Disease spread in small-size directed networks: Epidemic threshold, correlation between links to and from nodes, and clustering

Network epidemiology has mainly focused on large-scale complex networks. It is unclear whether findings of these investigations also apply to networks of small size. This knowledge gap is of relevance for many biological applications, including meta-communities, plant–pollinator interactions and the spread of the oomycete pathogen Phytophthora ramorum in networks of plant nurseries. Moreover, many small-size biological networks are inherently asymmetrical and thus cannot be realistically modelled with undirected networks. We modelled disease spread and establishment in directed networks of 100 and 500 nodes at four levels of connectance in six network structures (local, small-world, random, one-way, uncorrelated, and two-way scale-free networks). The model was based on the probability of infection persistence in a node and of infection transmission between connected nodes. Regardless of the size of the network, the epidemic threshold did not depend on the starting node of infection but was negatively related to the correlation coefficient between in- and out-degree for all structures, unless networks were sparsely connected. In this case clustering played a significant role. For small-size scale-free directed networks to have a lower epidemic threshold than other network structures, there needs to be a positive correlation between number of links to and from nodes. When this correlation is negative (one-way scale-free networks), the epidemic threshold for small-size networks can be higher than in non-scale-free networks. Clustering does not necessarily have an influence on the epidemic threshold if connectance is kept constant. Analyses of the influence of the clustering on the epidemic threshold in directed networks can also be spurious if they do not consider simultaneously the effect of the correlation coefficient between in- and out-degree.     

Spatial network structure and metapopulation persistence

We explore the relationship between network structure and dynamics by relating the topology of spatial networks with its underlying metapopulation abundance. Metapopulation abundance is largely affected by the architecture of the spatial network, although this effect depends on demographic parameters here represented by the extinction-to-colonization ratio (e/c). Thus, for moderate to large e/c-values, regional abundance grows with the heterogeneity of the network, with uniform or random networks having the lowest regional abundances, and scale-free networks having the largest abundance. However, the ranking is reversed for low extinction probabilities, with heterogeneous networks showing the lowest relative abundance. We further explore the mechanisms underlying such results by relating a node's incidence (average number of time steps the node is occupied) with its degree, and with the average degree of the nodes it interacts with. These results demonstrate the importance of spatial network structure to understanding metapopulation abundance, and serve to determine under what circumstances information on network structure should be complemented with information on the species life-history traits to understand persistence in heterogeneous environments.     

The number of links to and from the starting node as a predictor of epidemic size in small-size directed networks

Much recent modelling is focusing on epidemics in large-scale complex networks. Whether or not findings of these investigations also apply to networks of small size is still an open question. This is an important gap for many biological applications, including the spread of the oomycete pathogen Phytophthora ramorum in networks of plant nurseries. We use numerical simulations of disease spread and establishment in directed networks of 100 individual nodes at four levels of connectivity. Factors governing epidemic spread are network structure (local, small-world, random, scale-free) and the probabilities of infection persistence in a node and of infection transmission between connected nodes. Epidemic final size at equilibrium varies widely depending on the starting node of infection, although the latter does not affect the threshold condition for spread. The number of links from (out-degree) but not the number of links to (in-degree) the starting node of the epidemic explains a substantial amount of variation in final epidemic size at equilibrium irrespective of the structure of the network. The proportion of variance in epidemic size explained by the out-degree of the starting node increases with the level of connectivity. Targeting highly connected nodes is thus likely to make disease control more effective also in case of small-size populations, a result of relevance not just for the horticultural trade, but for epidemiology in general.     

Spatial network structure and amphibian persistence in stochastic environments

In the past few years, the framework of complex networks has provided new insight into the organization and function of biological systems. However, in spite of its potential, spatial ecology has not yet fully incorporated tools and concepts from network theory. In the present study, we identify a large spatial network of temporary ponds, which are used as breeding sites by several amphibian species. We investigate how the structural properties of the spatial network change as a function of the amphibian dispersal distance and the hydric conditions. Our measures of network topology suggest that the observed spatial structure of ponds is robust to drought (compared with similar random structures), allowing the movement of amphibians to and between flooded ponds, and hence, increasing the probability of reproduction even in dry seasons.     

