Experimental demonstration of chaos in a microbial food web

Cd indirectly affects the structure and function of plankton ecosystems by affecting trophic interactions at environmental concentrations

The toxic effects of potentially toxic elements have been observed at low concentrations; however, many studies have focused on single-species toxicity testing. Consequently, it is imperative to quantify toxicity at the community level at environmental concentrations. A microcosm approach was employed in conjunction with the Lotka-Volterra model to ascertain the impact of environmentally relevant concentrations of cadmium (Cd) on plankton abundance, community function, and stability. The results demonstrated that Cd led to a reduction in the abundance of Daphnia magna, yet unexpectedly resulted in an increase in the abundance of Brachionus calyciflorus and Paramecium caudatum. Additionally, Cd was observed to impede primary productivity, metabolic capacity and the stability of the planktonic community. Further model analyses revealed that the environmental concentration of Cd directly reduced intrinsic growth rates and intraspecific interactions. In particular, we found that the predation effects of Daphnia magna on Brachionus calyciflorus were significantly weakened. The findings of this study offer quantitative evidence that Cd exposure exerts an indirect influence on the structure and functioning of plankton ecosystems, mediated by alterations in trophic interactions. The findings indicate that the impact of environmental concentrations of potentially toxic elements may be underestimated in single-species experiments.

Deciphering soil environmental regulation on reassembly of the soil bacterial community during wetland restoration

Soil bacteria are vital to regulate biogeochemical processes in wetlands, however, little is known about the patterns and mechanisms of soil bacterial re-organization during wetland restoration. Here, we used a space-for-time substitution approach and examined the ecological processes that drive soil bacterial assembly from cultivated to restored to natural wetlands. Results showed a decrease of soil bacterial α diversity and increase of bacterial community similarity and bacterial interaction (cooperation vs. competition) with years of restoration, which was dominantly influenced by deterministic processes. Identified bacterial keystone taxa (e.g. Variibacter, Acidibacter) with nutrient metabolism capacity exerted strong positive effect on bacterial interaction. Furthermore, changes of soil water condition and nutrient status showed dominantly direct positive effects on soil bacterial reassembly, while falling soil pH significantly promoted bacterial reassembly by increasing keystone taxa and bacterial interaction during wetland restoration. Overall, findings highlighted the crucial role of environmental filtering and its pathway in influencing keystone bacterial taxa that promotes the reassembly of bacterial community during wetland restoration. Our work thus provides a new crucial and timely insight for improving the management of soil bacterial community assembly within the plethora of current and future wetland restoration projects.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations

Large stochastic population abundance fluctuations are ubiquitous across the tree of life1-7, impacting the predictability of population dynamics and influencing eco-evolutionary outcomes. It has generally been thought that these large abundance fluctuations do not strongly impact evolution, as the relative frequencies of alleles in the population will be unaffected if the abundance of all alleles fluctuate in unison. However, we argue that large abundance fluctuations can lead to significant genotype frequency fluctuations if different genotypes within a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related E. coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from models of genetic drift. We develop a flexible, effective model that explains the abundance fluctuations as arising from correlated offspring numbers between individuals, and the large frequency fluctuations result from even slight decoupling in offspring numbers between genotypes. This model accurately describes the observed abundance and frequency fluctuation scaling behaviors. Our findings suggest chaotic dynamics underpin these giant fluctuations, causing initially similar trajectories to diverge exponentially; subtle environmental changes can be magnified, leading to batch correlations in identical growth conditions. Furthermore, we present evidence that such decoupling noise is also present in mixed-genotype S. cerevisiae populations. We demonstrate that such decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of asynchronous fluctuations, we anticipate that they are widespread in biological populations, significantly affecting evolutionary and ecological dynamics.

Imprints of ecological processes in the taxonomic core community: an analysis of naturally replicated microbial communities enclosed in oil

It is widely assumed that a taxonomic core community emerges among microbial communities from similar habitats because similar environments select for the same taxa bearing the same traits. Yet, a core community itself is no indicator of selection because it may also arise from dispersal and neutral drift, i.e. by chance. Here, we hypothesize that a core community produced by either selection or chance processes should be distinguishable. While dispersal and drift should produce core communities with similar relative taxon abundances, especially when the proportional core community, i.e. the sum of the relative abundances of the core taxa, is large, selection may produce variable relative abundances. We analyzed the core community of 16S rRNA gene sequences of 193 microbial communities occurring in tiny water droplets enclosed in heavy oil from the Pitch Lake, Trinidad and Tobago. These communities revealed highly variable relative abundances along with a large proportional core community (68.0 ± 19.9%). A dispersal-drift null model predicted a negative relationship of proportional core community and compositional variability along a range of dispersal probabilities and was largely inconsistent with the observed data, suggesting a major role of selection for shaping the water droplet communities in the Pitch Lake.

Demographic fluctuations and selection during host-parasite co-evolution interactively increase genetic diversity

Host-parasite interactions can cause strong demographic fluctuations accompanied by selective sweeps of resistance/infectivity alleles. Both demographic bottlenecks and frequent sweeps are expected to reduce the amount of segregating genetic variation and therefore might constrain adaptation during co-evolution. Recent studies, however, suggest that the interaction of demographic and selective processes is a key component of co-evolutionary dynamics and may rather positively affect levels of genetic diversity available for adaptation. Here, we provide direct experimental testing of this hypothesis by disentangling the effects of demography, selection and their interaction in an experimental host-parasite system. We grew 12 populations of a unicellular, asexually reproducing algae (Chlorella variabilis) that experienced either growth followed by constant population sizes (three populations), demographic fluctuations (three populations), selection induced by exposure to a virus (three populations), or demographic fluctuations together with virus-induced selection (three populations). After 50 days (~50 generations), we conducted whole-genome sequencing of each algal host population. We observed more genetic diversity in populations that jointly experienced selection and demographic fluctuations than in populations where these processes were experimentally separated. In addition, in those three populations that jointly experienced selection and demographic fluctuations, experimentally measured diversity exceeds expected values of diversity that account for the cultures' population sizes. Our results suggest that eco-evolutionary feedbacks can positively affect genetic diversity and provide the necessary empirical measures to guide further improvements of theoretical models of adaptation during host-parasite co-evolution.

