A central tenet of ecology and biogeography is that the broad outlines of

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.conservation biology ͉ gene flow ͉ networks ͉ population genetics U nderstanding the connectivity between components of a metapopulation system and their role as weak or strong links remains a major challenge of population ecology (1-3). Advances in molecular biology fostered the use of indirect approaches to understand metapopulation structure, based on describing the distribution of gene variants (alleles) in space within the theoretical framework of population genetics (4-7). Yet, the premises of the classical Wright-Fisher model (4, 6), such as ''migration-drift'' and ''mutation-drift'' equilibrium (8), ''equal population sizes'' or symmetrical rate migration among populations, are often violated in real metapopulation systems. Threatened or pathogen species, for example, are precisely studied for their state of demographic disequilibrium due to decline and local extinctions in the first case, or to their complex dynamics of local decline and sudden pandemic burst in the second. Furthermore, the underlying hypotheses of equal population size and symmetrical migration rates hamper the identification of putative population ''hubs'' centralizing migration pathways or acting as sources in a metapopulation system, which is a central issue in ecology in general, and in conservation biology or epidemiology in particular. Finally, complementary methods of genetic structure analyses, such as hierarchical AMOVA and coalescent methods rely on a priori information (or priors) as to the clustering or demographic state of populations, requiring either subjective assumptions or the availability of reliable demographic, historical or ecological information that are seldom available.Network theory is emerging as a powerful tool to un...

Viable populations of species occur in a given place if three conditions are met: the environment at the place is suitable; the species is able to colonize it; co‐occurrence is possible despite or because of interactions with other species. Studies investigating the effects of climate change on species have mainly focused on measuring changes in climate suitability. Complex interactions among species have rarely been explored in such studies. We extend network theory to the analysis of complex patterns of co‐occurrence among species. The framework is used to explore the robustness of networks under climate change. With our data, we show that networks describing the geographic pattern of co‐occurrence among species display properties shared by other complex networks, namely that most species are poorly connected to other species in the network and only a few are highly connected. In our example, species more exposed to climate change tended to be poorly connected to other species within the network, while species more connected tended to be less exposed. Such high connectance would make the co‐occurrence networks more robust to climate change. The proposed framework illustrates how network analysis could be used, together with co‐occurrence data, to help addressing the potential consequences of species interactions in studies of climate change and biodiversity. However, more research is needed to test for links between co‐occurrence and network interactions.

A central tenet of ecology and biogeography is that the broad outlines of species ranges are determined by climate, whereas the effects of biotic interactions are manifested at local scales. While the first proposition is supported by ample evidence, the second is still a matter of controversy. To address this question, we develop a mathematical model that predicts the spatial overlap, i.e. co-occurrence, between pairs of species subject to all possible types of interactions. We then identify the scale of resolution in which predicted range overlaps are lost. We found that co-occurrence arising from positive interactions, such as mutualism (/) and commensalism (/0), are manifested across scales. Negative interactions, such as competition (2/2) and amensalism (2/0), generate checkerboard patterns of co-occurrence that are discernible at finer resolutions but that are lost and increasing scales of resolution. Scale dependence in consumer-resource interactions (/2) depends on the strength of positive dependencies between species. If the net positive effect is greater than the net negative effect, then interactions scale up similarly to positive interactions. Our results challenge the widely held view that climate alone is sufficient to characterize species distributions at broad scales, but also demonstrate that the spatial signature of competition is unlikely to be discernible beyond local and regional scales.

We suggest a method for embedding scale-free networks, with degree distribution P (k) ∼ k −λ , in regular Euclidean lattices. 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 λ > 2 can be successfully embedded up to an (Euclidean) distance ξ 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 d f = d), while the dimension of the shortest path between any two sites is smaller than one: dmin = λ−2 λ−1−1/d , contrary to all other known examples of fractals and disordered lattices.Many social, biological, and communication systems can be properly described by complex networks whose nodes represent individuals or organizations and links mimic the interactions among them [1]. An important class of complex networks are the scale-free networks, which exhibit a power-law connectivity distribution. Examples of scale-free networks include the Internet [2,3], WWW [4,5], metabolic [6] and cellular networks [7]. Most of the work done on scale free networks concerns off-lattice systems (graphs) where the Euclidean distance between nodes is irrelevant. However, real-life networks are often embedded in Euclidean space (e.g., the Internet is embedded in the two-dimensional network of routers, neuronal networks are embedded in a three-dimensional brain, etc.). Indeed, in the case of the Internet, indications for the relevance of embedding space is given in [8] In this Letter we develop a method for generating scalefree networks on Euclidean lattices and study some of its properties. As a guiding principle we impose the natural restriction that the total length of links in the system be minimal.Our model is defined as follows. To each site of a ddimensional lattice, of size R, and with periodic boundary conditions, we assign a random connectivity k taken from the scale-free distributionwhere the normalization constant C ≈ (λ − 1)m λ−1 (for K large) [9]. We then select a site at random and connect it to its closest neighbors until its (previously assigned) connectivity k is realized, or until all sites up to a distancehave been explored. (Links to some of the neighboring sites might prove impossible, in case that the connectivity quota of the target site is already filled.) This process is repeated for all sites of the lattice. We show that following this method networks with λ > 2 can be successfully embedded up to an (Euclidean) distance ξ which can be made as large as desired upon the changing of the external parameter A. Suppose that one attempts to embed a scale-free network, by the above recipe, in an infinite lattice, R → ∞. Sites with a connectivity larger than a certain cutoff k c (A) cannot be realized, because of saturation of the surrounding sites. Consider the number of links n(r) entering a generic site from a surrounding neighborhood of radius r. Sites at distance r ′ are linked to the origin with probability...

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.

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.

No abstract