Emergence of structural and dynamical properties of ecological mutualistic networks

The persistence of bipartite ecological communities with Lotka-Volterra dynamics

The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific interactions are organised according to a bipartite network. Considering the dynamics of species abundances to be governed by generalised Lotka-Volterra equations, we extend work on unipartite networks to we derive exact results for the phase diagram of this model. Focusing on antagonistic interactions, we describe factors that influence the persistence of the two guilds, locate transitions to multiple-attractor and unbounded phases, as well as identifying a region of parameter space in which consumers are essentially absent in the local community.

Latitudinal specificity of plant-avian frugivore interactions

Broad-scale assessments of plant-frugivore interactions indicate the existence of a latitudinal gradient in interaction specialization. The specificity (i.e. the similarity of the interacting partners) of plant-frugivore interactions could also change latitudinally given that differences in resource availability could favour species to become more or less specific in their interactions across latitudes. Species occurring in the tropics could be more taxonomically, phylogenetically and functionally specific in their interactions because of a wide range of resources that are constantly available in these regions that would allow these species to become more specialized in their resource usage. We used a data set on plant-avian frugivore interactions spanning a wide latitudinal range to examine these predictions, and we evaluated the relationship between latitude and taxonomic, phylogenetic and functional specificity of plant and frugivore interactions. These relationships were assessed using data on population interactions (population level), species means (species level) and community means (community level). We found that the specificity of plant-frugivore interactions is generally not different from null models. Although statistically significant relationships were often observed between latitude and the specificity of plant-frugivore interactions, the direction of these relationships was variable and they also were generally weak and had low explanatory power. These results were consistent across the three specificity measures and levels of organization, suggesting that there might be an interplay between different mechanisms driving the interactions between plants and frugivores across latitudes.

Structural dynamics of plant-pollinator mutualistic networks

The discourse surrounding the structural organization of mutualistic interactions mostly revolves around modularity and nestedness. The former is known to enhance the stability of communities, while the latter is related to their feasibility, albeit compromising the stability. However, it has recently been shown that the joint emergence of these structures poses challenges that can eventually lead to limitations in the dynamic properties of mutualistic communities. We hypothesize that considering compound arrangements-modules with internal nested organization-can offer valuable insights in this debate. We analyze the temporal structural dynamics of 20 plant-pollinator interaction networks and observe large structural variability throughout the year. Compound structures are particularly prevalent during the peak of the pollination season, often coexisting with nested and modular arrangements in varying degrees. Motivated by these empirical findings, we synthetically investigate the dynamics of the structural patterns across two control parameters-community size and connectance levels-mimicking the progression of the pollination season. Our analysis reveals contrasting impacts on the stability and feasibility of these mutualistic communities. We characterize the consistent relationship between network structure and stability, which follows a monotonic pattern. But, in terms of feasibility, we observe nonlinear relationships. Compound structures exhibit a favorable balance between stability and feasibility, particularly in mid-sized ecological communities, suggesting they may effectively navigate the simultaneous requirements of stability and feasibility. These findings may indicate that the assembly process of mutualistic communities is driven by a delicate balance among multiple properties, rather than the dominance of a single one.

Adaptive rewiring shapes structure and stability in a three-guild herbivore-plant-pollinator network

Animal species, encompassing both pollinators and herbivores, exhibit a preference for plants based on optimal foraging theory. Understanding the intricacies of these adaptive plant-animal interactions in the context of community assembly poses a main challenge in ecology. This study delves into the impact of adaptive interaction rewiring between species belonging to different guilds on the structure and stability of a 3-guild ecological network, incorporating both mutualistic and antagonistic interactions. Our findings reveal that adaptive rewiring results in sub-networks becoming more nested and compartmentalized. Furthermore, the rewiring of interactions uncovers a positive correlation between a plant's generalism concerning both pollinators and herbivores. Additionally, there is a positive correlation between a plant's degree centrality and its energy budget. Although network stability does not exhibit a clear relationship with non-random structures, it is primarily influenced by the balance of multiple interaction strengths. In summary, our results underscore the significance of adaptive interaction rewiring in shaping the structure of 3-guild networks. They emphasize the importance of considering the balance of multiple interactions for the stability of adaptive networks, providing valuable insights into the complex dynamics of ecological communities.

A personalized pharmaco-epistatic network model of precision medicine

Precision medicine, the utilization of targeted treatments to address an individual's disease, relies on knowledge about the genetic cause of that individual's drug response. Here, we present a functional graph (FunGraph) theory to chart comprehensive pharmacogenetic architecture for each and every patient. FunGraph is the combination of functional mapping - a dynamic model for genetic mapping and evolutionary game theory guiding interactive strategies. It coalesces all pharmacogenetic factors into multilayer and multiplex networks that fully capture bidirectional, signed and weighted epistasis. It can visualize and interrogate how epistasis moves in the cell and how this movement leads to patient- and context-specific genetic architecture in response to organismic physiology. We discuss the future implementation of FunGraph to achieve precision medicine. Teaser: We present a functional graph (FunGraph) theory to draw a complete picture of pharmacogenetic architecture underlying interindividual variability in drug response. FunGraph can characterize how each gene acts and interacts with every other gene to mediate therapeutic response.

The non-random assembly of network motifs in plant-pollinator networks

Ecological processes leave distinct structural imprints on the species interactions that shape the topology of animal-plant mutualistic networks. Detecting how direct and indirect interactions between animals and plants are organised is not trivial since they go beyond pairwise interactions, but may get blurred when considering global network descriptors. Recent work has shown that the meso-scale, the intermediate level of network complexity between the species and the global network, can capture this important information. The meso-scale describes network subgraphs representing patterns of direct and indirect interactions between a small number of species, and when these network subgraphs differ statistically from a benchmark, they are often referred to as 'network motifs'. Although motifs can capture relevant ecological information of species interactions, they remain overlooked in natural plant-pollinator networks. By exploring 60 empirical plant-pollinator networks from 18 different studies with wide geographical coverage, we show that some network subgraphs are consistently under- or over-represented, suggesting the presence of worldwide network motifs in plant-pollinator networks. In addition, we found a higher proportion of densely connected network subgraphs that, based on previous findings, could reflect that species relative abundances are the main driver shaping the structure of the meso-scale on plant-pollinator communities. Moreover, we found that distinct subgraph positions describing species ecological roles (e.g. generalisation and number of indirect interactions) are occupied by different groups of animal and plant species representing their main life-history strategies (i.e. functional groups). For instance, we found that the functional group of 'bees' was over-represented in subgraph positions with a lower number of indirect interactions in contrast to the rest of floral visitors groups. Finally, we show that the observed functional group combinations within a subgraph cannot be retrieved from their expected probabilities (i.e. joint probability distributions), indicating that plant and floral visitor associations within subgraphs are not random either. Our results highlight the presence of common network motifs in plant-pollinator communities that are formed by a non-random association of plants and floral visitors functional groups.

