Chaos is not rare in natural ecosystems

Robust Chaos in a Totally Symmetric Network of Four Phase Oscillators

The Kuramoto model and its generalizations are universal models of collective behavior in oscillatory networks. We provide conditions on the coupling function such that the Kuramoto system with four globally coupled identical oscillators has chaotic attractors: a pair of Lorenz attractors or a four-winged analog of the Lorenz attractor. The attractors emerge near the triple instability threshold of the splay-phase synchronization state of the oscillators. We provide theoretical arguments and verify numerically, based on the pseudohyperbolicity test, that the chaotic dynamics are robust with respect to small, e.g., time-dependent, perturbations of the system. The robust chaoticity should also be inherited by any network of weakly interacting systems with such attractors.

Spatio-temporal pattern formation of living organisms at the edge of chaos

Understanding spatio-temporal dynamics is essential for predicting how populations fluctuate over time and space. Theoretical models have highlighted the ecological complexity of spatio-temporal dynamics, which can lead to the emergence of complex patterns, including nonlinear dynamics and chaotic behavior, important mechanisms for maintaining of biodiversity. However, these dynamics are difficult to observe experimentally due to a lack of temporal and spatial resolution. Here, we show that even a single-species system exhibits complex spatio-temporal patterns without external forcing where order and chaos coexist (edge of chaos). Automated analyses of experimental dynamics of cells of a ciliate on a microfluidic chip environment with 50 interconnected patches documented pattern formation, including chaos-like dynamics, using several analytical methods. Different initial conditions caused changes in patterns, revealing the complexity and principal unpredictability of self-organized pattern formation. A model containing the stochastic fluctuations of the experiment verified the deterministic nature of patterns. The results show the intrinsic complexity of ecological systems, challenging predictions in nature conservation. Our results bridge the gap between theoretical models and experimental observations, offering new insights into the fundamental nature of living systems and their spatio-temporal organization.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations

Large stochastic population abundance fluctuations are ubiquitous across the tree of life, impacting the predictability and outcomes of population dynamics. It is generally thought that abundance fluctuations with a Taylor's law exponent of two do not strongly impact evolution. However, we argue that such abundance fluctuations can lead to substantial genotype frequency fluctuations if different genotypes in a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related Escherichia coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from genetic drift. We develop an effective model explaining that the abundance fluctuations arise from correlated offspring numbers between individuals, and the large frequency fluctuations result from (even slight) decoupling in offspring number correlations between genotypes. The model quantitatively predicts the observed abundance and frequency fluctuation scaling. Initially close trajectories diverge exponentially, suggesting that chaotic dynamics may underpin the excess frequency fluctuations. Our findings suggest that decoupling noise is also present in mixed-genotype Saccharomyces cerevisiae populations. Theoretical analyses demonstrate that decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of these frequency fluctuations, we expect them to be widespread across biological populations.

Distinct phytoplankton size classes respond differently to biotic and abiotic factors

The interplay between abiotic (resource supply, temperature) and biotic (grazing) factors determines growth and loss processes in phytoplankton through resource competition and trophic interactions, which are mediated by morphological traits like size. Here, we study the relative importance of grazers, water physics, and chemistry on the daily net accumulation rates (ARs) of individual phytoplankton from natural communities, grouped into six size classes from circa 10 to 500 μm. Using a Random Forest modelling approach and 4 years of daily data from a lake, we find that water temperature is generally a pivotal control of all phytoplankton ARs. At the same time, nutrients and light are important for the smallest and the largest classes. Mesozooplankton abundance is a key predictor of the AR for small phytoplankton, with microzooplankton being important for the middle-size range. In our data, large and small phytoplankton have different (seasonal) blooming patterns: small forms are favoured by low temperature and grazing, and high phosphorus levels. Larger forms show positive ARs at high temperatures and low phosphorus (being relatively insensitive to zooplankton grazing). These results help us understand the opportunities and limitations of using size to explain and model phytoplankton responses to biotic and abiotic environmental change.

