Complex networks: two ways to be robust?

Recent studies of biological networks have focused on the distribution of the number of links per node. However, the connectivity distribution does not uncover all the complexity of their topology. Here, we analyse the relation between the connectivity of a species and the average connectivity of its nearest neighbours in three of the most resolved community food webs. We compare the pattern arising with the one recently reported for protein networks and for a simple null model of a random network. Whereas two highly connected nodes are unlikely to be connected between each other in protein networks, the reverse happens in food webs. We discuss this difference in organization in relation to the robustness of biological networks to different types of perturbation.     

Population dynamics in migratory networks

Migratory animals are comprised of a complex series of interconnected breeding and nonbreeding populations. Because individuals in any given population can arrive from a variety of sites the previous season, predicting how different populations will respond to environmental change can be challenging. In this study, we develop a population model composed of a network of breeding and wintering sites to show how habitat loss affects patterns of connectivity and species abundance. When the costs of migration are evenly distributed, habitat loss at a single site can increase the degree of connectivity (mixing) within the entire network, which then acts to buffer global populations from declines. However, the degree to which populations are buffered depends on where habitat loss occurs within the network: a site that has the potential to receive individuals from multiple populations in the opposite season will lead to smaller declines than a site that is more isolated. In other cases when there are equal costs of migration to two or more sites in the opposite season, habitat loss can result in some populations becoming segregated (disconnected) from the rest of the network. The geographic structure of the network can have a significant influence on relative population sizes of sites in the same season and can also affect the overall degree of mixing in the network, even when sites are of equal intrinsic quality. When a migratory network is widely spaced and migration costs are high, an equivalent habitat loss will lead to a larger decline in global population size than will occur in a network where the overall costs of migration are low. Our model provides an important foundation to test predictions related to habitat loss in real-world migratory networks and demonstrates that migratory networks will likely produce different dynamics from traditional metapopulations. Our results provide strong evidence that estimating population connectivity is a prerequisite for successfully predicting changes in migratory populations.     

Role of African protected areas in maintaining connectivity for large mammals

The African protected area (PA) network has the potential to act as a set of functionally interconnected patches that conserve meta-populations of mammal species, but individual PAs are vulnerable to habitat change which may disrupt connectivity and increase extinction risk. Individual PAs have different roles in maintaining connectivity, depending on their size and location. We measured their contribution to network connectivity (irreplaceability) for carnivores and ungulates and combined it with a measure of vulnerability based on a 30-year trend in remotely sensed vegetation cover (Normalized Difference Vegetation Index). Highly irreplaceable PAs occurred mainly in southern and eastern Africa. Vegetation cover change was generally faster outside than inside PAs and particularly so in southern Africa. The extent of change increased with the distance from PAs. About 5% of highly irreplaceable PAs experienced a faster vegetation cover loss than their surroundings, thus requiring particular conservation attention. Our analysis identified PAs at risk whose isolation would disrupt the connectivity of the PA network for large mammals. This is an example of how ecological spatial modelling can be combined with large-scale remote sensing data to investigate how land cover change may affect ecological processes and species conservation.     

Active colonization dynamics and diversity patterns are influenced by dendritic network connectivity and species interactions

Habitat network connectivity influences colonization dynamics, species invasions, and biodiversity patterns. Recent theoretical work suggests dendritic networks, such as those found in rivers, alter expectations regarding colonization and dispersal dynamics compared with other network types. As many native and non‐native species are spreading along river networks, this may have important ecological implications. However, experimental studies testing the effects of network structure on colonization and diversity patterns are scarce. Up to now, experimental studies have only considered networks where sites are connected with small corridors, or dispersal was experimentally controlled, which eliminates possible effects of species interactions on colonization dynamics. Here, we tested the effect of network connectivity and species interactions on colonization dynamics using continuous linear and dendritic (i.e., river‐like) networks, which allow for active dispersal. We used a set of six protist species and one rotifer species in linear and dendritic microcosm networks. At the start of the experiment, we introduced species, either singularly or as a community within the networks. Species subsequently actively colonized the networks. We periodically measured densities of species throughout the networks over 2 weeks to track community dynamics, colonization, and diversity patterns. We found that colonization of dendritic networks was faster compared with colonization of linear networks, which resulted in higher local mean species richness in dendritic networks. Initially, community similarity was also greater in dendritic networks compared with linear networks, but this effect vanished over time. The presence of species interactions increased community evenness over time, compared with extrapolations from single‐species setups. Our experimental findings confirm previous theoretical work and show that network connectivity, species‐specific dispersal ability, and species interactions greatly influence the dispersal and colonization of dendritic networks. We argue that these factors need to be considered in empirical studies, where effects of network connectivity on colonization patterns have been largely underestimated.     

