Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions

Exploring the permanence of conservation covenants

Conservation on private land is a growing part of international efforts to stem the decline of biodiversity. In many countries, private land conservation policy often supports in-perpetuity covenants and easements, which are legally binding agreements used to protect biodiversity on private land by restricting activities that may negatively impact ecological values. With a view to understand the long-term security of these mechanisms, we examined release and breach data from all 13 major covenanting programs across Australia. We report that out of 6,818 multi-party covenants, only 8 had been released, contrasting with approximately 130 of 673 single-party covenants. Breach data was limited, with a minimum of 71 known cases where covenant obligations had not been met. With a focus on private land conservation policy, we use the results from this case study to argue that multi-party covenants appear an enduring conservation mechanism, highlight the important role that effective monitoring and reporting of the permanency of these agreements plays in contributing to their long-term effectiveness, and provide recommendations for organizations seeking to improve their monitoring programs. The collection of breach and release data is important for the continuing improvement of conservation policies and practices for private land

Optimal synchronization of directed complex networks

We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized synchrony alignment function that encodes the interplay between network structure and the oscillators' natural frequencies and serves as an objective measure for the network's degree of synchronization. Using the generalized synchrony alignment function, we show that a network's synchronization properties can be systematically optimized. This framework also allows us to study the properties of synchrony-optimized networks, and in particular, investigate the role of directed network properties such as nodal in- and out-degrees. For instance, we find that in optimally rewired networks the heterogeneity of the in-degree distribution roughly matches the heterogeneity of the natural frequency distribution, but no such relationship emerges for out-degrees. We also observe that a network's synchronization properties are promoted by a strong correlation between the nodal in-degrees and the natural frequencies of oscillators, whereas the relationship between the nodal out-degrees and the natural frequencies has comparatively little effect. This result is supported by our theory, which indicates that synchronization is promoted by a strong alignment of the natural frequencies with the left singular vectors corresponding to the largest singular values of the Laplacian matrix

k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects

We develop the theory of the k-core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the k-core percolation is an unusual, hybrid phase transition with a jump emergence of the k-core as at a first order phase transition but also with a critical singularity as at a continuous transition. We describe the properties of the k-core, explain the meaning of the order parameter for the k-core percolation, and reveal the origin of the specific critical phenomena. We demonstrate that a so-called ``corona'' of the k-core plays a crucial role (corona is a subset of vertices in the k-core which have exactly k neighbors in the k-core). It turns out that the k-core percolation threshold is at the same time the percolation threshold of finite corona clusters. The mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point. We show that a random removal of even one vertex from the k-core may result in the collapse of a vast region of the k-core around the removed vertex. The mean size of this region diverges at the critical point. We find an exact mapping of the k-core percolation to a model of cooperative relaxation. This model undergoes critical relaxation with a divergent rate at some critical moment.Comment: 11 pages, 8 figure

A novel configuration model for random graphs with given degree sequence

Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. Here, we present a specific realization of a class of random network models in which the connection probability between two vertices (i,j) is a specific function of degrees ki and kj. In the framework of the configuration model of random graphs, we find analytical expressions for the degree correlation and clustering as a function of the variance of the desired degree distribution. The expressions obtained are checked by means of numerical simulations. Possible applications of our model are discussed.Comment: 7 pages, 3 figure

Transparent planning for biodiversity and development in the urban fringe

In Australia, over 50% of threatened species occur within the urban fringe and accelerating urbanization is now a key threat. Biodiversity near and within urban areas brings much social benefit but its maintenance involves complex trade-offs between competing land uses. Urban design typically views biodiversity as a development constraint, not a value to be enhanced into the future. We argue that decisions could be more transparent and systematic and we demonstrate that efficient development solutions can be found that avoid areas important for biodiversity. We present a case study in the context of land use change across the city of Wyndham, a local Government west of Melbourne, Australia. We use reserve design tools in a novel way to identify priority development sites, based on a synthesis of ecological, social and economic data. Trade-offs between biodiversity conservation and other key development objectives and constraints (transport planning, flood risk and food production) are quantified. The analysis can be conducted dynamically with visually compelling output, facilitating more transparent, efficient and democratically derived urban planning solutions. We suggest that government agencies could adopt similar approaches to identify efficient planning solutions for both biodiversity and development in urban environments

The use of dynamic landscape metapopulation models for forest management: a case study of the red-backed salamander

Spatial models of population dynamics have been proposed as a useful method for predicting the impacts of environmental change on biodiversity. Here, we demonstrate advances in dynamic landscape metapopulation modelling and its use as a decision support tool for evaluating the impacts of forest management scenarios. This novel modelling framework incorporates both landscape and metapopulation model stochasticity and allows their relative contributions to model output variance to be characterized. It includes a detailed sensitivity analysis, allowing defensible uncertainty bounds and the prioritization of future data gathering to reduce model uncertainties. We demonstrate this framework by modelling the landscape-level impacts of eight forest management scenarios on the red-backed salamander (Plethodon cinereus (Green, 1818)) in the boreal forest of Ontario, Canada, using the RAMAS Landscape package. The 100 year forest management scenarios ranged in intensity of timber harvesting and fire suppression. All scenarios including harvesting predicted decreases in salamander population size and the current style of forest management is predicted to produce a 9%-17% decrease in expected minimum population size compared with scenarios without harvesting. This method is amenable to incorporating many forms of environmental change and allows a meaningful treatment of uncertainty

Generation of uncorrelated random scale-free networks

Uncorrelated random scale-free networks are useful null models to check the accuracy an the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable to generate random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two and three vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree $k$, respectively