Chaotic turnover of rare and abundant species in a strongly interacting model community

The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species toward rarity or abundance is crucial to assessing ecosystem resilience and adaptation to changing environmental conditions. In plankton communities in particular, large temporal fluctuations in species abundances have been associated with chaotic dynamics. On the other hand, microbial diversity is overwhelmingly sustained by a "rare biosphere" of species with very low abundances. We consider here the possibility that interactions within a species-rich community can relate both phenomena. We use a Lotka-Volterra model with weak immigration and strong, disordered, and mostly competitive interactions between hundreds of species to bridge single-species temporal fluctuations and abundance distribution patterns. We highlight a generic chaotic regime where a few species at a time achieve dominance but are continuously overturned by the invasion of formerly rare species. We derive a focal-species model that captures the intermittent boom-and-bust dynamics that every species undergoes. Although species cannot be treated as effectively uncorrelated in their abundances, the community's effect on a focal species can nonetheless be described by a time-correlated noise characterized by a few effective parameters that can be estimated from time series. The model predicts a nonunitary exponent of the power-law abundance decay, which varies weakly with ecological parameters, consistent with observation in marine protist communities. The chaotic turnover regime is thus poised to capture relevant ecological features of species-rich microbial communities.

Preliminary evidence for chaotic signatures in host-microbe interactions

Host-microbe interactions constitute dynamical systems that can be represented by mathematical formulations that determine their dynamic nature and are categorized as deterministic, stochastic, or chaotic. Knowing the type of dynamical interaction is essential for understanding the system under study. Very little experimental work has been done to determine the dynamical characteristics of host-microbe interactions, and its study poses significant challenges. The most straightforward experimental outcome involves an observation of time to death upon infection. However, in measuring this outcome, the internal parameters and the dynamics of each particular host-microbe interaction in a population of interactions are hidden from the experimentalist. To investigate whether a time-to-death (time-to-event) data set provides adequate information for searching for chaotic signatures, we first determined our ability to detect chaos in simulated data sets of time-to-event measurements and successfully distinguished the time-to-event distribution of a chaotic process from a comparable stochastic one. To do so, we introduced an inversion measure to test for a chaotic signature in time-to-event distributions. Next, we searched for chaos in the time-to-death of Caenorhabditis elegans and Drosophila melanogaster infected with Pseudomonas aeruginosa or Pseudomonas entomophila, respectively. We found suggestions of chaotic signatures in both systems but caution that our results are preliminary and highlight the need for more fine-grained and larger data sets in determining dynamical characteristics. If validated, chaos in host-microbe interactions would have important implications for the occurrence and outcome of infectious diseases, the reproducibility of experiments in the field of microbial pathogenesis, and the prediction of microbial threats.IMPORTANCEIs microbial pathogenesis a predictable scientific field? At a time when we are dealing with coronavirus disease 2019, there is intense interest in knowing about the epidemic potential of other microbial threats and new emerging infectious diseases. To know whether microbial pathogenesis will ever be a predictable scientific field requires knowing whether a host-microbe interaction follows deterministic, stochastic, or chaotic dynamics. If randomness and chaos are absent from virulence, there is hope for prediction in the future regarding the outcome of microbe-host interactions. Chaotic systems are inherently unpredictable, although it is possible to generate short-term probabilistic models, as is done in applications of stochastic processes and machine learning to weather forecasting. Information on the dynamics of a system is also essential for understanding the reproducibility of experiments, a topic of great concern in the biological sciences. Our study finds preliminary evidence for chaotic dynamics in infectious diseases.

Chaos in a bacterial stress response

Cellular responses to environmental changes are often highly heterogeneous and exhibit seemingly random dynamics. The astonishing insight of chaos theory is that such unpredictable patterns can, in principle, arise without the need for any random processes, i.e., purely deterministically without noise. However, while chaos is well understood in mathematics and physics, its role in cell biology remains unclear because the complexity and noisiness of biological systems make testing difficult. Here, we show that chaos explains the heterogeneous response of Escherichia coli cells to oxidative stress. We developed a theoretical model of the gene expression dynamics and demonstrate that chaotic behavior arises from rapid molecular feedbacks that are coupled with cell growth dynamics and cell-cell interactions. Based on theoretical predictions, we then designed single-cell experiments to show we can shift gene expression from periodic oscillations to chaos on demand. Our work suggests that chaotic gene regulation can be employed by cell populations to generate strong and variable responses to changing environments.

Chaotic signatures in host-microbe interactions

Host-microbe interactions constitute dynamical systems that can be represented by mathematical formulations that determine their dynamic nature, and are categorized as deterministic, stochastic, or chaotic. Knowing the type of dynamical interaction is essential for understanding the system under study. Very little experimental work has been done to determine the dynamical characteristics of host-microbe interactions and its study poses significant challenges. The most straightforward experimental outcome involves an observation of time to death upon infection. However, in measuring this outcome, the internal parameters, and the dynamics of each particular host-microbe interaction in a population of interactions are hidden from the experimentalist. To investigate whether a time-to-death (time to event) dataset provides adequate information for searching for chaotic signatures, we first determined our ability to detect chaos in simulated data sets of time-to-event measurements and successfully distinguished the time-to-event distribution of a chaotic process from a comparable stochastic one. To do so, we introduced an inversion measure to test for a chaotic signature in time-to-event distributions. Next, we searched for chaos, in time-to-death of Caenorhabditis elegans and Drosophila melanogaster infected with Pseudomonas aeruginosa or Pseudomonas entomophila, respectively. We found suggestions of chaotic signatures in both systems, but caution that our results are preliminary and highlight the need for more fine-grained and larger data sets in determining dynamical characteristics. If validated, chaos in host-microbe interactions would have important implications for the occurrence and outcome of infectious diseases, the reproducibility of experiments in the field of microbial pathogenesis and the prediction of microbial threats.

