Sample-Based Forest Landscape Diversity Indices.

Studies of spatial patterns of landscapes are useful to quantify human impact, predict wildlife effects, or describe various landscape features. A robust landscape index should quantify two distinct components of landscape diversity: composition and configuration. One category of landscape index is the contagion index. A generalized measure of contagion is defined as a function of concentration. From this definition two contagion indices, \Gamma\sb1 (a new index) and \Gamma\sb2 (an entropy formulation), are derived from expected values of geometric random variables. A widely used relative contagion index, RC\sb2, is shown to be a scaled version of \Gamma\sb2.. Distributional properties of \\Gamma\sb1,\ \\Gamma\sb2, and \\Gamma\sb{2({\rm scaled})} (i.e., R\ C\sb2) are derived. They are shown to be asymptotically unbiased, consistent, and asymptotically normally distributed. Variance formulas for \\Gamma\sb1,\ \\Gamma\sb2, and \\Gamma\sb{2\rm(scaled)} are derived using the delta method A Monte Carlo study using subseries analysis and replicate histograms, for variance and distribution assessment, was done as a validity check. Behavior of \Gamma\sb1,\ \Gamma\sb2, and RC\sb2 were investigated with simulated random, uniform, and aggregated landscapes. Both \Gamma\sb1 and \Gamma\sb2 provide acceptable measures of contagion. The index RC\sb2 is shown to be an index of evenness, and not of contagion. It is demonstrated that relativized contagion indices are mathematically untenable. As an application, the pattern and changes in forest cover types over the last two decades were analyzed on three landscape level physiographic provinces of the state of Alabama: (i) The Great Appalachian Valley Province, (ii) The Blue Ridge-Talladega Mountain Province, and (iii) The Piedmont Province. The USDA Forest Service conducts periodic surveys of forest resources nationwide from plots distributed on a 3-mile by 3-mile (4.8-km by 4.8-km) grid randomly established within each county. Using forest inventory and analysis survey data on forest cover types, stratified by physiographic province, the \\Gamma\sb1 and \\Gamma\sb2 contagion values and their variances were calculated for each province for the survey years 1972, 1982, and 1990. One-way analysis of variance was used for hypothesis testing of contagion values across time and between provinces. Contagion values were very similar indicating similar processes operating across the physiographic provinces over the last two decades. In comparing \\Gamma\sb1 and \\Gamma\sb2, use of \\Gamma\sb1 in analysis of variance gave a more conservative test of contagion

Advances in spatial entropy measures

open3noThis work is developed under the PRIN2015 supported project ’Environmental processes and human activities: capturing their interactions via statistical methods EPHASTAT)’ [Grant Number 20154X8K23] funded by MIUR (Italian Ministry of Education, University and Scientific Research).A very recent proposal of a set of entropy measures for spatial data, based on building pairs of realizations, allows to split the data heterogeneity that is usually assessed via Shannon's entropy into two components: spatial mutual information, identifying the role of space, and spatial residual entropy, measuring heterogeneity due to other sources. A further decomposition into partial terms deeply investigates the role of space at specific distance ranges. The present work proposes improvements to the method and adds relevant results proving that the new set of spatial entropies satisfies a list of desirable properties. We extend the methodology to sets of realizations greater than pairs. We also show that the approach is more general, better performing and more interpretable than the most popular proposals in the literature, thanks to the property of additivity and a new way of computing entropy that explicitly discards the order within sets. A novel procedure for building the necessary quantities for computations is also provided. A comparative study illustrates the superior performance of the new set of measures over representative spatial configurations. Practical questions are answered by means of a case study on land use data.embargoed_20200527Altieri L., Cocchi D., Roli G.Altieri L., Cocchi D., Roli G

Assessment of habitat quality and landscape connectivity for forest-dependent cracids in the Sierra Madre del Sur Mesoamerican biological corridor, Mexico

Assessing landscape connectivity allows us to identify critical areas that impede or facilitate the movement of organisms and their genes and to plan their conservation and management. In this article, we assessed landscape connectivity and ecological condition of the habitat patches of a highly biodiverse region in Chiapas, Mexico. We employed data of three cracid species with different characteristics in habitat use and mobility. The habitat map of each species was derived from a spatial intersection of the models of potential distribution and a high-resolution map of current land cover and land use. The ecological condition of vegetation types was evaluated using 75 field plots. Structure of landscape was estimated by fragmentation metrics, while functional connectivity was assessed using spatially explicit graph analysis. The extent of suitable habitat for Oreophasis derbianus, Penelopina nigra, and Penelope purpurascens correspond to 25%, 46%, and 55% of the study area (5,185.6 km2), respectively. Although the pine-oak forests were the most fragmented vegetation type, habitats of the three species were well connected, and only 4% to 9% of the fragments located on the periphery of the corridor had low connectivity. Landscape connectivity depends mainly on land uses with an intermediate and lower ecological condition (secondary forests and coffee agroforestry systems). Therefore, we suggest that in addition to promoting the improvement in connectivity in fragmented forests, conservation efforts should be aimed at preventing the conversion of mature forests into agricultural uses and maintaining agroforestry systems

