Two degrees of separation in complex food webs

Complexity does not affect stability in feasible model communities

The complexity-stability relation is a central issue in ecology. In this paper, we show how the sampling method most often used to parameterize an ecological community, can affect the conclusions about whether or not complexity promotes stability and we suggest a sampling algorithm that overcomes the problem. We also illustrate the importance of treating feasibility separately from stability when constructing model communities. Using model Lotka-Volterra competition communities we found that probability of feasibility decreases with increasing interaction strength and number of species in the community. However, for feasible systems we found that local stability probability and resilience do not significantly differ between communities with few or many species, in contrast with earlier studies that, did not account for feasibility and concluded that species-poor communities had higher probability of being locally stable than species-rich communities.

Macroecological patterns and niche structure in a new marine food web

The integration of detailed information on feeding interactions with measures of abundance and body mass of individuals provides a powerful platform for understanding ecosystem organisation. Metabolism and, by proxy, body mass constrain the flux, turnover and storage of energy and biomass in food webs. Here, we present the first food web data for Lough Hyne, a species rich Irish Sea Lough. Through the application of individual-and size-based analysis of the abundance-body mass relationship, we tested predictions derived from the metabolic theory of ecology. We found that individual body mass constrained the flux of biomass and determined its distribution within the food web. Body mass was also an important determinant of diet width and niche overlap, and predator diets were nested hierarchically, such that diet width increased with body mass. We applied a novel measure of predator-prey biomass flux which revealed that most interactions in Lough Hyne were weak, whereas only a few were strong. Further, the patterning of interaction strength between prey sharing a common predator revealed that strong interactions were nearly always coupled with weak interactions. Our findings illustrate that important insights into the organisation, structure and stability of ecosystems can be achieved through the theoretical exploration of detailed empirical data.

Success and its limits among structural models of complex food webs

1. Following the development of the relatively successful niche model, several other simple structural food web models have been proposed. These models predict the detailed structure of complex food webs given only two input parameters, the numbers of species and the number of feeding links among them. 2. The models claim different degrees of success but have not been compared consistently with each other or with the empirical data. We compared the performance of five structural models rigorously against 10 empirical food webs from a variety of aquatic and terrestrial habitats containing 25-92 species and 68-997 links. 3. All models include near-hierarchical ordering of species' consumption and have identical distributions of the number of prey of each consumer species, but differ in the extent to which species' diets are required to be contiguous and the rules used to assign feeding links. 4. The models perform similarly on a range of food-web properties, including the fraction of top, intermediate and basal species, the standard deviations of generality and connectivity and the fraction of herbivores and omnivores. 5. For other properties, including the standard deviation of vulnerability, the fraction of cannibals and species in loops, mean trophic level, path length, clustering coefficient, maximum similarity and diet discontinuity, there are significant differences in the performance of the different models. 6. While the empirical data do not support the niche model's assumption of diet contiguity, models which relax this assumption all have worse overall performance than the niche model. All the models under-estimate severely the fraction of species that are herbivores and exhibit other important failures that need to be addressed in future research.

Network structural properties mediate the stability of mutualistic communities

Key advances are being made on the structures of predator-prey food webs and competitive communities that enhance their stability, but little attention has been given to such complexity-stability relationships for mutualistic communities. We show, by way of theoretical analyses with empirically informed parameters, that structural properties can alter the stability of mutualistic communities characterized by nonlinear functional responses among the interacting species. Specifically, community resilience is enhanced by increasing community size (species diversity) and the number of species interactions (connectivity), and through strong, symmetric interaction strengths of highly nested networks. As a result, mutualistic communities show largely positive complexity-stability relationships, in opposition to the standard paradox. Thus, contrary to the commonly-held belief that mutualism's positive feedback destabilizes food webs, our results suggest that interplay between the structure and function of ecological networks in general, and consideration of mutualistic interactions in particular, may be key to understanding complexity-stability relationships of biological communities as a whole.

Functional integration of ecological networks through pathway proliferation

Large-scale structural patterns commonly occur in network models of complex systems including a skewed node degree distribution and small-world topology. These patterns suggest common organizational constraints and similar functional consequences. Here, we investigate a structural pattern termed pathway proliferation. Previous research enumerating pathways that link species determined that as pathway length increases, the number of pathways tends to increase without bound. We hypothesize that this pathway proliferation influences the flow of energy, matter, and information in ecosystems. In this paper, we clarify the pathway proliferation concept, introduce a measure of the node-node proliferation rate, describe factors influencing the rate, and characterize it in 17 large empirical food-webs. During this investigation, we uncovered a modular organization within these systems. Over half of the food-webs were composed of one or more subgroups that were strongly connected internally, but weakly connected to the rest of the system. Further, these modules had distinct proliferation rates. We conclude that pathway proliferation in ecological networks reveals subgroups of species that will be functionally integrated through cyclic indirect effects.

