Reconstructing large interaction networks from empirical time series data

Bioenergetically constrained dynamical microbial interactions govern the performance and stability of methane-producing bioreactors

Biogas generation from organic waste by anaerobic bioreactors as renewable energy largely depends on microbial community and species interplays involved. This microbial networking is complex and time-dependent, influencing community succession and reactor performance, but remains unexplored due to the challenges in quantifying dynamics. We employed empirical dynamic modeling to analyze daily networking from a newly established bioreactor converting sucrose to biogas. Over time, microbial interactions within the three trophic (fermentative, syntrophic, and methanogenic) groups varied substantially more than between groups. Notably, versatile syntrophic bacteria like Syntrophorhabdus exhibited stronger interaction strength (0.14 ± 0.22) to hydrogen-dependent methylotrophic Methanomassiliicoccus than strictly syntrophic bacteria associated with butyrate (0.01 ± 0.01 for Syntrophomonas) and propionate (0.00 ± 0.01 for Syntrophobacter). The time-varying interaction networks were closely linked to the system performance dynamics, particularly concerning hydrogen concentrations. As community succession progressed, the stability of interaction network increased through time, accompanied by increased complexity and higher interaction strength. Causal analyses revealed intricate feedback involving catabolic energetics, community structure, and microbial interactions. These feedback mechanisms played a crucial role in regulating anaerobic degradation processes, thereby offering strategies for manipulating microbial interactions to enhance bioreactor stability and efficiency.

Exploring interspecific interaction variability in microbiota: A review

Interspecific interactions are an important component and a strong selective force in microbial communities. Over the past few decades, there has been a growing awareness of the variability in microbial interactions, and various studies are already unraveling the inner working dynamics in microbial communities. This has prompted scientists to develop novel techniques for characterizing the varying interspecific interactions among microbes. Here, we review the precise definitions of pairwise and high-order interactions, summarize the key concepts related to interaction variability, and discuss the strengths and weaknesses of emerging characterization techniques. Specifically, we found that most methods can accurately predict or provide direct information about microbial pairwise interactions. However, some of these methods inevitably mask the underlying high-order interactions in the microbial community. Making reasonable assumptions and choosing a characterization method to explore varying microbial interactions should allow us to better understand and engineer dynamic microbial systems.

Multifaceted effects of variable biotic interactions on population stability in complex interaction webs

Recent studies have revealed that biotic interactions in ecological communities vary over time, possibly mediating community responses to anthropogenic disturbances. This study investigated the heterogeneity of such variability within a real community and its impact on population stability in the face of pesticide application, particularly focusing on density-dependence of the interaction effect. Using outdoor mesocosms with a freshwater community, we found considerable heterogeneity in density-dependent interaction variability among links in the same community. This variability mediated the stability of recipient populations, with negative density-dependent interaction variability stabilizing whereas positive density-dependence and density-independent interaction variability destabilizing populations. Unexpectedly, the mean interaction strength, which is typically considered crucial for stability, had no significant effect, suggesting that how organisms interact on average is insufficient to predict the ecological impacts of pesticides. Our findings emphasize the multifaceted role of interaction variability in predicting the ecological consequences of anthropogenic disturbances such as pesticide application.

Local-manifold-distance-based regression: an estimation method for quantifying dynamic biological interactions with empirical time series

Quantifying species interactions based on empirical observations is crucial for ecological studies. Advancements in nonlinear time-series analyses, particularly S-maps, are promising for high-dimensional and non-equilibrium ecosystems. S-maps sequentially perform a local linear model fitting to the time evolution of neighbouring points on the reconstructed attractor manifold, and the coefficients can approximate the Jacobian elements corresponding to interaction effects. However, despite that the advantages in nonlinear forecasting with noise-contaminated data, these methodologies have a limitation in the Jacobian estimation accuracy owing to non-equidistantly stretched local manifolds in the state space. Herein, we therefore introduced a local manifold distance (LMD) concept, a non-equidistant measure based on the multi-faceted state dependency. By integrating LMD with advanced computation techniques, we presented a robust and efficient analytical method, LMD-based regression (LMDr). To validate its advantages in prediction and Jacobian estimation, we analysed synthetic time series of model ecosystems with different noise levels and applied it to an experimental protozoan predator-prey system with established biological information. The robustness to noise was the highest for LMDr, which also showed a better correspondence to expected predator-prey interactions in the protozoan system. Thus, LMDr can be applied to study complex ecological networks under dynamic conditions.