Experimental evidence for the effect of habitat loss on the dynamics of migratory networks

Migratory animals present a unique challenge for understanding the consequences of habitat loss on population dynamics because individuals are typically distributed over a series of interconnected breeding and non‐breeding sites (termed migratory network). Using replicated breeding and non‐breeding populations of Drosophila melanogaster and a mathematical model, we investigated three hypotheses to explain how habitat loss influenced the dynamics of populations in networks with different degrees of connectivity between breeding and non‐breeding seasons. We found that habitat loss increased the degree of connectivity in the network and influenced population size at sites that were not directly connected to the site where habitat loss occurred. However, connected networks only buffered global population declines at high levels of habitat loss. Our results demonstrate why knowledge of the patterns of connectivity across a species range is critical for predicting the effects of environmental change and provide empirical evidence for why connected migratory networks are commonly found in nature.     

Synchronization study in ring-like and grid-like neuronal networks

In this paper, we study the synchronization status of both two gap-junction coupled neurons and neuronal network with two different network connectivity patterns. One of the network connectivity patterns is a ring-like neuronal network, which only considers nearest-neighbor neurons. The other is a grid-like neuronal network, with all nearest neighbor couplings. We show that by varying some key parameters, such as the coupling strength and the external current injection, the neuronal network will exhibit various patterns of firing synchronization. Different types of firing synchronization are diagnosed by means of a mean field potential, a bifurcation diagram, a correlation coefficient and the ISI-distance method. Numerical simulations demonstrate that the synchronization status of multiple neurons is much dependent on the network patters, when the number of neurons is the same. It is also demonstrated that the synchronization status of two coupled neurons is similar with the grid-like neuronal network, but differs radically from that of the ring-like neuronal network. These results may be instructive in understanding synchronization transitions in neuronal systems.     

Plant multiscale networks: charting plant connectivity by multi-level analysis and imaging techniques

In multicellular and even single-celled organisms, individual components are interconnected at multiscale levels to produce enormously complex biological networks that help these systems maintain homeostasis for development and environmental adaptation. Systems biology studies initially adopted network analysis to explore how relationships between individual components give rise to complex biological processes. Network analysis has been applied to dissect the complex connectivity of mammalian brains across different scales in time and space in The Human Brain Project. In plant science, network analysis has similarly been applied to study the connectivity of plant components at the molecular, subcellular, cellular, organic, and organism levels. Analysis of these multiscale networks contributes to our understanding of how genotype determines phenotype. In this review, we summarized the theoretical framework of plant multiscale networks and introduced studies investigating plant networks by various experimental and computational modalities. We next discussed the currently available analytic methodologies and multi-level imaging techniques used to map multiscale networks in plants. Finally, we highlighted some of the technical challenges and key questions remaining to be addressed in this emerging field.     

Oscillations and synchrony in a cortical neural network

In this paper, the oscillations and synchronization status of two different network connectivity patterns based on Izhikevich model are studied. One of the connectivity patterns is a randomly connected neuronal network, the other one is a small-world neuronal network. This Izhikevich model is a simple model which can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Detailed investigations reveal that by varying some key parameters, such as the connection weights of neurons, the external current injection, the noise of intensity and the neuron number, this neuronal network will exhibit various collective behaviors in randomly coupled neuronal network. In addition, we show that by changing the number of nearest neighbor and connection probability in small-world topology can also affect the collective dynamics of neuronal activity. These results may be instructive in understanding the collective dynamics of mammalian cortex.     

