Diversity in a complex ecological network with two interaction types

Most studies on ecological networks consider only a single interaction type (e.g. competitive, predatory or mutualistic), and try to developrules for system stability based exclusively on properties of this interaction type. However, the stability of ecological networks may be more dependent on the way different interaction types are combined in real communities. To address this issue, we start by compiling an ecological network in the Doñana Biological Reserve, southern Spain, with 390 species and 798 mu-tualistic and antagonistic interactions. We characterize network structure by looking at how mutualistic and antagonistic interactions are combined across all plant species. Both the ratio of mutualistic to antagonistic interactions per plant, and the number of basic modules with an antagonistic and a mutualistic interaction are very heterogeneous across plant species, with a few plant species showing very high values for these parameters. To assess the implications of these network patterns on species diversity, we study analytically and by simulation a model of this ecological network. We find that the observed correlation between strong interaction strengths and high mutualistic to antagonistic ratios in a few plant species significantly increases community diversity. Thus, to predict the persistence of biodiversity we need to understand how interaction strength and the architecture of ecological networks with different interaction types are combined.     

Discovering functional interaction patterns in protein-protein interaction networks

Background  

In recent years, a considerable amount of research effort has been directed to the analysis of biological networks with the availability of genome-scale networks of genes and/or proteins of an increasing number of organisms. A protein-protein interaction (PPI) network is a particular biological network which represents physical interactions between pairs of proteins of an organism. Major research on PPI networks has focused on understanding the topological organization of PPI networks, evolution of PPI networks and identification of conserved subnetworks across different species, discovery of modules of interaction, use of PPI networks for functional annotation of uncharacterized proteins, and improvement of the accuracy of currently available networks.     

Evolution of reproductive effort in a metapopulation with local extinctions and ecological succession

Abstract Using a metapopulation model, we study how local extinctions, limited population life span, and local demographic disequilibrium affect the evolution of the reproductive effort in a species with overlapping generations but no senescence. We show that in a metapopulation with saturation of all sites and an infinite deme maximal life span (no succession), local extinctions simply constitute an additional source of extrinsic mortality. When either the hypothesis of an infinite deme maximal life span or the saturation hypothesis is relaxed, nontrivial predictions arise. in particular, we find interactions between the evolutionarily stable reproductive effort strategy and the demographic dynamics in the metapopulation. We predict that larger reproductive effort may be selected for in habitats of poorer productivity, contrary to what would be predicted in a single population. Also, we predict that higher dispersal rates should favor selection for lower reproductive efforts. However, metapopulation parameters that favor high dispersal rates also favor larger reproductive efforts. Conflicting selection pressures in the metapopulation also allow maintaining evolutionarily stable polymorphism between a low and high reproductive effort for particular trade-offs between survival and fecundity.     

Pattern formation in associative neural networks with weak lateral interaction

A model is proposed for the formation of singularities in the director field of orientation-selective cells in the visual cortex. The model consists of a two-layer associative neural net. The forward connections converge to a continuum of steady states. The degeneracy is removed by lateral interactions. It is shown that in many cases the director field contains critical points which are identified as the vortex locations. Received: 1 January 1993/Accepted in revised form: 8 September 1993     

The effects of space and diversity of interaction types on the stability of complex ecological networks

The relationship between structure and stability in ecological networks and the effect of spatial dynamics on natural communities have both been major foci of ecological research for decades. Network research has traditionally focused on a single interaction type at a time (e.g. food webs, mutualistic networks). Networks comprising different types of interactions have recently started to be empirically characterized. Patterns observed in these networks and their implications for stability demand for further theoretical investigations. Here, we employed a spatially explicit model to disentangle the effects of mutualism/antagonism ratios in food web dynamics and stability. We found that increasing levels of plant-animal mutualistic interactions generally resulted in more stable communities. More importantly, increasing the proportion of mutualistic vs. antagonistic interactions at the base of the food web affects different aspects of ecological stability in different directions, although never negatively. Stability is either not influenced by increasing mutualism—for the cases of population stability and species’ spatial distributions—or is positively influenced by it—for spatial aggregation of species. Additionally, we observe that the relative increase of mutualistic relationships decreases the strength of biotic interactions in general within the ecological network. Our work highlights the importance of considering several dimensions of stability simultaneously to understand the dynamics of communities comprising multiple interaction types.     