Calibrated Ecosystem Models Cannot Predict the Consequences of Conservation Management Decisions

Ecosystem models are often used to predict the consequences of management interventions in applied ecology and conservation. These models are often high-dimensional and nonlinear, yet limited data are available to calibrate or validate them. Consequently, their utility as decision-support tools is unclear. In this paper, we calibrate ecosystem models to time series data from 110 different experimental microcosm ecosystems, each containing three to five interacting species. Then, we assess their ability to predict the consequences of management interventions. Our results show that for each time series dataset, multiple divergent parameter sets offer equivalent, good fits. However, these models have poor predictive accuracy when forecasting future dynamics or when predicting how the ecosystem will respond to management intervention. Closer inspection reveals that the models fail because calibration cannot determine the nature of the interspecific interactions. Our findings question whether ecosystem models can support applied ecological decision-making when calibrated against real-world datasets.

Assembly Graph as the Rosetta Stone of Ecological Assembly

Ecological assembly-the process of ecological community formation through species introductions-has recently seen exciting theoretical advancements across dynamical, informational, and probabilistic approaches. However, these theories often remain inaccessible to non-theoreticians, and they lack a unifying lens. Here, I introduce the assembly graph as an integrative tool to connect these emerging theories. The assembly graph visually represents assembly dynamics, where nodes symbolise species combinations and edges represent transitions driven by species introductions. Through the lens of assembly graphs, I review how ecological processes reduce uncertainty in random species arrivals (informational approach), identify graphical properties that guarantee species coexistence and examine how the class of dynamical models constrain the topology of assembly graphs (dynamical approach), and quantify transition probabilities with incomplete information (probabilistic approach). To facilitate empirical testing, I also review methods to decompose complex assembly graphs into smaller, measurable components, as well as computational tools for deriving empirical assembly graphs. In sum, this math-light review of theoretical progress aims to catalyse empirical research towards a predictive understanding of ecological assembly.

Increasing environmental fluctuations can dampen variability of endogenously cycling populations

Understanding how populations respond to increasingly variable conditions is a major objective for natural resource managers forecasting extinction risk. The lesson from current modelling is clear: increasing environmental variability increases population abundance variability. We show that this paradigm fails to describe a broad class of empirically observed dynamics, namely endogenously driven population cycles. In contrast to the dominant paradigm, these populations can exhibit reduced long-run population variance under increasing environmental variability. We provide evidence for a mechanistic explanation of this phenomenon that relies on how stochasticity interacts with long transient dynamics present in the deterministic cycling model. This interaction stands in contrast to the often assumed additivity of stochastic and deterministic drivers of population fluctuations. We show evidence for the phenomenon in two cyclical populations: flour beetles and Canadian lynx. We quantify the impact of the phenomenon with new theory that partitions the effects of nonlinear dynamics and stochastic variation on dynamical systems. In both empirical examples, the partitioning shows that the interaction between deterministic and stochastic dynamics reduces the variance in population size. Our results highlight that previous predictions about extinction under environmental variability may prove inadequate to understand the effects of climate change in some populations.

New insights into the prediction for the potential of soil organic carbon accumulation: From the perspective of non-equilibrium statistical mechanics

The accumulation of soil organic carbon (SOC) is significant for soil health and ecosystem services. Numerous studies have assessed the dynamic changes of SOC by considering the microbial system as an equilibrium system. However, they failed to reveal the complexity of the SOC accumulation/loss process, as the microbial system is a non-equilibrium system affected by stochastic fluctuations from the external environment. This study is the first to explore the complex non-equilibrium relationship between microbial carbon use efficiency (CUE) and SOC by using potential landscape and flux in non-equilibrium statistical mechanics. Nitrogen (N) was identified as the most critical environmental factor influencing CUE on a global scale, with the transition between the carbon loss state and the carbon sequestration state observed along N gradients. Random perturbations of other environmental factors could also trigger transition. Non-equilibrium thermodynamic quantities indicated that carbon sequestration had the potential to be achieved when N = 0.5 g/kg, where active soil management measures should be taken. Furthermore, the non-equilibrium relationship between CUE and SOC was clarified through potential energy analysis, where the average deviation between predictions and actual observations of SOC is about 1.9792 g/kg. This study provides an effective framework for predicting SOC accumulation.

