Correlated multiplexity and connectivity of multiplex random networks

Nodes in a complex networked system often engage in more than one type of interactions among them; they form a multiplex network with multiple types of links. In real-world complex systems, a node's degree for one type of links and that for the other are not randomly distributed but correlated, which we term correlated multiplexity. In this paper we study a simple model of multiplex random networks and demonstrate that the correlated multiplexity can drastically affect the properties of giant component in the network. Specifically, when the degrees of a node for different interactions in a duplex Erdos-Renyi network are maximally correlated, the network contains the giant component for any nonzero link densities. In contrast, when the degrees of a node are maximally anti-correlated, the emergence of giant component is significantly delayed, yet the entire network becomes connected into a single component at a finite link density. We also discuss the mixing patterns and the cases with imperfect correlated multiplexity.Comment: Revised version, 12 pages, 6 figure

Setting temporal baselines for biodiversity : the limits of available monitoring data for capturing the full impact of anthropogenic pressures

Temporal baselines are needed for biodiversity, in order for the change in biodiversity to be measured over time, the targets for biodiversity conservation to be defined and conservation progress to be evaluated. Limited biodiversity information is widely recognized as a major barrier for identifying temporal baselines, although a comprehensive quantitative assessment of this is lacking. Here, we report on the temporal baselines that could be drawn from biodiversity monitoring schemes in Europe and compare those with the rise of important anthropogenic pressures. Most biodiversity monitoring schemes were initiated late in the 20th century, well after anthropogenic pressures had already reached half of their current magnitude. Setting temporal baselines from biodiversity monitoring data would therefore underestimate the full range of impacts of major anthropogenic pressures. In addition, biases among taxa and organization levels provide a truncated picture of biodiversity over time. These limitations need to be explicitly acknowledged when designing management strategies and policies as they seriously constrain our ability to identify relevant conservation targets aimed at restoring or reversing biodiversity losses. We discuss the need for additional research efforts beyond standard biodiversity monitoring to reconstruct the impacts of major anthropogenic pressures and to identify meaningful temporal baselines for biodiversity

Epidemics in partially overlapped multiplex networks

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction $q$ of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted $T$. We also theoretically determine the dependence of the epidemic threshold on the fraction $q > 0$ of shared nodes in a system composed of two layers. We find that in the limit of $q \to 0$ the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.Comment: 13 pages, 4 figure

Multiplexity-facilitated cascades in networks

Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [D. J. Watts, Proc. Natl. Acad. Sci. U.S.A. 99, 5766 (2002)] to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active. We show that both combining layers (i.e., realizing other interactions play a role) and splitting a network into layers (i.e., recognizing distinct kinds of interactions) facilitate cascades. Notably, layers unsusceptible to global cascades can cooperatively achieve them if coupled. On one hand, this suggests fundamental limitations on predicting cascades without full knowledge of a system's multiplexity; on the other hand, it offers feasible means to control cascades by introducing or removing sparse layers in an existing network.Comment: Final version 4/30/12: 5 pages, 5 figure

Dynamic virtual ecosystems as a tool for detecting large-scale responses of biodiversity to environmental and land-use change

In the face of biodiversity loss, we rely upon measures of diversity to describe the health of ecosystems and to direct policymakers and conservation efforts. However, there are many complexities in natural systems that can easily confound biodiversity measures, giving misleading interpretations of the system status and, as a result, there is yet to be a consistent framework by which to measure this biodiversity loss. Ecosystems are governed by dynamic processes, such as reproduction, dispersal and competition for resources, that both shape their biodiversity and how the system responds to change. Here, we incorporate these processes into simulations of habitat and environmental change, in order to understand how well we can identify signals of biodiversity loss against the background inherent variability these processes introduce. We developed a tool for Ecosystem Simulation through Integrated Species Trait-Environment Modelling (EcoSISTEM), which models on the species-level for several sizes of ecosystem, from small islands and patches through to entire regions, and several different types of habitat. We tested a suite of traditionally-used and new biodiversity measures on simulated ecosystems against a range of different scenarios of population decline, invasion and habitat loss. We found that the response of biodiversity measures was generally stronger in larger, more heterogeneous habitats than in smaller or homogeneous habitats. We were also able to detect signals of increasing homogenisation in climate change scenarios, which contradicted the signal of increased heterogeneity and distinctiveness through habitat loss

The extreme vulnerability of interdependent spatially embedded networks

Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this "critical dependency" (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and \textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.Comment: 13 pages, 5 figure

Long-distance dispersal explains the bipolar disjunction in Carex macloviana

PREMISE OF THE STUDY: The sedge Carex macloviana d’Urv presents a bipolar distribution. To clarify the origin of its distribution, we consider the four main hypotheses: long-distance dispersal (either by mountain hopping or by direct dispersal), vicariance, parallel evolution, and human introduction. METHODS: Phylogenetic, phylogeographic, and divergence time estimation analyses were carried out based on two nuclear ribosomal (ETS and ITS) regions, one nuclear single copy gene (CATP), and three plastid DNA regions (rps 16 and 5′ trn K introns, and psb A-trn H spacer), using Bayesian inference, maximum likelihood, and statistical parsimony. Bioclimatic data were used to characterize the climatic niche of C. macloviana. KEY RESULTS: C arex macloviana constitutes a paraphyletic species, dating back to the Pleistocene (0.62 Mya, 95% highest posterior density: 0.29–1.00 Mya). This species displays strong genetic structure between hemispheres, wiThtwo different lineages in the Southern Hemisphere and limited genetic differentiation in Northern Hemisphere populations. Also, populations from the Southern Hemisphere show a narrower climatic niche wiThregards to the Northern Hemisphere populations. CONCLUSIONS: C arex macloviana reached its bipolar distribution by long-distance dispersal, although it was not possible to determine whether it was caused by mountain hopping or by direct dispersal. While there is some support that Carex macloviana might have colonized the Northern Hemisphere by south-to-norThtranshemisphere dispersal during the Pleistocene, unlike the southwards dispersal pattern inferred for other bipolar Carex L. species, we cannot entirely rule out north-to-souThdispersion.Ministerio de Economía y Competitividad CGL2016-77401-

Towards designing robust coupled networks

Natural and technological interdependent systems have been shown to be highly vulnerable due to cascading failures and an abrupt collapse of global connectivity under initial failure. Mitigating the risk by partial disconnection endangers their functionality. Here we propose a systematic strategy of selecting a minimum number of autonomous nodes that guarantee a smooth transition in robustness. Our method which is based on betweenness is tested on various examples including the famous 2003 electrical blackout of Italy. We show that, with this strategy, the necessary number of autonomous nodes can be reduced by a factor of five compared to a random choice. We also find that the transition to abrupt collapse follows tricritical scaling characterized by a set of exponents which is independent on the protection strategy