The Resilience of Plant-Pollinator Networks

There is growing awareness of pollinator declines worldwide. Conservation efforts have mainly focused on finding the direct causes, while paying less attention to building a systemic understanding of the fragility of these communities of pollinators. To fill this gap, we need operational measures of network resilience that integrate two different approaches in theoretical ecology. First, we should consider the range of conditions compatible with the stable coexistence of all of the species in a community. Second, we should address the rate and shape of network collapse once this safe operational space is exited. In this review, we describe this integrative approach and consider several mechanisms that may enhance the resilience of pollinator communities, chiefly rewiring the network of interactions, increasing heterogeneity, allowing variance, and enhancing coevolution. The most pressing need is to develop ways to reduce the gap between these theoretical recommendations and practical applications. This perspective shifts the emphasis from traditional approaches focusing on the equilibrium states to strategies that allow pollination networks to cope with global environmental change.

Inference of monopartite networks from bipartite systems with different link types

Many of the real-world data sets can be portrayed as bipartite networks. Since connections between nodes of the same type are lacking, they need to be inferred. The standard way to do this is by converting the bipartite networks to their monopartite projection. However, this simple approach renders an incomplete representation of all the information in the original network. To this end, we propose a new statistical method to identify the most critical links in the bipartite network projection. Our method takes into account the heterogeneity of node connections. Moreover, it can handle situations where links of different types are present. We compare our method against the state-of-the-art and illustrate the findings with synthetic data and empirical examples of investor and political data.

Effects of habitat destruction on coevolving metacommunities

Habitat destruction is a growing threat to biodiversity and ecosystem services. The ecological consequences of habitat loss and fragmentation involve reductions in species abundance and even the extinction of species and their interactions. However, we do not yet understand how habitat loss alters the coevolutionary trajectories of the remaining species or how coevolution, in turn, affects their response to habitat loss. To investigate this, we develop a spatially explicit model which couples metacommunity and coevolutionary dynamics. We show that, by changing the size, composition and structure of local networks, habitat destruction increases the diversity of coevolutionary trajectories of mutualists across the landscape. Conversely, in antagonistic communities, some species increase while others reduce their spatial trait heterogeneity. Furthermore, we show that while coevolution dampens the negative effects of habitat destruction in mutualistic networks, its effects on the persistence of antagonistic communities tend to be smaller and less predictable.

Estimating comparable distances to tipping points across mutualistic systems by scaled recovery rates

Mutualistic systems can experience abrupt and irreversible regime shifts caused by local or global stressors. Despite decades of efforts to understand ecosystem dynamics and determine whether a tipping point could occur, there are no current approaches to estimate distances (in state/parameter space) to tipping points and compare the distances across various mutualistic systems. Here we develop a general dimension-reduction approach that simultaneously compresses the natural control and state parameters of high-dimensional complex systems and introduces a scaling factor for recovery rates. Our theoretical framework places various systems with entirely different dynamical parameters, network structure and state perturbations on the same scale. More importantly, it compares distances to tipping points across different systems on the basis of data on abundance and topology. By applying the method to 54 real-world mutualistic networks, our analytical results unveil the network characteristics and system parameters that control a system's resilience. We contribute to the ongoing efforts in developing a general framework for mapping and predicting distance to tipping points of ecological and potentially other systems.

Generalism drives abundance: A computational causal discovery approach

A ubiquitous pattern in ecological systems is that more abundant species tend to be more generalist; that is, they interact with more species or can occur in wider range of habitats. However, there is no consensus on whether generalism drives abundance (a selection process) or abundance drives generalism (a drift process). As it is difficult to conduct direct experiments to solve this chicken-and-egg dilemma, previous studies have used a causal discovery method based on formal logic and have found that abundance drives generalism. Here, we refine this method by correcting its bias regarding skewed distributions, and employ two other independent causal discovery methods based on nonparametric regression and on information theory, respectively. Contrary to previous work, all three independent methods strongly indicate that generalism drives abundance when applied to datasets on plant-hummingbird communities and reef fishes. Furthermore, we find that selection processes are more important than drift processes in structuring multispecies systems when the environment is variable. Our results showcase the power of the computational causal discovery approach to aid ecological research.

Ever since Aristotle, the chicken-or-egg causality dilemma has baffled researchers. Such causality dilemmas are abundant in ecological research, where causal directions are often assumed but not tested. An archetypal example is whether being a generalist causes a species to be more abundant, or whether being more abundant causes a species to be generalists. Without doubt, the gold standard to establish causal directions is controlled experiments. However, controlled experiments that can disentangle the direction of causality in this case are challenging because it involves controlling biotic or abiotic niche breadth. These challenges create an opportunity for computational tools to detect the most likely causal direction. Here, by adapting a set of recently developed computational methods, we provide strong evidence that generalism drives abundance, overturning the previously established direction. We hope our work raises awareness of the potential for computational discovery methods to address long-standing questions in ecology, especially increasingly large datasets become available.

