Model for Heterogeneous Random Networks Using Continuous Latent Variables and an Application to a Tree–Fungus Network

Summary The mixture model is a method of choice for modeling heterogeneous random graphs, because it contains most of the known structures of heterogeneity: hubs, hierarchical structures, or community structure. One of the weaknesses of mixture models on random graphs is that, at the present time, there is no computationally feasible estimation method that is completely satisfying from a theoretical point of view. Moreover, mixture models assume that each vertex pertains to one group, so there is no place for vertices being at intermediate positions. The model proposed in this article is a grade of membership model for heterogeneous random graphs, which assumes that each vertex is a mixture of extremal hypothetical vertices. The connectivity properties of each vertex are deduced from those of the extreme vertices. In this new model, the vector of weights of each vertex are fixed continuous parameters. A model with a vector of parameters for each vertex is tractable because the number of observations is proportional to the square of the number of vertices of the network. The estimation of the parameters is given by the maximum likelihood procedure. The model is used to elucidate some of the processes shaping the heterogeneous structure of a well‐resolved network of host/parasite interactions.     

Frequentist model averaging for undirected Gaussian graphical models

Advances in information technologies have made network data increasingly frequent in a spectrum of big data applications, which is often explored by probabilistic graphical models. To precisely estimate the precision matrix, we propose an optimal model averaging estimator for Gaussian graphs. We prove that the proposed estimator is asymptotically optimal when candidate models are misspecified. The consistency and the asymptotic distribution of model averaging estimator, and the weight convergence are also studied when at least one correct model is included in the candidate set. Furthermore, numerical simulations and a real data analysis on yeast genetic data are conducted to illustrate that the proposed method is promising.     

Patterns of abundance and morphology as indicators of ecosystem status: A meta-analysis

A series of studies have suggested that abundance and morphology distributions approximate the lognormal in undisturbed communities and depart from the lognormal with disturbance. However, this proposed capability to indicate ecosystem status has been challenged on theoretical, methodological and statistical grounds. This paper quantifies the departure from the lognormal in natural communities, and the sensitivity of such departures to disturbance, species richness, sample size, temporal and spatial scale, taxa, methodological protocols and other confounding factors. We have conducted a rigorous test of the hypothesis that distance to the lognormal represents a powerful indicator of ecosystem status. We tested three measures of distance to the lognormal and their sensitivity by reviewing 38 case studies and simulated community patterns and examined the potential and pitfalls of the approach. The most robust parameter for measuring the departure from the lognormal was found to be the normalized distance to the lognormal (ΔL). ΔL proved to be a reliable and adaptable indicator of disturbance, which is effective over a broad range of biological systems (terrestrial and aquatic, most taxa, social and economic). We show that ΔL can be measured either by quantifying abundance or by organism size, a cheaper and easy to obtain metric. Abundance distributions provide an indication of system status on a shorter time scale than size distribution. Taken together, they provide clues to the direction in which the system is moving. The sensitivity analysis shows which methods will lead to consistent results across disciplines. Our simulations confirm that disturbance consistently pushes complex systems away from the lognormal pattern, as suggested by empirical data. We conclude that the departure from the lognormal can be used as an indicator of status of a dynamic ecosystem as long as appropriate procedures are followed. Systems approximating the lognormal (ΔL close to 0) can usually be considered self-organized and little disturbed by external influences.     

生物群落多样性的测度方法 V.生物群落物种数目的估计方法

群落的物种数目,即物种丰富度,是最古老、同时也是最基本的一个多样性概念,从对它的估计中可以得到关于物种灭绝速率方面的信息,这对生物多样性保护是非常重要的。已经提出了很多方法来估计群落中的物种数目,这些方法可以分为两大类,即基于理论抽样的方法和基于数据分析的方法。前者包括经典估计方法和贝叶斯估计方法;后者包括对数正态分布的积分方法、再抽样方法和种－面积曲线的外推方法。发现：（１）有些方法适用于动物群落,如大多数基于理论抽样的方法;有些方法则适用于植物群落,如大多数基于数据分析的方法;（２）这些方法还没有经过全面而系统地比较;（３）还没有一个普遍认为比较好的方法。因此,建议采用野外调查与模拟研究相结合的方法对各种估计方法进行系统地评价。     