Relation between complexity and stability in food webs with adaptive behavior

We investigate the influence of functional responses (Lotka-Volterra or Holling type), initial topological web structure (randomly connected or niche model), adaptive behavior (adaptive foraging and predator avoidance) and the type of constraints on the adaptive behavior (linear or nonlinear) on the stability and structure of food webs. Two kinds of stability are considered: one is the network robustness (i.e., the proportion of species surviving after population dynamics) and the other is the species deletion stability. When evaluating the network structure, we consider link density as well as the trophic level structure. We show that the types of functional responses and initial web structure do not have a large effect on the stability of food webs, but foraging behavior has a large stabilizing effect. It leads to a positive complexity-stability relationship whenever higher "complexity" implies more potential prey per species. The other type of adaptive behavior, predator avoidance behavior, makes food webs only slightly more stable. The observed link density after population dynamics depends strongly on the presence or absence of adaptive foraging, and on the type of constraints used. We also show that the trophic level structure is preserved under population dynamics with adaptive foraging.     

Partitioning the impact of abiotic factors and spatial patterns on species richness and community structure of ground ant assemblages in four Bornean rainforests

Contrasting theories have been proposed to explain the structure of ecological communities. Here, we studied the impact of environmental factors and spatial patterns on ground‐foraging ant communities in four different forest types of Gunung Mulu National Park in Sarawak, Borneo, Malaysia. Forest types differed in their environmental parameters and were inhabited by distinct ant communities, with various indicator species characteristic for single forest types. Three environmental parameters, soil volume, number of trees and amount of leaf litter, had the most influence on ant communities. Spatial patterns were correlated with environmental parameters and also influenced ant communities. Environmental parameters influenced community composition only moderately (r²=0.14), but had a high impact on species richness (r²=0.44). Spatial patterns explained only a small fraction of the total variance in species patterns, while much of the residual space in the ordination space of ant community patterns remained unexplained. We conclude that environmental parameters shape the number of niches within a tropical soil habitat, but identities of species that occupy those niches are accounted for by other factors like competition, traits and neutral processes that may further reduce unexplained variance in species ordination.     

The importance of forest patch networks for the conservation of the Thorn-tailed Rayaditos in central Chile

Conservation of forest birds in fragmented landscapes requires not only determining the critical patch characteristics influencing local population persistence but also identifying patch networks providing connectivity and suitable habitat conditions necessary to ensure regional persistence. In this study, we assessed the importance of patch attributes, patch connectivity, and network components (i.e., groups of interconnected patches) in explaining the occupancy pattern of the Thorn-tailed Rayadito (Aphrastura spinicauda), a forest bird species of central Chile. Using a daily movement threshold distance, we identified a total of 16 network components of sclerophyllous forest within the study area. Among those components, patch area and vegetation structure-composition were important predictors of patch occupancy. However, the inclusion of patch connectivity and component size (i.e., the area of a network component) into the models greatly increases the models’ accuracy and parsimony. Using the best-fitted model, a total of 33 patches were predicted to be occupied by rayaditos within the study area, but such occupied patches were distributed in only six network components. These results suggest that persistence of rayaditos in central Chile requires the maintenance of large single patches and patch networks providing habitat and connectivity.     

A network perspective on the topological importance of enzymes and their phylogenetic conservation

Background  

A metabolic network is the sum of all chemical transformations or reactions in the cell, with the metabolites being interconnected by enzyme-catalyzed reactions. Many enzymes exist in numerous species while others occur only in a few. We ask if there are relationships between the phylogenetic profile of an enzyme, or the number of different bacterial species that contain it, and its topological importance in the metabolic network. Our null hypothesis is that phylogenetic profile is independent of topological importance. To test our null hypothesis we constructed an enzyme network from the KEGG (Kyoto Encyclopedia of Genes and Genomes) database. We calculated three network indices of topological importance: the degree or the number of connections of a network node; closeness centrality, which measures how close a node is to others; and betweenness centrality measuring how frequently a node appears on all shortest paths between two other nodes.     