A framework for identifying factors controlling cyanobacterium Microcystis flos-aquae blooms by coupled CCM-ECCM Bayesian networks

Cyanobacterial blooms in freshwater sources are a global concern, and gaining insight into their causes is crucial for effective resource management and control. In this study, we present a novel computational framework for the causal analysis of cyanobacterial harmful algal blooms (cyanoHABs) in Lake Kinneret. Our framework integrates Convergent Cross Mapping (CCM) and Extended CCM (ECCM) causal networks with Bayesian Network (BN) models. The constructed CCM-ECCM causal networks and BN models unveil significant interactions among factors influencing cyanoHAB formation. These interactions have been validated by domain experts and supported by evidence from peer-reviewed publications. Our findings suggest that Microcystis flos-aquae levels are influenced not only by community structure but also by ammonium, phosphate, oxygen, and temperature levels in the weeks preceding bloom occurrences. We demonstrated a non-parametric computational framework for causal analysis of a multivariate ecosystem. Our framework offers a more comprehensive understanding of the underlying mechanisms driving M. flos-aquae blooms in Lake Kinneret. It captures complex interactions and provides an explainable prediction model. By considering causal relationships, temporal dynamics, and joint probabilities of environmental factors, the proposed framework enhances our understanding of cyanoHABs in Lake Kinneret.

An ecological network approach for detecting and validating influential organisms for rice growth

How to achieve sustainable food production while reducing environmental impacts is a major concern in agricultural science, and advanced breeding techniques are promising for achieving such goals. However, rice is usually grown under field conditions and influenced by surrounding ecological community members. How ecological communities influence the rice performance in the field has been underexplored despite the potential of ecological communities to establish an environment-friendly agricultural system. In the present study, we demonstrate an ecological-network-based approach to detect potentially influential, previously overlooked organisms for rice (Oryza sativa). First, we established small experimental rice plots, and measured rice growth and monitored ecological community dynamics intensively and extensively using quantitative environmental DNA metabarcoding in 2017 in Japan. We detected more than 1000 species (including microbes and macrobes such as insects) in the rice plots, and nonlinear time series analysis detected 52 potentially influential organisms with lower-level taxonomic information. The results of the time series analysis were validated under field conditions in 2019 by field manipulation experiments. In 2019, we focused on two species, Globisporangium nunn and Chironomus kiiensis, whose abundance was manipulated in artificial rice plots. The responses of rice, namely, the growth rate and gene expression patterns, were measured before and after the manipulation. We confirmed that, especially in the G. nunn-added treatment, rice growth rate and gene expression pattern were changed. In the present study, we demonstrated that intensive monitoring of an agricultural system and the application of nonlinear time series analysis were helpful to identify influential organisms under field conditions. Although the effects of the manipulations were relatively small, the research framework presented here has future potential to harness the ecological complexity and utilize it in agriculture. Our proof-of-concept study would be an important basis for the further development of field-basis system management.