Plant functional types and ecological strategies in Patagonian forbs

Abstract. We identified four major functional types of forbs in the Patagonian steppe, taking into account phenological and morphological traits: (1) shallow-rooted mesophytic species (annuals), (2) shallow-rooted non-mesophytic species, (3) deep-rooted evergreen species, and (4) deep-rooted deciduous species. The major attributes differentiating these groups were the date at which seasonal growth ended, rooting depth, sprouting depth, distance between shoots of the same plant, and degree of ‘mesophytism’. We used Cluster and Principal Components Analyses to identify the groups, and the attributes determining them. Late-growth-cycle types had deep roots and/or high ‘xerophytism’. Late-cycle-xerophytic types had a great sprouting depth, and late-cycle-deep-rooted types had a great distance between shoots of the same plant. On the basis of current knowledge of the structure and functioning of the Patagonian steppe, we suggested three explanations to account for these correlations. 1. Late-cycle forbs survive summer water deficit if they have xerophytic characteristics that reduce transpiration water losses, and/or they have deep roots that increase water uptake. 2. Sprouting depth results from the shift of active buds to dormant buds at the end of the cycle. Summer forbs have a great sprouting depth because only buds which are located deep in the soil survive hot and dry summers. 3. Distant shoots of summer forbs allow them simultaneously to use the high protection against desiccating winds provided by shrubs, and the ample water availability of bare soil patches. All the functional types of forbs depend on winter water recharge to begin their cycles, but each one completes its cycle by using a different portion of the water resources available in spring and summer.     

Species abundance and asymmetric interaction strength in ecological networks

The strength of interactions among species in a network tends to be highly asymmetric. We evaluate the hypothesis that this asymmetry results from the distribution of abundance among species, so that species interactions occur randomly among individuals. We used a database on mutualistic and antagonistic bipartite quantitative interaction networks. We show that across all types of networks asymmetry was correlated with abundance, so that rare species were asymmetrically affected by their abundant partners, while pairs of interacting abundant species tended to exhibit more symmetric, reciprocally strong effects. A null model shows that abundance provides a sufficient explanation of the asymmetry structure in some networks, but suggests the role of additional factors in others. Although not universal, our hypothesis holds for a substantial fraction of networks analyzed here, and should be considered as a null model in all studies aimed at evaluating the ecological and evolutionary consequences of species interactions.     

Exploring overlapping functional units with various structure in protein interaction networks

Revealing functional units in protein-protein interaction (PPI) networks are important for understanding cellular functional organization. Current algorithms for identifying functional units mainly focus on cohesive protein complexes which have more internal interactions than external interactions. Most of these approaches do not handle overlaps among complexes since they usually allow a protein to belong to only one complex. Moreover, recent studies have shown that other non-cohesive structural functional units beyond complexes also exist in PPI networks. Thus previous algorithms that just focus on non-overlapping cohesive complexes are not able to present the biological reality fully. Here, we develop a new regularized sparse random graph model (RSRGM) to explore overlapping and various structural functional units in PPI networks. RSRGM is principally dominated by two model parameters. One is used to define the functional units as groups of proteins that have similar patterns of connections to others, which allows RSRGM to detect non-cohesive structural functional units. The other one is used to represent the degree of proteins belonging to the units, which supports a protein belonging to more than one revealed unit. We also propose a regularizer to control the smoothness between the estimators of these two parameters. Experimental results on four S. cerevisiae PPI networks show that the performance of RSRGM on detecting cohesive complexes and overlapping complexes is superior to that of previous competing algorithms. Moreover, RSRGM has the ability to discover biological significant functional units besides complexes.     

