The multilayer nature of ecological networks

Multilayer biological networks to upscale marine research to global change-smart management and sustainable resource use

Human activities are having a massive negative impact on biodiversity and ecological processes worldwide. The rate and magnitude of ecological transformations induced by climate change, habitat destruction, overexploitation and pollution are now so substantial that a sixth mass extinction event is currently underway. The biodiversity crisis of the Anthropocene urges scientists to put forward a transformative vision to promote the conservation of biodiversity, and thus indirectly the preservation of ecosystem functions. Here, we identify pressing issues in global change biology research and propose an integrative framework based on multilayer biological networks as a tool to support conservation actions and marine risk assessments in multi-stressor scenarios. Multilayer networks can integrate different levels of environmental and biotic complexity, enabling us to combine information on molecular, physiological and behaviour responses, species interactions and biotic communities. The ultimate aim of this framework is to link human-induced environmental changes to species physiology, fitness, biogeography and ecosystem impacts across vast seascapes and time frames, to help guide solutions to address biodiversity loss and ecological tipping points. Further, we also define our current ability to adopt a widespread use of multilayer networks within ecology, evolution and conservation by providing examples of case-studies. We also assess which approaches are ready to be transferred and which ones require further development before use. We conclude that multilayer biological networks will be crucial to inform (using reliable multi-levels integrative indicators) stakeholders and support their decision-making concerning the sustainable use of resources and marine conservation.

Connected interactions: enriching food web research by spatial and social interactions

This theme issue features 18 papers exploring ecological interactions, encompassing metabolic, social, and spatial connections alongside traditional trophic networks. This integration enriches food web research, offering insights into ecological dynamics. By examining links across organisms, populations, and ecosystems, a hierarchical approach emerges, connecting horizontal effects within organizational levels vertically across biological organization levels. The inclusion of interactions involving humans is a key focus, highlighting the need for their integration into ecology given the complex interactions between human activities and ecological systems in the Anthropocene. The comprehensive exploration in this theme issue sheds light on the interconnectedness of ecological systems and the importance of considering diverse interactions in understanding ecosystem dynamics. This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'.

A highly resolved network reveals the role of terrestrial herbivory in structuring aboveground food webs

Comparative studies suggest remarkable similarities among food webs across habitats, including systematic changes in their structure with diversity and complexity (scale-dependence). However, historic aboveground terrestrial food webs (ATFWs) have coarsely grouped plants and insects such that these webs are generally small, and herbivory is disproportionately under-represented compared to vertebrate predator-prey interactions. Furthermore, terrestrial herbivory is thought to be structured by unique processes compared to size-structured feeding in other systems. Here, we present the richest ATFW to date, including approximately 580 000 feeding links among approximately 3800 taxonomic species, sourced from approximately 27 000 expert-vetted interaction records annotated as feeding upon one of six different resource types: leaves, flowers, seeds, wood, prey and carrion. By comparison to historical ATFWs and null ecological hypotheses, we show that our temperate forest web displays a potentially unique structure characterized by two properties: (i) a large fraction of carnivory interactions dominated by a small number of hyper-generalist, opportunistic bird and bat predators; and (ii) a smaller fraction of herbivory interactions dominated by a hyper-rich community of insects with variably sized but highly specific diets. We attribute our findings to the large-scale, even resolution of vertebrate, insect and plant guilds in our food web.This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'.

Limited function of road verges as habitat for species connecting plant-bee networks in remnant semi-natural grasslands

Species-rich natural and semi-natural ecosystems are under threat owing to land use change. To conserve the biodiversity associated with these ecosystems, we must identify and target conservation efforts towards functionally important species and supporting habitats that create connections between remnant patches in the landscape. Here, we use a multi-layer network approach to identify species that connect a metanetwork of plant-bee interactions in remnant semi-natural grasslands which are biodiversity hotspots in European landscapes. We investigate how these landscape connecting species, and their interactions, persist in their proposed supporting habitat, road verges, across a landscape with high human impact. We identify 11 plant taxa and nine bee species that connect semi-natural grassland patches. We find the beta diversity of these connector species to be low across road verges, indicating a poor contribution of these habitats to the landscape-scale diversity in semi-natural grasslands. We also find a significant influence of the surrounding landscape on the beta diversity of connector species and their interactions with implications for landscape-scale management. Conservation actions targeted toward species with key functional roles as connectors of fragmented ecosystems can provide cost-effective management of the diversity and functioning of threatened ecosystems.This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'.

Biodiversity in changing environments: An external-driver internal-topology framework to guide intervention

Accompanying the climate crisis is the more enigmatic biodiversity crisis. Rapid reorganization of biodiversity due to global environmental change has defied prediction and tested the basic tenets of conservation and restoration. Conceptual and practical innovation is needed to support decision making in the face of these unprecedented shifts. Critical questions include: How can we generalize biodiversity change at the community level? When are systems able to reorganize and maintain integrity, and when does abiotic change result in collapse or restructuring? How does this understanding provide a template to guide when and how to intervene in conservation and restoration? To this end, we frame changes in community organization as the modulation of external abiotic drivers on the internal topology of species interactions, using plant-plant interactions in terrestrial communities as a starting point. We then explore how this framing can help translate available data on species abundance and trait distributions to corresponding decisions in management. Given the expectation that community response and reorganization are highly complex, the external-driver internal-topology (EDIT) framework offers a way to capture general patterns of biodiversity that can help guide resilience and adaptation in changing environments.

