A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement

Nestedness has been widely reported for both metacommunities and networks of interacting species. Even though the concept of this ecological pattern has been well-defined, there are several metrics by which it can be quantified. We noted that current metrics do not correctly quantify two major properties of nestedness: (1) whether marginal totals (i.e. fills) differ among columns and/or among rows, and (2) whether the presences (1's) in less-filled columns and rows coincide, respectively, with those found in the more-filled columns and rows. We propose a new metric directly based on these properties and compare its behavior with that of the most used metrics, using a set of model matrices ranging from highly-nested to alternative structures in which no nestedness should be detected. We also used an empirical dataset to explore possible biases generated by the metrics as well as to evaluate correlations between metrics. We found that nestedness has been quantified by metrics that inappropriately detect this pattern, even for matrices in which there is no nestedness. In addition, the most used metrics are prone to type I statistical errors while our new metric has better statistical properties and consistently rejects a nested pattern for different types of random matrices. The analysis of the empirical data showed that two nestedness metrics, matrix temperature and the discrepancy measure, tend to overestimate the degrees of nestedness in metacommunities. We emphasize and discuss some implications of these biases for the theoretical understanding of the processes shaping species interaction networks and metacommunity structure.     

Nestedness of eco‐industrial networks: Exploring linkage distribution to promote sustainable industrial growth

Eco‐industrial networks (EINs, of which eco‐industrial parks are a subset) have gained support as a solution that simultaneously reduces environmental burdens and promotes economic interests. EINs operate under a mutualistic framework, where waste materials and energy are exchanged between industries to their mutual benefit, creating a diverse web of flows. Recent studies have focused on analogies between food webs (FWs) and EINs, measuring a network's success at ecological imitation as representative of its sustainability. Studies have focused heavily on the number of links and nodes in a network, but have neglected the economic reality that each investment comes at the opportunity cost of all alternatives. This analysis focuses on the nestedness metric as used by ecologists to address this pivotal facet to the FW‐EIN analogy. Nestedness describes an ecological strategy for the position of links between nodes in a network in a way that maximizes network cycling for a given number of connections. This metric presents many advantages for EIN design and analysis, including maturity independence, size normalization, and a strong statistical record in highly mutualistic ecological systems. Application of nestedness to EINs indicates a lower presence of nested structures and more randomness than what is typically seen in FWs. The industrial networks also display a correlation between high nestedness and internal cycles, suggesting that the reuse of materials and energy in EINs can be improved upon by increasing the nestedness of structures.     

False Correlates of Nested Patterns: A Case Study Using Temporary Pond Microcrustaceans

Nestedness analysis is a popular tool for inferring spatial species distributions, and therefore has management and conservation relevance. Ecologists frequently compute nestedness and subsequently use Spearman rank correlations for inferring relationships between the observed nested ranks of sites with biogeographic and environmental variables. Using temporary pond microcrustaceans hatched from microcosms as a case study, this paper shows that the application of this method can be problematic. While the overall degree and significance of nestedness was robust against a statistical error, the results obtained from randomly generated matrices, in which community structure from the original microcrustacean incidence matrix was maintained (fixed rows –fixed columns constraints), showed that rank correlations of observed nested patterns can be vulnerable to a Type 1 error (detecting an effect when there is none). Using expected nestedness patterns derived from rarefied original matrices to control for sample size effects did not change this result. This problem may have arisen as a result of a quantitative bias related to the disproportionate impact of rank positions of individual ponds in the analysis. Future extensive simulations studies, involving different community structures, should help identify the general reliability of rank correlation results in nestedness analyses. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new algorithm to calculate the nestedness temperature of presence–absence matrices