Possible beneficial interactions of ciliated protozoans with coral health and resilience

Microbial interactions contribute significantly to coral health in the marine environment. Most beneficial associations have been described with their bacterial communities, but knowledge of beneficial associations between protozoan ciliates and corals is still lacking. Ciliates are important bacterial predators and provide nutrition to higher trophic-level organisms. The mucus secreted by corals and the microenvironment of the coral surface layer attract ciliates based on their food preferences. The mixotrophic and heterotrophic ciliates play a major role in nutrient cycling by increasing nitrogen, phosphorus, and extractable sulfur, which can enhance the proliferation of coral beneficial microbe. Besides, bacterial predator ciliates reduce the pathogenic bacterial population that infects the coral and also act as bioindicators for assessing the toxicity of the reef ecosystem. Thus, these ciliates can be used as a beneficial partner in influencing coral health and resilience under various stress conditions. Herein, we explore the urgent need to understand the complex beneficial interactions of ciliates that may occur in the coral reef ecosystem.

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.

Dynamics-based characterization and classification of biodiversity indicators

Various biodiversity indicators, such as species richness, total abundance, and species diversity indices, have been developed to capture the state of ecological communities over space and time. As biodiversity is a multifaceted concept, it is important to understand the dimension of biodiversity reflected by each indicator for successful conservation and management. Here we utilized the responsiveness of biodiversity indicators' dynamics to environmental changes (i.e., environmental responsiveness) as a signature of the dimension of biodiversity. We present a method for characterizing and classifying biodiversity indicators according to environmental responsiveness and apply the methodology to monitoring data for a marine fish community under intermittent anthropogenic warm water discharge. Our analysis showed that 10 biodiversity indicators can be classified into three super-groups based on the dimension of biodiversity that is reflected. Group I (species richness and community mean of latitudinal center of distribution (cCOD)) showed the greatest robustness to temperature changes; Group II (species diversity and total abundance) showed an abrupt change in the middle of the monitoring period, presumably due to a change in temperature; Group III (species evenness) exhibited the highest sensitivity to environmental changes, including temperature. These results had several ecological implications. First, the responsiveness of species diversity and species evenness to temperature changes might be related to changes in the species abundance distribution. Second, the similar environmental responsiveness of species richness and cCOD implies that fish migration from lower latitudes is a major driver of species compositional changes. The study methodology may be useful in selecting appropriate indicators for efficient biodiversity monitoring.

Wavelet clustering analysis as a tool for characterizing community structure in the human microbiome

Human microbiome research is helped by the characterization of microbial networks, as these may reveal key microbes that can be targeted for beneficial health effects. Prevailing methods of microbial network characterization are based on measures of association, often applied to limited sampling points in time. Here, we demonstrate the potential of wavelet clustering, a technique that clusters time series based on similarities in their spectral characteristics. We illustrate this technique with synthetic time series and apply wavelet clustering to densely sampled human gut microbiome time series. We compare our results with hierarchical clustering based on temporal correlations in abundance, within and across individuals, and show that the cluster trees obtained by using either method are significantly different in terms of elements clustered together, branching structure and total branch length. By capitalizing on the dynamic nature of the human microbiome, wavelet clustering reveals community structures that remain obscured in correlation-based methods.

Computational capability of ecological dynamics

Ecological dynamics is driven by complex ecological networks. Computational capabilities of artificial networks have been exploited for machine learning purposes, yet whether an ecological network possesses a computational capability and whether/how we can use it remain unclear. Here, we developed two new computational/empirical frameworks based on reservoir computing and show that ecological dynamics can be used as a computational resource. In silico ecological reservoir computing (ERC) reconstructs ecological dynamics from empirical time series and uses simulated system responses for information processing, which can predict near future of chaotic dynamics and emulate nonlinear dynamics. The real-time ERC uses real population dynamics of a unicellular organism, Tetrahymena thermophila. The temperature of the medium is an input signal and population dynamics is used as a computational resource. Intriguingly, the real-time ecological reservoir has necessary conditions for computing (e.g. synchronized dynamics in response to the same input sequences) and can make near-future predictions of empirical time series, showing the first empirical evidence that population-level phenomenon is capable of real-time computations. Our finding that ecological dynamics possess computational capability poses new research questions for computational science and ecology: how can we efficiently use it and how is it actually used, evolved and maintained in an ecosystem?

Intermittent instability is widespread in plankton communities

Chaotic dynamics appear to be prevalent in short-lived organisms including plankton and may limit long-term predictability. However, few studies have explored how dynamical stability varies through time, across space and at different taxonomic resolutions. Using plankton time series data from 17 lakes and 4 marine sites, we found seasonal patterns of local instability in many species, that short-term predictability was related to local instability, and that local instability occurred most often in the spring, associated with periods of high growth. Taxonomic aggregates were more stable and more predictable than finer groupings. Across sites, higher latitude locations had higher Lyapunov exponents and greater seasonality in local instability, but only at coarser taxonomic resolution. Overall, these results suggest that prediction accuracy, sensitivity to change and management efficacy may be greater at certain times of year and that prediction will be more feasible for taxonomic aggregates.

Technical versus biological variability in a synthetic human gut community

Synthetic communities grown in well-controlled conditions are an important tool to decipher the mechanisms driving community dynamics. However, replicate time series of synthetic human gut communities in chemostats are rare, and it is thus still an open question to what extent stochasticity impacts gut community dynamics. Here, we address this question with a synthetic human gut bacterial community using an automated fermentation system that allows for a larger number of biological replicates. We collected six biological replicates for a community initially consisting of five common gut bacterial species that fill different metabolic niches. After an initial 12 hours in batch mode, we switched to chemostat mode and observed the community to stabilize after 2-3 days. Community profiling with 16S rRNA resulted in high variability across replicate vessels and high technical variability, while the variability across replicates was significantly lower for flow cytometric data. Both techniques agree on the decrease in the abundance of Bacteroides thetaiotaomicron, accompanied by an initial increase in Blautia hydrogenotrophica. These changes occurred together with reproducible metabolic shifts, namely a fast depletion of glucose and trehalose concentration in batch followed by a decrease in formic acid and pyruvic acid concentrations within the first 12 hours after the switch to chemostat mode. In conclusion, the observed variability in the synthetic bacterial human gut community, as assessed with 16S rRNA gene sequencing, is largely due to technical variability. The low variability seen in HPLC and flow cytometry data suggests a highly deterministic system.