A framework for the detection and attribution of biodiversity change

The causes of biodiversity change are of great scientific interest and central to policy efforts aimed at meeting biodiversity targets. Changes in species diversity and high rates of compositional turnover have been reported worldwide. In many cases, trends in biodiversity are detected, but these trends are rarely causally attributed to possible drivers. A formal framework and guidelines for the detection and attribution of biodiversity change is needed. We propose an inferential framework to guide detection and attribution analyses, which identifies five steps-causal modelling, observation, estimation, detection and attribution-for robust attribution. This workflow provides evidence of biodiversity change in relation to hypothesized impacts of multiple potential drivers and can eliminate putative drivers from contention. The framework encourages a formal and reproducible statement of confidence about the role of drivers after robust methods for trend detection and attribution have been deployed. Confidence in trend attribution requires that data and analyses used in all steps of the framework follow best practices reducing uncertainty at each step. We illustrate these steps with examples. This framework could strengthen the bridge between biodiversity science and policy and support effective actions to halt biodiversity loss and the impacts this has on ecosystems. This article is part of the theme issue 'Detecting and attributing the causes of biodiversity change: needs, gaps and solutions'.

Relationships of temperature and biodiversity with stability of natural aquatic food webs

Temperature and biodiversity changes occur in concert, but their joint effects on ecological stability of natural food webs are unknown. Here, we assess these relationships in 19 planktonic food webs. We estimate stability as structural stability (using the volume contraction rate) and temporal stability (using the temporal variation of species abundances). Warmer temperatures were associated with lower structural and temporal stability, while biodiversity had no consistent effects on either stability property. While species richness was associated with lower structural stability and higher temporal stability, Simpson diversity was associated with higher temporal stability. The responses of structural stability were linked to disproportionate contributions from two trophic groups (predators and consumers), while the responses of temporal stability were linked both to synchrony of all species within the food web and distinctive contributions from three trophic groups (predators, consumers, and producers). Our results suggest that, in natural ecosystems, warmer temperatures can erode ecosystem stability, while biodiversity changes may not have consistent effects.

Alternative stable states, nonlinear behavior, and predictability of microbiome dynamics

BACKGROUND

Microbiome dynamics are both crucial indicators and potential drivers of human health, agricultural output, and industrial bio-applications. However, predicting microbiome dynamics is notoriously difficult because communities often show abrupt structural changes, such as "dysbiosis" in human microbiomes.

METHODS

We integrated theoretical frameworks and empirical analyses with the aim of anticipating drastic shifts of microbial communities. We monitored 48 experimental microbiomes for 110 days and observed that various community-level events, including collapse and gradual compositional changes, occurred according to a defined set of environmental conditions. We analyzed the time-series data based on statistical physics and non-linear mechanics to describe the characteristics of the microbiome dynamics and to examine the predictability of major shifts in microbial community structure.

RESULTS

We confirmed that the abrupt community changes observed through the time-series could be described as shifts between "alternative stable states" or dynamics around complex attractors. Furthermore, collapses of microbiome structure were successfully anticipated by means of the diagnostic threshold defined with the "energy landscape" analysis of statistical physics or that of a stability index of nonlinear mechanics.

CONCLUSIONS

The results indicate that abrupt microbiome events in complex microbial communities can be forecasted by extending classic ecological concepts to the scale of species-rich microbial systems. Video Abstract.

Anticipating the occurrence and type of critical transitions

Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition. However, no effective method allows to establish practical threshold indicating the condition when the critical transition is most likely to occur. Here, we introduce a powerful EWS, named dynamical eigenvalue (DEV), that is rooted in bifurcation theory of dynamical systems to estimate the dominant eigenvalue of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, while its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and also test the DEV approach on various critical transitions in real-world systems.

Ranking species based on sensitivity to perturbations under non-equilibrium community dynamics

Managing ecological communities requires fast detection of species that are sensitive to perturbations. Yet, the focus on recovery to equilibrium has prevented us from assessing species responses to perturbations when abundances fluctuate over time. Here, we introduce two data-driven approaches (expected sensitivity and eigenvector rankings) based on the time-varying Jacobian matrix to rank species over time according to their sensitivity to perturbations on abundances. Using several population dynamics models, we demonstrate that we can infer these rankings from time-series data to predict the order of species sensitivities. We find that the most sensitive species are not always the ones with the most rapidly changing or lowest abundance, which are typical criteria used to monitor populations. Finally, using two empirical time series, we show that sensitive species tend to be harder to forecast. Our results suggest that incorporating information on species interactions can improve how we manage communities out of equilibrium.