Quantifying compositional variability in microbial communities with FAVA

Microbial communities vary across space, time, and individual hosts, presenting new challenges for the development of statistics measuring the variability of community composition. To understand differences across microbiome samples from different host individuals, sampling times, spatial locations, or experimental replicates, we present FAVA, a new normalized measure for characterizing compositional variability across multiple microbiome samples. FAVA quantifies variability across many samples of taxonomic or functional relative abundances in a single index ranging between 0 and 1, equaling 0 when all samples are identical and equaling 1 when each sample is entirely comprised of a single taxon. Its definition relies on the population-genetic statisticF S T , with samples playing the role of "populations" and taxa playing the role of "alleles." Its convenient mathematical properties allow users to compare disparate data sets. For example, FAVA values are commensurable across different numbers of taxonomic categories and different numbers of samples considered. We introduce extensions that incorporate phylogenetic similarity among taxa and spatial or temporal distances between samples. We illustrate how FAVA can be used to describe across-individual taxonomic variability in ruminant microbiomes at different regions along the gastrointestinal tract. In a second example, a longitudinal analysis of gut microbiomes of healthy human adults taking an antibiotic, we use FAVA to quantify the increase in temporal variability of microbiomes following the antibiotic course and to measure the duration of the antibiotic's influence on microbial variability. We have implemented this tool in an R package, FAVA, which can fit easily into existing pipelines for the analysis of microbial relative abundances.

Multiple interaction networks reveal that Lepidoptera larvae and adults prefer various host plants for diet and pollination

Plant-Lepidoptera interactions are often studied using the pollination or herbivore networks only. Lepidoptera species are involved in two types of plant-insect interactions because they are herbivores as larvae and pollinators as adults. The study of entangled networks is critical, since the interaction of different networks can affect the overall network and community stability. Here, we studied the interaction of plants and Lepidoptera on the Yongxing Island, South China Sea. A plant-lepidopteran pollination network and a plant-lepidopteran herbivore network were built by using data from flower-pollinator and leaf-herbivore interactions. We then combined the two networks into a single network. We measured plant composition similarity within each sub-network and across sub-networks for Lepidoptera species. Our findings indicate that the plant-Lepidoptera pollination network and the herbivory network share significant proportions of Lepidoptera but small proportions of plant assemblages. The pollination network had higher nestedness and connectance than the herbivore network. Agrius convolvuli was the most specialized species, while Zizina otis had the highest species strength in the pollination network. Most Lepidoptera species were highly specialized in the herbivore network and their importance positively correlated across the two networks. Furthermore, there was no dietary composition similarity between the two networks for most Lepidoptera species. Our findings highlight the visible structural difference between the pollination and the herbivore networks. Adult Lepidoptera selects different plants for oviposition and feeding, a strategy that may benefit their reproduction and survival by sustaining adequate resources for their two life stages and the diversity of both plants and insects in oceanic island communities.

Hyper-brain hyper-frequency network topology dynamics when playing guitar in quartet

Ensemble music performance is a highly coordinated form of social behavior requiring not only precise motor actions but also synchronization of different neural processes both within and between the brains of ensemble players. In previous analyses, which were restricted to within-frequency coupling (WFC), we showed that different frequencies participate in intra- and inter-brain coordination, exhibiting distinct network topology dynamics that underlie coordinated actions and interactions. However, many of the couplings both within and between brains are likely to operate across frequencies. Hence, to obtain a more complete picture of hyper-brain interaction when musicians play the guitar in a quartet, cross-frequency coupling (CFC) has to be considered as well. Furthermore, WFC and CFC can be used to construct hyper-brain hyper-frequency networks (HB-HFNs) integrating all the information flows between different oscillation frequencies, providing important details about ensemble interaction in terms of network topology dynamics (NTD). Here, we reanalyzed EEG (electroencephalogram) data obtained from four guitarists playing together in quartet to explore changes in HB-HFN topology dynamics and their relation to acoustic signals of the music. Our findings demonstrate that low-frequency oscillations (e.g., delta, theta, and alpha) play an integrative or pacemaker role in such complex networks and that HFN topology dynamics are specifically related to the guitar quartet playing dynamics assessed by sound properties. Simulations by link removal showed that the HB-HFN is relatively robust against loss of connections, especially when the strongest connections are preserved and when the loss of connections only affects the brain of one guitarist. We conclude that HB-HFNs capture neural mechanisms that support interpersonally coordinated action and behavioral synchrony.

The propagation of disturbances in ecological networks

Despite the development of network science, we lack clear heuristics for how far different disturbance types propagate within and across species interaction networks. We discuss the mechanisms of disturbance propagation in ecological networks, and propose that disturbances can be categorized into structural, functional, and transmission types according to their spread and effect on network structure and functioning. We describe the properties of species and their interaction networks and metanetworks that determine the indirect, spatial, and temporal extent of propagation. We argue that the sampling scale of ecological studies may have impeded predictions regarding the rate and extent that a disturbance spreads, and discuss directions to help ecologists to move towards a predictive understanding of the propagation of impacts across interacting communities and ecosystems.

Motif-based community detection in heterogeneous multilayer networks

Multilayer networks composed of intralayer edges and interlayer edges are an important type of complex networks. Considering the heterogeneity of nodes and edges, it is necessary to design more reasonable and diverse community detection methods for multilayer networks. Existing research on community detection in multilayer networks mainly focuses on multiplexing networks (where the nodes are homogeneous and the edges are heterogeneous), but few studies have focused on heterogeneous multilayer networks where both nodes and edges represent different semantics. In this paper, we studied community detection on heterogeneous multilayer networks and proposed a motif-based detection algorithm. First, the communities and motifs of multilayer networks are defined, especially the interlayer motifs. Then, the modularity of multilayer networks based on these motifs is designed, and the community structure of the multilayer network is detected by maximizing the modularity of multilayer networks. Finally, we verify the effectiveness of the detection algorithm on synthetic networks. In the experiments on synthetic networks, comparing with the classical community detection algorithms (without considering interlayer heterogeneity), the motif-based modularity community detection algorithm can obtain better results under different evaluation indexes, and we found that there exists a certain relationship between motifs and communities. In addition, the proposed algorithm is applied in the empirical network, which shows its practicability in the real world. This study provides a solution for the investigation of heterogeneous information in multilayer networks.