The role of mathematical modelling in understanding prokaryotic predation

With increasing levels of antimicrobial resistance impacting both human and animal health, novel means of treating resistant infections are urgently needed. Bacteriophages and predatory bacteria such as Bdellovibrio bacteriovorus have been proposed as suitable candidates for this role. Microbes also play a key environmental role as producers or recyclers of nutrients such as carbon and nitrogen, and predators have the capacity to be keystone species within microbial communities. To date, many studies have looked at the mechanisms of action of prokaryotic predators, their safety in in vivo models and their role and effectiveness under specific conditions. Mathematical models however allow researchers to investigate a wider range of scenarios, including aspects of predation that would be difficult, expensive, or time-consuming to investigate experimentally. We review here a history of modelling in prokaryote predation, from simple Lotka-Volterra models, through increasing levels of complexity, including multiple prey and predator species, and environmental and spatial factors. We consider how models have helped address questions around the mechanisms of action of predators and have allowed researchers to make predictions of the dynamics of predator-prey systems. We examine what models can tell us about qualitative and quantitative commonalities or differences between bacterial predators and bacteriophage or protists. We also highlight how models can address real-world situations such as the likely effectiveness of predators in removing prey species and their potential effects in shaping ecosystems. Finally, we look at research questions that are still to be addressed where models could be of benefit.

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.

Limited predictability of body length in a fish population

Recent theoretical studies have identified chaotic dynamics in eco-evolutionary models. Yet, empirical evidence for eco-evolutionary chaos in natural ecosystems is lacking. In this study, we combine analyses of empirical data and an eco-evolutionary model to uncover chaotic dynamics of body length in a fish population (northeast Arctic cod: Gadus morhua). Consistent with chaotic attractors, the largest Lyapunov exponent (LE) of empirical data is positive, and approximately matches the LE of the model calculation, thus suggesting the potential for chaotic dynamics in this fish population. We also find that the autocorrelation function (ACF) of both empirical data and eco-evolutionary model shows a similar lag of approximately 7 years. Our combined analyses of natural time series and mathematical models suggest that chaotic dynamics of a phenotypic trait may be driven by trait evolution. This finding supports a growing theory that eco-evolutionary feedbacks can produce chaotic dynamics.

Intrinsic nonlinear dynamics drive single-species systems

The importance of oscillations and deterministic chaos in natural biological systems has been discussed for several decades and was originally based on discrete-time population growth models (May 1974). Recently, all types of nonlinear dynamics were shown for experimental communities where several species interact. Yet, there are no data exhibiting the whole range of nonlinear dynamics for single-species systems without trophic interactions. Up until now, ecological experiments and models ignored the intracellular dimension, which includes multiple nonlinear processes even within one cell type. Here, we show that dynamics of single-species systems of protists in continuous experimental chemostat systems and corresponding continuous-time models reveal typical characteristics of nonlinear dynamics and even deterministic chaos, a very rare discovery. An automatic cell registration enabled a continuous and undisturbed analysis of dynamic behavior with a high temporal resolution. Our simple and general model considering the cell cycle exhibits a remarkable spectrum of dynamic behavior. Chaos-like dynamics were shown in continuous single-species populations in experimental and modeling data on the level of a single type of cells without any external forcing. This study demonstrates how complex processes occurring in single cells influence dynamics on the population level. Nonlinearity should be considered as an important phenomenon in cell biology and single-species dynamics and also, for the maintenance of high biodiversity in nature, a prerequisite for nature conservation.

Chaos in synthetic microbial communities

Predictability is a fundamental requirement in biological engineering. As we move to building coordinated multicellular systems, the potential for such systems to display chaotic behaviour becomes a concern. Therefore understanding which systems show chaos is an important design consideration. We developed a methodology to explore the potential for chaotic dynamics in small microbial communities governed by resource competition, intercellular communication and competitive bacteriocin interactions. Our model selection pipeline uses Approximate Bayesian Computation to first identify oscillatory behaviours as a route to finding chaotic behaviour. We have shown that we can expect to find chaotic states in relatively small synthetic microbial systems, understand the governing dynamics and provide insights into how to control such systems. This work is the first to query the existence of chaotic behaviour in synthetic microbial communities and has important ramifications for the fields of biotechnology, bioprocessing and synthetic biology.

Species abundance correlations carry limited information about microbial network interactions

Unraveling the network of interactions in ecological communities is a daunting task. Common methods to infer interspecific interactions from cross-sectional data are based on co-occurrence measures. For instance, interactions in the human microbiome are often inferred from correlations between the abundances of bacterial phylogenetic groups across subjects. We tested whether such correlation-based methods are indeed reliable for inferring interaction networks. For this purpose, we simulated bacterial communities by means of the generalized Lotka-Volterra model, with variation in model parameters representing variability among hosts. Our results show that correlations can be indicative for presence of bacterial interactions, but only when measurement noise is low relative to the variation in interaction strengths between hosts. Indication of interaction was affected by type of interaction network, process noise and sampling under non-equilibrium conditions. The sign of a correlation mostly coincided with the nature of the strongest pairwise interaction, but this is not necessarily the case. For instance, under rare conditions of identical interaction strength, we found that competitive and exploitative interactions can result in positive as well as negative correlations. Thus, cross-sectional abundance data carry limited information on specific interaction types. Correlations in abundance may hint at interactions but require independent validation.

The bacteria in and on our body (the human microbiome) largely determine how our body functions, and whether we stay healthy or get sick. These bacteria do not live on their own, but interact among each other and with their human host. Finding out which bacteria interact with each other is cumbersome, but patterns of joint occurrence between species might provide a clue to their ecological dependencies. We investigated whether correlations in species abundance can be used for the purpose of ecological network reconstruction. We simulated different bacterial communities with known interactions according to a theoretical population model. After having collected virtual samples from our simulated data, we performed a correlation analysis and then compared the correlation network with our known interaction network. We found that correlations can be informative for underlying interactions, but ecological conclusions should be drawn carefully. An obvious limitation of correlation analysis is that direction of interaction cannot be recovered from co-occurrence data, making correlations insensitive for detection of asymmetric interactions. In addition, we found that competitive and exploitative interactions can induce positive as well as negative correlations. We recommend careful interpretation and validation when inferring networks from cross-sectional abundance data.