Aim The nestedness temperature of presence–absence matrices is currently calculated with the nestedness temperature calculator (NTC). In the algorithm implemented by the NTC: (1) the line of perfect order is not uniquely defined, (2) rows and columns are reordered in such a way that the packed matrix is not the one with the lowest temperature, and (3) the null model used to determine the probabilities of finding random matrices with the same or lower temperature is not adequate for most applications. We develop a new algorithm, BINMATNEST (binary matrix nestedness temperature calculator), that overcomes these difficulties. Methods BINMATNEST implements a line of perfect order that is uniquely defined, uses genetic algorithms to determine the reordering of rows and columns that leads to minimum matrix temperature, and provides three alternative null models to calculate the statistical significance of matrix temperature. Results The NTC performs poorly when the input matrix has checkerboard patterns. The more efficient packing of BINMATNEST translates into matrix temperatures that are lower than those computed with the NTC. The null model implemented in the NTC is associated with a large frequency of type I error, while the other null models implemented in BINMATNEST (null models 2 and 3) are conservative. Overall, null model 3 provides the best performance. The nestedness temperature of a matrix is affected by its size and fill, but the probability that such a temperature is obtained by chance is not. BINMATNEST reorders the input matrix in such a way that, if fragment size/isolation plays a role in determining community structure, there will be a significant rank correlation between the size/isolation of the fragments and the way that they are ordered in the packed matrix. Main conclusions The nestedness temperature of presence–absence matrices should not be calculated with the NTC. The algorithm implemented by BINMATNEST is more robust, allowing for across‐study comparisons of the extent to which the nestedness of communities departs from randomness. The sequence in which BINMATNEST reorders habitat fragments provides information about the causal role of immigration and extinction in shaping the community under study.     

A waterfowl seed-dispersal network from the Neotropical region is nested and modular

Seed dispersal by vertebrates is fundamental for the persistence of plant species, forming networks of interactions that are often nested and modular. Networks involving angiosperms and frugivorous birds are relatively well-studied in the Neotropical region, but there are no previous studies of networks involving waterbirds. Here, we describe the structure of a Neotropical waterfowl seed-dispersal network and identify the species that have an important role for the network structure. We used information on 40 plant taxa found in fecal samples of five common waterfowl species to calculate the nestedness (NODF), weighted nestedness (WNODF), modularity, and weighted modularity of the network. We found that the network was nested, with yellow-billed teal showing the highest contribution both to nestedness and weighted nestedness. Twenty-four plant species contributed positively to weighted nestedness, with Salzmann's mille graines presenting the highest influence both to nestedness and weighted nestedness. The network was modular, but the weighted modularity was not significant. These results need to be considered with caution due to incomplete interaction sampling for two species. Ringed teal, Brazilian teal, and yellow-billed teal were considered hub modular species. Among plants, beak sedges and water snowflake were considered modular hub species, while Salzmann's mille graines and spikerush were network connectors. The structure of this Neotropical waterbird seed-dispersal network differed from the only previous waterfowl network study, from Europe, which found similar level of nestedness but no significant modularity. We include several possible explanations for this discrepancy and identified priorities for future research into waterbird–plant interaction networks. Abstract in Portuguese is available with online material.     

Dung beetle-megafauna trophic networks in Singapore’s fragmented forests

We investigated trophic networks between dung beetles and megafauna species in five forest fragments in Singapore varying in size and isolation. We found that Singapore's dung beetle communities were attracted to extant and extinct dung types from different dietary groups. All forest fragment networks were similar and displayed high generalism and high nestedness.     

Individual variation in resource use by opossums leading to nested fruit consumption