A taxonomy of multiple stable states in complex ecological communities

Natural systems are built from multiple interconnected units, making their dynamics, functioning and fragility notoriously hard to predict. A fragility scenario of particular relevance concerns so-called regime shifts: abrupt transitions from healthy to degraded ecosystem states. An explanation for these shifts is that they arise as transitions between alternative stable states, a process that is well-understood in few-species models. However, how multistability upscales with system complexity remains a debated question. Here, we identify that four different multistability regimes generically emerge in models of species-rich communities and other archetypical complex biological systems assuming random interactions. Across the studied models, each regime consistently emerges under a specific interaction scheme and leaves a distinct set of fingerprints in terms of the number of observed states, their species richness and their response to perturbations. Our results help clarify the conditions and types of multistability that can be expected to occur in complex ecological communities.

Novel community data in ecology-properties and prospects

New technologies for monitoring biodiversity such as environmental (e)DNA, passive acoustic monitoring, and optical sensors promise to generate automated spatiotemporal community observations at unprecedented scales and resolutions. Here, we introduce 'novel community data' as an umbrella term for these data. We review the emerging field around novel community data, focusing on new ecological questions that could be addressed; the analytical tools available or needed to make best use of these data; and the potential implications of these developments for policy and conservation. We conclude that novel community data offer many opportunities to advance our understanding of fundamental ecological processes, including community assembly, biotic interactions, micro- and macroevolution, and overall ecosystem functioning.

Analysis of subgingival bacterial and fungal diversity in patients with peri-implantitis based on 16sRNA and internal transcribed spacer sequencing

Aim: To analyze subgingival fungal diversity in peri-implant inflammation patients and their relationship with bacteria. Methods: We collected saliva samples from four groups. 16sRNA and internal transcribed spacer sequencing was performed preceded by quantitative PCR and enzyme-linked immunosorbent assay tests. Analyses were done using R and Cytoscape software. Results: Significant differences were observed in the Abundance-based Coverage Estimator (ACE) index between control and peri-implantitis samples. Basidiomycota was the dominant fungal species, while Firmicutes dominated the bacteria. The most abundant fungal and bacterial species were 's_unclassified g Apiotrichum' and 's_unclassified g Streptococcus', respectively. Dothiorella was strongly associated with immunoglobulin G levels, with positive correlations between specific microorganisms and peri-implantitis in Q-PCR. Conclusion: Our findings have significant clinical implications, suggesting specific fungal and bacterial taxa roles in peri-implant inflammation.

A quantitative framework for identifying the role of individual species in Nature's Contributions to People

It is widely acknowledged that biodiversity change is affecting human well-being by altering the supply of Nature's Contributions to People (NCP). Nevertheless, the role of individual species in this relationship remains obscure. In this article, we present a framework that combines the cascade model from ecosystem services research with network theory from community ecology. This allows us to quantitatively link NCP demanded by people to the networks of interacting species that underpin them. We show that this "network cascade" framework can reveal the number, identity and importance of the individual species that drive NCP and of the environmental conditions that support them. This information is highly valuable in demonstrating the importance of biodiversity in supporting human well-being and can help inform the management of biodiversity in social-ecological systems.

Using individual-based trait frequency distributions to forecast plant-pollinator network responses to environmental change

Determining how and why organisms interact is fundamental to understanding ecosystem responses to future environmental change. To assess the impact on plant-pollinator interactions, recent studies have examined how the effects of environmental change on individual interactions accumulate to generate species-level responses. Here, we review recent developments in using plant-pollinator networks of interacting individuals along with their functional traits, where individuals are nested within species nodes. We highlight how these individual-level, trait-based networks connect intraspecific trait variation (as frequency distributions of multiple traits) with dynamic responses within plant-pollinator communities. This approach can better explain interaction plasticity, and changes to interaction probabilities and network structure over spatiotemporal or other environmental gradients. We argue that only through appreciating such trait-based interaction plasticity can we accurately forecast the potential vulnerability of interactions to future environmental change. We follow this with general guidance on how future studies can collect and analyse high-resolution interaction and trait data, with the hope of improving predictions of future plant-pollinator network responses for targeted and effective conservation.

Mitigating the impacts of street lighting on biodiversity and ecosystem functioning

Street lights are not only a major source of direct light pollution emissions, but stock has been transitioning to light-emitting diode (LED) technology in many parts of the world, resulting in increases in the blue part of the visible spectrum that is more harmful to biodiversity and human health. But LEDs can be modified more easily than conventional sodium lamps by adjusting their intensity, spectral output and other features of street light systems. In this Opinion piece, I provide an updated overview of street light mitigation strategies and contend that research in this area has been slow. I show how experimental lighting rigs that mimic real street lights can be used for mitigation testing, since invertebrate behaviour, abundances and interactions can respond quickly and measurably. I demonstrate how advances in network ecology that use species interaction data can provide much-needed assessments of the impacts of street lights on biodiversity and ecosystem functioning, and ultimately provide new tools and metrics for biomonitoring. I acknowledge the limitations of measuring local, short-term responses of biodiversity and identify promising avenues for collaborating with industry and government agencies in new or existing road lighting schemes, to minimize the negative long-term impacts at marginal cost. This article is part of the theme issue 'Light pollution in complex ecological systems'.

Discrete-Time Quantum Walk on Multilayer Networks

A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures.

Desynchrony induced by higher-order interactions in triplex metapopulations

In a predator-prey metapopulation, two traits are adversely related: synchronization and persistence. A decrease in synchrony apparently leads to an increase in persistence and, therefore, necessitates the study of desynchrony in a metapopulation. In this article, we study predator-prey patches that communicate with one another while being interconnected through distinct dispersal structures in the layers of a three-layer multiplex network. We investigate the synchronization phenomenon among the patches of the outer layers by introducing higher-order interactions (specifically three-body interactions) in the middle layer. We observe a decrease in the synchronous behavior or, alternatively, an increase in desynchrony due to the inclusion of group interactions among the patches of the middle layer. The advancement of desynchrony becomes more prominent with increasing strength and numbers of three-way interactions in the middle layer. We analytically validate our numerical results by performing a stability analysis of the referred synchronous solution using the master stability function approach. Additionally, we verify our findings by taking into account two distinct predator-prey models and dispersal topologies, which ultimately supports that the findings are generalizable across various models and dispersal structures.