Drivers and consequences of structure in plant-lemur ecological networks

Species interactions shape the diversity and resilience of ecological networks. Plant and animal traits, as well as phylogeny, affect interaction likelihood, driving variation in network structure and tolerance to disturbance. We investigated how traits and phylogenetic effects influenced network-wide interaction probabilities and examined the consequences of extinction on the structure and robustness of ecological networks. We combined both mutualistic and antagonistic interactions of animals (55 species, Infraorder Lemuriformes, Order Primates) and their food plants (590 genera) throughout Madagascar to generate ecological networks. We tested the effects of both lemur and plant traits, biogeographic factors, and phylogenetic relatedness on interaction probability in these networks using exponential random graph models. Next, we simulated animal and plant extinction to analyze the effects of extinction on network structure (connectance, nestedness, and modularity) and robustness for mutualistic, antagonistic, and combined plant-animal networks. Both animal and plant traits affected their interaction probabilities. Large, frugivorous lemurs with a short gestation length, occurring in arid habitats, and with a Least Concern threat level had a high interaction probability in the network, given all other variables. Closely related plants were more likely to interact with the same lemur species than distantly related plants, but closely related lemurs were not more likely to interact with the same plant genus. Simulated lemur extinction tended to increase connectance and modularity, but decrease nestedness and robustness, compared to pre-extinction networks. Networks were more tolerant to plant than lemur extinctions. Lemur-plant interactions were highly trait-structured and the loss of both lemurs and plants threatened the tolerance of mutualistic, antagonistic, and combined networks to future disturbance.

Effect of delay on the emergent stability patterns in generalized Lotka-Volterra ecological dynamics

Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the existence of emergent universal patterns of both stability and feasibility in ecological dynamics. However, only a few studies have investigated the role of delay coupled with population dynamics in the emergence of feasible and stable states. In this work, we study the effects of delay on generalized Loka-Volterra population dynamics of several interacting species in closed ecological environments. First, we investigate the relation between feasibility and stability of the modelled ecological community in the absence of delay and find a simple analytical relation when intra-species interactions are dominant. We then show how, by increasing the time delay, there is a transition in the stability phases of the population dynamics: from an equilibrium state to a stable non-point attractor phase. We calculate analytically the critical delay of that transition and show that it is in excellent agreement with numerical simulations. Finally, following a similar approach to characterizing stability in empirical studies, we investigate the coefficient of variation, which quantifies the magnitude of population fluctuations. We show that in the oscillatory regime induced by the delay, the variability at community level decreases for increasing diversity. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

From the origin of life to pandemics: emergent phenomena in complex systems

When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This non-trivial phenomenon, known as emergence, characterizes a broad range of distinct complex systems-from physical to biological and social-and is often related to collective behaviour. It is ubiquitous, from non-living entities such as oscillators that under specific conditions synchronize, to living ones, such as birds flocking or fish schooling. Despite the ample phenomenological evidence of the existence of systems' emergent properties, central theoretical questions to the study of emergence remain unanswered, such as the lack of a widely accepted, rigorous definition of the phenomenon or the identification of the essential physical conditions that favour emergence. We offer here a general overview of the phenomenon of emergence and sketch current and future challenges on the topic. Our short review also serves as an introduction to the theme issue Emergent phenomena in complex physical and socio-technical systems: from cells to societies, where we provide a synthesis of the contents tackled in the issue and outline how they relate to these challenges, spanning from current advances in our understanding on the origin of life to the large-scale propagation of infectious diseases. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Stochastic block models reveal a robust nested pattern in healthy human gut microbiomes

A key question in human gut microbiome research is what are the robust structural patterns underlying its taxonomic composition. Herein, we use whole metagenomic datasets from healthy human guts to show that such robust patterns do exist, albeit not in the conventional enterotype sense. We first introduce the concept of mixed-membership enterotypes using a network inference approach based on stochastic block models. We find that gut microbiomes across a group of people (hosts) display a nested structure, which has been observed in a number of ecological systems. This finding led us to designate distinct ecological roles to both microbes and hosts: generalists and specialists. Specifically, generalist hosts have microbiomes with most microbial species, while specialist hosts only have generalist microbes. Moreover, specialist microbes are only present in generalist hosts. From the nested structure of microbial taxonomies, we show that these ecological roles of microbes are generally conserved across datasets. Our results show that the taxonomic composition of healthy human gut microbiomes is associated with robustly structured combinations of generalist and specialist species.

Global structural stability and the role of cooperation in mutualistic systems

Dynamical systems on graphs allow to describe multiple phenomena from different areas of Science. In particular, many complex systems in Ecology are studied by this approach. In this paper we analize the mathematical framework for the study of the structural stability of each stationary point, feasible or not, introducing a generalization for this concept, defined as Global Structural Stability. This approach would fit with the proper mathematical concept of structural stability, in which we find a full description of the complex dynamics on the phase space due to nonlinear dynamics. This fact can be analyzed as an informational field grounded in a global attractor whose structure can be completely characterized. These attractors are stable under perturbation and suppose the minimal structurally stable sets. We also study in detail, mathematically and computationally, the zones characterizing different levels of biodiversity in bipartite graphs describing mutualistic antagonistic systems of population dynamics. In particular, we investigate the dependence of the region of maximal biodiversity of a system on its connectivity matrix. On the other hand, as the network topology does not completely determine the robustness of the dynamics of a complex network, we study the correlation between structural stability and several graph measures. A systematic study on synthetic and biological graphs is presented, including 10 mutualistic networks of plants and seed-dispersal and 1000 random synthetic networks. We compare the role of centrality measures and modularity, concluding the importance of just cooperation strength among nodes when describing areas of maximal biodiversity. Indeed, we show that cooperation parameters are the central role for biodiversity while other measures act as secondary supporting functions.

OxDNA to Study Species Interactions

Molecular ecology uses molecular genetic data to answer traditional ecological questions in biogeography and biodiversity, among others. Several ecological principles, such as the niche hypothesis and the competitive exclusions, are based on the fact that species compete for resources. More in generally, it is now recognized that species interactions play a crucial role in determining the coexistence and abundance of species. However, experimentally controllable platforms, which allow us to study and measure competitions among species, are rare and difficult to implement. In this work, we suggest exploiting a Molecular Dynamics coarse-grained model to study interactions among single strands of DNA, representing individuals of different species, which compete for binding to other oligomers considered as resources. In particular, the well-established knowledge of DNA–DNA interactions at the nanoscale allows us to test the hypothesis that the maximum consecutive overlap between pairs of oligomers measure the species’ competitive advantages. However, we suggest that a more complex structure also plays a role in the ability of the species to successfully bind to the target resource oligomer. We complement the simulations with experiments on populations of DNA strands which qualitatively confirm our hypotheses. These tools constitute a promising starting point for further developments concerning the study of controlled, DNA-based, artificial ecosystems.