Ancient Amazonian populations left lasting impacts on forest structure

Amazonia contains a vast expanse of contiguous tropical forest and is influential in global carbon and hydrological cycles. Whether ancient Amazonia was highly disturbed or modestly impacted, and how ancient disturbances have shaped current forest ecosystem processes, is still under debate. Amazonian Dark Earths (ADEs), which are anthropic soil types with enriched nutrient levels, are one of the primary lines of evidence for ancient human presence and landscape modifications in settings that mostly lack stone structures and which are today covered by vegetation. We assessed the potential of using moderate spatial resolution optical satellite imagery to predict ADEs across the Amazon Basin. Maximum entropy modeling was used to develop a predictive model using locations of ADEs across the basin and satellite‐derived remotely sensed indices. Amazonian Dark Earth sites were predicted to be primarily along the main rivers and in eastern Amazonia. Amazonian Dark Earth sites, when compared with randomly selected forested sites located within 50 km of ADE sites, were less green canopies (lower normalized difference vegetation index) and had lower canopy water content. This difference was accentuated in two drought years, 2005 and 2010. This is contrary to our expectation that ADE sites would have nutrient‐rich soils that support trees with greener canopies and forests on ADE soils being more resilient to drought. Biomass and tree height were lower on ADE sites in comparison with randomly selected adjacent sites. Our results suggested that ADE‐related ancient human impact on the forest is measurable across the entirety of the 6 million km2 of Amazon Basin using remotely sensed data

Computation in Complex Networks

Complex networks are one of the most challenging research focuses of disciplines, including physics, mathematics, biology, medicine, engineering, and computer science, among others. The interest in complex networks is increasingly growing, due to their ability to model several daily life systems, such as technology networks, the Internet, and communication, chemical, neural, social, political and financial networks. The Special Issue “Computation in Complex Networks" of Entropy offers a multidisciplinary view on how some complex systems behave, providing a collection of original and high-quality papers within the research fields of: • Community detection • Complex network modelling • Complex network analysis • Node classification • Information spreading and control • Network robustness • Social networks • Network medicin

EFFECTS OF SPATIAL RESOLUTION AND LANDSCAPE STRUCTURE ON LAND COVER CHARACTERIZATION

This dissertation addressed problems in scaling, problems that are among the main challenges in remote sensing. The principal objective of the research was to investigate the effects of changing spatial scale on the representation of land cover. A second objective was to determine the relationship between such effects, characteristics of landscape structure and scaling procedures. Four research issues related to spatial scaling were examined. They included: 1) the upscaling of Normalized Difference Vegetation Index (NDVI); 2) the effects of spatial scale on indices of landscape structure; 3) the representation of land cover databases at different spatial scales; and 4) the relationships between landscape indices and land cover area estimations. The overall bias resulting from non-linearity of NDVI in relation to spatial resolution is generally insignificant as compared to other factors such as influences of aerosols and water vapor. The bias is, however, related to land surface characteristics. Significant errors may be introduced in heterogeneous areas where different land cover types exhibit strong spectral contrast. Spatially upscaled SPOT and TM NDVIs have information content comparable with the AVHRR-derived NDVI: Indices of landscape structure and spatial resolution are generally related, but the exact forms of the relationships are subject to changes in other factors including the basic patch unit constituting a landscape and the proportional area of foreground land cover under consideration. The extent of agreement between spatially aggregated coarse resolution land cover datasets and full resolution datasets changes with the properties of the original datasets, including the pixel size and class definition. There are close relationships between landscape structure and class areas estimated from spatially aggregated land cover databases. The relationships, however, do not permit extension from one area to another. Inversion calibration across different geographic/ecological areas is, therefore, not feasible. Different rules govern the land cover area changes across resolutions when different upscaling methods are used. Special attention should be given to comparison between land cover maps derived using different methods

The Physics of Communicability in Complex Networks

A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network. Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantum-mechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks.Comment: Review Article. 90 pages, 14 figures. Contents: Introduction; Communicability in Networks; Physical Analogies; Comparing Communicability Functions; Communicability and the Analysis of Networks; Communicability and Localization in Complex Networks; Computability of Communicability Functions; Conclusions and Prespective

Containing epidemic outbreaks by message-passing techniques

The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected infection under a given epidemic model. Although computing the expected infection is a hard computational problem, simple and efficient mean-field approximations have been put forward in the literature in recent years. The optimization problem can be recast into a constrained one in which the constraints enforce local mean-field equations describing the average stationary state of the epidemic process. For a wide class of epidemic models, including the susceptible-infected-removed and the susceptible-infected-susceptible models, we define a message-passing approach to network immunization that allows us to study the statistical properties of epidemic outbreaks in the presence of immunized nodes as well as to find (nearly) optimal immunization sets for a given choice of parameters and costs. The algorithm scales linearly with the size of the graph and it can be made efficient even on large networks. We compare its performance with topologically based heuristics, greedy methods, and simulated annealing