Hydrophobic, hydrophilic, and charged amino acid networks within protein

The native three-dimensional structure of a single protein is determined by the physicochemical nature of its constituent amino acids. The 20 different types of amino acids, depending on their physicochemical properties, can be grouped into three major classes: hydrophobic, hydrophilic, and charged. The anatomy of the weighted and unweighted networks of hydrophobic, hydrophilic, and charged residues separately for a large number of proteins were studied. Results showed that the average degree of the hydrophobic networks has a significantly larger value than that of hydrophilic and charged networks. The average degree of the hydrophilic networks is slightly higher than that of the charged networks. The average strength of the nodes of hydrophobic networks is nearly equal to that of the charged network, whereas that of hydrophilic networks has a smaller value than that of hydrophobic and charged networks. The average strength for each of the three types of networks varies with its degree. The average strength of a node in a charged network increases more sharply than that of the hydrophobic and hydrophilic networks. Each of the three types of networks exhibits the "small-world" property. Our results further indicate that the all-amino-acids networks and hydrophobic networks are of assortative type. Although most of the hydrophilic and charged networks are of the assortative type, few others have the characteristics of disassortative mixing of the nodes. We have further observed that all-amino-acids networks and hydrophobic networks bear the signature of hierarchy, whereas the hydrophilic and charged networks do not have any hierarchical signature.

Ecological networks and their fragility

Darwin used the metaphor of a 'tangled bank' to describe the complex interactions between species. Those interactions are varied: they can be antagonistic ones involving predation, herbivory and parasitism, or mutualistic ones, such as those involving the pollination of flowers by insects. Moreover, the metaphor hints that the interactions may be complex to the point of being impossible to understand. All interactions can be visualized as ecological networks, in which species are linked together, either directly or indirectly through intermediate species. Ecological networks, although complex, have well defined patterns that both illuminate the ecological mechanisms underlying them and promise a better understanding of the relationship between complexity and ecological stability.

Applying network analysis to the conservation of habitat trees in urban environments: a case study from Brisbane, Australia

In Australia more than 300 vertebrates, including 43 insectivorous bat species, depend on hollows in habitat trees for shelter with many species using a network of multiple trees as roosts. We used roost-switching data on white-striped freetail bats (Tadarida australis; Microchiroptera: Molossidae) to construct a network representation of day roosts in suburban Brisbane, Australia. Bats were caught from a communal roost tree with a roosting group of several hundred individuals and released with transmitters. Each roost used by the bats represented a node in the network, and the movements of bats between roosts formed the links between nodes. Despite differences in gender and reproductive stages, the bats exhibited the same behavior throughout three radiotelemetry periods and over 500 bat days of radio tracking: each roosted in separate roosts, switched roosts very infrequently, and associated with other bats only at the communal roost. This network resembled a scale-free network in which the distribution of the number of links from each roost followed a power law. Despite being spread over a large geographic area (> 200 km2), each roost was connected to others by less than three links. One roost (the hub or communal roost) defined the architecture of the network because it had the most links. That the network showed scale-free properties has profound implications for the management of the habitat trees of this roosting group. Scale-free networks provide high tolerance against stochastic events such as random roost removals but are susceptible to the selective removal of hub nodes. Network analysis is a useful tool for understanding the structural organization of habitat tree usage and allows the informed judgment of the relative importance of individual trees and hence the derivation of appropriate management decisions. Conservation planners and managers should emphasize the differential importance of habitat trees and think of them as being analogous to vital service centers in human societies.

Multi-target strategies for the improved treatment of depressive states: Conceptual foundations and neuronal substrates, drug discovery and therapeutic application