Year-Long Microbial Succession on Microplastics in Wastewater: Chaotic Dynamics Outweigh Preferential Growth

Microplastics are a globally-ubiquitous aquatic pollutant and have been heavily studied over the last decade. Of particular interest are the interactions between microplastics and microorganisms, especially the pursuit to discover a plastic-specific biome, the so-called plastisphere. To follow this up, a year-long microcosm experimental setup was deployed to expose five different microplastic types (and silica beads control) to activated aerobic wastewater in controlled conditions, with microbial communities being measured four times over the course of the year using 16S rDNA (bacterial) and ITS (fungal) amplicon sequencing. The biofilm community shows no evidence of a specific plastisphere, even after a year of incubation. Indeed, the microbial communities (particularly bacterial) show a clear trend of increasing dissimilarity between plastic types as time increases. Despite little evidence for a plastic-specific community, there was a slight grouping observed for polyolefins (PE and PP) in 6–12-month biofilms. Additionally, an OTU assigned to the genus Devosia was identified on many plastics, increasing over time while showing no growth on silicate (natural particle) controls, suggesting this could be either a slow-growing plastic-specific taxon or a symbiont to such. Both substrate-associated findings were only possible to observe in samples incubated for 6–12 months, which highlights the importance of studying long-term microbial community dynamics on plastic surfaces.

Chaos is not rare in natural ecosystems

Chaotic dynamics are thought to be rare in natural populations but this may be due to methodological and data limitations, rather than the inherent stability of ecosystems. Following extensive simulation testing, we applied multiple chaos detection methods to a global database of 172 population time series and found evidence for chaos in >30%. In contrast, fitting traditional one-dimensional models identified <10% as chaotic. Chaos was most prevalent among plankton and insects and least among birds and mammals. Lyapunov exponents declined with generation time and scaled as the -1/6 power of body mass among chaotic populations. These results demonstrate that chaos is not rare in natural populations, indicating that there may be intrinsic limits to ecological forecasting and cautioning against the use of steady-state approaches to conservation and management.

Microbial fuel cell compared to a chemostat

Microbial Fuel Cells (MFCs) represent a green and sustainable energy conversion system that integrate bacterial biofilms within an electrochemical two-electrode set-up to produce electricity from organic waste. In this review, we focus on a novel exploratory model, regarding "thin" biofilms forming on highly perfusable (non-diffusible) anodes in small-scale, continuous flow MFCs due to the unique properties of the electroactive biofilm. We discuss how this type of MFC can behave as a chemostat in fulfilling common properties including steady state growth and multiple steady states within the limit of biological physicochemical conditions imposed by the external environment. With continuous steady state growth, there is also continuous metabolic rate and continuous electrical power production, which like the chemostat can be controlled. The model suggests that in addition to controlling growth rate and power output by changing the external resistive load, it will be possible instead to change the flow rate/dilution rate.

Strong Selection and High Mutation Supply Characterize Experimental Chlorovirus Evolution

Characterizing how viruses evolve expands our understanding of the underlying fundamental processes, such as mutation, selection and drift. One group of viruses whose evolution has not yet been extensively studied is the Phycodnaviridae, a globally abundant family of aquatic large double-stranded (ds) DNA viruses. Here we studied the evolutionary change of Paramecium bursaria chlorella virus 1 during experimental coevolution with its algal host. We used pooled genome sequencing of six independently evolved populations to characterize genomic change over five time points. Across six experimental replicates involving either strong or weak demographic fluctuations, we found single nucleotide polymorphisms (SNPs) at sixty-seven sites. The occurrence of genetic variants was highly repeatable, with just two of the SNPs found in only a single experimental replicate. Three genes A122/123R, A140/145R and A540L showed an excess of variable sites, providing new information about potential targets of selection during Chlorella–Chlorovirus coevolution. Our data indicated that the studied populations were not mutation-limited and experienced strong positive selection. Our investigation highlighted relevant processes governing the evolution of aquatic large dsDNA viruses, which ultimately contributes to a better understanding of the functioning of natural aquatic ecosystems.

Novel high throughput sequencing - fluorometric approach demonstrates Microcystis blooms across western Lake Erie are promoted by grazing resistance and nutrient enhanced growth

Cyanobacterial harmful algal blooms (CHABs) are a global public health threat. While CHABs are often promoted by nutrients, an important and often overlooked influence on bloom dynamics is zooplankton grazing. In the present study, zooplankton grazing and nutrient enrichment experiments were combined with next generation sequencing and fluorometric analyses to quantify differential grazing and nutrient effects on specific cyanobacterial genera across the western basin of Lake Erie. Grazing by two different sized daphnids, Daphnia magna and Daphnia pulex, was compared to protozooplankton grazing effects assessed via a dilution approach at sites within the Maumee and Sandusky Bays where Planktothrix, Microcystis, Synechococcus, and Dolichospermum were the dominant genera. Daphnid grazing significantly reduced Synechococcus net growth rates at most sites as well as Planktothrix net growth in Sandusky Bay and Dolichospermum in Maumee Bay. Dilution resulted in significant growth increase of Synechococcus at half of the sites and Planktothrix at most sites evidencing substantial grazing pressure by the protozooplankton community on these genera. In contrast, Microcystis populations were largely unaffected by daphnids and protozooplankton grazing but benefitted from nutrient enrichment more than other CHAB genera. When diatoms were present in moderate abundance, grazing rates by daphnids on diatoms were significantly greater than grazing rates on cyanobacteria. The novel approach used in this study established differences in grazing pressure and nutrient effects on differing taxa and revealed that, while many taxa were grazed by multiple classes of zooplankton (e.g. Planktothrix, Synechococcus, Dolichospermum, diatoms), the lack of grazing pressure on Microcystis coupled with nutrient-enhanced growth in western Lake Erie promotes the occurrence of CHABs of this genus.

