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Register a new userHybrid structural arrangements mediate stability and feasibility in mutualistic networks
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Perhaps the largest debate in network Ecology, the emergence of structural patterns stands out as a multifaceted problem. To the methodological challenges -- pattern identification, statistical significance -- one has to add the relationship between candidate architectures and dynamical performance. In the case of mutualistic communities, the debate revolves mostly around two structural arrangements (nestedness and modularity) and two requirements for persistence, namely feasibility and stability. So far, it is clear that the former is strongly related to nestedness, while the latter is enhanced in modular systems. Adding to this, it has recently become clear that nestedness and modularity are antagonistic patterns -- or, at the very least, their coexistence in a single system is problematic. In this context, this work addresses the role of the interaction architecture in the emergence and maintenance of both properties, introducing the idea of hybrid architectural configurations. Specifically, we examine in-block nestedness, compound by disjoint subsets of species (modules) with internal nested organization, and prove that it grants a balanced trade-off between stability and feasibility. Remarkably, we analyze a large amount of empirical communities and find that a relevant fraction of them exhibits a marked in-block nested structure. We elaborate on the implications of these results, arguing that they provide new insights about the key properties ruling community assembly.
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Mutualistic networks have attracted increasing attention in the ecological literature in the last decades as they play a key role in the maintenance of biodiversity. Here, we develop an analytical framework to study the structural stability of these networks including both mutualistic and competitive interactions. Analytical and numerical analyses show that the structure of the competitive network fundamentally alters the necessary conditions for species coexistence in communities. Using 50 real mutualistic networks, we show that when the relative importance of shared partners is incorporated via weighted competition, the feasibility area in the parameter space is highly correlated with Mays stability criteria and can be predicted by a functional relationship between the number of species, the network connectance and the average interaction strength in the community. Our work reopens a decade-long debate about the complexity-stability relationship in ecological communities, and highlights the role of the relative structures of different interaction types.
We study how large functional networks can grow stably under possible cascading overload failures and evaluated the maximum stable network size above which even a small-scale failure would cause a fatal breakdown of the network. Employing a model of cascading failures induced by temporally fluctuating loads, the maximum stable size $n_{text{max}}$ has been calculated as a function of the load reduction parameter $r$ that characterizes how quickly the total load is reduced during the cascade. If we reduce the total load sufficiently fast ($rge r_{text{c}}$), the network can grow infinitely. Otherwise, $n_{text{max}}$ is finite and increases with $r$. For a fixed $r,(<r_{text{c}})$, $n_{text{max}}$ for a scale-free network is larger than that for an exponential network with the same average degree. We also discuss how one detects and avoids the crisis of a fatal breakdown of the network from the relation between the sizes of the initial network and the largest component after an ordinarily occurring cascading failure.
One of the most important tasks of urban and hazard planning is to mitigate the damages and minimize the costs of the recovery process after catastrophic events. The rapidity and the efficiency of the recovery process are commonly referred to as resilience. Despite the problem of resilience quantification has received a lot of attention, a mathematical definition of the resilience of an urban community, which takes into account the social aspects of a urban environment, has not yet been identified. In this paper we provide and test a methodology for the assessment of urban resilience to catastrophic events which aims at bridging the gap between the engineering and the ecosystem approaches to resilience. We propose to model a urban system by means of different hybrid social-physical complex networks, obtained by enriching the urban street network with additional information about the social and physical constituents of a city, namely citizens, residential buildings and services. Then, we introduce a class of efficiency measures on these hybrid networks, inspired by the definition of global efficiency given in complex network theory, and we show that these measures can be effectively used to quantify the resilience of a urban system, by comparing their respective values before and after a catastrophic event and during the reconstruction process. As a case study, we consider simulated earthquakes in the city of Acerra, Italy, and we use these efficiency measures to compare the ability of different reconstruction strategies in restoring the original performance of the urban system.
Link failures repeatedly induce large-scale outages in power grids and other supply networks. Yet, it is still not well understood, which links are particularly prone to inducing such outages. Here we analyze how the nature and location of each link impact the networks capability to maintain stable supply. We propose two criteria to identify critical links on the basis of the topology and the load distribution of the network prior to link failure. They are determined via a links redundant capacity and a renormalized linear response theory we derive. These criteria outperform critical link prediction based on local measures such as loads. The results not only further our understanding of the physics of supply networks in general. As both criteria are available before any outage from the state of normal operation, they may also help real-time monitoring of grid operation, employing counter-measures and support network planning and design.
Understanding the resilience of infrastructures such as transportation network has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with characteristic link length such as power-grids and the brain. However, although many real-world networks are spatially embedded and their links have characteristics length such as pipelines, power lines or ground transportation lines they are not homogeneous but rather heterogeneous. For example, density of links within cities are significantly higher than between cities. Here we present and study numerically and analytically a similar realistic heterogeneous spatial modular model using percolation process to better understand the effect of heterogeneity on such networks. The model assumes that inside a city there are many lines connecting different locations, while long lines between the cities are sparse and usually directly connecting only a few nearest neighbours cities in a two dimensional plane. We find that this model experiences two distinct continues transitions, one when the cities disconnect from each other and the second when each city breaks apart. Although the critical threshold for site percolation in 2D grid remains an open question we analytically find the critical threshold for site percolation in this model. In addition, while the homogeneous model experience a single transition having a unique phenomenon called textit{critical stretching} where a geometric crossover from random to spatial structure in different scales found to stretch non-linearly with the characteristic length at criticality. Here we show that the heterogeneous model does not experience such a phenomenon indicating that critical stretching strongly depends on the network structure.
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