Boosting biodiversity monitoring using smartphone-driven, rapidly accumulating community-sourced data

Comprehensive biodiversity data is crucial for ecosystem protection. The Biome mobile app, launched in Japan, efficiently gathers species observations from the public using species identification algorithms and gamification elements. The app has amassed >6 million observations since 2019. Nonetheless, community-sourced data may exhibit spatial and taxonomic biases. Species distribution models (SDMs) estimate species distribution while accommodating such bias. Here, we investigated the quality of Biome data and its impact on SDM performance. Species identification accuracy exceeds 95% for birds, reptiles, mammals, and amphibians, but seed plants, molluscs, and fishes scored below 90%. Our SDMs for 132 terrestrial plants and animals across Japan revealed that incorporating Biome data into traditional survey data improved accuracy. For endangered species, traditional survey data required >2000 records for accurate models (Boyce index ≥ 0.9), while blending the two data sources reduced this to around 300. The uniform coverage of urban-natural gradients by Biome data, compared to traditional data biased towards natural areas, may explain this improvement. Combining multiple data sources better estimates species distributions, aiding in protected area designation and ecosystem service assessment. Establishing a platform for accumulating community-sourced distribution data will contribute to conserving and monitoring natural ecosystems.

Evolutionary ecology of masting: mechanisms, models, and climate change

Many perennial plants show mast seeding, characterized by synchronous and highly variable reproduction across years. We propose a general model of masting, integrating proximate factors (environmental variation, weather cues, and resource budgets) with ultimate drivers (predator satiation and pollination efficiency). This general model shows how the relationships between masting and weather shape the diverse responses of species to climate warming, ranging from no change to lower interannual variation or reproductive failure. The role of environmental prediction as a masting driver is being reassessed; future studies need to estimate prediction accuracy and the benefits acquired. Since reproduction is central to plant adaptation to climate change, understanding how masting adapts to shifting environmental conditions is now a central question.

Duality between predictability and reconstructability in complex systems

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. We provide analytical calculations of the uncertainty coefficients for many different systems, including continuous deterministic systems, and describe a numerical procedure when exact calculations are intractable. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process. Finally, we provide evidence that predictability-reconstruction dualities may exist in dynamical processes on real networks close to criticality.

Using neural ordinary differential equations to predict complex ecological dynamics from population density data

Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modelling bias due to simplifying assumptions or unaccounted factors, limiting their predictive power. Neural ordinary differential equations (NODEs) have surged as a machine-learning algorithm that preserves the dynamic nature of the data (Chen et al. 2018 Adv. Neural Inf. Process. Syst.). Although preserving the dynamics in the data is an advantage, the question of how NODEs perform as a forecasting tool of ecological communities is unanswered. Here, we explore this question using simulated time series of competing species in a time-varying environment. We find that NODEs provide more precise forecasts than autoregressive integrated moving average (ARIMA) models. We also find that untuned NODEs have a similar forecasting accuracy to untuned long-short term memory neural networks and both are outperformed in accuracy and precision by empirical dynamical modelling . However, we also find NODEs generally outperform all other methods when evaluating with the interval score, which evaluates precision and accuracy in terms of prediction intervals rather than pointwise accuracy. We also discuss ways to improve the forecasting performance of NODEs. The power of a forecasting tool such as NODEs is that it can provide insights into population dynamics and should thus broaden the approaches to studying time series of ecological communities.

Enhancing Predictability Assessment: An Overview and Analysis of Predictability Measures for Time Series and Network Links

Driven by the variety of available measures intended to estimate predictability of diverse objects such as time series and network links, this paper presents a comprehensive overview of the existing literature in this domain. Our overview delves into predictability from two distinct perspectives: the intrinsic predictability, which represents a data property independent of the chosen forecasting model and serves as the highest achievable forecasting quality level, and the realized predictability, which represents a chosen quality metric for a specific pair of data and model. The reviewed measures are used to assess predictability across different objects, starting from time series (univariate, multivariate, and categorical) to network links. Through experiments, we establish a noticeable relationship between measures of realized and intrinsic predictability in both generated and real-world time series data (with the correlation coefficient being statistically significant at a 5% significance level). The discovered correlation in this research holds significant value for tasks related to evaluating time series complexity and their potential to be accurately predicted.

Combining multiple data sources with different biases in state-space models for population dynamics

The resolution at which animal populations can be modeled can be increased when multiple datasets corresponding to different life stages are available, allowing, for example, seasonal instead of annual descriptions of dynamics. However, the abundance estimates used for model fitting can have multiple sources of error, both random and systematic, namely bias. We focus here on the consequences of, and how to address, differing and unknown observation biases when fitting models.State-space models (SSMs) separate process variation and observation error, thus providing a framework to account for different and unknown estimate biases across multiple datasets. Here we study the effects on the inference of including or excluding bias parameters for a sequential life stage population dynamics SSM using a combination of theory, simulation experiments, and an empirical example.When the data, that is, abundance estimates, are unbiased, including bias parameters leads to increased imprecision compared to a model that correctly excludes bias parameters. But when observations are biased and no bias parameters are estimated, recruitment and survival processes are inaccurately estimated and estimates of process variance become biased high. These problems are substantially reduced by including bias parameters and fixing one of them at even an incorrect value. The primary inferential challenge is that models with bias parameters can show properties of being parameter redundant even when they are not in theory.Combining multiple datasets into a single analysis by using bias parameters to rescale data can offer significant improvements to inference and model diagnostics. Because their estimability in practice is dataset specific and will likely require more precise estimates than might be expected from ecological datasets, we outline some strategies for characterizing process uncertainty when it is confounded by bias parameters.