From resonance to chaos by modulating spatiotemporal patterns through a synthetic optogenetic oscillator

Oscillations are a recurrent phenomenon in biological systems across scales, but deciphering their fundamental principles is very challenging. Here, we tackle this challenge by redesigning the wellcharacterised synthetic oscillator known as "repressilator" in Escherichia coli and controlling it using optogenetics, creating the "optoscillator". Bacterial colonies manifest oscillations as spatial ring patterns. When we apply periodic light pulses, the optoscillator behaves as a forced oscillator and we systematically investigate the properties of the rings under various light conditions. Combining experiments with mathematical modeling, we demonstrate that this simple oscillatory circuit can generate complex dynamics that are transformed into distinct spatial patterns. We report the observation of synchronisation, resonance, subharmonic resonance and period doubling. Furthermore, we present evidence of a chaotic regime. This work highlights the intricate spatiotemporal patterns accessible by synthetic oscillators and underscores the potential of our approach in revealing fundamental principles of biological oscillations.

Warming increases the compositional and functional variability of a temperate protist community

Phototrophic protists are a fundamental component of the world's oceans by serving as the primary source of energy, oxygen, and organic nutrients for the entire ecosystem. Due to the high thermal seasonality of their habitat, temperate protists could harbour many well-adapted species that tolerate ocean warming. However, these species may not sustain ecosystem functions equally well. To address these uncertainties, we conducted a 30-day mesocosm experiment to investigate how moderate (12 °C) and substantial (18 °C) warming compared to ambient conditions (6 °C) affect the composition (18S rRNA metabarcoding) and ecosystem functions (biomass, gross oxygen productivity, nutritional quality - C:N and C:P ratio) of a North Sea spring bloom community. Our results revealed warming-driven shifts in dominant protist groups, with haptophytes thriving at 12 °C and diatoms at 18 °C. Species responses primarily depended on the species' thermal traits, with indirect temperature effects on grazing being less relevant and phosphorus acting as a critical modulator. The species Phaeocystis globosa showed highest biomass on low phosphate concentrations and relatively increased in some replicates of both warming treatments. In line with this, the C:P ratio varied more with the presence of P. globosa than with temperature. Examining further ecosystem responses under warming, our study revealed lowered gross oxygen productivity but increased biomass accumulation whereas the C:N ratio remained unaltered. Although North Sea species exhibited resilience to elevated temperatures, a diminished functional similarity and heightened compositional variability indicate potential ecosystem repercussions for higher trophic levels. In conclusion, our research stresses the multifaceted nature of temperature effects on protist communities, emphasising the need for a holistic understanding that encompasses trait-based responses, indirect effects, and functional dynamics in the face of exacerbating temperature changes.

Explaining empirical dynamic modelling using verbal, graphical and mathematical approaches

Empirical dynamic modelling (EDM) is becoming an increasingly popular method for understanding the dynamics of ecosystems. It has been applied to laboratory, terrestrial, freshwater and marine systems, used to forecast natural populations and has addressed fundamental ecological questions. Despite its increasing use, we have not found full explanations of EDM in the ecological literature, limiting understanding and reproducibility. Here we expand upon existing work by providing a detailed introduction to EDM. We use three progressively more complex approaches. A short verbal explanation of EDM is then explicitly demonstrated by graphically working through a simple example. We then introduce a full mathematical description of the steps involved. Conceptually, EDM translates a time series of data into a path through a multi-dimensional space, whose axes are lagged values of the time series. A time step is chosen from which to make a prediction. The state of the system at that time step corresponds to a 'focal point' in the multi-dimensional space. The set (called the library) of candidate nearest neighbours to the focal point is constructed, to determine the nearest neighbours that are then used to make the prediction. Our mathematical explanation explicitly documents which points in the multi-dimensional space should not be considered as focal points. We suggest a new option for excluding points from the library that may be useful for short-term time series that are often found in ecology. We focus on the core simplex and S-map algorithms of EDM. Our new R package, pbsEDM, enhances understanding (by outputting intermediate calculations), reproduces our results and can be applied to new data. Our work improves the clarity of the inner workings of EDM, a prerequisite for EDM to reach its full potential in ecology and have wide uptake in the provision of advice to managers of natural resources.

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.