Urbanization alters the spatiotemporal dynamics of plant-pollinator networks in a tropical megacity

Urbanization is a major driver of biodiversity change but how it interacts with spatial and temporal gradients to influence the dynamics of plant-pollinator networks is poorly understood, especially in tropical urbanization hotspots. Here, we analysed the drivers of environmental, spatial and temporal turnover of plant-pollinator interactions (interaction β-diversity) along an urbanization gradient in Bengaluru, a South Indian megacity. The compositional turnover of plant-pollinator interactions differed more between seasons and with local urbanization intensity than with spatial distance, suggesting that seasonality and environmental filtering were more important than dispersal limitation for explaining plant-pollinator interaction β-diversity. Furthermore, urbanization amplified the seasonal dynamics of plant-pollinator interactions, with stronger temporal turnover in urban compared to rural sites, driven by greater turnover of native non-crop plant species (not managed by people). Our study demonstrates that environmental, spatial and temporal gradients interact to shape the dynamics of plant-pollinator networks and urbanization can strongly amplify these dynamics.

Spatial analysis enables priority selection in conservation practices for landscapes that need ecological security

Global urbanization has not only promoted social and economic development, but also contributed to seriously ecological challenges. As a type of sustainable landscape patterns, ecological security pattern is considered as an effective spatial pathway to simultaneously conserve ecological security and maintain social-economic development. However, the fragmentation issue of ecological sources of ecological security pattern has not been effectively addressed, although many case studies have been conducted to identify ecological security pattern. In this study, we used spatial conservation prioritization to identify the ecological security pattern of the city belt along the Yellow River in Ningxia, China. Ecological sources were selected using Zonation model while ecological corridors and key ecological nodes were identified with circuit model. The results showed that the ecological security pattern was composed of 97 ecological sources, 226 ecological corridors, 267 pinch points and 22 barriers, covering a total area of 7713.1 km2 and accounting for 34% of the study area. Ecological sources were concentrated in the Helan Mountain, Xiang Mountain and along the Yellow River. Besides, ecological corridors were dense in the southern and eastern part of the study area. Both indicated that the Yellow River and Helan Mountain were the conservation hotspots. Landscape connectivity of ecological sources identified through Zonation-based spatial conservation prioritization was better than that with the scoring approach based on ecosystem service importance. Particularly, in the Zonation approach the landscape connectivity increased with 44% while the average patch area increased with 28% when comparing with the scoring approach. The spatial conservation prioritization approach proposed in this study provides a new effective tool to construct ecological security pattern, which is conducive to the synergic enhancement of landscape connectivity and ecosystem services conservation.

Five fundamental ways in which complex food webs may spiral out of control

Theory suggests that increasingly long, negative feedback loops of many interacting species may destabilize food webs as complexity increases. Less attention has, however, been paid to the specific ways in which these 'delayed negative feedbacks' may affect the response of complex ecosystems to global environmental change. Here, we describe five fundamental ways in which these feedbacks might pave the way for abrupt, large-scale transitions and species losses. By combining topological and bioenergetic models, we then proceed by showing that the likelihood of such transitions increases with the number of interacting species and/or when the combined effects of stabilizing network patterns approach the minimum required for stable coexistence. Our findings thus shift the question from the classical question of what makes complex, unaltered ecosystems stable to whether the effects of, known and unknown, stabilizing food-web patterns are sufficient to prevent abrupt, large-scale transitions under global environmental change.

Dynamics of species-rich predator-prey networks and seasonal alternations of core species

In nature, entangled webs of predator-prey interactions constitute the backbones of ecosystems. Uncovering the network architecture of such trophic interactions has been recognized as the essential step for exploring species with great impacts on ecosystem-level phenomena and functions. However, it has remained a major challenge to reveal how species-rich networks of predator-prey interactions are continually reshaped through time in the wild. Here, we show that dynamics of species-rich predator-prey interactions can be characterized by remarkable network structural changes and alternations of species with greatest impacts on community processes. On the basis of high-throughput detection of prey DNA from 1,556 spider individuals collected in a grassland ecosystem, we reconstructed dynamics of interaction networks involving, in total, 50 spider species and 974 prey species and strains through 8 months. The networks were compartmentalized into modules (groups) of closely interacting predators and prey in each month. Those modules differed in detritus/grazing food chain properties, forming complex fission-fusion dynamics of belowground and aboveground energy channels across the seasons. The substantial shifts of network structure entailed alternations of spider species located at the core positions within the entangled webs of interactions. These results indicate that knowledge of dynamically shifting food webs is crucial for understanding temporally varying roles of 'core species' in ecosystem processes.

Eco-evolution from deep time to contemporary dynamics: The role of timescales and rate modulators

Eco-evolutionary dynamics, or eco-evolution for short, are often thought to involve rapid demography (ecology) and equally rapid heritable phenotypic changes (evolution) leading to novel, emergent system behaviours. We argue that this focus on contemporary dynamics is too narrow: Eco-evolution should be extended, first, beyond pure demography to include all environmental dimensions and, second, to include slow eco-evolution which unfolds over thousands or millions of years. This extension allows us to conceptualise biological systems as occupying a two-dimensional time space along axes that capture the speed of ecology and evolution. Using Hutchinson's analogy: Time is the 'theatre' in which ecology and evolution are two interacting 'players'. Eco-evolutionary systems are therefore dynamic: We identify modulators of ecological and evolutionary rates, like temperature or sensitivity to mutation, which can change the speed of ecology and evolution, and hence impact eco-evolution. Environmental change may synchronise the speed of ecology and evolution via these rate modulators, increasing the occurrence of eco-evolution and emergent system behaviours. This represents substantial challenges for prediction, especially in the context of global change. Our perspective attempts to integrate ecology and evolution across disciplines, from gene-regulatory networks to geomorphology and across timescales, from today to deep time.