Despite recent findings on the ecological relevance of within population diet variation far less attention has been devoted to the role diet variation for ecological services. Seed dispersal is a key ecological service, affecting plant fitness and regeneration based on foraging by fruit‐eating vertebrates. Here we used a network approach, widely used to understand how seed‐dispersal is organized at the species level, to gain insights into the patterns that emerge at the individual‐level. We studied the individual fruit consumption behavior of a South American didelphid Didelphis albiventris, during the cool–dry and warm–wet seasons. In species–species networks the heterogeneity in specialization levels generates patterns such as nestedness and asymmetry. Because generalist populations may be comprised of specialized individuals, we hypo thesized that network structural properties, such as nestedness, should also emerge at the individual level. We detected variation in fruit consumption that was not related to resource availability, ontogenetic or sexual factors or sampling biases. Such variation resulted in the structural patterns often found in species–species seed‐dispersal networks: low connectance, a high degree of nestedness and the absence of modules. Moreover structure varied between the warm–wet and cool–dry seasons, presumably as a consequence of seasonal fluctuation in fruit availability. Our findings suggest individuals may differ in selectivity causing asymmetries in seed dispersal efficiency within the population. In this sense the realized dispersal would differ from the expected dispersal estimated from their average dispersal potential. Additionally the results suggest possible frequency‐dependent effects on seed dispersal that might affect individual plant performance and plant community composition.     

Chronological change of resource metabolism and decarbonization patterns in Pakistan: Perspectives from a typical developing country

With economic growth in many developing countries, not all are making similar progress with regard to material and environmental efficiencies. This study examines material use and CO₂ emission patterns and intensities from 1971 to 2015 in a typical developing country, Pakistan, and investigates national‐level and multi‐country‐level efficiency improvements using data envelopment analysis. The results are used to derive key policy insights for a sustainable economic transition with higher resource and carbon efficiencies. Results show that material intensity has reduced by 39.1% while CO₂ intensity has risen by 21.5% in the country. Pakistan, when compared with its top 10 export countries, was relatively more material and CO₂ intensive. National‐level efficiency was found to be low in most of the periods due to material/energy intensive agriculture and industries, low value‐added exports, etc. Insights from the national‐level efficiency analysis indicate that surging CO₂ intensities have started to decline since 2010 and the economy has greatly stabilized. Multi‐country analysis revealed that the efficiency gap between Pakistan and its developed export countries (such as the United Kingdom and France) has widened during the study period. Insights from the multi‐country analysis suggest that the economic growth and industrialization improves material and environmental efficiencies to some extent, yet these improvements are not equally distributed among all countries. As a way forward, integrated policies on sustainable resource consumption, carbon mitigation, and economic growth are necessary for accruing higher benefits from rising global trade and resource connectedness.     

Resource Use in Small Island States

Iceland and Trinidad and Tobago are small open, high‐income island economies with very specific resource‐use patterns. This article presents a material flow analysis (MFA) for the two countries covering a time period of nearly five decades. Both countries have a narrow domestic resource base, their economy being largely based on the exploitation of one or two key resources for export production. In the case of Trinidad and Tobago, the physical economy is dominated by oil and natural gas extraction and petrochemical industries, whereas Iceland's economy for centuries has been based on fisheries. More recently, abundant hydropower and geothermal heat were the basis for the establishment of large export‐oriented metal processing industries, which fully depend on imported raw materials and make use of domestic renewable electricity. Both countries are highly dependent on these natural resources and vulnerable to overexploitation and price developments. We show how the export‐oriented industries lead to high and growing levels of per capita material and energy use and carbon dioxide emissions resulting from large amounts of processing wastes and energy consumption in production processes. The example of small open economies with an industrial production system focused on few, but abundant, key resources and of comparatively low complexity provides interesting insights of how resource endowment paired with availability or absence of infrastructure and specific institutional arrangements drives domestic resource‐use patterns. This also contributes to a better understanding and interpretation of MFA indicators, such as domestic material consumption.     