Emergence of community structure in terrestrial mammal-dominated ecosystems

We present a paper that combines empirical and theoretical research about the trophic organization of biological communities. Some regularities are observed in the analysis of the relationship between the trophic structure (how the species are distributed among a set of feeding groups) of a number of African large mammal communities and the type of ecosystem. Different types of ecosystems are characterized by specific patterns in the trophic structure of the mammal community. In order to explain the origin of these patterns, we propose a model defining the underlying dynamic of mammal-dominated ecosystems. The main aim of this study is to show that it is possible to obtain a dynamic explanation of those patterns. The model is shown to spontaneously define different types of structures in community organization, related to those observed. We propose a model that could help to explain the correlation between different environmental factors and the abundance or diversity of herbivores, and which establishes a general mechanism that makes it possible to understand how some rules constrain the assembly of the communities. In addition, the proposed model leads us to see how biological communities can operate in an integrated way, which allows for the acceptance of their changes on large time-scales as evolutionary. In summary, we suggest that communities are unitary structures with coherent properties that result from the self-organizing dynamic of the whole system.     

Discovering Link Communities in Complex Networks by an Integer Programming Model and a Genetic Algorithm

Identification of communities in complex networks is an important topic and issue in many fields such as sociology, biology, and computer science. Communities are often defined as groups of related nodes or links that correspond to functional subunits in the corresponding complex systems. While most conventional approaches have focused on discovering communities of nodes, some recent studies start partitioning links to find overlapping communities straightforwardly. In this paper, we propose a new quantity function for link community identification in complex networks. Based on this quantity function we formulate the link community partition problem into an integer programming model which allows us to partition a complex network into overlapping communities. We further propose a genetic algorithm for link community detection which can partition a network into overlapping communities without knowing the number of communities. We test our model and algorithm on both artificial networks and real-world networks. The results demonstrate that the model and algorithm are efficient in detecting overlapping community structure in complex networks.     

A complex speciation-richness relationship in a simple neutral model

Speciation is the "elephant in the room" of community ecology. As the ultimate source of biodiversity, its integration in ecology's theoretical corpus is necessary to understand community assembly. Yet, speciation is often completely ignored or stripped of its spatial dimension. Recent approaches based on network theory have allowed ecologists to effectively model complex landscapes. In this study, we use this framework to model allopatric and parapatric speciation in networks of communities. We focus on the relationship between speciation, richness, and the spatial structure of communities. We find a strong opposition between speciation and local richness, with speciation being more common in isolated communities and local richness being higher in more connected communities. Unlike previous models, we also find a transition to a positive relationship between speciation and local richness when dispersal is low and the number of communities is small. We use several measures of centrality to characterize the effect of network structure on diversity. The degree, the simplest measure of centrality, is the best predictor of local richness and speciation, although it loses some of its predictive power as connectivity grows. Our framework shows how a simple neutral model can be combined with network theory to reveal complex relationships between speciation, richness, and the spatial organization of populations.     

Protein-RNA interface residue prediction using machine learning: an assessment of the state of the art

Background

Understanding the interaction among different species within a community and their responses to environmental changes is a central goal in ecology. However, defining the network structure in a microbial community is very challenging due to their extremely high diversity and as-yet uncultivated status. Although recent advance of metagenomic technologies, such as high throughout sequencing and functional gene arrays, provide revolutionary tools for analyzing microbial community structure, it is still difficult to examine network interactions in a microbial community based on high-throughput metagenomics data.

Results

Here, we describe a novel mathematical and bioinformatics framework to construct ecological association networks named molecular ecological networks (MENs) through Random Matrix Theory (RMT)-based methods. Compared to other network construction methods, this approach is remarkable in that the network is automatically defined and robust to noise, thus providing excellent solutions to several common issues associated with high-throughput metagenomics data. We applied it to determine the network structure of microbial communities subjected to long-term experimental warming based on pyrosequencing data of 16?S rRNA genes. We showed that the constructed MENs under both warming and unwarming conditions exhibited topological features of scale free, small world and modularity, which were consistent with previously described molecular ecological networks. Eigengene analysis indicated that the eigengenes represented the module profiles relatively well. In consistency with many other studies, several major environmental traits including temperature and soil pH were found to be important in determining network interactions in the microbial communities examined. To facilitate its application by the scientific community, all these methods and statistical tools have been integrated into a comprehensive Molecular Ecological Network Analysis Pipeline (MENAP), which is open-accessible now (http://ieg2.ou.edu/MENA).