Major depression is a debilitating and recurrent disorder with a substantial lifetime risk and a high social cost. Depressed patients generally display co-morbid symptoms, and depression frequently accompanies other serious disorders. Currently available drugs display limited efficacy and a pronounced delay to onset of action, and all provoke distressing side effects. Cloning of the human genome has fuelled expectations that symptomatic treatment may soon become more rapid and effective, and that depressive states may ultimately be "prevented" or "cured". In pursuing these objectives, in particular for genome-derived, non-monoaminergic targets, "specificity" of drug actions is often emphasized. That is, priority is afforded to agents that interact exclusively with a single site hypothesized as critically involved in the pathogenesis and/or control of depression. Certain highly selective drugs may prove effective, and they remain indispensable in the experimental (and clinical) evaluation of the significance of novel mechanisms. However, by analogy to other multifactorial disorders, "multi-target" agents may be better adapted to the improved treatment of depressive states. Support for this contention is garnered from a broad palette of observations, ranging from mechanisms of action of adjunctive drug combinations and electroconvulsive therapy to "network theory" analysis of the etiology and management of depressive states. The review also outlines opportunities to be exploited, and challenges to be addressed, in the discovery and characterization of drugs recognizing multiple targets. Finally, a diversity of multi-target strategies is proposed for the more efficacious and rapid control of core and co-morbid symptoms of depression, together with improved tolerance relative to currently available agents.

The neurocognitive bases of human multimodal food perception: sensory integration

This review addresses a fundamental neuroscientific question in food perception: how multimodal features of food are integrated. Much research and conceptualization has emerged related to multisensory integration in vision, audition and somatosensation, while it remains poorly understood and researched within the chemical and mouth feel senses. This review aims to bridge this gap. We discuss the main concepts in the fields of auditory, visual and somatosensory multisensory integration and relate them to oral-sensory (gustatory and somatosensory) and olfactory (orolfactory) interactions. We systematically review the psychophysical literature pertaining to intra- and intermodal interactions related to food perception, while making explicit distinctions between peripheral and central interactions. As the neural bases of crossmodal orolfaction currently are poorly understood, we introduce several plausible neuroscientific models, which provide a framework for further neuroscientific exploration in this area. We are guided by a new meta-analysis of the odor-taste neuroimaging literature, as well as by single-unit, anatomical and psychophysical studies. Finally, we propose strong involvement of recurrent neural networks in multisensory integration and make suggestions for future research.

The smallest of all worlds: pollination networks

A pollination network may be either 2-mode, describing trophic and reproductive interactions between communities of flowering plants and pollinator species within a well-defined habitat, or 1-mode, describing interactions between either plants or pollinators. In a 1-mode pollinator network, two pollinator species are linked to each other if they both visit the same plant species, and vice versa for plants. Properties of 2-mode networks and their derived 1-mode networks are highly correlated and so are properties of 1-mode pollinator and 1-mode plant networks. Most network properties are scale-dependent, i.e. they are dependent upon network size. Pollination networks have the strongest small-world properties of any networks yet studied, i.e. all species are close to each other (short average path length) and species are highly clustered. Species in pollination networks are much more densely linked than species in traditional food webs, i.e. they have a higher density of links, a shorter distance between species, and species are more clustered.

Stochastic opinion formation in scale-free networks

The dynamics of opinion formation in large groups of people is a complex nonlinear phenomenon whose investigation is just beginning. Both collective behavior and personal views play an important role in this mechanism. In the present work we mimic the dynamics of opinion formation of a group of agents, represented by two states +/-1, as a stochastic response of each agent to the opinion of his/her neighbors in the social network and to feedback from the average opinion of the whole. In the light of recent studies, a scale-free Barabási-Albert network has been selected to simulate the topology of the interactions. A turbulent-like dynamics, characterized by an intermittent behavior, is observed for a certain range of the model parameters. The problem of uncertainty in decision taking is also addressed both from a topological point of view, using random and targeted removal of agents from the network, and by implementing a three-state model, where the third state, zero, is related to the information available to each agent. Finally, the results of the model are tested against the best known network of social interactions: the stock market. A time series of daily closures of the Dow-Jones index has been used as an indicator of the possible applicability of our model in the financial context. Good qualitative agreement is found.

Maximal planar networks with large clustering coefficient and power-law degree distribution

In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called random Apollonian networks (RANs) as they can be considered as a variation of Apollonian networks. We obtain the analytic results of power-law exponent gamma=3 and clustering coefficient C= (46/3)-36 ln 3/2 approximately 0.74, which agree with the simulation results very well. We prove that the increasing tendency of average distance of RANs is a little slower than the logarithm of the number of nodes in RANs. Since most real-life networks are both scale-free and small-world networks, RANs may perform well in mimicking the reality. The RANs possess hierarchical structure as C(k) approximately k(-1) that are in accord with the observations of many real-life networks. In addition, we prove that RANs are maximal planar networks, which are of particular practicability for layout of printed circuits and so on. The percolation and epidemic spreading process are also studied and the comparisons between RANs and Barabási-Albert (BA) as well as Newman-Watts (NW) networks are shown. We find that, when the network order N (the total number of nodes) is relatively small (as N approximately 10(4)), the performance of RANs under intentional attack is not sensitive to N , while that of BA networks is much affected by N. And the diseases spread slower in RANs than BA networks in the early stage of the susceptible-infected process, indicating that the large clustering coefficient may slow the spreading velocity, especially in the outbreaks.

