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Many technological, biological, social, and information networks fall into the broad class of 'small-world' networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction ('small/not-small') rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network's small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model--the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified. We defined a precise measure of 'small-world-ness' S based on the trade off between high local clustering and short path length. A network is now deemed a 'small-world' if S>1--an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process. We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing.

Interactions between microbial species are sometimes mediated by the exchange of small molecules, secreted by one species and metabolized by another. Both one-way (commensal) and two-way (mutualistic) interactions may contribute to complex networks of interdependencies. Understanding these interactions constitutes an open challenge in microbial ecology, with applications ranging from the human microbiome to environmental sustainability. In parallel to natural communities, it is possible to explore interactions in artificial microbial ecosystems, e.g. pairs of genetically engineered mutualistic strains. Here we computationally generate artificial microbial ecosystems without re-engineering the microbes themselves, but rather by predicting their growth on appropriately designed media. We use genome-scale stoichiometric models of metabolism to identify media that can sustain growth for a pair of species, but fail to do so for one or both individual species, thereby inducing putative symbiotic interactions. We first tested our approach on two previously studied mutualistic pairs, and on a pair of highly curated model organisms, showing that our algorithms successfully recapitulate known interactions, robustly predict new ones, and provide novel insight on exchanged molecules. We then applied our method to all possible pairs of seven microbial species, and found that it is always possible to identify putative media that induce commensalism or mutualism. Our analysis also suggests that symbiotic interactions may arise more readily through environmental fluctuations than genetic modifications. We envision that our approach will help generate microbe-microbe interaction maps useful for understanding microbial consortia dynamics and evolution, and for exploring the full potential of natural metabolic pathways for metabolic engineering applications.

Ecological niche models (ENMs) provide a means of characterizing the spatial distribution of suitable conditions for species, and have recently been applied to the challenge of locating potential distributional areas at the Last Glacial Maximum (LGM) when unfavorable climate conditions led to range contractions and fragmentation. Here, we compare and contrast ENM-based reconstructions of LGM refugial locations with those resulting from the more traditional molecular genetic and phylogeographic predictions. We examined 20 North American terrestrial vertebrate species from different regions and with different range sizes for which refugia have been identified based on phylogeographic analyses, using ENM tools to make parallel predictions. We then assessed the correspondence between the two approaches based on spatial overlap and areal extent of the predicted refugia. In 14 of the 20 species, the predictions from ENM and predictions based on phylogeographic studies were significantly spatially correlated, suggesting that the two approaches to development of refugial maps are converging on a similar result. Our results confirm that ENM scenario exploration can provide a useful complement to molecular studies, offering a less subjective, spatially explicit hypothesis of past geographic patterns of distribution.

As the global human population grows and its consumption patterns change, additional land will be needed for living space and agricultural production. A critical question facing global society is how to meet growing human demands for living space, food, fuel, and other materials while sustaining ecosystem services and biodiversity [1]. We spatially allocate two scenarios of 2000 to 2015 global areal change in urban land and cropland at the grid cell-level and measure the impact of this change on the provision of ecosystem services and biodiversity. The models and techniques used to spatially allocate land-use/land-cover (LULC) change and evaluate its impact on ecosystems are relatively simple and transparent [2]. The difference in the magnitude and pattern of cropland expansion across the two scenarios engenders different tradeoffs among crop production, provision of species habitat, and other important ecosystem services such as biomass carbon storage. For example, in one scenario, 5.2 grams of carbon stored in biomass is released for every additional calorie of crop produced across the globe; under the other scenario this tradeoff rate is 13.7. By comparing scenarios and their impacts we can begin to identify the global pattern of cropland and irrigation development that is significant enough to meet future food needs but has less of an impact on ecosystem service and habitat provision. Urban area and croplands will expand in the future to meet human needs for living space, livelihoods, and food. In order to jointly provide desired levels of urban land, food production, and ecosystem service and species habitat provision the global society will have to become much more strategic in its allocation of intensively managed land uses. Here we illustrate a method for quickly and transparently evaluating the performance of potential global futures.

Avian influenza virus (AIV) persists in North American wild waterfowl, exhibiting major outbreaks every 2-4 years. Attempts to explain the patterns of periodicity and persistence using simple direct transmission models are unsuccessful. Motivated by empirical evidence, we examine the contribution of an overlooked AIV transmission mode: environmental transmission. It is known that infectious birds shed large concentrations of virions in the environment, where virions may persist for a long time. We thus propose that, in addition to direct fecal/oral transmission, birds may become infected by ingesting virions that have long persisted in the environment. We design a new host-pathogen model that combines within-season transmission dynamics, between-season migration and reproduction, and environmental variation. Analysis of the model yields three major results. First, environmental transmission provides a persistence mechanism within small communities where epidemics cannot be sustained by direct transmission only (i.e., communities smaller than the critical community size). Second, environmental transmission offers a parsimonious explanation of the 2-4 year periodicity of avian influenza epidemics. Third, very low levels of environmental transmission (i.e., few cases per year) are sufficient for avian influenza to persist in populations where it would otherwise vanish.

