Pollination networks of oil-flowers: a tiny world within the smallest of all worlds

1.   In the Neotropics, most plants depend on animals for pollination. Solitary bees are the most important vectors, and among them members of the tribe Centridini depend on oil from flowers (mainly Malpighiaceae) to feed their larvae. This specialized relationship within 'the smallest of all worlds' (a whole pollination network) could result in a 'tiny world' different from the whole system. This 'tiny world' would have higher nestedness, shorter path lengths, lower modularity and higher resilience if compared with the whole pollination network.
2.   In the present study, we contrasted a network of oil-flowers and their visitors from a Brazilian steppe ('caatinga') to whole pollination networks from all over the world.
3.   A network approach was used to measure network structure and, finally, to test fragility. The oil-flower network studied was more nested ( NODF  = 0·84, N  =   0·96) than all of the whole pollination networks studied. Average path lengths in the two-mode network were shorter (one node, both for bee and plant one-mode network projections) and modularity was lower ( M  =   0·22 and four modules) than in all of the whole pollination networks. Extinctions had no or small effects on the network structure, with an average change in nestedness smaller than 2% in most of the cases studied; and only two species caused coextinctions. The higher the degree of the removed species, the stronger the effect and the higher the probability of a decrease in nestedness.
4.   We conclude that the oil-flower subweb is more cohesive and resilient than whole pollination networks. Therefore, the Malpighiaceae have a robust pollination service in the Neotropics. Our findings reinforce the hypothesis that each ecological service is in fact a mosaic of different subservices with a hierarchical structure ('webs within webs').     

Effects of dynamics on ecological networks

Ecological food webs define the feeding patterns of interacting species. The architecture of such networks may be affected by dynamical processes operating within them, ultimately influencing the capacity of the networks to persist. As yet relatively little is known about these effects. We compared the architecture of ecological networks with a fixed number of species, constructed in four contrasting ways: (I) topological networks, which required only that species had prey to eat; (II) persistent networks, in which species had also to persist under a simple model of population dynamics; (III) assembled networks, built up by sequential addition of species with dynamical persistence at each step in the sequence; (IV) evolved networks where, in addition to dynamical persistence, body size of species was determined by a simple mutation-selection process. Dynamics had fundamental effects on architecture, the networks of classes II, III and IV being restricted to a small number of trophic levels, in contrast to the non-dynamic, topological class I networks. Class III assembled networks tended to have fewer trophic levels and a more pyramidal biomass distribution than networks of classes II and IV. In evolved class IV networks, the smallest consumers converged to similar body sizes, whereas larger consumers evolved more slowly and did not show such convergence. The results indicate that dynamics affect the architecture of food webs, and that assumptions about simultaneous arrival, sequential arrival and evolution lead to different outcomes. Sequential assembly was shown to have a special property of finding rare sets of persistent species in a small number of steps, suggesting that the rarity of stable communities is not a serious problem in the development of complex communities.     

生物神经系统的编码特性和小世界特性

本文主要研究视网膜神经系统和七鳃鳗脊椎神经系统的电位发放特性和网络特性,首先利用抑制神经系统的Winner Less Competition（WLC）模型,分析视网膜和七鳃鳗脊椎神经系统的电位发放．得到视网膜神经元和脊椎神经元的电位发放模式．然后利用Watts-Strogatz小世界网络的特性,分析两个生物神经系统的群集系数和特征路长,说明这些生物系统神经元之间的信息传递具有小世界网络的特性．     

Edge vulnerability in neural and metabolic networks

Biological networks, such as cellular metabolic pathways or networks of corticocortical connections in the brain, are intricately organized, yet remarkably robust toward structural damage. Whereas many studies have investigated specific aspects of robustness, such as molecular mechanisms of repair, this article focuses more generally on how local structural features in networks may give rise to their global stability. In many networks the failure of single connections may be more likely than the extinction of entire nodes, yet no analysis of edge importance (edge vulnerability) has been provided so far for biological networks. We tested several measures for identifying vulnerable edges and compared their prediction performance in biological and artificial networks. Among the tested measures, edge frequency in all shortest paths of a network yielded a particularly high correlation with vulnerability and identified intercluster connections in biological but not in random and scale-free benchmark networks. We discuss different local and global network patterns and the edge vulnerability resulting from them.     