Measuring the Intangibles: A Metrics for the Economic Complexity of Countries and Products

We investigate a recent methodology we have proposed to extract valuable information on the competitiveness of countries and complexity of products from trade data. Standard economic theories predict a high level of specialization of countries in specific industrial sectors. However, a direct analysis of the official databases of exported products by all countries shows that the actual situation is very different. Countries commonly considered as developed ones are extremely diversified, exporting a large variety of products from very simple to very complex. At the same time countries generally considered as less developed export only the products also exported by the majority of countries. This situation calls for the introduction of a non-monetary and non-income-based measure for country economy complexity which uncovers the hidden potential for development and growth. The statistical approach we present here consists of coupled non-linear maps relating the competitiveness/fitness of countries to the complexity of their products. The fixed point of this transformation defines a metrics for the fitness of countries and the complexity of products. We argue that the key point to properly extract the economic information is the non-linearity of the map which is necessary to bound the complexity of products by the fitness of the less competitive countries exporting them. We present a detailed comparison of the results of this approach directly with those of the Method of Reflections by Hidalgo and Hausmann, showing the better performance of our method and a more solid economic, scientific and consistent foundation.     

A protocol to compare nestedness among submatrices

Searching for nestedness has become a popular exercise in community ecology. Significance of a nestedness index is usually evaluated using z values, and finding that a matrix is nested is typically a common result. However, nestedness is not likely to be spread uniformly within a matrix of species presence/absence per site. Selected parts of the matrix may show a degree of nestedness significantly higher (or lower) than expected from the overall pattern. Here we describe a procedure to assess if a particular submatrix (i.e., a peculiar combination of rows and columns extracted from the complete matrix) is more or less nested than expected for an assortment of sites and species taken at random from the same overall matrix. The idea is to obtain several submatrices of different sizes from the same overall matrix and to calculate their z values. A regression is then performed between z values of submatrices and their sizes. A nestedness index independent of matrix size is suggested as the deviation of the z value of a particular submatrix from that expected according to the regression line. We applied our protocol to 55 matrices with different nestedness indices under various null-models and, for purpose of demonstration, we discussed in detail a single case study regarding various animal groups of the Aegean Islands (Greece). The obtained results strongly encourage further research to focus not only on the question whether a matrix is nested or not, but also on where and why nestedness is confined.     

Historical climate‐change influences modularity and nestedness of pollination networks

The structure of species interaction networks is important for species coexistence, community stability and exposure of species to extinctions. Two widespread structures in ecological networks are modularity, i.e. weakly connected subgroups of species that are internally highly interlinked, and nestedness, i.e. specialist species that interact with a subset of those species with which generalist species also interact. Modularity and nestedness are often interpreted as evolutionary ecological structures that may have relevance for community persistence and resilience against perturbations, such as climate‐change. Therefore, historical climatic fluctuations could influence modularity and nestedness, but this possibility remains untested. This lack of research is in sharp contrast to the considerable efforts to disentangle the role of historical climate‐change and contemporary climate on species distributions, richness and community composition patterns. Here, we use a global database of pollination networks to show that historical climate‐change is at least as important as contemporary climate in shaping modularity and nestedness of pollination networks. Specifically, on the mainland we found a relatively strong negative association between Quaternary climate‐change and modularity, whereas nestedness was most prominent in areas having experienced high Quaternary climate‐change. On islands, Quaternary climate‐change had weak effects on modularity and no effects on nestedness. Hence, for both modularity and nestedness, historical climate‐change has left imprints on the network structure of mainland communities, but had comparably little effect on island communities. Our findings highlight a need to integrate historical climate fluctuations into eco‐evolutionary hypotheses of network structures, such as modularity and nestedness, and then test these against empirical data. We propose that historical climate‐change may have left imprints in the structural organisation of species interactions in an array of systems important for maintaining biological diversity.     

From Innovation to Diversification: A Simple Competitive Model

Few attempts have been proposed in order to describe the statistical features and historical evolution of the export bipartite matrix countries/products. An important standpoint is the introduction of a products network, namely a hierarchical forest of products that models the formation and the evolution of commodities. In the present article, we propose a simple dynamical model where countries compete with each other to acquire the ability to produce and export new products. Countries will have two possibilities to expand their export: innovating, i.e. introducing new goods, namely new nodes in the product networks, or copying the productive process of others, i.e. occupying a node already present in the same network. In this way, the topology of the products network and the country-product matrix evolve simultaneously, driven by the countries push toward innovation.     