Cooperation and Lateral Forces: Moving Beyond Bottom-Up and Top-Down Drivers of Animal Population Dynamics

Biologists have long known that animal population dynamics are regulated by a combination of bottom-up (resource availability) and top-down forces (predation). Yet, economists have argued that human population dynamics can also be influenced by intraspecific cooperation. Despite awareness of the role of interspecific cooperation (mutualism) in influencing resource availability and animal population dynamics, the role of intraspecific cooperation (sociality) under different environmental conditions has rarely been considered. Here we examine the role of what we call “lateral forces” that act within populations and interact with external top-down and bottom-up forces in influencing population dynamics using an individual-based model linking environmental quality, intraspecific cooperation, and population size. We find that the proportion of cooperators is higher when the environment is poor and population sizes are greatest under intermediate resources levels due to the contrasting effects of resource availability on behavior and population size. We also show that social populations are more resilient to environmental change than non-social ones because the benefits of intraspecific cooperation can outweigh the effects of constrained resource availability. Our study elucidates the complex relationship between environmental harshness, cooperation, and population dynamics, which is important for understanding the ecological consequences of cooperation.

Long-term dynamics of the network structures in seed dispersal associated with fluctuations in bird migration and fruit abundance patterns

In temperate zones, seed-dispersal networks by migratory birds are formed on long time scale. In mid-October from 2005 to 2016, to explore the dynamics of the network structures, we examined interannual variability of fruit abundance, bird migration, and seed-dispersal networks in central Japan. For 12 years, the fruit abundance exhibited a remarkable fluctuation across years, with the number of fruiting plants and matured fruits fluctuating repeatedly every other year, leading to the periodic fluctuations. The abundance of migratory birds was also fluctuated. According to the abundance of fruits and migratory birds, the 12 years was classified into three types: frugivores and fruits were abundant, frugivores were abundant but fruits were scarce, and frugivores were scarce. The seed-dispersal networks were investigated by collecting faeces and vomits of migrants. Of the 6652 samples collected from 15 bird species, 1671 (25.1%) included seeds from 60 plant species. Main dispersers were composed of Turdus pallidus, T. obscurus, and Zosterops japonicus. The network structures were almost nested for 12 years. Specifically, the nested structure was developed in years when fruit abundance was low. GLM analyses showed the abundance of migrants, particularly T. pallidus and T. obscurus, had strong positive effects on nested structure. It may be caused by the fact the two Turdus species were more frequently functioning as generalist dispersers when fruit abundance was lower. Our study suggested fruit abundance and foraging behaviour of frugivores determine the network structures of seed dispersal on long time scale.

Stability and selective extinction in complex mutualistic networks

We study species abundance in the empirical plant-pollinator mutualistic networks exhibiting broad degree distributions, with uniform intragroup competition assumed, by the Lotka-Volterra equation. The stability of a fixed point is found to be identified by the signs of its nonzero components and those of its neighboring fixed points. Taking the annealed approximation, we derive the nonzero components to be formulated in terms of degrees and the rescaled interaction strengths, which lead us to find different stable fixed points depending on parameters, and we obtain the phase diagram. The selective extinction phase finds small-degree species extinct and effective interaction reduced, maintaining stability and hindering the onset of instability. The nonzero minimum species abundances from different empirical networks show data collapse when rescaled as predicted theoretically.

Managing food-ecosystem synergies to sustain water resource systems

Measures implemented to restore ecosystem services are widely believed to conflict with food production in the world's irrigated regions because of their competition for scarce water. However, little integrated analysis has been conducted to test this hypothesis. This work tests that hypothesis by presenting results of a basin-scale hydroeconomic analysis linking biophysical, hydrologic, agronomic, ecological, economic, policy, and institutional dimensions of the partially-restored Mesopotamian Marshes of Western Asia. Results serve to partly reject the hypothesis: Here we find that an economically-optimized ecosystem restoration trajectory can be achieved with a minimal loss in food production or farm income where restored wetlands complement important dimensions of food production. Moreover, we find that where water shortage sharing rules can be made more flexible, ecosystem restoration more nearly complements improved food security. Our results point to previously unexplored synergies among food production, ecosystem restoration, and water laws in arid and semi-arid regions internationally.

Machine learning dismantling and early-warning signals of disintegration in complex systems

From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features - e.g., heterogeneous connectivity, mesoscale organization, hierarchy - affect their robustness to external perturbations, such as targeted attacks to their units. Identifying the minimal set of units to attack to disintegrate a complex network, i.e. network dismantling, is a computationally challenging (NP-hard) problem which is usually attacked with heuristics. Here, we show that a machine trained to dismantle relatively small systems is able to identify higher-order topological patterns, allowing to disintegrate large-scale social, infrastructural and technological networks more efficiently than human-based heuristics. Remarkably, the machine assesses the probability that next attacks will disintegrate the system, providing a quantitative method to quantify systemic risk and detect early-warning signals of system's collapse. This demonstrates that machine-assisted analysis can be effectively used for policy and decision-making to better quantify the fragility of complex systems and their response to shocks.

Nestedness-Based Measurement of Evolutionarily Stable Equilibrium of Global Production System

A nested structure is a structural feature that is conducive to system stability formed by the coevolution of biological species in mutualistic ecosystems The coopetition relationship and value flow between industrial sectors in the global value chain are similar to the mutualistic ecosystem in nature. That is, the global economic system is always changing to form one dynamic equilibrium after another. In this paper, a nestedness-based analytical framework is used to define the generalist and specialist sectors for the purpose of analyzing the changes in the global supply pattern. We study why the global economic system can reach a stable equilibrium, what the role of different sectors play in the steady status, and how to enhance the stability of the global economic system. In detail, the domestic trade network, export trade network and import trade network of each country are extracted. Then, an econometric model is designed to analyze how the microstructure of the production system affects a country’s macroeconomic performance.