Conclusions

The RMT-based molecular ecological network analysis provides powerful tools to elucidate network interactions in microbial communities and their responses to environmental changes, which are fundamentally important for research in microbial ecology and environmental microbiology.     

Effects of predator confusion on functional responses

A number of experiments have addressed how increases in nitrogen availability increase the productivity and decrease the diversity of plant communities. We lack, however, a rigorous mechanistic understanding of how changes in abundance of particular species combine to produce changes in community productivity and diversity. Single experiments cannot provide insight into this issue because each species occurs only once per experiment, and each experiment is conducted in only one location; thus, it is impossible from single experiments to determine whether responses of particular species are consistent across environments or dependent on the particular environmental context in which the experiment was conducted. To address this issue, we assembled a dataset of 20 herbaceous species that were each represented in at least 6 different fertilization experiments and tested whether responses were general across experiments. Of the 20 species, one consistently increased in relative abundance and five consistently decreased across replicate experiments. A partially-overlapping group of 8 species displayed responses to nitrogen that varied predictably among experiments as a function of geographic location, neighboring species, or a handful of other community characteristics (ANPP, precipitation, species richness, relative abundance of focal species in control plots, and community composition). Thus, despite modest replication and a limited number of predictor variables, we were able to identify consistent patterns in response of 10 out of 20 species across multiple experiments. We conclude that the responses of individual species to nitrogen addition are often predictable, but that in most cases these responses are functions of the abiotic or biotic environment. Thus, a rigorous understanding of how plant species respond to nitrogen addition will have to consider not only the traits of individual plant species, but also aspects of the communities in which those plants live.     

Habitat loss and the structure of plant-animal mutualistic networks

Recent papers have described the structure of plant–animal mutualistic networks. However, no study has yet explored the dynamical implications of network structure for the persistence of such mutualistic communities. Here, we develop a patch-model of a whole plant–animal community and explore its persistence. To assess the role of network structure, we build three versions of the model. In the first version, we use the exact network of interactions of two real mutualistic communities. In the other versions, we randomize the observed network of interactions using two different null models. We show that the community response to habitat loss is affected by network structure. Real communities start to decay sooner than random communities, but persist for higher destruction levels. There is a destruction threshold at which the community collapses. Our model is the first attempt to describe the dynamics of whole mutualistic metacommunities interacting in realistic ways.     

Evaluating the performance of neutrality tests of a local community using a niche‐structured simulation model

Understanding the processes that underlie species diversity and abundance in a community is a fundamental issue in community ecology. While the species abundance distributions (SADs) of various natural communities may be well explained by Hubbell's neutral model, it has been repeatedly pointed out that Hubbell's SAD‐fitting approach lacks the ability to detect the effects of non‐neutral factors such as niche differentiation; however, our understanding of its quantitative effect is limited. Herein, we conducted extensive simulations to quantitatively evaluate the performance of the SAD‐fitting method and other recently developed tests. For simulations, we developed a niche model that incorporates the random stochastic demography of individuals and the nonrandom replacements of those individuals, i.e. niche differentiation. It therefore allows us to explore situations with various degrees of niche differentiation. We found that niche differentiation has strong effects on SADs and the number of species in the community under this model. We then examined the performance of these neutrality tests, including Hubbell's SAD‐fitting method, using extensive simulations. It was demonstrated that all these tests have relatively poor performance except for the cases with very strong niche structure, which is in accordance with previous studies. This is likely because two important parameters in Hubbell's model are usually unknown and are commonly estimated from the data to be tested. To demonstrate this point, we showed that the precise estimation of the two parameters substantially improved the performance of these neutrality tests, indicating that poor performance can be owed to overfitting Hubbell's neutral model with unrealistic parameters. Our results therefore emphasize the importance of accurate parameter estimation, which should be obtained from data independent of the local community to be tested.     