Offset boosting in a discrete system

Offset boosting plays an important role in chaos application in electronic engineering. A direct variable substitution typically will destroy the dynamics of a discrete map even though the initial condition is well considered. The internal fundamental reason is that the left-hand side of a discrete system does not have the dimension of variable differentiation (DVD) like the one of a continuous system. When the key property of DVD is completely preserved, the offset boosting based on a parameter or the initial condition can be reasonably achieved like in a differential system. Consequently, by the initial condition-oriented offset boosting, flexible multistability like attractor self-reproducing or attractor doubling can be further realized. A circuit experiment is completed for the verification of reliable offset boosting. The systematic exploration of offset boosting in a map will cast a new light on chaos regulation and attractor transportation in a discrete map. As a simple case, a two-dimensional Hénon map is taken as the example demonstrating the achievement of offset boosting via the parameter or initial condition.

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.

Enhancement of solid-liquid mixing state quality in a mechanical stirred reactor with serial-chaotic rotation generated by basic speed method

In this work, a novel controllable chaotic stirring strategy that basic speed with chaotic mappings is proposed to enhance the solid-liquid mixing state quality. Specially, the modern statistical image analysis technique is introduced to explore the intensification mechanism of the mixing process. Results show that the best experimental conditions are obtained by studying the influence of factors such as the type of chaotic mapping, the speed change time, and the basic speed on the mixing state quality. Moreover, the case in which the basic speed is set to 150 r/min generated by the cascaded Logistic-Cubic chaotic mapping is the best while the speed change time is set to 5 s and the fluctuation threshold is 30. The mixing time of this case is 50 s and the shortest, energy consumption is 1.64 × 104 W/m3 and appropriate, the solid particle suspension quality is 83 and the best.

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.

Finding analytical approximations for discrete, stochastic, individual-based models of ecology

Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be approximated by 'top down' models of dynamics. Here, we study a class of spatially explicit individual-based models with contest competition: where species compete for space in local cells and then disperse to nearby cells. We start by describing simulations of the model, which exhibit large-scale discrete oscillations and characterize these oscillations by measuring spatial correlations. We then develop two new approximate descriptions of the resulting spatial population dynamics. The first is based on local interactions of the individuals and allows us to give a difference equation approximation of the system over small dispersal distances. The second approximates the long-range interactions of the individual-based model. These approximations capture demographic stochasticity from the individual-based model and show that dispersal stabilizes population dynamics. We calculate extinction probability for the individual-based model and show convergence between the local approximation and the non-spatial global approximation of the individual-based model as dispersal distance and population size simultaneously tend to infinity. Our results provide new approximate analytical descriptions of a complex bottom-up model and deepen understanding of spatial population dynamics.

Artificial selection of communities drives the emergence of structured interactions

Species-rich communities, such as the microbiota or microbial ecosystems, provide key functions for human health and climatic resilience. Increasing effort is being dedicated to design experimental protocols for selecting community-level functions of interest. These experiments typically involve selection acting on populations of communities, each of which is composed of multiple species. If numerical simulations started to explore the evolutionary dynamics of this complex, multi-scale system, a comprehensive theoretical understanding of the process of artificial selection of communities is still lacking. Here, we propose a general model for the evolutionary dynamics of communities composed of a large number of interacting species, described by disordered generalised Lotka-Volterra equations. Our analytical and numerical results reveal that selection for scalar community functions leads to the emergence, along an evolutionary trajectory, of a low-dimensional structure in an initially featureless interaction matrix. Such structure reflects the combination of the properties of the ancestral community and of the selective pressure. Our analysis determines how the speed of adaptation scales with the system parameters and the abundance distribution of the evolved communities. Artificial selection for larger total abundance is thus shown to drive increased levels of mutualism and interaction diversity. Inference of the interaction matrix is proposed as a method to assess the emergence of structured interactions from experimentally accessible measures.

Toward a cohesive understanding of ecological complexity

Ecological systems are quintessentially complex systems. Understanding and being able to predict phenomena typical of complex systems is, therefore, critical to progress in ecology and conservation amidst escalating global environmental change. However, myriad definitions of complexity and excessive reliance on conventional scientific approaches hamper conceptual advances and synthesis. Ecological complexity may be better understood by following the solid theoretical basis of complex system science (CSS). We review features of ecological systems described within CSS and conduct bibliometric and text mining analyses to characterize articles that refer to ecological complexity. Our analyses demonstrate that the study of complexity in ecology is a highly heterogeneous, global endeavor that is only weakly related to CSS. Current research trends are typically organized around basic theory, scaling, and macroecology. We leverage our review and the generalities identified in our analyses to suggest a more coherent and cohesive way forward in the study of complexity in ecology.