Synchronization Induced by Layer Mismatch in Multiplex Networks

Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in terms of parameter mismatch among the layers, has not been adequately investigated. Here, we study the intralayer synchrony in multiplex networks, where the layers are different from one other, due to parameter mismatch in their local dynamics. In such a multiplex network, the intralayer coupling strength for the emergence of intralayer synchronization decreases upon the introduction of impurity among the layers, which is caused by a parameter mismatch in their local dynamics. Furthermore, the area of occurrence of intralayer synchronization also widens with increasing mismatch. We analytically derive a condition under which the intralayer synchronous solution exists, and we even sustain its stability. We also prove that, in spite of the mismatch among the layers, all the layers of the multiplex network synchronize simultaneously. Our results indicate that a multiplex network with mismatched layers can induce synchrony more easily than a multiplex network with identical layers.

Epidemiological connectivity between humans and animals across an urban landscape

Urbanization is predicted to be a key driver of disease emergence through human exposure to novel, animal-borne pathogens. However, while we suspect that urban landscapes are primed to expose people to novel animal-borne diseases, evidence for the mechanisms by which this occurs is lacking. To address this, we studied how bacterial genes are shared between wild animals, livestock, and humans (n = 1,428) across Nairobi, Kenya-one of the world's most rapidly developing cities. Applying a multilayer network framework, we show that low biodiversity (of both natural habitat and vertebrate wildlife communities), coupled with livestock management practices and more densely populated urban environments, promotes sharing of Escherichia coli-borne bacterial mobile genetic elements between animals and humans. These results provide empirical support for hypotheses linking resource provision, the biological simplification of urban landscapes, and human and livestock demography to urban dynamics of cross-species pathogen transmission at a landscape scale. Urban areas where high densities of people and livestock live in close association with synanthropes (species such as rodents that are more competent reservoirs for zoonotic pathogens) should be prioritized for disease surveillance and control.

The synchronizing role of multiplexing noise: Exploring Kuramoto oscillators and breathing chimeras

The synchronization of spatiotemporal patterns in a two-layer multiplex network of identical Kuramoto phase oscillators is studied, where each layer is a non-locally coupled ring. Particular focus is on the role played by a noisy inter-layer communication. It is shown that modulating the inter-layer coupling strength by uncommon noise has a significant impact on the dynamics of the network, in particular, that modulating the interlayer coupling by noise can counter-intuitively induce synchronization in networks. It is further shown that increasing the noise intensity has many other analogous effects to that of increasing the interlayer coupling strength. For example, the noise intensity can also induce state transitions in a similar way, in some cases causing the layers to completely synchronize within themselves. It is discussed how such disturbances may in many cases be beneficial to multilayer systems. These effects are demonstrated both for white noise and for other kinds of colored noise. A "floating" breathing chimera state is also discovered in this system.

Structure and function in artificial, zebrafish and human neural networks

Network science provides a set of tools for the characterization of the structure and functional behavior of complex systems. Yet a major problem is to quantify how the structural domain is related to the dynamical one. In other words, how the diversity of dynamical states of a system can be predicted from the static network structure? Or the reverse problem: starting from a set of signals derived from experimental recordings, how can one discover the network connections or the causal relations behind the observed dynamics? Despite the advances achieved over the last two decades, many challenges remain concerning the study of the structure-dynamics interplay of complex systems. In neuroscience, progress is typically constrained by the low spatio-temporal resolution of experiments and by the lack of a universal inferring framework for empirical systems. To address these issues, applications of network science and artificial intelligence to neural data have been rapidly growing. In this article, we review important recent applications of methods from those fields to the study of the interplay between structure and functional dynamics of human and zebrafish brain. We cover the selection of topological features for the characterization of brain networks, inference of functional connections, dynamical modeling, and close with applications to both the human and zebrafish brain. This review is intended to neuroscientists who want to become acquainted with techniques from network science, as well as to researchers from the latter field who are interested in exploring novel application scenarios in neuroscience.

Dense Sampling Approaches for Psychiatry Research: Combining Scanners and Smartphones

Together, data from brain scanners and smartphones have sufficient coverage of biology, psychology, and environment to articulate between-person differences in the interplay within and across biological, psychological, and environmental systems thought to underlie psychopathology. An important next step is to develop frameworks that combine these two modalities in ways that leverage their coverage across layers of human experience to have maximum impact on our understanding and treatment of psychopathology. We review literature published in the last 3 years highlighting how scanners and smartphones have been combined to date, outline and discuss the strengths and weaknesses of existing approaches, and sketch a network science framework heretofore underrepresented in work combining scanners and smartphones that can push forward our understanding of health and disease.

Non-random interactions within and across guilds shape the potential to coexist in multi-trophic ecological communities

Theory posits that the persistence of species in ecological communities is shaped by their interactions within and across trophic guilds. However, we lack empirical evaluations of how the structure, strength and sign of biotic interactions drive the potential to coexist in diverse multi-trophic communities. Here, we model community feasibility domains, a theoretically informed measure of multi-species coexistence probability, from grassland communities comprising more than 45 species on average from three trophic guilds (plants, pollinators and herbivores). Contrary to our hypothesis, increasing community complexity, measured either as the number of guilds or community richness, did not decrease community feasibility. Rather, we observed that high degrees of species self-regulation and niche partitioning allow for maintaining larger levels of community feasibility and higher species persistence in more diverse communities. Our results show that biotic interactions within and across guilds are not random in nature and both structures significantly contribute to maintaining multi-trophic diversity.