Effect of mutation supply on population dynamics and trait evolution in an experimental microbial community

Mutation supply can influence evolutionary and thereby ecological dynamics in important ways which have received little attention. Mutation supply influences features of population genetics, such as the pool of adaptive mutations, evolutionary pathways and importance of processes, such as clonal interference. The resultant trait evolutionary dynamics, in turn, can alter population size and species interactions. However, controlled experiments testing for the importance of mutation supply on rapid adaptation and thereby population and community dynamics have primarily been restricted to the first of these aspects. To close this knowledge gap, we performed a serial passage experiment with wild-type Pseudomonas fluorescens and a mutant with reduced mutation rate. Bacteria were grown at two resource levels in combination with the presence of a ciliate predator. A higher mutation supply enabled faster adaptation to the low-resource environment and anti-predatory defence. This was associated with higher population size at the ecological level and better access to high-recurrence mutational targets at the genomic level with higher mutation supply. In contrast, mutation rate did not affect growth under high-resource level. Our results demonstrate that intrinsic mutation rate influences population dynamics and trait evolution particularly when population size is constrained by extrinsic conditions.

Mathematical analysis of laboratory microbial experiments demonstrating deterministic chaotic dynamics

Presented is a system of four ordinary differential equations and a mathematical analysis of microbiological experiments in a four-component chemostat-nutrient n, rods r, cocci c, and predators p. The analysis is consistent with the conclusion that previous experiments produced features of deterministic chaotic and classical dynamics depending on dilution rate. The surrogate model incorporates as much experimental detail as possible, but necessarily contains unmeasured parameters. The objective is to understand better the differences between model simulations and experimental results in complex microbial populations. The key methodology for simulation of chaotic dynamics, consistent with the measured dilution rate and microbial volume averages, was to cause the preference of p for r vs. c to vary with the r and c concentrations, to make r more competitive for nutrient than c, and to recycle some dying p biomass, leading to a modified version of the Monod kinetics model. Our mathematical model demonstrated that the occurrence of chaotic dynamics requires a predator, p, preference for r versus c to increase significantly with increases in r and c populations. Also included is a discussion of several generalizations of the existing model and a possible involvement of the minimum energy dissipation principle. This principle appears fundamental to thermodynamic systems including living systems. Several new experiments are suggested.

A computational framework for finding parameter sets associated with chaotic dynamics

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we use existing software tools (COPASI, R) to explore dynamical systems and uncover regions with positive Lyapunov exponents where thus chaos exists. We evaluate the ability of the software's optimization algorithms to find these positive values with several dynamical systems used to model biological populations. The algorithms have been able to identify parameter sets which lead to positive Lyapunov exponents, even when those exponents lie in regions with small support. For one of the examined systems, we observed that positive Lyapunov exponents were not uncovered when executing a search over the parameter space with small spacings between values of the independent variables.

Origin of exponential growth in nonlinear reaction networks

Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. Here, we describe a general theoretical framework that reveals underlying principles of long-term growth: scalability of flux functions and ergodicity of the rescaled systems. Our theory shows that nonlinear fluxes can generate not only balanced growth but also oscillatory or chaotic growth modalities, explaining nonequilibrium dynamics observed in cell cycles and ecosystems. Our mathematical framework is broadly useful in predicting long-term growth rates from natural and synthetic networks, analyzing the effects of system noise and perturbations, validating empirical and phenomenological laws on growth rate, and studying autocatalysis and network evolution.

Discovery, development and exploitation of steady-state biofilms

Early in vitro biofilm models go back even beyond the invention of the word 'biofilm'. In the dental field, biofilms were simply known as dental plaque and many of the first in vitro models were termed 'artificial mouth microcosm plaques'. The purpose of this review is to highlight important elements of research from over the years regarding in vitro biofilm models, including data from our own laboratories. This helps us to interpret the models and point the way to the future development of biofilm testing. Many hypotheses regarding biofilm phenomena, particularly ecology, metabolism and physiology of volatile sulphur compounds (VSCs) and volatile organic compound (VOC) production could potentially be supported or disproved. In this way, the methods we use for screening biologically active agents including inhibitors, biocides and antimicrobial compounds in general can be improved. Hopefully, any lessons learnt in the past may be of value for the future. In this review, we focus around the need for growth rate controlled long-term biofilms; being continuously monitored using recent technical advances in bioluminescence, selective real-time electrodes, pH electrodes and continuous on-line analysis of the gas phase (both qualitatively and quantitatively). These features allow for accurate determination of growth rate and/or metabolic rate as well as pave the way towards automated assays and fine control of metabolism; impossible to achieve according to conventional biofilm theory. We also attempt to address the questions; can biofilm systems be improved to maintain long term 'real' or 'true' steady states over weeks or months, or are we limited to quasi-steady state systems for a limited period of time.

Evolution in interacting species alters predator life-history traits, behaviour and morphology in experimental microbial communities

Predator-prey interactions heavily influence the dynamics of many ecosystems. An increasing body of evidence suggests that rapid evolution and coevolution can alter these interactions, with important ecological implications, by acting on traits determining fitness, including reproduction, anti-predatory defence and foraging efficiency. However, most studies to date have focused only on evolution in the prey species, and the predator traits in (co)evolving systems remain poorly understood. Here, we investigated changes in predator traits after approximately 600 generations in a predator-prey (ciliate-bacteria) evolutionary experiment. Predators independently evolved on seven different prey species, allowing generalization of the predator's evolutionary response. We used highly resolved automated image analysis to quantify changes in predator life history, morphology and behaviour. Consistent with previous studies, we found that prey evolution impaired growth of the predator, although the effect depended on the prey species. By contrast, predator evolution did not cause a clear increase in predator growth when feeding on ancestral prey. However, predator evolution affected morphology and behaviour, increasing size, speed and directionality of movement, which have all been linked to higher prey search efficiency. These results show that in (co)evolving systems, predator adaptation can occur in traits relevant to foraging efficiency without translating into an increased ability of the predator to grow on the ancestral prey type.