The reduction of food web robustness by parasitism: fact and artefact

A robust food web is one which suffers few secondary extinctions after primary species losses. While recent research has shown that a food web with parasitism is less robust than one without, it still remains unclear whether the reduction in robustness is due to changes in network complexity or unique characteristics associated with parasitism. Here, using several published food webs, simulation experiments with different food web models and extinction scenarios were conducted to elucidate how such reduction can be achieved. Our results show that, regardless of changes in network complexity and preferential parasitism, the reduction in food web robustness is mainly due to the life cycle constraint of parasites. Our findings further demonstrate that parasites are prone to secondary extinctions and that their extinctions occur earlier than those involving free-living species. These findings suggest that the vulnerable nature of parasites to species loss makes them highly sensitive indicators of food web integrity.     

Cutoff variation induces different topological properties: A new discovery of amino acid network within protein

An increasing attention has been dedicated to the characterization of complex networks within the protein world. Before now most investigations about protein structures were only considered where the interactive cutoff distance R_c=5 or 7 Å. It is noteworthy that the length of peptide bond is about 1.5 Å, the length of hydrogen bond is about 3 Å, the range of London-van der Waals force is about 5 Å and the range of hydrophobic effect can reach to 12 Å in protein molecule. Present work reports a study on the topological properties of the amino acid network constructed by different interactions above. The results indicate that the small-world property of amino acid network constructed by the peptide and hydrogen bond, London-van der Waals force and the hydrophobic effect is strong, very strong and relatively weak, respectively. Besides, there exists a precise exponential relation C∝k^−0.5 at R_c=12 Å. It means that the amino acid network constructed by the hydrophobic effect tend to be hierarchical. Functional modules could be the cause for hierarchical modularity architecture in protein structures. This study on amino acid interactive network for different interactions facilitates the identification of binding sites which is strongly linked with protein function, and furthermore provides reasonable understanding of the underlying laws of evolution in genomics and proteomics.     

Emergence of non-random structure in local food webs generated from randomly structured regional webs

Previous studies have shown that high-resolution, empirical food webs possess a non-random network structure, typically characterized by uniform or exponential degree distributions. However, the empirical food webs that have been investigated for their structural properties represent local communities that are only a subset of a larger pool of regionally coexisting species. Here, we use a simple model to investigate the effects of regional food web structure on local food webs that are assembled by two simple processes: random immigration of species from a source web (regional food web), and random extinction of species within the local web. The model shows that local webs with non-random degree distributions can arise from randomly structured source webs. A comparison of local webs assembled from randomly structured source webs with local webs assembled from source webs generated by the niche model shows that the former have higher species richness at equilibrium, but have a nonlinear response to changing extinction rates. These results imply that the network structure of regional food webs can play a significant role in the assembly and dynamics of local webs in natural ecosystems. With natural landscapes becoming increasingly fragmented, understanding such structure may be a necessary key to understanding the maintenance and stability of local species diversity.     

Modelling the unpredictability of future biodiversity in ecological networks

We consider the question of how accurately we can hope to predict future biodiversity in a world in which many interacting species are at risk of extinction. Simple models assuming that species’ extinctions occur independently are easily analysed, but do not account for the fact that many species depend on or otherwise interact with each other. In this paper we evaluate the effect of explicitly incorporating ecological dependencies on the predictive ability of models of extinction. In particular, we compare a model in which species’ extinction rates increase because of the extinction of their prey to a model in which the same average rate increase takes place, but in which extinctions occur independently from species to species. One might expect that including this ecological information would make the prediction of future biodiversity more accurate, but instead we find that accounting for food web dependencies reveals greater uncertainty. The expected loss of biodiversity over time is similar between the two models, but the variance in future biodiversity is considerably higher in the model that includes species interactions. This increased uncertainty is because of the non-independence of species—the tendency of two species to respond similarly to the loss of a species on which both depend. We use simulations to show that this increase in variance is robust to many variations of the model, and that its magnitude should be largest in food webs that are highly dependent on a few basal species. Our results should hold whenever ecological dependencies cause most species’ extinction risks to covary positively, and illustrate how more information does not necessarily improve our ability to predict future biodiversity loss.     