Predicting primate-parasite associations using exponential random graph models

Ecological associations between hosts and parasites are influenced by host exposure and susceptibility to parasites, and by parasite traits, such as transmission mode. Advances in network analysis allow us to answer questions about the causes and consequences of traits in ecological networks in ways that could not be addressed in the past. We used a network-based framework (exponential random graph models or ERGMs) to investigate the biogeographic, phylogenetic and ecological characteristics of hosts and parasites that affect the probability of interactions among nonhuman primates and their parasites. Parasites included arthropods, bacteria, fungi, protozoa, viruses and helminths. We investigated existing hypotheses, along with new predictors and an expanded host-parasite database that included 213 primate nodes, 763 parasite nodes and 2319 edges among them. Analyses also investigated phylogenetic relatedness, sampling effort and spatial overlap among hosts. In addition to supporting some previous findings, our ERGM approach demonstrated that more threatened hosts had fewer parasites, and notably, that this effect was independent of hosts also having a smaller geographic range. Despite having fewer parasites, threatened host species shared more parasites with other hosts, consistent with loss of specialist parasites and threat arising from generalist parasites that can be maintained in other, non-threatened hosts. Viruses, protozoa and helminths had broader host ranges than bacteria, or fungi, and parasites that infect non-primates had a higher probability of infecting more primate species. The value of the ERGM approach for investigating the processes structing host-parasite networks provided a more complete view on the biogeographic, phylogenetic and ecological traits that influence parasite species richness and parasite sharing among hosts. The results supported some previous analyses and revealed new associations that warrant future research, thus revealing how hosts and parasites interact to form ecological networks.

Conceptualizing microbe-plasmid communities as complex adaptive systems

Plasmids shape microbial communities' diversity, structure, and function. Nevertheless, we lack a mechanistic understanding of how community structure and dynamics emerge from local microbe-plasmid interactions and coevolution. Addressing this gap is challenging because multiple processes operate simultaneously at multiple levels of organization. For example, immunity operates between a plasmid and a cell, but incompatibility mechanisms regulate coexistence between plasmids. Conceptualizing microbe-plasmid communities as complex adaptive systems is a promising approach to overcoming these challenges. I illustrate how agent-based evolutionary modeling, extended by network analysis, can be used to quantify the relative importance of local processes governing community dynamics. These theoretical developments can advance our understanding of plasmid ecology and evolution, especially when combined with empirical data.

Multilayer networks of plasmid genetic similarity reveal potential pathways of gene transmission

Antimicrobial resistance (AMR) is a significant threat to public health. Plasmids are principal vectors of AMR genes, significantly contributing to their spread and mobility across hosts. Nevertheless, little is known about the dynamics of plasmid genetic exchange across animal hosts. Here, we use theory and methodology from network and disease ecology to investigate the potential of gene transmission between plasmids using a data set of 21 plasmidomes from a single dairy cow population. We constructed a multilayer network based on pairwise plasmid genetic similarity. Genetic similarity is a signature of past genetic exchange that can aid in identifying potential routes and mechanisms of gene transmission within and between cows. Links between cows dominated the transmission network, and plasmids containing mobility genes were more connected. Modularity analysis revealed a network cluster where all plasmids contained a mobM gene, and one where all plasmids contained a beta-lactamase gene. Cows that contain both clusters also share transmission pathways with many other cows, making them candidates for super-spreading. In support, we found signatures of gene super-spreading in which a few plasmids and cows are responsible for most gene exchange. An agent-based transmission model showed that a new gene invading the cow population will likely reach all cows. Finally, we showed that edge weights contain a non-random signature for the mechanisms of gene transmission, allowing us to differentiate between dispersal and genetic exchange. These results provide insights into how genes, including those providing AMR, spread across animal hosts.

Stability of multi-layer ecosystems

Community structure is reported to play a critical role in ecosystem stability, which indicates the ability of a system to return to equilibrium after perturbations. However, current studies rely on the assumption that the community consists of only a single-layer structure. In practice, multi-layer structures are common in ecosystems, e.g. the distributions of both microorganisms in strata and fish in the ocean usually stratify into multi-layer structures. Here we use multi-layer networks to model species interactions within each layer and between different layers, and study the stability of multi-layer ecosystems under different interaction types. We show that competitive interactions within each layer have a more substantial stabilizing effect in multi-layer ecosystems relative to their impact in single-layer ecosystems. Surprisingly, between different layers, we find that competition between species destabilizes the ecosystem. We further provide a theoretical analysis of the stability of multi-layer ecosystems and confirm the robustness of our findings for different connectances between layers, numbers of species in each layer, and numbers of layers. Our work provides a general framework for investigating the stability of multi-layer ecosystems and uncovers the double-sided role of competitive interactions in the stability of multi-layer ecosystems.

Impacts of extreme climatic events on trophic network complexity and multidimensional stability

Untangling the relationship between network complexity and ecological stability under climate change is an arduous challenge for theoretical and empirical ecology. Even more so, when considering extreme climatic events. Here, we studied the effects of extreme climatic events (heatwaves) on the complexity of realistic freshwater ecosystems using topological and quantitative trophic network metrics. Next, we linked changes in network complexity with the investigation of four stability components (temporal stability, resistance, resilience, and recovery) of community's functional, compositional, and energy flux stability. We found reduction in topological network complexity to be correlated with reduction of functional and compositional resistance. However, temperature-driven increase in link-weighted network complexity increased functional and energy flux recovery and resilience, but at the cost of increased compositional instability. Overall, we propose an overarching approach to elucidate the effects of climate change on multidimensional stability through the lens of network complexity, providing helpful insights for preserving ecosystems stability under climate change.