Subnets of scale-free networks are not scale-free: sampling properties of networks

Most studies of networks have only looked at small subsets of the true network. Here, we discuss the sampling properties of a network's degree distribution under the most parsimonious sampling scheme. Only if the degree distributions of the network and randomly sampled subnets belong to the same family of probability distributions is it possible to extrapolate from subnet data to properties of the global network. We show that this condition is indeed satisfied for some important classes of networks, notably classical random graphs and exponential random graphs. For scale-free degree distributions, however, this is not the case. Thus, inferences about the scale-free nature of a network may have to be treated with some caution. The work presented here has important implications for the analysis of molecular networks as well as for graph theory and the theory of networks in general.

Scaling of directed dynamical small-world networks with random responses

A dynamical model of small-world networks, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of sites to the input message are introduced to simulate real systems. The interplay of these ingredients results in the collective dynamical evolution of a spinlike variable S(t) of the whole network. The global average spreading length <L>(s) and average spreading time <T>(s) are found to scale as p(-alpha)ln(N with different exponents. Meanwhile, S(t) behaves in a duple scaling form for N>>N(*): S approximately f(p(-beta)q(gamma)t), where p and q are rewiring and external parameters, alpha, beta, and gamma are scaling exponents, and f(t) is a universal function. Possible applications of the model are discussed.

Diversity and dynamics of microbial communities in engineered environments and their implications for process stability

The availability of molecular biological tools for studying microbial communities in bioreactors and other engineered systems has resulted in remarkable insights linking diversity and dynamics to process stability. As engineered systems are often more manageable than large-scale ecosystems, and because parallels between engineered environments and other ecosystems exist, the former can be used to elucidate some unresolved ecological issues. For example, the process stability of methanogenic bioreactors containing well-defined trophic groups appears to depend on the diversity of the functional groups within each trophic level as well as on how these functional groups complement each other. In addition to using engineered systems to study general ecological questions, microbial ecologists and environmental engineers need to investigate conditions, processes, and interactions in engineered environments in order to make the ecological engineering of bioreactor design and operation more practicable.

Universal scaling relations in food webs

The structure of ecological communities is usually represented by food webs. In these webs, we describe species by means of vertices connected by links representing the predations. We can therefore study different webs by considering the shape (topology) of these networks. Comparing food webs by searching for regularities is of fundamental importance, because universal patterns would reveal common principles underlying the organization of different ecosystems. However, features observed in small food webs are different from those found in large ones. Furthermore, food webs (except in isolated cases) do not share general features with other types of network (including the Internet, the World Wide Web and biological webs). These features are a small-world character and a scale-free (power-law) distribution of the degree (the number of links per vertex). Here we propose to describe food webs as transportation networks by extending to them the concept of allometric scaling (how branching properties change with network size). We then decompose food webs in spanning trees and loop-forming links. We show that, whereas the number of loops varies significantly across real webs, spanning trees are characterized by universal scaling relations.

Food-web structure and network theory: The role of connectance and size

Networks from a wide range of physical, biological, and social systems have been recently described as "small-world" and "scale-free." However, studies disagree whether ecological networks called food webs possess the characteristic path lengths, clustering coefficients, and degree distributions required for membership in these classes of networks. Our analysis suggests that the disagreements are based on selective use of relatively few food webs, as well as analytical decisions that obscure important variability in the data. We analyze a broad range of 16 high-quality food webs, with 25-172 nodes, from a variety of aquatic and terrestrial ecosystems. Food webs generally have much higher complexity, measured as connectance (the fraction of all possible links that are realized in a network), and much smaller size than other networks studied, which have important implications for network topology. Our results resolve prior conflicts by demonstrating that although some food webs have small-world and scale-free structure, most do not if they exceed a relatively low level of connectance. Although food-web degree distributions do not display a universal functional form, observed distributions are systematically related to network connectance and size. Also, although food webs often lack small-world structure because of low clustering, we identify a continuum of real-world networks including food webs whose ratios of observed to random clustering coefficients increase as a power-law function of network size over 7 orders of magnitude. Although food webs are generally not small-world, scale-free networks, food-web topology is consistent with patterns found within those classes of networks.