areas such as conservation biology and epidemiology, where targeting specific populations is crucial.

Spectrum of genetic diversity and networks of clonal organisms.

Clonal reproduction characterizes a wide range of species including clonal plants in terrestrial and aquatic ecosystems, and clonal microbes such as bacteria and parasitic protozoa, with a key role in human health and ecosystem processes. Clonal organisms present a particular challenge in population genetics because, in addition to the possible existence of replicates of the same genotype in a given sample, some of the hypotheses and concepts underlying classical population genetics models are irreconcilable with clonality. The genetic structure and diversity of clonal populations were examined using a combination of new tools to analyse microsatellite data in the marine angiosperm Posidonia oceanica. These tools were based on examination of the frequency distribution of the genetic distance among ramets, termed the spectrum of genetic diversity (GDS), and of networks built on the basis of pairwise genetic distances among genets. Clonal growth and outcrossing are apparently dominant processes, whereas selfing and somatic mutations appear to be marginal, and the contribution of immigration seems to play a small role in adding genetic diversity to populations. The properties and topology of networks based on genetic distances showed a 'small-world' topology, characterized by a high degree of connectivity among nodes, and a substantial amount of substructure, revealing organization in subfamilies of closely related individuals. The combination of GDS and network tools proposed here helped in dissecting the influence of various evolutionary processes in shaping the intra-population genetic structure of the clonal organism investigated; these therefore represent promising analytical tools in population genetics.

Dynamic critical approach to self-organized criticality.

A dynamic scaling ansatz for the approach to the self-organized critical (SOC) regime is proposed and tested by means of extensive simulations applied to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering the short-time scaling behavior of the density of sites [rho(t)] below the critical value, it is shown that (i) starting the dynamics with configurations such that rho(t=0)-->0 one observes an initial increase of the density with exponent theta=0.12(2); (ii) using initial configurations with rho(t=0)-->1, the density decays with exponent delta=0.47(2). It is also shown that the temporal autocorrelation decays with exponent Ca=0.35(2). Using these dynamically determined critical exponents and suitable scaling relationships, all known exponents of the BS model can be obtained, e.g., the dynamical exponent z=2.10(5), the mass dimension exponent D=2.42(5), and the exponent of all returns of the activity tauALL=0.39(2), in excellent agreement with values already accepted and obtained within the SOC regime.

Scale-free networks on lattices.

We suggest a method for embedding scale-free networks, with degree distribution Pk approximately k(-lambda), in regular Euclidean lattices accounting for geographical properties. The embedding is driven by a natural constraint of minimization of the total length of the links in the system. We find that all networks with lambda>2 can be successfully embedded up to a (Euclidean) distance xi which can be made as large as desired upon the changing of an external parameter. Clusters of successive chemical shells are found to be compact (the fractal dimension is df=d), while the dimension of the shortest path between any two sites is smaller than 1: dmin=(lambda-2)/(lambda-1-1/d), contrary to all other known examples of fractals and disordered lattices.