Correlation between interaction strengths drives stability in large ecological networks

Food webs have markedly non‐random network structure. Ecologists maintain that this non‐random structure is key for stability, since large random ecological networks would invariably be unstable and thus should not be observed empirically. Here we show that a simple yet overlooked feature of natural food webs, the correlation between the effects of consumers on resources and those of resources on consumers, substantially accounts for their stability. Remarkably, random food webs built by preserving just the distribution and correlation of interaction strengths have stability properties similar to those of the corresponding empirical systems. Surprisingly, we find that the effect of topological network structure on stability, which has been the focus of countless studies, is small compared to that of correlation. Hence, any study of the effects of network structure on stability must first take into account the distribution and correlation of interaction strengths.     

Tolerance of pollination networks to species extinctions

Mutually beneficial interactions between flowering plants and animal pollinators represent a critical 'ecosystem service' under threat of anthropogenic extinction. We explored probable patterns of extinction in two large networks of plants and flower visitors by simulating the removal of pollinators and consequent loss of the plants that depend upon them for reproduction. For each network, we removed pollinators at random, systematically from least-linked (most specialized) to most-linked (most generalized), and systematically from most- to least-linked. Plant species diversity declined most rapidly with preferential removal of the most-linked pollinators, but declines were no worse than linear. This relative tolerance to extinction derives from redundancy in pollinators per plant and from nested topology of the networks. Tolerance in pollination networks contrasts with catastrophic declines reported from standard food webs. The discrepancy may be a result of the method used: previous studies removed species from multiple trophic levels based only on their linkage, whereas our preferential removal of pollinators reflects their greater risk of extinction relative to that of plants. In both pollination networks, the most-linked pollinators were bumble-bees and some solitary bees. These animals should receive special attention in efforts to conserve temperate pollination systems.     

The ecological and evolutionary implications of merging different types of networks

Interactions among species drive the ecological and evolutionary processes in ecological communities. These interactions are effectively key components of biodiversity. Studies that use a network approach to study the structure and dynamics of communities of interacting species have revealed many patterns and associated processes. Historically these studies were restricted to trophic interactions, although network approaches are now used to study a wide range of interactions, including for example the reproductive mutualisms. However, each interaction type remains studied largely in isolation from others. Merging the various interaction types within a single integrative framework is necessary if we want to further our understanding of the ecological and evolutionary dynamics of communities. Dividing the networks up is a methodological convenience as in the field the networks occur together in space and time and will be linked by shared species. Herein, we outline a conceptual framework for studying networks composed of more than one type of interaction, highlighting key questions and research areas that would benefit from their study.     

城市生态网络功能性连接辨识方法

城市生态网络是景观生态学应用领域研究的热点和重点之一,识别、评估生境之间的连接是构建生态网络的关键环节。在总结已有连接辨识方法的基础上,提出采用最小费用模型和图论分析相结合的方法,探讨功能性连接的辨识和优先恢复途径。以新西兰基督城为案例,分别利用景观发展强度指数建立阻力面,新西兰鸡毛松(Dacrycarpus dacrydioides)种子最大传播距离作为连接阈值来模拟、评价网络连接。结果表明:在1200 m距离阈值下,共有408条连接,其重要性分为10类。其中Richmond—Petrie公园,Hansons—Auburn保护地,Centaurus公园—King George保护地是整个生态网络的关键连接;若去除,景观整体连接度将下降31.73%。此外,研究发现连接重要值与两端的源面积之和没有显著相关性,即面积大的源斑块之间的连接不一定对网络构建起关键作用,这一结论还有待进一步证明。针对缺少动物迁移资料的城市环境,改进最小费用模型和网络连接分析的部分参数;可操作性与实用性强,对中国城市区域生态恢复建设、栖息地选择具有借鉴意义。     