Revealing the role of Plant Growth Promoting Rhizobacteria in suppressive soils against Fusarium oxysporum f.sp. cubense based on metagenomic analysis

Fusarium oxysporum f.sp. cubense (Foc) is a soil-borne pathogen causing fusarium wilt banana disease. Management of soil-borne disease generally required the application of toxic pesticides or fungicides strongly affect the soil microbiomes ecosystem. Suppressive soil is a promising method for controlling soil-borne pathogens in which soil microbiomes may affect the suppressiveness. The comparative analysis of microbial diversity was conducted from suppressive and conducive soils by analyzing whole shotgun metagenomic DNA data. Two suppressive soil samples and two conducive soil samples were collected from a banana plantation in Sukabumi, West Java, Indonesia. Each soil sample was prepared by mixing the soil samples collected from three points sampling sites with 20 cm depth. Analysis of microbial abundance, diversity, co-occurrence network using Metagenome Analyzer 6 (MEGAN6) and functional analysis using Kyoto Encyclopedia of Genes and Genomes (KEGG) was performed. Data showed the abundance of Actinobacteria, Betaproteobacteria, Rhizobiales, Burkholderiales, Bradyrhizobiaceae, Methylobacteriaceae, Rhodopseudomonas palustris, and Methylobacterium nodulans were higher in the suppressive than conducive soils. Interestingly, those bacteria groups are known functionally as members of Plant Growth Promoting Rhizobacteria (PGPR). The co-occurrence analysis showed Pseudomonas, Burkholderia, and Streptomyces were present in the suppressive soils, while Bacillus and more Streptomyces were found in the conducive soils. Furthermore, the relative abundance of Pseudomonas, Burkholderia, Bacillus, and Streptomyces was performed. The analysis showed that the relative abundance of Pseudomonas and Burkholderia was higher in the suppressive than conducive soils. Therefore, it assumed Pseudomonas and Burkholderia play a role in suppressing Foc based on co-occurrence and abundance analysis. Functional analysis of Pseudomonas and Burkholderia showed that the zinc/manganese transport system was higher in the suppressive than conducive soils. In contrast, the phosphate transport system was not found in conducive soils. Both functions are may be responsible for the synthesis of a siderophore and phosphate solubilization. In conclusion, this study provides information that PGPR may be contributing to Foc growth suppressing by releasing secondary metabolites.

Complex Interaction Networks Among Cyanolichens of a Tropical Biodiversity Hotspot

Interactions within lichen communities include, in addition to close mutualistic associations between the main partners of specific lichen symbioses, also more elusive relationships between members of a wider symbiotic community. Here, we analyze association patterns of cyanolichen symbionts in the tropical montane forests of Taita Hills, southern Kenya, which is part of the Eastern Afromontane biodiversity hotspot. The cyanolichen specimens analyzed represent 74 mycobiont taxa within the order Peltigerales (Ascomycota), associating with 115 different variants of the photobionts genus Nostoc (Cyanobacteria). Our analysis demonstrates wide sharing of photobionts and reveals the presence of several photobiont-mediated lichen guilds. Over half of all mycobionts share photobionts with other fungal species, often from different genera or even families, while some others are strict specialists and exclusively associate with a single photobiont variant. The most extensive symbiont network involves 24 different fungal species from five genera associating with 38 Nostoc photobionts. The Nostoc photobionts belong to two main groups, the Nephroma-type Nostoc and the Collema/Peltigera-type Nostoc, and nearly all mycobionts associate only with variants of one group. Among the mycobionts, species that produce cephalodia and those without symbiotic propagules tend to be most promiscuous in photobiont choice. The extent of photobiont sharing and the structure of interaction networks differ dramatically between the two major photobiont-mediated guilds, being both more prevalent and nested among Nephroma guild fungi and more compartmentalized among Peltigera guild fungi. This presumably reflects differences in the ecological characteristics and/or requirements of the two main groups of photobionts. The same two groups of Nostoc have previously been identified from many lichens in various lichen-rich ecosystems in different parts of the world, indicating that photobiont sharing between fungal species is an integral part of lichen ecology globally. In many cases, symbiotically dispersing lichens can facilitate the dispersal of sexually reproducing species, promoting establishment and adaptation into new and marginal habitats and thus driving evolutionary diversification.

Pollinator interaction flexibility across scales affects patch colonization and occupancy

Global change alters ecological communities and may disrupt ecological interactions and the provision of ecosystem functions. As ecological communities respond to global change, species may either go locally extinct or form novel interactions. To date, few studies have assessed how flexible species are in their interaction patterns, mainly due to the scarcity of data spanning long time series. Using a ten-year species-level dataset on the assembly of mutualistic networks from the Central Valley in California, we test whether interaction flexibility affects pollinators' colonization and persistence and their resulting habitat occupancy in a highly modified landscape. We propose three metrics of interaction flexibility associated with different scales of organization within ecological communities and explore which species' traits affect them. Our results provide empirical evidence linking species' ability to colonize habitat patches across a landscape to the role they play in networks. Phenological breadth and body size had contrasting effects on interaction flexibility. We demonstrate the relationship between mutualistic networks and species' ability to colonize and persist in the landscape, suggesting interaction flexibility as a potential mechanism for communities to maintain ecosystem function despite changes in community composition.