传粉网络的研究进展:网络的结构和动态

植物与传粉者之间相互作用,构成了复杂的传粉网络。近年来,社会网络分析技术的发展使得复杂生态网络的研究成为可能。从群落水平上研究植物与传粉者之间的互惠关系,为理解群落的结构和动态以及花部特征的演化提供了全新的视角。传粉网络的嵌套结构说明自然界的传粉服务存在冗余,而且是相对泛化的物种主导了传粉。在多年或者多季度的传粉网络中,虽然有很高的物种替换率,但是其网络结构仍然保持相对稳定,说明传粉网络对干扰有很强的抗性。尽管有关网络结构和动态的研究逐渐增多,但传粉网络维持的机制仍不清楚。网络结构可以部分由花部特征与传粉者的匹配来解释,也受到系统发生的制约,影响因素还包括群落构建的时间和物种多样性,以及物种在群落中的位置。开展大尺度群落动态的研究,为探索不同时间尺度、不同物种多样性水平上的传粉网络的生态学意义提供了条件。但已有的研究仍存在不足,比如基于访问观察的网络无法准确衡量传粉者的访问效率和植物间的花粉流动,以及结果受到调查精度区域研究不平衡的制约等。目前的研究只深入到传粉者携带花粉构成成分的水平,传粉者访问植物的网络不能代表植物的整个传粉过程。因此,研究应当更多地深入到物种之间关系对有性生殖的切实影响上。     

Disease persistence in epidemiological models: the interplay between vaccination and migration

We consider the interplay of vaccination and migration rates on disease persistence in epidemiological systems. We show that short-term and long-term migration can inhibit disease persistence. As a result, we show how migration changes how vaccination rates should be chosen to maintain herd immunity. In a system of coupled SIR models, we analyze how disease eradication depends explicitly on vaccine distribution and migration connectivity. The analysis suggests potentially novel vaccination policies that underscore the importance of optimal placement of finite resources.     

The interplay between microscopic and mesoscopic structures in complex networks

Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from properties shared by groups of nodes. Disentangling the determinants of network structure on these different scales has remained a major, and so far unsolved, challenge. Here we show how multiscale generative probabilistic exponential random graph models combined with efficient, distributive message-passing inference techniques can be used to achieve this separation of scales, leading to improved detection accuracy of latent classes as demonstrated on benchmark problems. It sheds new light on the statistical significance of motif-distributions in neural networks and improves the link-prediction accuracy as exemplified for gene-disease associations in the highly consequential Online Mendelian Inheritance in Man database.     

Scales of persistence: transmission and the microbiome

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Finding quasi-optimal network topologies for information transmission in active networks

This work clarifies the relation between network circuit (topology) and behaviour (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.     

Dendritic network structure and dispersal affect temporal dynamics of diversity and species persistence

Landscape connectivity structure, specifically the dendritic network structure of rivers, is expected to influence community diversity dynamics by altering dispersal patterns, and subsequently the unfolding of species interactions. However, previous comparative and experimental work on dendritic metacommunities has studied diversity mostly from an equilibrium perspective. Here we investigated the effect of dendritic versus linear network structure on local (α‐diversity), among (β‐diversity) and total (γ‐diversity) temporal species community diversity dynamics. Using a combination of microcosm experiments, which allowed for active dispersal of 14 protists and a rotifer species, and numerical analyses, we demonstrate the general importance of spatial network configuration and basic life history tradeoffs as driving factors of different diversity patterns in linear and dendritic systems. We experimentally found that community diversity patterns were shaped by the interaction of dispersal within the networks and local species interactions. Specifically, α‐diversity remained higher in dendritic networks over time, especially at highly connected sites. β‐diversity was initially greater in linear networks, due to increased dispersal limitation, but became more similar to β‐diversity in dendritic networks over time. Comparing the experimental results with a neutral metacommunity model we found that dispersal and network connectivity alone may, to a large extent, explain α‐ and β‐diversity dynamics. However, additional mechanisms, such as variation in carrying capacity and competition–colonization tradeoffs, were needed in the model to capture the detailed temporal diversity dynamics of the experiments, such as a general decline in γ‐diversity and long‐term dynamics in α‐diversity.     