A consumer's guide to nestedness analysis

Nestedness analysis has become increasingly popular in the study of biogeographic patterns of species occurrence. Nested patterns are those in which the species composition of small assemblages is a nested subset of larger assemblages. For species interaction networks such as plant–pollinator webs, nestedness analysis has also proven a valuable tool for revealing ecological and evolutionary constraints. Despite this popularity, there has been substantial controversy in the literature over the best methods to define and quantify nestedness, and how to test for patterns of nestedness against an appropriate statistical null hypothesis. Here we review this rapidly developing literature and provide suggestions and guidelines for proper analyses. We focus on the logic and the performance of different metrics and the proper choice of null models for statistical inference. We observe that traditional 'gap-counting' metrics are biased towards species loss among columns (occupied sites) and that many metrics are not invariant to basic matrix properties. The study of nestedness should be combined with an appropriate gradient analysis to infer possible causes of the observed presence–absence sequence. In our view, statistical inference should be based on a null model in which row and columns sums are fixed. Under this model, only a relatively small number of published empirical matrices are significantly nested. We call for a critical reassessment of previous studies that have used biased metrics and unconstrained null models for statistical inference.     

Nestedness of Ectoparasite-Vertebrate Host Networks

Determining the structure of ectoparasite-host networks will enable disease ecologists to better understand and predict the spread of vector-borne diseases. If these networks have consistent properties, then studying the structure of well-understood networks could lead to extrapolation of these properties to others, including those that support emerging pathogens. Borrowing a quantitative measure of network structure from studies of mutualistic relationships between plants and their pollinators, we analyzed 29 ectoparasite-vertebrate host networks—including three derived from molecular bloodmeal analysis of mosquito feeding patterns—using measures of nestedness to identify non-random interactions among species. We found significant nestedness in ectoparasite-vertebrate host lists for habitats ranging from tropical rainforests to polar environments. These networks showed non-random patterns of nesting, and did not differ significantly from published estimates of nestedness from mutualistic networks. Mutualistic and antagonistic networks appear to be organized similarly, with generalized ectoparasites interacting with hosts that attract many ectoparasites and more specialized ectoparasites usually interacting with these same “generalized” hosts. This finding has implications for understanding the network dynamics of vector-born pathogens. We suggest that nestedness (rather than random ectoparasite-host associations) can allow rapid transfer of pathogens throughout a network, and expand upon such concepts as the dilution effect, bridge vectors, and host switching in the context of nested ectoparasite-vertebrate host networks.     

Habitat heterogeneity drives bird species richness,nestedness and habitat selection by individual species in fluvial wetlands of the Paraná River,Argentina

We assessed the relationship between habitat heterogeneity and bird species richness and composition within wetlands of the floodplain of the Middle Paraná River, Argentina. Given the high habitat heterogeneity in these wetland systems, we sought to determine whether (i) there was a positive relationship between bird species richness and habitat heterogeneity; (ii) whether bird species richness was associated with certain types of individual habitat types; (iii) whether there was a pattern of species nestedness and turnover between sites as a function of habitat heterogeneity and composition, respectively; and (iv) whether individual species exhibited associations with habitat heterogeneity. Point counts were used to survey birds at 60 sites. We estimated the area of eight habitat types found within a 200‐m radius from the centre of each site and calculated number and Pielou's evenness of habitat types. These indices, together with area proportion of each habitat type, were used as explanatory factors of bird species richness in linear regression models. Habitat heterogeneity per se rather than area of individual habitat types was a more important predictor of species richness in these fluvial wetlands. Sites with more habitat types supported more bird species. Results showed that individual bird species were associated with different habitat types and, therefore, sites that contained more habitat types contained more species. Number of habitat types accounted for species nestedness between sites whereas composition of habitat types accounted for species turnover between sites. Results suggest that selection of heterogeneous sites by individual species could help explain the positive heterogeneity–species richness relationship. Our findings highlight the importance of habitat heterogeneity per se resulting from flood disturbances in maintaining bird richness in fluvial systems.     