Human impacts on minimum subsets of species critical for maintaining ecosystem structure

Humans have indirectly influenced species at lower trophic levels by driving losses of apex consumers. Furthermore, humans have indirectly influenced species at higher trophic levels by driving losses of primary producers. Beyond these broad classes of apex consumers and primary producers, it remains challenging to identify minimum subsets of species that are particularly important for maintaining ecosystem structure and functioning. Here we use a novel method at the intersection of control theory and network theory to identify a minimum set of driver node species upon which ecosystem structure strongly depends. Specifically, humans could unintentionally completely restructure ecosystems (i.e., change species abundances from any initial values to any final values, including zero) by altering the abundances of these few critical driver node species. We then quantify the proportion of these driver nodes that are influenced by humans, top predators, and primary producers in several marine food webs. We find that humans could unintentionally completely restructure marine food webs while only directly influencing less than one in four species. Additionally, humans directly influence: (1) most or all of the species necessary to completely restructure each network, (2) more driver nodes than top predators, and at least as many driver nodes as primary producers, and (3) an increasing proportion of driver nodes over time in the Adriatic Sea. We conclude that humans have potentially huge impacts on marine ecosystems while directly influencing only the relatively small subset of species that are currently fished. It may be possible to reduce unintentional and undesirable cascading human influences by decreasing human impacts on driver node species in these and other food webs.     

The growth and form of tunnelling networks in ants

Many biological networks grow under strong spatial constraints, where the large-scale structure emerges from the extension, the branching and intersection of growing parts of the network. One example is provided by ant tunnelling networks, which represent the most common nest architecture in ants. Our goal was to understand how these network structures emerge from the tunnel growth dynamics. We used a standardized two-dimensional set-up shaped as a disk and studied the characteristics of tunnel growth in terms of initiation, propagation and termination of new digging sites and found that they can be described with simple probabilistic laws. We show that a model based on these simple laws and for which parameters were measured from the sand disks experiments can account for the emergence of several topological properties that were observed in experimental networks. In particular, the model accurately reproduced an allometric relation between the number of edges and the number of nodes, as well as an invariance of the node degree distribution. The model was then used to make predictions about the resulting networks' topology when the geometry of the sand substrate was shaped as a square. Experiments aimed at testing the model's predictions showed that the predictions were indeed validated. Both in the model and in the experiments, there was a similar trend for the node degree distribution tail to be steeper in the square sand patch than in the disk sand patch, while other characteristics such as the meshedness (i.e. how densely the network is internally connected) remained constant. Because network growth based on branching/fusion events is widespread in biological systems, this general model might provide useful insights for the study of other systems and, more generally, the evolution of spatial networks in biological systems.     

Food webs robustness to biodiversity loss: the roles of connectance, expansibility and degree distribution

We analyse the robustness of food webs against species loss by considering the influence of several structural factors of the networks, such as connectance, degree distribution and expansibility. The last concept refers to the absence of structural bottlenecks in the food web, whose removal separate the network into large isolate clusters. In theory networks with identical connectance can display different expansibility characteristics. Using the spectral scaling method we studied 17 food networks and classified them as good expansion (GE) and not-GE networks. The combination of GE properties and degree distribution of species permitted the classification of food webs into six different classes. These classes characterize the differences in robustness of food webs to species loss. While the webs having uniform degree distributions and displaying GE properties are the most robust to species loss, the presence of bottlenecks and skewed distribution of the number of links per species make food webs very vulnerable to primary removal of species.     

The importance of quantifying inherent variability when interpreting stable isotope field data

Stable isotope data are often used to assess diet, trophic level, trophic niche width and the extent of omnivory. Notwithstanding ongoing discussions about the value of these approaches, variations in isotopic signatures among individuals depend on inherent variability as well as differences in feeding habitats. Remarkably, the relative contributions of diet variation and inherent variability to differences in δ¹⁵N and δ¹³C among individuals have not been quantified for the same species at the same life history stages, and inherent variability has been ignored or assumed. We quantified inherent variability in δ¹³C and δ¹⁵N among individuals of a marine fish (the European sea bass, Dicentrarchus labrax) reared in a controlled environment on a diet of constant isotopic composition and compared it with variability in δ¹³C and δ¹⁵N among individuals from wild bass populations. The analysis showed that inherent variability among reared individuals on a controlled diet was equivalent to a large proportion of the observed variability among wild individuals and, therefore, that inherent variability should be measured to establish baseline variability in wild populations before any assumptions are made about the influence of diet. Given that inherent variability is known to be dependent on species, life history stage and the environment, our results show that it should be quantified on a case-by-case basis if diet studies are intended to provide absolute assessments of dietary habits.     

The structure of a plant-pollinator food web

The pollination biology literature is dominated by examples of specialization between plants and their pollinators. However, a recent review shows that it is generalization that prevails in the field, with most plants having a number of pollinators and most pollinators visiting a number of plants. Consequently, the vast majority of plant–pollinator interactions are embedded in a complex web of plant–pollinator interactions. These plant-pollinator webs can be studied in the manner of conventional food webs and the aim of this paper is to illustrate how contemporary methods of web construction and analysis can be applied to plant-pollinator communities.     