Biodiversity conservation in metacommunity networks: linking pattern and persistence

A central goal of conservation science is to identify the most important habitat patches for maintaining biodiversity on a landscape. Spatial biodiversity patterns are often used for such assessments, and patches that harbor unique diversity are generally prioritized over those with high community similarity to other areas. This places an emphasis on biodiversity representation, but removing a patch can have cascading effects on biodiversity persistence in the remaining ecological communities. Metacommunity theory provides a mechanistic route to the linking of biodiversity patterns on a landscape with the subsequent dynamics of diversity loss after habitat is degraded. Using spatially explicit neutral theory, I focus on the situation where spatial patterns of diversity and similarity are generated by the structure of dispersal networks and not environmental gradients. I find that gains in biodiversity representation are nullified by losses in persistence, and as a result the effects of removing a patch on metacommunity diversity are essentially independent of complementarity or other biodiversity patterns. In this scenario, maximizing protected area and not biodiversity representation is the key to maintaining diversity in the long term. These results highlight the need for a broader understanding of how conservation paradigms perform under different models of metacommunity dynamics.     

Identification of directed interactions in networks

Multichannel data collection in the neurosciences is routine and has necessitated the development of methods to identify the direction of interactions among processes. The most widely used approach for detecting these interactions in such data is based on autoregressive models of stochastic processes, although some work has raised the possibility of serious difficulties with this approach. This article demonstrates that these difficulties are present and that they are intrinsic features of the autoregressive method. Here, we introduce a new method taking into account unobserved processes and based on coherence. Two examples of three-process networks are used to demonstrate that although coherence measures are intrinsically non-directional, a particular network configuration will be associated with a particular set of coherences. These coherences may not specify the network uniquely, but in principle will specify all network configurations consistent with their values and will also specify the relationships among the unobserved processes. Moreover, when new information becomes available, the values of the measures of association already in place do not change, but the relationships among the unobserved processes may become further resolved.     

The interplay between structure and function in intrinsically unstructured proteins

Intrinsically unstructured proteins (IUPs) are common in various proteomes and occupy a unique structural and functional niche in which function is directly linked to structural disorder. The evidence that these proteins exist without a well-defined folded structure in vitro is compelling, and justifies considering them a separate class within the protein world. In this paper, novel advances in the rapidly advancing field of IUPs are reviewed, with the major attention directed to the evidence of their unfolded character in vivo, the interplay of their residual structure and their various functional modes and the functional benefits their malleable structural state provides. Via all these details, it is demonstrated that in only a couple of years after its conception, the idea of protein disorder has already come of age and transformed our basic concepts of protein structure and function.     

The interplay between microevolution and community structure in microbial populations

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Highlights► The action of industrial processes depends on microbial community structure. ► Microbes evolve very rapidly. ► Microbial evolution is affected by community structure. ► Community structure is affected by microbial evolution. ► This feedback may be crucial when considering microbial communities in industry.     

Effects of network and dynamical model structure on species persistence in large model food webs

Four models of network structure are combined with models of bioenergetic dynamics to study the role of food web topology and nonlinear dynamics on species coexistence in complex ecological networks. Network models range from the highly structured niche model to loosely constrained energetically feasible random networks. Bioenergetic models differ in how they represent primary production, functional responses, and consumption by generalists. Network structure weakly influenced the ability of species to coexist. Species persistence is strongly affected by functional responses and generalists’ consumption rates but weakly affected by models and amounts of primary production. Despite these generalities, specific mechanisms that determine persistence under one dynamical regime, such as top-down control by consumers, may play an insignificant role under different dynamical conditions. Future research is needed to strengthen the weak empirical basis for various functional forms and parameter values that strongly influence whether species can coexist in complex food webs. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Theory of interface: Category theory,directed networks and evolution of biological networks

Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this paper, first we discuss that these two modes can be associated with the category theoretic duality (adjunction) and derive a natural network structure (a path notion) for each mode by appealing to the category theoretic universality. The path notion corresponding to the static mode is just the usual directed path. The path notion for the dynamic mode is called lateral path which is the alternating path considered on the set of arcs. Their general functionalities in a network are transport and coherence, respectively. Second, we introduce a betweenness centrality of arcs for each mode and see how the two modes are embedded in various real biological network data. We find that there is a trade-off relationship between the two centralities: if the value of one is large then the value of the other is small. This can be seen as a kind of division of labor in a network into transport on the network and coherence of the network. Finally, we propose an optimization model of networks based on a quality function involving intensities of the two modes in order to see how networks with the above trade-off relationship can emerge through evolution. We show that the trade-off relationship can be observed in the evolved networks only when the dynamic mode is dominant in the quality function by numerical simulations. We also show that the evolved networks have features qualitatively similar to real biological networks by standard complex network analysis.     

On the limit cycle structure of threshold boolean networks over complete graphs

In previous work, the limit structure of positive and negative finite threshold boolean networks without inputs (TBNs) over the complete digraph K(n) was analyzed and an algorithm was presented for computing this structure in polynomial time. Those results are generalized in this paper to cover the case of arbitrary TBNs over K(n). Although the limit structure is now more complicated, containing, not only fixed-points and cycles of length 2, but possibly also cycles of arbitrary length, a simple algorithm is still available for its determination in polynomial time. Finally, the algorithm is generalized to cover the case of symmetric finite boolean networks over K(n).     

The effects of connectivity on metapopulation persistence: network symmetry and degree correlations

A spatial metapopulation is a mosaic of interconnected patch populations. The complex routes of colonization between the patches are governed by the metapopulation''s dispersal network. Over the past two decades, there has been considerable interest in uncovering the effects of dispersal network topology and its symmetry on metapopulation persistence. While most studies find that the level of symmetry in dispersal pattern enhances persistence, some have reached the conclusion that symmetry has at most a minor effect. In this work, we present a new perspective on the debate. We study properties of the in- and out-degree distribution of patches in the metapopulation which define the number of dispersal routes into and out of a particular patch, respectively. By analysing the spectral radius of the dispersal matrices, we confirm that a higher level of symmetry has only a marginal impact on persistence. We continue to analyse different properties of the in–out degree distribution, namely the ‘in–out degree correlation’ (IODC) and degree heterogeneity, and find their relationship to metapopulation persistence. Our analysis shows that, in contrast to symmetry, the in–out degree distribution and particularly, the IODC are dominant factors controlling persistence.     

Metapopulation persistence and species spread in river networks

River networks define ecological corridors characterised by unidirectional streamflow, which may impose downstream drift to aquatic organisms or affect their movement. Animals and plants manage to persist in riverine ecosystems, though, which in fact harbour high biological diversity. Here, we study metapopulation persistence in river networks analysing stage‐structured populations that exploit different dispersal pathways, both along‐stream and overland. Using stability analysis, we derive a novel criterion for metapopulation persistence in arbitrarily complex landscapes described as spatial networks. We show how dendritic geometry and overland dispersal can promote population persistence, and that their synergism provides an explanation of the so‐called `drift paradox’. We also study the geography of the initial spread of a species and place it in the context of biological invasions. Applications concerning the persistence of stream salamanders in the Shenandoah river, and the spread of two invasive species in the Mississippi‐Missouri are also discussed.     

The interplay of fold recognition and experimental structure determination in structural genomics

Achieving the goals of structural genomics initiatives depends on the outcomes of two groups of factors: the number and distribution of experimentally determined protein structures, and our ability to assign novel proteins to known structures (fold recognition) and use them to build models (modeling). The quality of the tools used for fold recognition defines the scope of experimental effort - the more distant the templates that can be recognized, the smaller the number of proteins that have to be solved. Recent improvements in fold recognition may have suggested that the goals of structural genomics initiatives are getting closer. However, problems that surfaced during the first few years of active work have put many of the early estimates in doubt and new ones are still slow in coming.