Predicting cascading extinctions and efficient restoration strategies in plant-pollinator networks via generalized positive feedback loops

The extinction of a species in a plant-pollinator mutualistic community can cause cascading effects and lead to major biodiversity loss. The ecologically important task of predicting the severity of the cascading effects is made challenging by the complex network of interactions among the species. In this work, we analyze an ensemble of models of communities of plant and pollinator species. These models describe the mutualistic inter-species interactions by Boolean threshold functions. We show that identifying generalized positive feedback loops can help pinpoint the species whose extinction leads to catastrophic and substantial damage to the whole community. We compare these results with the damage percentage caused by the loss of species identified as important by previously studied structural measures and show that positive feedback loops and the information gained from them can identify certain crucial species that the other measures fail to find. We also suggest mitigation measures for two specific purposes: (1) prevent the damage to the community by protecting a subset of the species, and (2) restore the community after the damage by restoring a subset of species. Our analyses indicate that the generalized positive feedback loops predict the most efficient strategies to achieve these purposes. The correct identification of species in each category has important implications for conservation efforts and developing community management strategies.

Ectophagous folivores do not profit from rich resources on phylogenetically isolated trees

Resource use by consumers across patches is often proportional to the quantity or quality of the resource within these patches. In folivores, such proportional use of resources is likely to be more efficient when plants are spatially proximate, such as trees forming a forest canopy. However, resources provided by forest-trees are often not used proportionally. We hypothesised that proportional use of resources is reduced when host trees are isolated among phylogenetically distant neighbours that mask olfactory and visual search cues, and reduce folivore movement between trees. Such phylogenetically distant neighbourhoods might sort out species that are specialists, poor dispersers, or have poor access to information about leaf quality. We studied individual oaks, their leaf size and quality, their folivory and abundance of folivores (mostly Lepidopteran ectophages, gallers and miners), and parasitism of folivores. We found that leaf consumption by ectophages hardly increased with increasing leaf size when host trees were phylogenetically isolated. We found a similar effect on host use by parasitoids in 1 year. In contrast, we found no consistent effects in other folivore guilds. Relative abundances of specialists and species with wingless females declined with phylogenetic isolation. However, resource use within each of these groups was inconsistently affected by phylogenetic isolation. We suggest that phylogenetic isolation prevents ectophages from effectively choosing trees with abundant resources, and also sorts out species likely to recruit in situ on their host tree. Trees in phylogenetically distant neighbourhoods may be selected for larger leaves and greater reliance on induced defences.

Plant Virus Adaptation to New Hosts: A Multi-scale Approach

Viruses are studied at each level of biological complexity: from within-cells to ecosystems. The same basic evolutionary forces and principles operate at each level: mutation and recombination, selection, genetic drift, migration, and adaptive trade-offs. Great efforts have been put into understanding each level in great detail, hoping to predict the dynamics of viral population, prevent virus emergence, and manage their spread and virulence. Unfortunately, we are still far from this. To achieve these ambitious goals, we advocate for an integrative perspective of virus evolution. Focusing in plant viruses, we illustrate the pervasiveness of the above-mentioned principles. Beginning at the within-cell level, we describe replication modes, infection bottlenecks, and cellular contagion rates. Next, we move up to the colonization of distal tissues, discussing the fundamental role of random events. Then, we jump beyond the individual host and discuss the link between transmission mode and virulence. Finally, at the community level, we discuss properties of virus-plant infection networks. To close this review we propose the multilayer network theory, in which elements at different layers are connected and submit to their own dynamics that feed across layers, resulting in new emerging properties, as a way to integrate information from the different levels.

Studying Plant-Insect Interactions through the Analyses of the Diversity, Composition, and Functional Inference of Their Bacteriomes

As with many other trophic interactions, the interchange of microorganisms between plants and their herbivorous insects is unavoidable. To test the hypothesis that the composition and diversity of the insect bacteriome are driven by the bacteriome of the plant, the bacteriomes of both the plant Datura inoxia and its specialist insect Lema daturaphila were characterised using 16S sRNA gene amplicon sequencing. Specifically, the bacteriomes associated with seeds, leaves, eggs, guts, and frass were described and compared. Then, the functions of the most abundant bacterial lineages found in the samples were inferred. Finally, the patterns of co-abundance among both bacteriomes were determined following a multilayer network approach. In accordance with our hypothesis, most genera were shared between plants and insects, but their abundances differed significantly within the samples collected. In the insect tissues, the most abundant genera were Pseudomonas (24.64%) in the eggs, Serratia (88.46%) in the gut, and Pseudomonas (36.27%) in the frass. In contrast, the most abundant ones in the plant were Serratia (40%) in seeds, Serratia (67%) in foliar endophytes, and Hymenobacter (12.85%) in foliar epiphytes. Indeed, PERMANOVA analysis showed that the composition of the bacteriomes was clustered by sample type (F = 9.36, p < 0.001). Functional inferences relevant to the interaction showed that in the plant samples, the category of Biosynthesis of secondary metabolites was significantly abundant (1.4%). In turn, the category of Xenobiotics degradation and metabolism was significantly present (2.5%) in the insect samples. Finally, the phyla Proteobacteria and Actinobacteriota showed a pattern of co-abundance in the insect but not in the plant, suggesting that the co-abundance and not the presence−absence patterns might be more important when studying ecological interactions.

Statistical inference links data and theory in network science

The number of network science applications across many different fields has been rapidly increasing. Surprisingly, the development of theory and domain-specific applications often occur in isolation, risking an effective disconnect between theoretical and methodological advances and the way network science is employed in practice. Here we address this risk constructively, discussing good practices to guarantee more successful applications and reproducible results. We endorse designing statistically grounded methodologies to address challenges in network science. This approach allows one to explain observational data in terms of generative models, naturally deal with intrinsic uncertainties, and strengthen the link between theory and applications.

Theoretical models and structures recovered from measured data serve for analysis of complex networks. The authors discuss here existing gaps between theoretical methods and real-world applied networks, and potential ways to improve the interplay between theory and applications.