Interaction generalisation and demographic feedbacks drive the resilience of plant-insect networks to extinctions

Understanding the processes driving ecological resilience, that is the extent to which systems retain their structure while absorbing perturbations, is a central challenge for theoretical and applied ecologists. Plant-insect assemblages are well-suited for the study of ecological resilience as they are species-rich and encompass a variety of ecological interactions that correspond to essential ecosystem functions. Mechanisms affecting community response to perturbations depend on both the natural history and structure of ecological interactions. Natural history attributes of the interspecific interactions, for example whether they are mutualistic or antagonistic, may affect the ecological resilience by controlling the demographic feedbacks driving ecological dynamics at the community level. Interaction generalisation may also affect resilience, by defining opportunities for interaction rewiring, the extent to which species are able to switch interactions in fluctuating environments. These natural history attributes may also interact with network structure to affect ecological resilience. Using adaptive network models, we investigated the resilience of plant-pollinator and plant-herbivore networks to species loss. We specifically investigated how fundamental natural history differences between these systems, namely the demographic consequences of the interaction and their level of generalisation-mediating rewiring opportunities-affect the resilience of dynamic ecological networks to extinctions. We also create a general benchmark for the effect of network structure on resilience simulating extinctions on theoretical networks with controlled structures. When network structure was static, pollination networks were less resilient than herbivory networks; this is related to their high levels of nestedness and the reciprocally positive feedbacks that define mutualisms, which made co-extinction cascades more likely and longer in plant-pollinator assemblages. When considering interaction rewiring, the high generalisation and the structure of pollination networks boosted their resilience to extinctions, which approached those of herbivory networks. Simulation results using theoretical networks suggested that the empirical structure of herbivory networks may protect them from collapse. Elucidating the ecological and evolutionary processes driving interaction rewiring is key to understanding the resilience of plant-insect assemblages. Accounting for rewiring requires ecologists to combine natural history with network models that incorporate feedbacks between species abundances, traits and interactions. This combination will elucidate how perturbations propagate at community level, reshaping biodiversity structure and ecosystem functions.

An ecological approach to structural flexibility in online communication systems

Human cognitive abilities are limited resources. Today, in the age of cheap information-cheap to produce, to manipulate, to disseminate-this cognitive bottleneck translates into hypercompetition for rewarding outcomes among actors. These incentives push actors to mutualistically interact with specific memes, seeking the virality of their messages. In turn, memes' chances to persist and spread are subject to changes in the communication environment. In spite of all this complexity, here we show that the underlying architecture of empirical actor-meme information ecosystems evolves into recurring emergent patterns. We then propose an ecology-inspired modelling framework, bringing to light the precise mechanisms causing the observed flexible structural reorganisation. The model predicts-and the data confirm-that users' struggle for visibility induces a re-equilibration of the network's mesoscale towards self-similar nested arrangements. Our final microscale insights suggest that flexibility at the structural level is not mirrored at the dynamical one.

Dimensionality reduction of complex dynamical systems

One of the outstanding problems in complexity science and engineering is the study of high-dimensional networked systems and of their susceptibility to transitions to undesired states as a result of changes in external drivers or in the structural properties. Because of the incredibly large number of parameters controlling the state of such complex systems and the heterogeneity of its components, the study of their dynamics is extremely difficult. Here we propose an analytical framework for collapsing complex N-dimensional networked systems into an S+1-dimensional manifold as a function of S effective control parameters with S << N. We test our approach on a variety of real-world complex problems showing how this new framework can approximate the system's response to changes and correctly identify the regions in the parameter space corresponding to the system's transitions. Our work offers an analytical method to evaluate optimal strategies in the design or management of networked systems.

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We analytically collapse N-dimensional networked dynamics in low-dimensional manifolds

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We test this approach on a variety of real-world complex problems

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We accurately predict the system's response to changes in parameter values

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We identify regions in parameter space corresponding to system's critical transitions

Stability of ecosystems enhanced by species-interaction constraints

Ecosystem stability is a central question both in theoretical and applied biology. Dynamical systems theory can be used to analyze how growth rates, carrying capacities, and patterns of species interactions affect the stability of an ecosystem. The response to increasing complexity has been extensively studied and the general conclusion is that there is a limit. While there is a complexity limit to stability at which global destabilisation occurs, the collapse rarely happens suddenly if a system is fully viable (no species is extinct). In fact, when complexity is successively increased, we find that the generic response is to go through multiple single-species extinctions before a global collapse. In this paper we demonstrate this finding via both numerical simulations and elaborations of theoretical predictions. We explore more biological interaction patterns, and, perhaps most importantly, we show that constrained interaction structures-a constant row sum in the interaction matrix-prevent extinctions from occurring. This makes an ecosystem more robust in terms of allowed complexity, but it also means singles-species extinctions do not precede or signal collapse-a drastically different behavior compared to the generic and commonly assumed case. We further argue that this constrained interaction structure-limiting the total interactions for each species-is biologically plausible.

The ambiguity of nestedness under soft and hard constraints

Many real networks feature the property of nestedness, i.e. the neighbours of nodes with a few connections are hierarchically nested within the neighbours of nodes with more connections. Despite the abstract simplicity of this notion, various mathematical definitions of nestedness have been proposed, sometimes giving contrasting results. Moreover, there is an ongoing debate on the statistical significance of nestedness, since random networks where the number of connections (degree) of each node is fixed to its empirical value are typically as nested as real ones. By using only ergodic and unbiased null models, we propose a clarification that exploits the recent finding that random networks where the degrees are enforced as hard constraints (microcanonical ensembles) are thermodynamically different from random networks where the degrees are enforced as soft constraints (canonical ensembles). Indeed, alternative definitions of nestedness can be negatively correlated in the microcanonical one, while being positively correlated in the canonical one. This result disentangles distinct notions of nestedness captured by different metrics and highlights the importance of making a principled choice between hard and soft constraints in null models of ecological networks.

Mutualistic networks emerging from adaptive niche-based interactions

Mutualistic networks are vital ecological and social systems shaped by adaptation and evolution. They involve bipartite cooperation via the exchange of goods or services between actors of different types. Empirical observations of mutualistic networks across genres and geographic conditions reveal correlated nested and modular patterns. Yet, the underlying mechanism for the network assembly remains unclear. We propose a niche-based adaptive mechanism where both nestedness and modularity emerge simultaneously as complementary facets of an optimal niche structure. Key dynamical properties are revealed at different timescales. Foremost, mutualism can either enhance or reduce the network stability, depending on competition intensity. Moreover, structural adaptations are asymmetric, exhibiting strong hysteresis in response to environmental change. Finally, at the evolutionary timescale we show that the adaptive mechanism plays a crucial role in preserving the distinctive patterns of mutualism under species invasions and extinctions.