Indirect effects in ecological interaction networks I. The chain rule approach

A mathematical method for evaluating indirect effects propagated through ecosystems consisting of multiple species is developed. The time-backward expansion of the sensitivity matrix of a system at steady state represents the tracking back of the total effects received by species. Aggregating those portions of the total effect between two species that travel through a common path with various schedules gives the path partitioning of the total effect. From this path partitioning, a chain rule is derived that expresses the indirect effect transmitted through an individual path as the products of direct effects associated with the links constituting the path. The evaluation of indirect effects by this chain rule is applied to example systems to reveal the entire structure of influence propagation through the systems. The results of this application suggest three basic mechanisms through which indirect effects contribute to the complexity and contingency of species interactions: (i) the globalization of influence by bundles of long indirect paths, (ii) the amplification (or reduction) of effects by positive (or negative) cycles, and (iii) the alteration in sign of interactions between a pair of species due to the change in dominance among the effects carried by parallel paths connecting the species.     

Dynamic functional modules in co-expressed protein interaction networks of dilated cardiomyopathy

Background  

Molecular networks represent the backbone of molecular activity within cells and provide opportunities for understanding the mechanism of diseases. While protein-protein interaction data constitute static network maps, integration of condition-specific co-expression information provides clues to the dynamic features of these networks. Dilated cardiomyopathy is a leading cause of heart failure. Although previous studies have identified putative biomarkers or therapeutic targets for heart failure, the underlying molecular mechanism of dilated cardiomyopathy remains unclear.     

Stability of a diamond-shaped module with multiple interaction types

Indirect interactions among species emerge from the complexity of ecological networks and can strongly affect the response of communities to disturbances. To determine these indirect interactions and understand better community dynamics, ecologists focused on the interactions within small sets of species or modules. Thanks to their analytical tractability, modules bring insights on the mechanisms occurring in complex interaction networks. So far, most studies have considered modules with a single type of interaction although numerous species are involved in mutualistic and antagonistic interactions simultaneously. In this study, we analyse the dynamics of a diamond-shaped module with multiple interaction types: two resource species sharing a mutualist and a consumer. We describe the different types of indirect interaction occurring between the resource species and the conditions for a stable coexistence of all species. We show that the nature of indirect interactions between resource species (i.e. apparent facilitation, competition or antagonism), as well as stable coexistence, depend on the species generalism and asymmetry of interactions, or in other words, on the distribution of interaction strengths among species. We further unveil that a balance between mutualistic and antagonistic interactions at the level of resource species favours stable coexistence, and that species are more likely to coexist stably if there is apparent facilitation between the two resource species rather than apparent competition. Our results echo existing knowledge on the trophic diamond-shaped module, and confirm that our understanding of communities combining different interaction types can gain from module analyses.     

Semantic integration to identify overlapping functional modules in protein interaction networks

Background  

The systematic analysis of protein-protein interactions can enable a better understanding of cellular organization, processes and functions. Functional modules can be identified from the protein interaction networks derived from experimental data sets. However, these analyses are challenging because of the presence of unreliable interactions and the complex connectivity of the network. The integration of protein-protein interactions with the data from other sources can be leveraged for improving the effectiveness of functional module detection algorithms.     

Construction of reliable protein-protein interaction networks with a new interaction generality measure

MOTIVATION: Recent screening techniques have made large amounts of protein-protein interaction data available, from which biologically important information such as the function of uncharacterized proteins, the existence of novel protein complexes, and novel signal-transduction pathways can be discovered. However, experimental data on protein interactions contain many false positives, making these discoveries difficult. Therefore computational methods of assessing the reliability of each candidate protein-protein interaction are urgently needed. RESULTS: We developed a new 'interaction generality' measure (IG2) to assess the reliability of protein-protein interactions using only the topological properties of their interaction-network structure. Using yeast protein-protein interaction data, we showed that reliable protein-protein interactions had significantly lower IG2 values than less-reliable interactions, suggesting that IG2 values can be used to evaluate and filter interaction data to enable the construction of reliable protein-protein interaction networks.