A Method of Profiling Microbial Communities Based on a Most-Probable-Number Assay That Uses BIOLOG Plates and Multiple Sole Carbon Sources

A new approach to the community-level BIOLOG assay was proposed. This assay, which we call the BIOLOG-MPN assay, is a most-probable-number (MPN) assay that uses BIOLOG plates and multiple sole carbon sources, and the profiles obtained by this assay consist of MPNs estimated for the substrates in the BIOLOG plates. In order to demonstrate the performance of the BIOLOG-MPN assay, it was applied to pure cultures, model bacterial communities that contain two strains in different ratios, and microbial community samples. MPN estimation using BIOLOG plates worked well for the substrates on which utilizers can grow at a sufficiently high rate for color development under the conditions of the assay procedure. Furthermore, the results obtained using model communities showed that the MPNs obtained reflected the mixing ratios of pure cultures in the model communities. The profiles obtained using model communities and community samples were differentiated properly by statistical analyses. The results suggest that the BIOLOG-MPN assay is a promising procedure for obtaining a quantitative picture of the community structure.     

A method of profiling microbial communities based on a most-probable-number assay that uses BIOLOG plates and multiple sole carbon sources.

A new approach to the community-level BIOLOG assay was proposed. This assay, which we call the BIOLOG-MPN assay, is a most-probable-number (MPN) assay that uses BIOLOG plates and multiple sole carbon sources, and the profiles obtained by this assay consist of MPNs estimated for the substrates in the BIOLOG plates. In order to demonstrate the performance of the BIOLOG-MPN assay, it was applied to pure cultures, model bacterial communities that contain two strains in different ratios, and microbial community samples. MPN estimation using BIOLOG plates worked well for the substrates on which utilizers can grow at a sufficiently high rate for color development under the conditions of the assay procedure. Furthermore, the results obtained using model communities showed that the MPNs obtained reflected the mixing ratios of pure cultures in the model communities. The profiles obtained using model communities and community samples were differentiated properly by statistical analyses. The results suggest that the BIOLOG-MPN assay is a promising procedure for obtaining a quantitative picture of the community structure.     

植物群落动态的模型分析

植物群落的动态是植物群落学的中心问题之一,包括更新、波动、演替、进化等主要内容。空间格局对种群和群落的动态起着至关重要的作用,种群空间格局和群落空间结构是群落中各种过程相互作用的产物。模型是描述群落动态、认识植物群落组建和维持机理的有效工具。本文阐述和比较了描述群落动态的四种具有代表性的经验模型,即镶嵌循环模型、随意游走模型、同资源种团比例模型、空间抢先占有模型及其机理。四种经验模型的空间性及缺陷分别是:(1)“镶嵌循环模型”考虑到了相邻斑块之间的植被空间结合在群落动态中的作用,而另外三种模型没有考虑到这一点;(2)在一定程度上,四种植物群落动态模型对各自针对的植物群落可能是适合的,但要作为描述群落动态发展的一般性模型还需要不断完善和发展;因为四种模型均没有考虑到自然干扰和人类干扰对植物群落动态的影响。作者对将来植物群落动态的研究及实践意义做出以下展望:(1)在不同空间尺度上,更加有效地评价控制群落动态变化的各种过程的相对重要性,并进一步将它们之间的复杂相互作用整合到群落动态模型中;(2)充分认识植物群落中存在的各种自然环境条件和生物群体的结构配置对植物群落动态发展的重要性;(3)重视植物群落动态发展中自然干扰过程和人类干扰过程的整合以     

Link Community Detection Using Generative Model and Nonnegative Matrix Factorization