Nested and modular patterns are vastly observed in mutualistic networks across genres and geographic conditions. Here, the authors show a unified mechanism that underlies the assembly and evolution of such networks, based on adaptive niche interactions of the participants.

An individual-based model for the eco-evolutionary emergence of bipartite interaction networks

How ecological interaction networks emerge on evolutionary time scales remains unclear. Here we build an individual-based eco-evolutionary model for the emergence of mutualistic, antagonistic and neutral bipartite interaction networks. Exploring networks evolved under these scenarios, we find three main results. First, antagonistic interactions tend to foster species and trait diversity, while mutualistic interactions reduce diversity. Second, antagonistic interactors evolve higher specialisation, which results in networks that are often more modular than neutral ones; resource species in these networks often display phylogenetic conservatism in interaction partners. Third, mutualistic interactions lead to networks that are more nested than neutral ones, with low phylogenetic conservatism in interaction partners. These results tend to match overall empirical trends, demonstrating that structures of empirical networks that have most often been explained by ecological processes can result from an evolutionary emergence. Our model contributes to the ongoing effort of better integrating ecological interactions and macroevolution.

Co-adaptation enhances the resilience of mutualistic networks

Mutualistic networks, which describe the ecological interactions between multiple types of species such as plants and pollinators, play a paramount role in the generation of Earth's biodiversity. The resilience of a mutualistic network denotes its ability to retain basic functionality when errors and failures threaten the persistence of the community. Under the disturbances of mass extinctions and human-induced disasters, it is crucial to understand how mutualistic networks respond to changes, which enables the system to increase resilience and tolerate further damages. Despite recent advances in the modelling of the structure-based adaptation, we lack mathematical and computational models to describe and capture the co-adaptation between the structure and dynamics of mutualistic networks. In this paper, we incorporate dynamic features into the adaptation of structure and propose a co-adaptation model that drastically enhances the resilience of non-adaptive and structure-based adaptation models. Surprisingly, the reason for the enhancement is that the co-adaptation mechanism simultaneously increases the heterogeneity of the mutualistic network significantly without changing its connectance. Owing to the broad applications of mutualistic networks, our findings offer new ways to design mechanisms that enhance the resilience of many other systems, such as smart infrastructures and social-economical systems.

The stability of mutualism

Positive interactions are observed at high frequencies in nearly all living systems, ranging from human and animal societies down to the scale of microbial organisms. However, historically, detailed ecological studies of mutualism have been relatively unrepresented. Moreover, while ecologists have long portrayed competition as a stabilizing process, mutualism is often deemed destabilizing. Recently, several key modelling studies have applied random matrix methods, and have further corroborated the instability of mutualism. Here, I reassess these findings by factoring in species densities into the “community matrix,” a practice which has almost always been ignored in random matrix analyses. With this modification, mutualistic interactions are found to boost equilibrium population densities and stabilize communities by increasing their resilience. By taking into account transient dynamics after a strong population perturbation, it is found that mutualists have the ability to pull up communities by their bootstraps when species are dangerously depressed in numbers.

Mutualism is typically portrayed as a destabilizing process in community ecology. Here, via a random matrix model that considers species density, the author shows that mutualistic interactions can, in fact, enhance population density at equilibrium and increase community resilience to perturbation.

Predicting collapse of complex ecological systems: quantifying the stability-complexity continuum

Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability-species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the extinction continuum. We also develop a metric that locates the position of the system within the extinction continuum-thus quantifying proximity to stability or collapse-in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system's behaviour in comparison with other existing methods-such as May's stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

Telling ecological networks apart by their structure: An environment-dependent approach

The network architecture of an ecological community describes the structure of species interactions established in a given place and time. It has been suggested that this architecture presents unique features for each type of ecological interaction: e.g., nested and modular architectures would correspond to mutualistic and antagonistic interactions, respectively. Recently, Michalska-Smith and Allesina (2019) proposed a computational challenge to test whether it is indeed possible to differentiate ecological interactions based on network architecture. Contrary to the expectation, they found that this differentiation is practically impossible, moving the question to why it is not possible to differentiate ecological interactions based on their network architecture alone. Here, we show that this differentiation becomes possible by adding the local environmental information where the networks were sampled. We show that this can be explained by the fact that environmental conditions are a confounder of ecological interactions and network architecture. That is, the lack of association between network architecture and type of ecological interactions changes by conditioning on the local environmental conditions. Additionally, we find that environmental conditions are linked to the stability of ecological networks, but the direction of this effect depends on the type of interaction network. This suggests that the association between ecological interactions and network architectures exists, but cannot be fully understood without attention to the environmental conditions acting upon them.

It has been suggested that different types of species interactions lead to ecological networks with different architectures. For example, mutualistic and antagonistic interaction networks have been shown to have nested and modular architectures, respectively. Importantly, this differentiation can provide clues about the link between the dynamics and structures shaping ecological communities. Recently, Michalska-Smith and Allesina (2019) turned this assumption into a serious computational challenge for the scientific community. Here, we embrace this challenge. We confirm that network architecture alone is not enough to differentiate interaction networks. However, we show that network architectures can differentiate between mutualistic and antagonistic interaction networks by using information about their local environmental conditions. In other words, ignoring environmental information throws out the predictable patterns of network architectures along environmental gradients. Thus, this response is also a reminder that ecological networks may only make sense in the light of environmental information.