Effects of phytoplankton, viral communities, and warming on free-living and particle-associated marine prokaryotic community structure

Free-living and particle-associated marine prokaryotes have physiological, genomic, and phylogenetic differences, yet factors influencing their temporal dynamics remain poorly constrained. In this study, we quantify the entire microbial community composition monthly over several years, including viruses, prokaryotes, phytoplankton, and total protists, from the San-Pedro Ocean Time-series using ribosomal RNA sequencing and viral metagenomics. Canonical analyses show that in addition to physicochemical factors, the double-stranded DNA viral community is the strongest factor predicting free-living prokaryotes, explaining 28% of variability, whereas the phytoplankton (via chloroplast 16S rRNA) community is strongest with particle-associated prokaryotes, explaining 31% of variability. Unexpectedly, protist community explains little variability. Our findings suggest that biotic interactions are significant determinants of the temporal dynamics of prokaryotes, and the relative importance of specific interactions varies depending on lifestyles. Also, warming influenced the prokaryotic community, which largely remained oligotrophic summer-like throughout 2014-15, with cyanobacterial populations shifting from cold-water ecotypes to warm-water ecotypes.

Differences in initial abundances reveal divergent dynamic structures in Gause's predator-prey experiments

Improved understanding of complex dynamics has revealed insights across many facets of ecology, and has enabled improved forecasts and management of future ecosystem states. However, an enduring challenge in forecasting complex dynamics remains the differentiation between complexity and stochasticity, that is, to determine whether declines in predictability are caused by stochasticity, nonlinearity, or chaos. Here, we show how to quantify the relative contributions of these factors to prediction error using Georgii Gause's iconic predator-prey microcosm experiments, which, critically, include experimental replicates that differ from one another only in initial abundances. We show that these differences in initial abundances interact with stochasticity, nonlinearity, and chaos in unique ways, allowing us to identify the impacts of these factors on prediction error. Our results suggest that jointly analyzing replicate time series across multiple, distinct starting points may be necessary for understanding and predicting the wide range of potential dynamic types in complex ecological systems.

Decomposing predictability to identify dominant causal drivers in complex ecosystems

Ecosystems are complex systems of various physical, biological, and chemical processes. Since ecosystem dynamics are composed of a mixture of different levels of stochasticity and nonlinearity, handling these data is a challenge for existing methods of time series-based causal inferences. Here, we show that, by harnessing contemporary machine learning approaches, the concept of Granger causality can be effectively extended to the analysis of complex ecosystem time series and bridge the gap between dynamical and statistical approaches. The central idea is to use an ensemble of fast and highly predictive artificial neural networks to select a minimal set of variables that maximizes the prediction of a given variable. It enables decomposition of the relationship among variables through quantifying the contribution of an individual variable to the overall predictive performance. We show how our approach, EcohNet, can improve interaction network inference for a mesocosm experiment and simulated ecosystems. The application of the method to a long-term lake monitoring dataset yielded interpretable results on the drivers causing cyanobacteria blooms, which is a serious threat to ecological integrity and ecosystem services. Since performance of EcohNet is enhanced by its predictive capabilities, it also provides an optimized forecasting of overall components in ecosystems. EcohNet could be used to analyze complex and hybrid multivariate time series in many scientific areas not limited to ecosystems.