Lassa fever is caused by a viral haemorrhagic arenavirus that affects two to three million people in West Africa, causing a mortality of between 5,000 and 10,000 each year. The natural reservoir of Lassa virus is the multi-mammate rat Mastomys natalensis, which lives in houses and surrounding fields. With the aim of gaining more information to control this disease, we here carry out a spatial analysis of Lassa fever data from human cases and infected rodent hosts covering the period 1965-2007. Information on contemporary environmental conditions (temperature, rainfall, vegetation) was derived from NASA Terra MODIS satellite sensor data and other sources and for elevation from the GTOPO30 surface for the region from Senegal to the Congo. All multi-temporal data were analysed using temporal Fourier techniques to generate images of means, amplitudes and phases which were used as the predictor variables in the models. In addition, meteorological rainfall data collected between 1951 and 1989 were used to generate a synoptic rainfall surface for the same region. Three different analyses (models) are presented, one superimposing Lassa fever outbreaks on the mean rainfall surface (Model 1) and the other two using non-linear discriminant analytical techniques. Model 2 selected variables in a step-wise inclusive fashion, and Model 3 used an information-theoretic approach in which many different random combinations of 10 variables were fitted to the Lassa fever data. Three combinations of absenceratiopresence clusters were used in each of Models 2 and 3, the 2 absenceratio1 presence cluster combination giving what appeared to be the best result. Model 1 showed that the recorded outbreaks of Lassa fever in human populations occurred in zones receiving between 1,500 and 3,000 mm rainfall annually. Rainfall, and to a much lesser extent temperature variables, were most strongly selected in both Models 2 and 3, and neither vegetation nor altitude seemed particularly important. Both Models 2 and 3 produced mean kappa values in excess of 0.91 (Model 2) or 0.86 (Model 3), making them 'Excellent'. The Lassa fever areas predicted by the models cover approximately 80% of each of Sierra Leone and Liberia, 50% of Guinea, 40% of Nigeria, 30% of each of Côte d'Ivoire, Togo and Benin, and 10% of Ghana.

Background: Winter chill is one of the defining characteristics of a location's suitability for the production of many tree crops. We mapped and investigated observed historic and projected future changes in winter chill in California, quantified with two different chilling models (Chilling Hours, Dynamic Model). Methodology/Principal Findings: Based on hourly and daily temperature records, winter chill was modeled for two past temperature scenarios (1950 and 2000), and 18 future scenarios (average conditions during 2041–2060 and 2080–2099 under each of the B1, A1B and A2 IPCC greenhouse gas emissions scenarios, for the CSIRO-MK3, HadCM3 and MIROC climate models). For each scenario, 100 replications of the yearly temperature record were produced, using a stochastic weather generator. We then introduced and mapped a novel climatic statistic, “safe winter chill”, the 10% quantile of the resulting chilling distributions. This metric can be interpreted as the amount of chilling that growers can safely expect under each scenario. Winter chill declined substantially for all emissions scenarios, with the area of safe winter chill for many tree species or cultivars decreasing 50–75% by mid-21st century, and 90–100% by late century. Conclusions/Significance: Both chilling models consistently projected climatic conditions by the middle to end of the 21st century that will no longer support some of the main tree crops currently grown in California, with the Chilling Hours Model projecting greater changes than the Dynamic Model. The tree crop industry in California will likely need to develop agricultural adaptation measures (e.g. low-chill varieties and dormancy-breaking chemicals) to cope with these projected changes. For some crops, production might no longer be possible.

Understanding the role of humans in the dispersal of predominantly animal pathogens is essential for their control. We used newly developed Bayesian phylogeographic methods to unravel the dynamics and determinants of the spread of dog rabies virus (RABV) in North Africa. Each of the countries studied exhibited largely disconnected spatial dynamics with major geopolitical boundaries acting as barriers to gene flow. Road distances proved to be better predictors of the movement of dog RABV than accessibility or raw geographical distance, with occasional long distance and rapid spread within each of these countries. Using simulations that bridge phylodynamics and spatial epidemiology, we demonstrate that the contemporary viral distribution extends beyond that expected for RABV transmission in African dog populations. These results are strongly supportive of human-mediated dispersal, and demonstrate how an integrated phylogeographic approach will turn viral genetic data into a powerful asset for characterizing, predicting, and potentially controlling the spatial spread of pathogens.

  [...]these studies are difficult to compare and impossible to synthesize globally. Records of the presence or absence of a DVS at a particular site and on a particular date were entered into the database so that information collected at different times from a locality was documented. Because abundance data have not been reported using methods that can be readily standardized across entomological surveys, only presence and absence data were used to generate the maps.\\n It is clear that subregional ecological diversity, coupled with the behavioural plasticity of many DVS, will require that any maps, and associated bionomics information provided, be interpreted and acted on cautiously with local expert knowledge.

Despite a long history of investigation, considerable debate revolves around whether Neanderthals became extinct because of climate change or competition with anatomically modern humans (AMH). We apply a new methodology integrating archaeological and chronological data with high-resolution paleoclimatic simulations to define eco-cultural niches associated with Neanderthal and AMH adaptive systems during alternating cold and mild phases of Marine Isotope Stage 3. Our results indicate that Neanderthals and AMH exploited similar niches, and may have continued to do so in the absence of contact. The southerly contraction of Neanderthal range in southwestern Europe during Greenland Interstadial 8 was not due to climate change or a change in adaptation, but rather concurrent AMH geographic expansion appears to have produced competition that led to Neanderthal extinction.