Network Dynamics Contribute to Structure: Nestedness in Mutualistic Networks

Both ecological and evolutionary timescales are of importance when considering an ecological system; population dynamics affect the evolution of species traits, and vice versa. Recently, these two timescales have been used to explain structural patterns in host-parasite networks, where the evolution of the manner in which species balance the use of their resources in interactions with each other was examined. One of these patterns was nestedness, in which the set of parasite species within a particular host forms a subset of those within a more species-rich host. Patterns of both nestedness and anti-nestedness have been observed significantly more often than expected due to chance in host-parasite networks. In contrast, mutualistic networks tend to display a significant degree of nestedness, but are rarely anti-nested. Within networks with different interaction types, therefore, there appears to be a feature promoting non-random structural patterns, such as nestedness and anti-nestedness, depending on the interaction types involved. Here, we invoke the co-evolution of species trait-values when allocating resources to interactions to explain the structural pattern of nestedness in a mutualistic community. We look at a bipartite, multi-species system, in which the strength of an interaction between two species is determined by the resources that each species invests in that relationship. We then analyze the evolution of these interactions using adaptive dynamics. We found that the evolution of these interactions, reflecting the trade-off of resources, could be used to accurately predict that nestedness occurs significantly more often than expect due to chance alone in a mutualistic network. This complements previous results applying the same concept to an antagonistic network. We conclude that population dynamics and resource trade-offs could be important promoters of structural patterns in ecological networks of different types.     

中国征收碳税应对碳关税的经济分析——以美国为例

碳税和碳关税作为一种价格调整机制,长期而言会对经济系统中各主体产生较强的约束力。通过GTAP-E模型的模拟分析,得出以下结论:在目前的发展阶段,碳关税并非有效的低碳经济发展政策,尤其是美国对中国征收碳关税对降低世界碳排放量的影响有限;美国针对中国采取的碳关税政策将在一定程度上对我国出口贸易产生负向影响,尤其是对中国的高碳产业影响较大;当中美采取相同的碳税政策时,碳税的征收对中国GDP造成较大的负面影响,且中国自主采取节能减排方案不足以应对美国碳关税的负面效应;而当两者采取差异化政策时,中国主动采取节能减排行动可以有效应对美国碳关税的威胁。     

Plant life history stage and nurse age change the development of ecological networks in an arid ecosystem

Understanding how ecological networks are organised over the course of an organism's lifetime is crucial for predicting the dynamics of interacting populations and communities across temporal scales. However, most studies so far considered only one life history stage at a time, such as adult, when studying networks of interacting species. Therefore, knowledge about how multiple life history stages affect the development and stability of plant–plant association networks is lacking. We measured the understory adult plant community and the soil seed bank across a plant age gradient of the nurse shrub Retama sphaerocarpa in an arid ecosystem in Spain. Using a multilayer network approach, we built adult understory–nurse and seed bank–nurse networks and analysed how network nestedness, species’ role, and species specificity varied between them and with nurse plant age. We found that seed bank and adult understory networks changed depending on nurse plant age in two different ways. With increasing nurse plant age, adult understory networks became significantly more nested than seed bank networks. The nested architecture of seed bank networks was therefore a poor predictor of adult understory network nestedness. The contribution and specificity of species to network nestedness increased with increasing nurse plant age more in the adult understory than in seed bank networks, despite high species turnover. Our data show that life history and ontogeny affect the development of plant–plant association networks. Niche construction and environmental filtering along nurse ontogeny seem pivotal mechanisms structuring adult understory networks while the assembly of seed bank networks seems rather stochastic. We highlight the importance of mature plant communities for maintaining rare species populations and supporting the stability of ecological communities through time.