Chaos theory discloses triggers and drivers of plankton dynamics in stable environment

Despite the enticing discoveries of chaos in nature, triggers and drivers of this phenomenon remain a classical enigma which needs irrefutable empirical evidence. Here we analyze results of the yearlong replicated mesocosm experiment with multi-species plankton community that allowed revealing signs of chaos at different trophic levels in strictly controlled abiotic environment. In mesocosms without external stressors, we observed the “paradox of chaos” when biotic interactions (internal drivers) were acting as generators of internal abiotic triggers of complex plankton dynamics. Chaos was registered as episodes that vanished unpredictably or were substituted by complex behaviour of other candidates when longer time series were considered. Remarkably, episodes of chaos were detected even in the most abiotically stable conditions. We developed the Integral Chaos Indicator to validate the results of the Lyapunov exponent analysis. These findings are essential for modelling and forecasting behaviour of a variety of natural and other global systems.

Long-term cyclic persistence in an experimental predator-prey system

Predator-prey cycles rank among the most fundamental concepts in ecology, are predicted by the simplest ecological models and enable, theoretically, the indefinite persistence of predator and prey^1-4. However, it remains an open question for how long cyclic dynamics can be self-sustained in real communities. Field observations have been restricted to a few cycle periods^5-8 and experimental studies indicate that oscillations may be short-lived without external stabilizing factors^9-19. Here we performed microcosm experiments with a planktonic predator-prey system and repeatedly observed oscillatory time series of unprecedented length that persisted for up to around 50 cycles or approximately 300 predator generations. The dominant type of dynamics was characterized by regular, coherent oscillations with a nearly constant predator-prey phase difference. Despite constant experimental conditions, we also observed shorter episodes of irregular, non-coherent oscillations without any significant phase relationship. However, the predator-prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply. Our findings empirically demonstrate the potential for infinite persistence of predator and prey populations in a cyclic dynamic regime that shows resilience in the presence of stochastic events.

EFFECT OF TIME DELAY IN A CANNIBALISTIC STAGE-STRUCTURED PREDATOR–PREY MODEL WITH HARVESTING OF AN ADULT PREDATOR: THE CASE OF LIONFISH

The progressive and increasing invasion of an opportunistic predator, the lionfish (Pterois volitans) has become a major threat for the delicate coral-reef ecosystem. The herbivore fish populations, in particular of Parrotfish, are taking the consequences of the lionfish invasion and then their control function on macro-algae growth is threatened. In this paper, we developed and analyzed a stage-structured mathematical model including P. volitans (lionfish), a cannibalistic predator, and a Parrotfish, its potential prey. As control upon the over predation, a rational harvest term has been considered. Further, to make the system more realistic, a delay in the growth rate of juvenile P. volitans population has been incorporated. We performed a global sensitivity analysis to identify important parameters of the system having significant correlations with the fishes. We observed that the system generates transcritical bifurcation, which takes the P. volitans-free equilibrium to the coexistence equilibrium on increasing the values of predation rate of adult P. volitans on Parrotfish. Further increase in the values of the predation rate of adult P. volitans on Parrotfish drives the system into Hopf bifurcation, which induces oscillation around the coexistence equilibrium. Moreover, the conversion efficiency due to cannibalism also has the property to alter the stability behavior of the system through Hopf bifurcation. The effect of time delay on the dynamics of the system is extensively studied and it is observed that the system develops chaotic dynamics through period-doubling oscillations for large values of time delay. However, if the system is already oscillatory, then the large values of time delay causes extinction of P. volitans from the system. To illustrate the occurrence of chaotic dynamics in the system, we drew the Poincaré map and also computed the Lyapunov exponents.

Artificial Microbial Arenas: Materials for Observing and Manipulating Microbial Consortia

From the smallest ecological niche to global scale, communities of microbial life present a major factor in system regulation and stability. As long as laboratory studies remain restricted to single or few species assemblies, however, very little is known about the interaction patterns and exogenous factors controlling the dynamics of natural microbial communities. In combination with microfluidic technologies, progress in the manufacture of functional and stimuli-responsive materials makes artificial microbial arenas accessible. As habitats for natural or multispecies synthetic consortia, they are expected to not only enable detailed investigations, but also the training and the directed evolution of microbial communities in states of balance and disturbance, or under the effects of modulated stimuli and spontaneous response triggers. Here, a perspective on how materials research will play an essential role in generating answers to the most pertinent questions of microbial engineering is presented, and the concept of adaptive microbial arenas and possibilities for their construction from particulate microniches to 3D habitats is introduced. Materials as active and tunable components at the interface of living and nonliving matter offer exciting opportunities in this field. Beyond forming the physical horizon for microbial cultivates, they will enable dedicated intervention, training, and observation of microbial consortia.

Multistability driven by inhibitory kinetics in a discrete-time size-structured chemostat model

In this paper, we consider a discrete size-structured nonlinear chemostat model with inhibitory kinetics and multiple competing species. We show that, same as in models with monotone increasing nutrient uptake response functionals studied in the literature, one essential growth-limiting nutrient can support at most one species. More interestingly, we show that, differing from monotone increasing kinetics, inhibitory kinetics can induce several types of multistability and the competitive outcome is initial condition dependent. The species with the smallest lower break-even value is not always the winning species, and the winning species can exhibit sustained periodic oscillations and even chaotic irregular oscillations.

Transcriptome analysis of activated sludge microbiomes reveals an unexpected role of minority nitrifiers in carbon metabolism

Although metagenomics researches have illuminated microbial diversity in numerous biospheres, understanding individual microbial functions is yet difficult due to the complexity of ecosystems. To address this issue, we applied a metagenome-independent, de novo assembly-based metatranscriptomics to a complex microbiome, activated sludge, which has been used for wastewater treatment for over a century. Even though two bioreactors were operated under the same conditions, their performances differed from each other with unknown causes. Metatranscriptome profiles in high- and low-performance reactors demonstrated that denitrifiers contributed to the anaerobic degradation of heavy oil; however, no marked difference in the gene expression was found. Instead, gene expression-based nitrification activities that fueled the denitrifiers by providing the respiratory substrate were notably high in the high-performance reactor only. Nitrifiers-small minorities with relative abundances of <0.25%-governed the heavy-oil degradation performances of the reactors, unveiling an unexpected linkage of carbon- and nitrogen-metabolisms of the complex microbiome.