Discovery of communities in complex networks is a fundamental data analysis problem with applications in various domains. While most of the existing approaches have focused on discovering communities of nodes, recent studies have shown the advantages and uses of link community discovery in networks. Generative models provide a promising class of techniques for the identification of modular structures in networks, but most generative models mainly focus on the detection of node communities rather than link communities. In this work, we propose a generative model, which is based on the importance of each node when forming links in each community, to describe the structure of link communities. We proceed to fit the model parameters by taking it as an optimization problem, and solve it using nonnegative matrix factorization. Thereafter, in order to automatically determine the number of communities, we extend the above method by introducing a strategy of iterative bipartition. This extended method not only finds the number of communities all by itself, but also obtains high efficiency, and thus it is more suitable to deal with large and unexplored real networks. We test this approach on both synthetic benchmarks and real-world networks including an application on a large biological network, and compare it with two highly related methods. Results demonstrate the superior performance of our approach over competing methods for the detection of link communities.     

Species assembly and the evolution of community structure

Summary In this paper I consider the evolutionary and ecological implications of an assembly rule which was derived empirically from studies on a heathland small-mammal community in south-eastern Australia. This rule has been tested successfully against 52 heathland small-mammal assemblages. Here it is shown to hold also for 80 forest assemblages of small mammals spanning a latitudinal range from 27°S to 43°S in south-eastern Australia. The observed forest communities are predicted by the rule and they deviate significantly from random assemblages. I suggest that the unique evolutionary history of the Australian fauna has made these patterns more apparent. The rule is simply stated as: There is a much higher probability that each species entering a community will be drawn from a different functional group (genus or other taxonomically related group of species with similar diets) until each group is represented, before the cycle repeats. A theoretical basis for the rule is proposed which extends the niche compression hypothesis to cover evolutionary time. Evolutionary constraints on adaptations for diet selection are greater than those operating on habitat selection. Successful tests in North America for the granivorous desert rodent guild and the mixed-forest insectivore guild support a wider application of this rule than the Australian communities from which it was derived. A speculative model is proposed in which the mechanisms involved in the operation of this rule shape the evolution of community structure.     

Examining the effects of species richness on community stability: an assembly model approach

We build dynamic models of community assembly by starting with one species in our model ecosystem and adding colonists. We find that the number of species present first increases, then fluctuates about some level. We ask: how large are these fluctuations and how can we characterize them statistically? As in Robert May's work, communities with weaker interspecific interactions permit a greater number of species to coexist on average. We find that as this average increases, however, the relative variation in the number of species and return times to mean community levels decreases. In addition, the relative frequency of large extinction events to small extinction events decreases as mean community size increases. While the model reproduces several of May's results, it also provides theoretical support for Charles Elton's idea that diverse communities such as those found in the tropics should be less variable than depauperate communities such as those found in arctic or agricultural settings.     

A Novel Top-k Strategy for Influence Maximization in Complex Networks with Community Structure

In complex networks, it is of great theoretical and practical significance to identify a set of critical spreaders which help to control the spreading process. Some classic methods are proposed to identify multiple spreaders. However, they sometimes have limitations for the networks with community structure because many chosen spreaders may be clustered in a community. In this paper, we suggest a novel method to identify multiple spreaders from communities in a balanced way. The network is first divided into a great many super nodes and then k spreaders are selected from these super nodes. Experimental results on real and synthetic networks with community structure show that our method outperforms the classic methods for degree centrality, k-core and ClusterRank in most cases.     

Building clone-consistent ecosystem models

Many ecological studies employ general models that can feature an arbitrary number of populations. A critical requirement imposed on such models is clone consistency: If the individuals from two populations are indistinguishable, joining these populations into one shall not affect the outcome of the model. Otherwise a model produces different outcomes for the same scenario. Using functional analysis, we comprehensively characterize all clone-consistent models: We prove that they are necessarily composed from basic building blocks, namely linear combinations of parameters and abundances. These strong constraints enable a straightforward validation of model consistency. Although clone consistency can always be achieved with sufficient assumptions, we argue that it is important to explicitly name and consider the assumptions made: They may not be justified or limit the applicability of models and the generality of the results obtained with them. Moreover, our insights facilitate building new clone-consistent models, which we illustrate for a data-driven model of microbial communities. Finally, our insights point to new relevant forms of general models for theoretical ecology. Our framework thus provides a systematic way of comprehending ecological models, which can guide a wide range of studies.