State-Space-Based Framework for Predicting Microbial Interaction Variability in Wastewater Treatment Plants

Substantial attempts have been made to control microbial communities for environmental integrity, biosystem performance, and human health. However, it is difficult to manipulate microbial communities in practice due to the varying and nonlinear nature of interspecific interaction networks. Here, we develop a manifold-based framework to investigate the patterns of microbial interaction variability in wastewater treatment plants using manifold geometric properties and design a simple control strategy to manipulate the microbes in nonlinear communities. We validate our framework using the readily available and nonsequential microbiome profiles of wastewater treatment plants. Our results show that some microbes in the activated sludge and anammox communities display deterministic rival or cooperative relationships and constitute a stable subnetwork within the whole nonlinear community network. We further use a simulation to demonstrate that these microbes can be used to drive a microbe in a target direction regardless of the community dynamics. Overall, our framework can provide a time-efficient solution to select effective control inputs for reliable manipulation in varying microbial networks, opening up new possibilities across a range of biological fields, including wastewater treatment plants.

Forecasting in the face of ecological complexity: Number and strength of species interactions determine forecast skill in ecological communities

The potential for forecasting the dynamics of ecological systems is currently unclear, with contrasting opinions regarding its feasibility due to ecological complexity. To investigate forecast skill within and across systems, we monitored a microbial system exposed to either constant or fluctuating temperatures in a 5-month-long laboratory experiment. We tested how forecasting of species abundances depends on the number and strength of interactions and on model size (number of predictors). We also tested how greater system complexity (i.e. the fluctuating temperatures) impacted these relations. We found that the more interactions a species had, the weaker these interactions were and the better its abundance was predicted. Forecast skill increased with model size. Greater system complexity decreased forecast skill for three out of eight species. These insights into how abundance prediction depends on the connectedness of the species within the system and on overall system complexity could improve species forecasting and monitoring.

Causal networks of phytoplankton diversity and biomass are modulated by environmental context

Untangling causal links and feedbacks among biodiversity, ecosystem functioning, and environmental factors is challenging due to their complex and context-dependent interactions (e.g., a nutrient-dependent relationship between diversity and biomass). Consequently, studies that only consider separable, unidirectional effects can produce divergent conclusions and equivocal ecological implications. To address this complexity, we use empirical dynamic modeling to assemble causal networks for 19 natural aquatic ecosystems (N24^◦~N58^◦) and quantified strengths of feedbacks among phytoplankton diversity, phytoplankton biomass, and environmental factors. Through a cross-system comparison, we identify macroecological patterns; in more diverse, oligotrophic ecosystems, biodiversity effects are more important than environmental effects (nutrients and temperature) as drivers of biomass. Furthermore, feedback strengths vary with productivity. In warm, productive systems, strong nitrate-mediated feedbacks usually prevail, whereas there are strong, phosphate-mediated feedbacks in cold, less productive systems. Our findings, based on recovered feedbacks, highlight the importance of a network view in future ecosystem management.

Disentangling causal interactions among biodiversity, ecosystem functioning and environmental factors is key to understanding how ecosystems respond to changing environment. This study presents a global scale analysis quantifying causal interactions and feedbacks among phytoplankton diversity, biomass and nutrients along environmental gradients of aquatic ecosystems.

Interaction capacity as a potential driver of community diversity

How patterns in community diversity emerge is a long-standing question in ecology. Studies suggested that community diversity and interspecific interactions are interdependent. However, evidence from high-diversity ecological communities is lacking because of practical challenges in characterizing speciose communities and their interactions. Here, I analysed time-varying interaction networks that were reconstructed using 1197 species, DNA-based ecological time series taken from experimental rice plots and empirical dynamic modelling, and introduced 'interaction capacity', namely, the sum of interaction strength that a single species gives and receives, as a potential driver of community diversity. As community diversity increases, the number of interactions increases exponentially but the mean interaction capacity of a community becomes saturated, weakening interspecific interactions. These patterns are modelled with simple mathematical equations, based on which I propose the 'interaction capacity hypothesis': that interaction capacity and network connectance can be two fundamental properties that influence community diversity. Furthermore, I show that total DNA abundance and temperature influence interaction capacity and connectance nonlinearly, explaining a large proportion of diversity patterns observed in various systems. The interaction capacity hypothesis enables mechanistic explanations of community diversity. Therefore, analysing ecological community data from the viewpoint of interaction capacity would provide new insight into community diversity.