Neural action fields for optic flow based navigation: a simulation study of the fly lobula plate network

Optic flow based navigation is a fundamental way of visual course control described in many different species including man. In the fly, an essential part of optic flow analysis is performed in the lobula plate, a retinotopic map of motion in the environment. There, the so-called lobula plate tangential cells possess large receptive fields with different preferred directions in different parts of the visual field. Previous studies demonstrated an extensive connectivity between different tangential cells, providing, in principle, the structural basis for their large and complex receptive fields. We present a network simulation of the tangential cells, comprising most of the neurons studied so far (22 on each hemisphere) with all the known connectivity between them. On their dendrite, model neurons receive input from a retinotopic array of Reichardt-type motion detectors. Model neurons exhibit receptive fields much like their natural counterparts, demonstrating that the connectivity between the lobula plate tangential cells indeed can account for their complex receptive field structure. We describe the tuning of a model neuron to particular types of ego-motion (rotation as well as translation around/along a given body axis) by its 'action field'. As we show for model neurons of the vertical system (VS-cells), each of them displays a different type of action field, i.e., responds maximally when the fly is rotating around a particular body axis. However, the tuning width of the rotational action fields is relatively broad, comparable to the one with dendritic input only. The additional intra-lobula-plate connectivity mainly reduces their translational action field amplitude, i.e., their sensitivity to translational movements along any body axis of the fly.     

The effect of mutational robustness on the evolvability of multicellular organisms and eukaryotic cells

Canalization involves mutational robustness, the lack of phenotypic change as a result of genetic mutations. Given the large divergence in phenotype across species, understanding the relationship between high robustness and evolvability has been of interest to both theorists and experimentalists. Although canalization was originally proposed in the context of multicellular organisms, the effect of multicellularity and other classes of hierarchical organization on evolvability has not been considered by theoreticians. We address this issue using a Boolean population model with explicit representation of an environment in which individuals with explicit genotype and a hierarchical phenotype representing multicellularity evolve. Robustness is described by a single real number between zero and one which emerges from the genotype–phenotype map. We find that high robustness is favoured in constant environments, and lower robustness is favoured after environmental change. Multicellularity and hierarchical organization severely constrain robustness: peak evolvability occurs at an absolute level of robustness of about 0.99 compared with values of about 0.5 in a classical neutral network model. These constraints result in a sharp peak of evolvability in which the maximum is set by the fact that the fixation of adaptive mutations becomes more improbable as robustness decreases. When robustness is put under genetic control, robustness levels leading to maximum evolvability are selected for, but maximal relative fitness appears to require recombination.     

The effects of habitat fragmentation on persistence of source-sink metapopulations in systems with predators and prey or apparent competitors.

We consider systems with one predator and one prey, or a common predator and two prey species (apparent competitors) in source and sink habitats. In both models, the predator species is vulnerable to extinction, if productivity in the source is insufficient to rescue demographically deficient sink populations. Conversely, in the model with two prey species, if the source is too rich, one of the prey species may be driven extinct by apparent competition, since the predator can maintain a large population because of the alternative prey. Increasing the rate of predator movement from the source population has opposite effects on prey and predator persistence. High emigration rate exposes the predator population to danger of extinction, reducing the number of individuals that breed and produce offspring in the source habitat. This may promote coexistence of prey by relaxing predation pressure and apparent competition between the two prey species. The number of sinks and spatial arrangement of patches, or connectivity between patches, also influence persistence of the species. More sinks favor the prey and fewer sinks are advantageous to the predator. A linear pattern with the source at one end is profitable for the predator, and a centrifugal pattern in which the source is surrounded by sinks is advantageous to the prey. When the dispersal rate is low, effects of the spatial structure may exceed those of the number of sinks. In brief, productivity in patches and patterns of connectivity between patches differentially influence persistence of populations in different trophic levels.     