The effects of energy input,immigration and habitat size on food web structure: a microcosm experiment

It has been hypothesised that larger habitats should support more complex food webs. We consider three mechanisms which could lead to this pattern. These are increased immigration rates, increased total productivity and spatial effects on the persistence of unstable interactions. Experiments designed to discriminate between these mechanisms were carried out in laboratory aquatic microcosm communities of protista and bacteria, by independently manipulating habitat size, total productivity and immigration rate. Larger habitats supported more complex food webs, with more species, more links per species and longer maximum and mean food chains, even in the absence of differences in total energy input. Increased immigration rate resulted in more complex food webs, but habitats with higher energy input per unit area supported less complex food webs. We conclude that spatial effects on the persistence of unstable interactions, and variation in immigration rates, are plausible mechanisms by which habitat size could affect food web structure. Variation in total productivity with habitat area seems a less likely explanation for variation in food web structure.     

The relative importance of herbivory and carnivory on the distribution of energy in a stochastic tri-trophic food web

A three-state, discrete-time Markov chain is used to model the dynamics of energy flow in a tri-trophic food web. The distribution of energy in the three trophic levels is related to the rates of flow between the trophic levels and calculated for the entire range of possible flow values. These distributions are then analysed for stability and used to test the idea that plants are resource-limited and herbivores are predation-limited. Low rates of death and decomposition, when coupled with low rates of herbivory and carnivory, tend to destabilize this food web. Food webs with higher rates of death and decomposition are relatively more stable regardless of rates of herbivory and carnivory. Plants are more prone to resource-limitation and herbivores are, in general, limited by their predators, which supports Hairston et al. (Am. Nat. 94 (1960) 421). The rate of decomposition often mediates the roles of top-down and bottom-up control of energy flow in the food web.     

The influence of environmental water on the hydrogen stable isotope ratio in aquatic consumers

Aquatic food webs are subsidized by allochthonous resources but the utilization of these resources by consumers can be difficult to quantify. Stable isotope ratios of hydrogen (deuterium:hydrogen; δD) potentially distinguish allochthonous inputs because δD differs between terrestrial and aquatic primary producers. However, application of this tracer is limited by uncertainties regarding the trophic fractionation of δD and the contributions of H from environmental water (often called “dietary water”) to consumer tissue H. We addressed these uncertainties using laboratory experiments, field observations, modeling, and a literature synthesis. Laboratory experiments that manipulated the δD of water and food for insects, cladoceran zooplankton, and fishes provided strong evidence that trophic fractionation of δD was negligible. The proportion of tissue H derived from environmental water was substantial yet variable among studies; estimates of this proportion, inclusive of lab, field, and literature data, ranged from 0 to 0.39 (mean 0.17 ± 0.12 SD). There is a clear need for additional studies of environmental water. Accounting for environmental water in mixing models changes estimates of resource use, although simulations suggest that uncertainty about the environmental water contribution does not substantially increase the uncertainty in estimates of resource use. As long as this uncertainty is accounted for, δD may be a powerful tool for estimating resource use in food webs.     

Response of epiphytic algae to nutrient loading and fish density in a shallow lake: a mesocosm experiment

Studies on the effect of eutrophication on the ecology of shallow lakes, usually pay scant attention to changes within the epiphytic algal community, though the contribution of this to the ecosystem dynamics is transcendental. In order to test the influence of nutrient loadings and fish densities in the structure of algal epiphyton in a shallow lake, an experiment was performed using in situ mesocosms. Nutrient additions were related to significant decreases in the total epiphyton biovolume and that of bacillariophyceans and zygnematophyceans, but with increases in the abundance of cyanobacteria. The different response of algal groups at the higher nutrient concentrations (increases or decreases in their abundance and/or biovolume) can be related to their ecophysiological constraints such as different resistance to toxicant ammonium accumulation. Plant-associated macroinvertebrates numbers were positively correlated with total numbers of epiphyton. The presence of planktivorous fish enhanced the abundance and biovolume of all algal groups, except cyanobacteria. Fishes enhanced the abundance of plant-associated animals and of total epiphyton. Fish indirect effects (e.g., nutrients release) and their dietary particularities were among the factors that together with nutrients influenced epiphyton growth. The role of indirect effects of fishes and the importance of their dietary particularities are stressed as key factors to understand the processes controlling epiphyton ecology and the food web structure of shallow lakes. Handling editor: D. Ryder.