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.

Natural Exponential and Three-Dimensional Chaotic System

Existing chaotic system exhibits unpredictability and nonrepeatability in a deterministic nonlinear architecture, presented as a combination of definiteness and stochasticity. However, traditional two-dimensional chaotic systems cannot provide sufficient information in the dynamic motion and usually feature low sensitivity to initial system input, which makes them computationally prohibitive in accurate time series prediction and weak periodic component detection. Here, a natural exponential and three-dimensional chaotic system with higher sensitivity to initial system input conditions showing astonishing extensibility in time series prediction and image processing is proposed. The chaotic performance evaluated theoretically and experimentally by Poincare mapping, bifurcation diagram, phase space reconstruction, Lyapunov exponent, and correlation dimension provides a new perspective of nonlinear physical modeling and validation. The complexity, robustness, and consistency are studied by recursive and entropy analysis and comparison. The method improves the efficiency of time series prediction, nonlinear dynamics-related problem solving and expands the potential scope of multi-dimensional chaotic systems.

Experimental evidence of size-selective harvest and environmental stochasticity effects on population demography, fluctuations and non-linearity

Theory and analyses of fisheries data sets indicate that harvesting can alter population structure and destabilise non-linear processes, which increases population fluctuations. We conducted a factorial experiment on the population dynamics of Daphnia magna in relation to size-selective harvesting and stochasticity of food supply. Harvesting and stochasticity treatments both increased population fluctuations. Timeseries analysis indicated that fluctuations in control populations were non-linear, and non-linearity increased substantially in response to harvesting. Both harvesting and stochasticity induced population juvenescence, but harvesting did so via the depletion of adults, whereas stochasticity increased the abundance of juveniles. A fitted fisheries model indicated that harvesting shifted populations towards higher reproductive rates and larger-magnitude damped oscillations that amplify demographic noise. These findings provide experimental evidence that harvesting increases the non-linearity of population fluctuations and that both harvesting and stochasticity increase population variability and juvenescence.

A predictive timeline of wildlife population collapse

Contemporary rates of biodiversity decline emphasize the need for reliable ecological forecasting, but current methods vary in their ability to predict the declines of real-world populations. Acknowledging that stressor effects start at the individual level, and that it is the sum of these individual-level effects that drives populations to collapse, shifts the focus of predictive ecology away from using predominantly abundance data. Doing so opens new opportunities to develop predictive frameworks that utilize increasingly available multi-dimensional data, which have previously been overlooked for ecological forecasting. Here, we propose that stressed populations will exhibit a predictable sequence of observable changes through time: changes in individuals' behaviour will occur as the first sign of increasing stress, followed by changes in fitness-related morphological traits, shifts in the dynamics (for example, birth rates) of populations and finally abundance declines. We discuss how monitoring the sequential appearance of these signals may allow us to discern whether a population is increasingly at risk of collapse, or is adapting in the face of environmental change, providing a conceptual framework to develop new forecasting methods that combine multi-dimensional (for example, behaviour, morphology, life history and abundance) data.

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.

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.

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.

Rethinking the Prevalence and Relevance of Chaos in Ecology

Chaos was proposed in the 1970s as an alternative explanation for apparently noisy fluctuations in population size. Although readily demonstrated in models, the search for chaos in nature proved challenging and led many to conclude that chaos is either rare or nigh impossible to detect. However, in the intervening half-century, it has become clear that ecosystems are replete with the enabling conditions for chaos. Chaos has been repeatedly demonstrated under laboratory conditions and has been found in field data using updated detection methods. Together, these developments indicate that the apparent rarity of chaos was an artifact of data limitations and overreliance on low-dimensional population models. We invite readers to reevaluate the relevance of chaos in ecology, and we suggest that chaos is not as rare or undetectable as previously believed.

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.