城市生态网络空间评价及其格局优化

合理的城市生态网络空间格局对于保障城市生态环境可持续发展具有重要意义。以哈尔滨中心城区为研究区,基于景观生态学"斑块-廊道-基质"理论,识别研究区生态源、生态廊道、生态节点和生态基质,分析生态网络连接度强弱的空间分布情况,运用GIS技术和CA-Marcov模型对生态网络格局进行模拟优化。研究结果表明:(1)研究区内部生态源较外部生态源与外界联系较密切;周边地区生态源或生态节点与生态廊道连接数目较少;中北部与西南部生态廊道连接度较差,东部生态廊道连接度处于中等水平,中部个别生态廊道连接度较好;转入的大型生态用地大片集中,转入的小型生态用地零星分布。(2)优化后的生态源地在东西方向与南北方向形成集中连片态势,大型生态源地间彼此连接程度较高;大型生态源之间,以及大型生态源与小型生态源之间构成大型生态廊道,是研究区内主要生态廊道网络;研究区小型生态源之间构成小型生态廊道,是研究区内次要生态廊道网络;研究区周边及研究区中心处60%的区域为生态节点盲区,应加强生态节点盲区生态建设;新增加的大部分生态用地,主要集中分布在水域生态源地周边,还有部分分布在绿地生态源地和风景区生态源地周边,其余少量新增加的生态用地零星分布在林地生态源地周边。研究成果为中心城区尺度的生态环境保护和城市规划提供科学的依据。     

Plant–pollinator networks: adding the pollinator's perspective

Pollination network studies are based on pollinator surveys conducted on focal plants. This plant-centred approach provides insufficient information on flower visitation habits of rare pollinator species, which are the majority in pollinator communities. As a result, pollination networks contain very high proportions of pollinator species linked to a single plant species (extreme specialists), a pattern that contrasts with the widely accepted view that plant–pollinator interactions are mostly generalized. In this study of a Mediterranean scrubland community in NE Spain we supplement data from an intensive field survey with the analysis of pollen loads carried by pollinators. We observed 4265 contacts corresponding to 19 plant and 122 pollinator species. The addition of pollen data unveiled a very significant number of interactions, resulting in important network structural changes. Connectance increased 1.43-fold, mean plant connectivity went from 18.5 to 26.4, and mean pollinator connectivity from 2.9 to 4.1. Extreme specialist pollinator species decreased 0.6-fold, suggesting that ecological specialization is often overestimated in plant–pollinator networks. We expected a greater connectivity increase in rare species, and consequently a decrease in the level of asymmetric specialization. However, new links preferentially attached to already highly connected nodes and, as a result, both nestedness and centralization increased. The addition of pollen data revealed the existence of four clearly defined modules that were not apparent when only field survey data were used. Three of these modules had a strong phenological component. In comparison to other pollination webs, our network had a high proportion of connector links and species. That is, although significant, the four modules were far from isolated.     

Evaluating the sufficiency of protected lands for maintaining wildlife population connectivity in the U.S. northern Rocky Mountains

Aim The goal of this study was to evaluate the sufficiency of the network of protected lands in the U.S. northern Rocky Mountains in providing protection for habitat connectivity for 105 hypothetical organisms. A large proportion of the landscape falls into one of several categories of protected lands. However, protected lands in the region are primarily higher elevation forest and mountain habitats. Little is known about how the network of protected lands may maintain connectivity for a broad spectrum of species expressing different habitat requirements and dispersal abilities. Location The study was conducted across the states of Montana and northern Idaho, USA, comprising an area of 30.2 million hectares. Methods We used resistant kernel modelling to map the extent of the study area predicted to be connected by dispersal for each of 35 species groups with different ecological associations. We evaluated the effect of vagility on protected area sufficiency by varying dispersal ability across three levels for each species group. We evaluated the degree of vulnerability of each of the 105 hypothetical species (35 species groups × 3 dispersal abilities) in terms of the extent of the total study area predicted to be connected by dispersal. We defined nine categories of risk as the combination of species vulnerability because of the extent of connected habitat and the degree to which that habitat was protected. Results We found high variation in the vulnerability of species because of the extent of connected habitat, and the extent to which connected habitat overlapped protected lands. Species associated with high elevations and species associated with lower elevations were predicted to have limited extent of connected habitat. Species associated with high elevations were predicted to have the vast majority of their connected habitat protected by federal Forest Service and National Park Service lands. In contrast, species associated with lower elevations were poorly protected by the existing network of protected lands. Main conclusions Low elevation and non‐forest habitats are at highest risk of human‐induced habitat loss and fragmentation in the study area. Conservation efforts in the region may be most effective if they focus on expanding the network of lower elevation protected lands in such a way that maximizes connectivity across the landscape.