Evolving complexity: how tinkering shapes cells, software and ecological networks

A common trait of complex systems is that they can be represented by means of a network of interacting parts. It is, in fact, the network organization (more than the parts) that largely conditions most higher-level properties, which are not reducible to the properties of the individual parts. Can the topological organization of these webs provide some insight into their evolutionary origins? Both biological and artificial networks share some common architectural traits. They are often heterogeneous and sparse, and most exhibit different types of correlations, such as nestedness, modularity or hierarchical patterns. These properties have often been attributed to the selection of functionally meaningful traits. However, a proper formulation of generative network models suggests a rather different picture. Against the standard selection-optimization argument, some networks reveal the inevitable generation of complex patterns resulting from reuse and can be modelled using duplication-rewiring rules lacking functionality. These give rise to the observed heterogeneous, scale-free and modular architectures. Here, we examine the evidence for tinkering in cellular, technological and ecological webs and its impact in shaping their architecture. Our analysis suggests a serious consideration of the role played by selection as the origin of network topology. Instead, we suggest that the amplification processes associated with reuse might shape these graphs at the topological level. In biological systems, selection forces would take advantage of emergent patterns. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

manta: a Clustering Algorithm for Weighted Ecological Networks

Microbial network inference and analysis have become successful approaches to extract biological hypotheses from microbial sequencing data. Network clustering is a crucial step in this analysis. Here, we present a novel heuristic network clustering algorithm, manta, which clusters nodes in weighted networks. In contrast to existing algorithms, manta exploits negative edges while differentiating between weak and strong cluster assignments. For this reason, manta can tackle gradients and is able to avoid clustering problematic nodes. In addition, manta assesses the robustness of cluster assignment, which makes it more robust to noisy data than most existing tools. On noise-free synthetic data, manta equals or outperforms existing algorithms, while it identifies biologically relevant subcompositions in real-world data sets. On a cheese rind data set, manta identifies groups of taxa that correspond to intermediate moisture content in the rinds, while on an ocean data set, the algorithm identifies a cluster of organisms that were reduced in abundance during a transition period but did not correlate strongly to biochemical parameters that changed during the transition period. These case studies demonstrate the power of manta as a tool that identifies biologically informative groups within microbial networks.IMPORTANCE manta comes with unique strengths, such as the abilities to identify nodes that represent an intermediate between clusters, to exploit negative edges, and to assess the robustness of cluster membership. manta does not require parameter tuning, is straightforward to install and run, and can be easily combined with existing microbial network inference tools.

Connectance and nestedness as stabilizing factors in response to pulse disturbances in adaptive antagonistic networks

Understanding how network architectures are related to community robustness is essential to investigating the effects of disturbances on biological systems. Regarding the perturbations that are observed in disturbance regimes, frequency and intensity are two main descriptors, specifically for those events with short duration. Here, I used the architecture of 45 real-world weighted bipartite networks to assess whether network size, connectance, and nestedness are related to the effects of pulse disturbances in antagonistic communities. Networks were simulated under five scenarios with different combinations of frequency and intensity of perturbations. The dynamics of resource-consumer interactions followed the adaptive interaction switching behavior, which is the key topological process underlying most of the architectures of antagonistic webs. As opposed to most studies considering the effects of disturbances as species extinctions explicitly, the effects of disturbances here were modeled as changes in the abundance of consumers following immediate reductions in the abundance of resources. Simulations revealed that community robustness to pulse disturbances increased with both connectance and nestedness overall, with no effect of network size. Community networks with highly connected and nested topologies were more robust to disturbances, particularly under high frequency and intensity perturbations. By considering disturbances that are not directly related to species' extinctions, this study provides valuable insights that connectance and nestedness have an important stabilizing role in ecological networks.

Fragility Limits Performance in Complex Networks

While numerous studies have suggested that large natural, biological, social, and technological networks are fragile, convincing theories are still lacking to explain why natural evolution and human design have failed to optimize networks and avoid fragility. In this paper we provide analytical and numerical evidence that a tradeoff exists in networks with linear dynamics, according to which general measures of robustness and performance are in fact competitive features that cannot be simultaneously optimized. Our findings show that large networks can either be robust to variations of their weights and parameters, or efficient in responding to external stimuli, processing noise, or transmitting information across long distances. As illustrated in our numerical studies, this performance tradeoff seems agnostic to the specific application domain, and in fact it applies to simplified models of ecological, neuronal, and traffic networks.

Macro- and mesoscale pattern interdependencies in complex networks

Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other arrangements-e.g. nestedness or core-periphery-have been studied in parallel, but to a much lesser extent. However, empirical evidence increasingly suggests that characterizing a network with a unique pattern typology may be too simplistic, since a system can integrate properties from distinct organizations at different scales. Here, we explore the relationship between some of these different organizational patterns: two at the mesoscale (modularity and in-block nestedness); and one at the macroscale (nestedness). We show experimentally and analytically that nestedness imposes bounds to modularity, with exact analytical results in idealized scenarios. Specifically, we show that nestedness and modularity are interdependent. Furthermore, we analytically evidence that in-block nestedness provides a natural combination between nested and modular networks, taking structural properties of both. Far from a mere theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy dynamical effects on processes, such as species abundances and stability in ecology.

Online division of labour: emergent structures in Open Source Software

The development Open Source Software fundamentally depends on the participation and commitment of volunteer developers to progress on a particular task. Several works have presented strategies to increase the on-boarding and engagement of new contributors, but little is known on how these diverse groups of developers self-organise to work together. To understand this, one must consider that, on one hand, platforms like GitHub provide a virtually unlimited development framework: any number of actors can potentially join to contribute in a decentralised, distributed, remote, and asynchronous manner. On the other, however, it seems reasonable that some sort of hierarchy and division of labour must be in place to meet human biological and cognitive limits, and also to achieve some level of efficiency. These latter features (hierarchy and division of labour) should translate into detectable structural arrangements when projects are represented as developer-file bipartite networks. Thus, in this paper we analyse a set of popular open source projects from GitHub, placing the accent on three key properties: nestedness, modularity and in-block nestedness -which typify the emergence of heterogeneities among contributors, the emergence of subgroups of developers working on specific subgroups of files, and a mixture of the two previous, respectively. These analyses show that indeed projects evolve into internally organised blocks. Furthermore, the distribution of sizes of such blocks is bounded, connecting our results to the celebrated Dunbar number both in off- and on-line environments. Our conclusions create a link between bio-cognitive constraints, group formation and online working environments, opening up a rich scenario for future research on (online) work team assembly (e.g. size, composition, and formation). From a complex network perspective, our results pave the way for the study of time-resolved datasets, and the design of suitable models that can mimic the growth and evolution of OSS projects.