Non-parametric estimation of the structural stability of non-equilibrium community dynamics

Environmental factors are important drivers of community dynamics. Yet, despite extensive research, it is still extremely challenging to predict the effect of environmental changes on the dynamics of ecological communities. Equilibrium- and model-based approaches have provided a theoretical framework with which to investigate this problem systematically. However, the applicability of this framework to empirical data has been limited because equilibrium dynamics of populations within communities are seldom observed in nature and exact equations for community dynamics are rarely known. To overcome these limitations, here we develop a data-driven non-parametric framework to estimate the tolerance of non-equilibrium community dynamics to environmental perturbations (that is, their structural stability). Following our approach, we show that in non-equilibrium systems, structural stability can vary significantly across time. As a case study, we investigate the structural stability of a rocky intertidal community with dynamics at the edge of chaos. The structural stability of the community as a whole exhibited a clear seasonal pattern, despite the persistent chaotic dynamics of individual populations. Importantly, we show that this seasonal pattern of structural stability is causally driven by sea temperature. Overall, our approach provides novel opportunities for estimating the tolerance of ecological communities to environmental changes within a non-parametric framework.

Seeking a Chaotic Order in the Cryptocurrency Market

In this study, we investigate the existence of chaos in the global cryptocurrency market. Specifically, we analyze parameters of chaotic order, nonlinearity, sensitivity to the initial conditions, monofractality, and multifractality. For this purpose, we conduct a comprehensive series of tests, including Brock–Dechert–Scheinkman (BDS) test, largest Lyapunov exponent, box-counting, and monogram analysis for fractal dimension, and multiple tests for long-range dependence (Aggregated Variances, Peng, Higuchi, R/S Analysis, and Multifractal Detrended Fluctuation Analysis (MFDFA)). All tests are performed over a variety of major cryptocurrencies: Bitcoin, Litecoin, Ethereum, and Ripple. The empirical results support the existence of chaos in the cryptocurrency market. Accordingly, cryptocurrency returns are not random and follow a chaotic order. Therefore, long term predictions are not possible, contrary to most of the discussions ongoing in the media and the public.

Asexual reproduction changes predator population dynamics in a life predator-prey system

Many organisms display oscillations in population size. Theory predicts that these fluctuations can be generated by predator-prey interactions, and empirical studies using life model systems, such as a rotifer-algae community consisting of Brachionus calyciflorus as predator and Chlorella vulgaris as prey, have been successfully used for studying such dynamics. B. calyciflorus is a cyclical parthenogen (CP) and clones often differ in their sexual propensity, that is, the degree to which they engage into sexual or asexual (clonal) reproduction. Since sexual propensities can affect growth rates and population sizes, we hypothesized that this might also affect population oscillations. Here, we studied the dynamical behaviour of B. calyciflorus clones representing either CPs (regularly inducing sex) or obligate parthenogens (OPs). We found that the amplitudes of population cycles to be increased in OPs at low nutrient levels. Several other population dynamic parameters seemed unaffected. This suggests that reproductive mode might be an important additional variable to be considered in future studies of population oscillations.

Temporal inactivation enhances robustness in an evolving system

We study the robustness of an evolving system that is driven by successive inclusions of new elements or constituents with m random interactions to older ones. Each constitutive element in the model stays either active or is temporarily inactivated depending upon the influence of the other active elements. If the time spent by an element in the inactivated state reaches T _W , it gets extinct. The phase diagram of this dynamic model as a function of m and T _W is investigated by numerical and analytical methods and as a result both growing (robust) as well as non-growing (volatile) phases are identified. It is also found that larger time limit T _W enhances the system's robustness against the inclusion of new elements, mainly due to the system's increased ability to reject 'falling-together' type attacks. Our results suggest that the ability of an element to survive in an unfavourable situation for a while, either as a minority or in a dormant state, could improve the robustness of the entire system.

Three-species competition with non-deterministic outcomes

Theoretical and experimental research studies have shown that ecosystems governed by non-transitive competition networks tend to maintain high levels of biodiversity. The theoretical body of work, however, has mainly focused on competition networks in which the outcomes of competition events are predetermined and hence deterministic, and where all species are identical up to their competitive relationships, an assumption that may limit the applicability of theoretical results to real-life situations. In this paper, we aim to probe the robustness of the link between biodiversity and non-transitive competition by introducing a three-dimensional winning probability parameter space, making the outcomes of competition events in a three-species in silico ecosystem uncertain. While two degenerate points in this parameter space have been the subject of previous studies, we investigate the remaining settings, which equip the species with distinct competitive abilities. We find that the impact of this modification depends on the spatial dimension of the system. When the system is well mixed, it collapses to monoculture, as is also the case in the non-transitive deterministic setting. In one dimension, chaotic patterns emerge, which tend to maintain biodiversity, and a power law relates the time that species manage to coexist to the degree of uncertainty regarding competition event outcomes. In two dimensions, the formation of spiral wave patterns ensures that biodiversity is maintained for moderate degrees of uncertainty, while considerable deviations from the non-transitive deterministic setting have strong negative effects on species coexistence. It can hence be concluded that non-transitive competition can still produce coexistence when the assumption of deterministic competition is abandoned. When the system collapses to monoculture, one observes a "survival of the strongest" law, as the species that has the highest probability of defeating its competitors has the best odds to become the sole survivor.

Model Microbial Consortia as Tools for Understanding Complex Microbial Communities

A major biological challenge in the postgenomic era has been untangling the composition and functions of microbes that inhabit complex communities or microbiomes. Multi-omics and modern bioinformatics have provided the tools to assay molecules across different cellular and community scales; however, mechanistic knowledge over microbial interactions often remains elusive. This is due to the immense diversity and the essentially undiminished volume of not-yet-cultured microbes. Simplified model communities hold some promise in enabling researchers to manage complexity so that they can mechanistically understand the emergent properties of microbial community interactions. In this review, we surveyed several approaches that have effectively used tractable model consortia to elucidate the complex behavior of microbial communities. We go further to provide some perspectives on the limitations and new opportunities with these approaches and highlight where these efforts are likely to lead as advances are made in molecular ecology and systems biology.