Nonadditive effects of two contrasting introduced herbivores on the reproduction of a pollination-specialized palm

Plant-animal interactions fall within a mutualism-antagonism continuum, exerting a wide range of effects on plant reproductive success. These effects become even more complex and diverse when several disparate animal species interact with the same plant species. Despite the increasing number of studies about the influence of herbivory on plant performance, the outcomes mediated by pollination and the combined impact of multiple herbivores on pollination-specialized plants are underexplored. In this study, we chose the Mediterranean dwarf palm Chamaerops humilis (Arecaceae) to illustrate the isolated and joint effect of two contrasting introduced herbivores, the palm borer Paysandisia archon (Lepidoptera, Castniidae) and feral goats, on pollinator abundance and plant reproductive success. To this aim, we monitored moth herbivory and goat herbivory in four palm populations in Mallorca (Balearic Islands) during 2019 and 2020. The effect of herbivory varied widely depending on both the herbivore and the pollinator species. Moth herbivory had a positive effect on pollinator abundance and fruit initiation, whereas goat herbivory had a negative effect on inflorescence production, pollinator abundance and fruit initiation. In addition, both herbivores exerted unexpected nonadditive effects on palm reproduction. Palms attacked by both herbivore species produced many more inflorescences (up to 18-fold) but had a lower fruit initiation success (close to zero) than unattacked palms or those attacked by a single herbivore species. Interestingly, only one of the two main pollinator species (the nitidulid beetle Meligethinus pallidulus) was impacted by herbivory. Our study highlights the need to investigate the possible nonadditive effects of all coexisting herbivores on plant performance, especially when establishing conservation plans and pest control strategies.

Multilayer Networks Assisting to Untangle Direct and Indirect Pathogen Transmission in Bats

The importance of species that connect the different types of interactions is becoming increasingly recognized, and this role may be related to specific attributes of these species. Multilayer networks have two or more layers, which represent different types of interactions, for example, between different parasites and hosts that are nonetheless connected. The understanding of the ecological relationship between bats, ectoparasites, and vector-borne bacteria could shed some light on the complex transmission cycles of these pathogens. In this study, we investigated a multilayer network in Brazil formed by interactions between bat-bacteria, bat-ectoparasite, and ectoparasite-bacteria, and asked how these interactions overlap considering different groups and transmission modes. The multilayer network was composed of 31 nodes (12 bat species, 14 ectoparasite species, and five bacteria genera) and 334 links, distributed over three layers. The multilayer network has low modularity and shows a core-periphery organization, that is, composed of a few generalist species with many interactions and many specialist species participating in few interactions in the multilayer network. The three layers were needed to accurately describe the multilayer structure, while aggregation leads to loss of information. Our findings also demonstrated that the multilayer network is influenced by a specific set of species that can easily be connected to the behavior, life cycle, and type of existing interactions of these species. Four bat species (Artibeus lituratus, A. planirostris, Phyllostomus discolor, and Platyrrhinus lineatus), one ectoparasite species (Steatonyssus) and three bacteria genera (Ehrlichia, hemotropic Mycoplasma and Neorickettsia) are the most important species for the multilayer network structure. Finally, our study brings an ecological perspective under a multilayer network approach on the interactions between bats, ectoparasites, and pathogens. By using a multilayer approach (different types of interactions), it was possible to better understand these different ecological interactions and how they affect each other, advancing our knowledge on the role of bats and ectoparasites as potential pathogen vectors and reservoirs, as well as the modes of transmission of these pathogens.

The fundamental benefits of multiplexity in ecological networks

A tipping point presents perhaps the single most significant threat to an ecological system as it can lead to abrupt species extinction on a massive scale. Climate changes leading to the species decay parameter drifts can drive various ecological systems towards a tipping point. We investigate the tipping-point dynamics in multi-layer ecological networks supported by mutualism. We unveil a natural mechanism by which the occurrence of tipping points can be delayed by multiplexity that broadly describes the diversity of the species abundances, the complexity of the interspecific relationships, and the topology of linkages in ecological networks. For a double-layer system of pollinators and plants, coupling between the network layers occurs when there is dispersal of pollinator species. Multiplexity emerges as the dispersing species establish their presence in the destination layer and have a simultaneous presence in both. We demonstrate that the new mutualistic links induced by the dispersing species with the residence species have fundamental benefits to the well-being of the ecosystem in delaying the tipping point and facilitating species recovery. Articulating and implementing control mechanisms to induce multiplexity can thus help sustain certain types of ecosystems that are in danger of extinction as the result of environmental changes.

Sharp thresholds limit the benefit of defector avoidance in cooperation on networks

Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors, or they may lead to self-organized patterns, where some patches become safe havens that maintain an elevated cooperator density. Here we analyze the transition between these states mathematically. We show that safe havens form once a certain threshold in connectivity is crossed. This threshold can be analytically linked to the structure of the patch network and specifically to certain network motifs. Surprisingly, a forgiving defector avoidance strategy may be most favorable for cooperators. Our results demonstrate that the analysis of cooperation games in ecological metacommunity models is mathematically tractable and has the potential to link topics such as macroecological patterns, behavioral evolution, and network topology.

Scaling up our understanding of tipping points

Anthropogenic activities are increasingly affecting ecosystems across the globe. Meanwhile, empirical and theoretical evidence suggest that natural systems can exhibit abrupt collapses in response to incremental increases in the stressors, sometimes with dramatic ecological and economic consequences. These catastrophic shifts are faster and larger than expected from the changes in the stressors and happen once a tipping point is crossed. The primary mechanisms that drive ecosystem responses to perturbations lie in their architecture of relationships, i.e. how species interact with each other and with the physical environment and the spatial structure of the environment. Nonetheless, existing theoretical work on catastrophic shifts has so far largely focused on relatively simple systems that have either few species and/or no spatial structure. This work has laid a critical foundation for understanding how abrupt responses to incremental stressors are possible, but it remains difficult to predict (let alone manage) where or when they are most likely to occur in more complex real-world settings. Here, we discuss how scaling up our investigations of catastrophic shifts from simple to more complex-species rich and spatially structured-systems could contribute to expanding our understanding of how nature works and improve our ability to anticipate the effects of global change on ecological systems. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'.