Quantifying the predictability of renewable energy data for improving power systems decision-making

Decision-making in the power systems domain often relies on predictions of renewable generation. While sophisticated forecasting methods have been developed to improve the accuracy of such predictions, their accuracy is limited by the inherent predictability of the data used. However, the predictability of time series data cannot be measured by existing prediction techniques. This important measure has been overlooked by researchers and practitioners in the power systems domain. In this paper, we systematically assess the suitability of various predictability measures for renewable generation time series data, revealing the best method and providing instructions for tuning it. Using real-world examples, we then illustrate how predictability could save end users and investors millions of dollars in the electricity sector.

The fitness value of ecological information in a variable world

Information processing is increasingly recognized as a fundamental component of life in variable environments, including the evolved use of environmental cues, biomolecular networks, and social learning. Despite this, ecology lacks a quantitative framework for understanding how population, community, and ecosystem dynamics depend on information processing. Here, we review the rationale and evidence for 'fitness value of information' (FVOI), and synthesize theoretical work in ecology, information theory, and probability behind this general mathematical framework. The FVOI quantifies how species' per capita population growth rates can depend on the use of information in their environment. FVOI is a breakthrough approach to linking information processing and ecological and evolutionary outcomes in a changing environment, addressing longstanding questions about how information mediates the effects of environmental change and species interactions.

Quantifying inherent predictability and spatial synchrony in the aphid vector Myzus persicae: field-scale patterns of abundance and regional forecasting error in the UK

BACKGROUND

Sugar beet is threatened by virus yellows, a disease complex vectored by aphids that reduces sugar content. We present an analysis of Myzus persicae population dynamics with and without neonicotinoid seed treatment. We use 6 years' yellow water trap and field-collected aphid data and two decades of 12.2 m suction-trap aphid migration data. We investigate both spatial synchrony and forecasting error to understand the structure and spatial scale of field counts and why forecasting aphid migrants lacks accuracy. Our aim is to derive statistical parameters to inform regionwide pest management strategies.

RESULTS

Spatial synchrony, indicating the coincident change in counts across the region over time, is rarely present and is best described as stochastic. Uniquely, early season field populations in 2019 did show spatial synchrony to 90 km compared to the overall average weekly correlation length of 23 km. However, 70% of the time series were spatially heterogenous, indicating patchy between-field dynamics. Field counts lacked the same seasonal trend and did not peak in the same week. Forecasts tended to under-predict mid-season log10 counts. A strongly negative correlation between forecasting error and the proportion of zeros was shown.

CONCLUSION

Field populations are unpredictable and stochastic, regardless of neonicotinoid seed treatment. This outcome presents a problem for decision-support that cannot usefully provide a single regionwide solution. Weighted permutation entropy inferred that M. persicae 12.2 m suction-trap time series had moderate to low intrinsic predictability. Early warning using a migration model tended to predict counts at lower levels than observed. © 2022 The Authors. Pest Management Science published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Progress and opportunities in advancing near-term forecasting of freshwater quality

Near-term freshwater forecasts, defined as sub-daily to decadal future predictions of a freshwater variable with quantified uncertainty, are urgently needed to improve water quality management as freshwater ecosystems exhibit greater variability due to global change. Shifting baselines in freshwater ecosystems due to land use and climate change prevent managers from relying on historical averages for predicting future conditions, necessitating near-term forecasts to mitigate freshwater risks to human health and safety (e.g., flash floods, harmful algal blooms) and ecosystem services (e.g., water-related recreation and tourism). To assess the current state of freshwater forecasting and identify opportunities for future progress, we synthesized freshwater forecasting papers published in the past 5 years. We found that freshwater forecasting is currently dominated by near-term forecasts of water quantity and that near-term water quality forecasts are fewer in number and in the early stages of development (i.e., non-operational) despite their potential as important preemptive decision support tools. We contend that more freshwater quality forecasts are critically needed and that near-term water quality forecasting is poised to make substantial advances based on examples of recent progress in forecasting methodology, workflows, and end-user engagement. For example, current water quality forecasting systems can predict water temperature, dissolved oxygen, and algal bloom/toxin events 5 days ahead with reasonable accuracy. Continued progress in freshwater quality forecasting will be greatly accelerated by adapting tools and approaches from freshwater quantity forecasting (e.g., machine learning modeling methods). In addition, future development of effective operational freshwater quality forecasts will require substantive engagement of end users throughout the forecast process, funding, and training opportunities. Looking ahead, near-term forecasting provides a hopeful future for freshwater management in the face of increased variability and risk due to global change, and we encourage the freshwater scientific community to incorporate forecasting approaches in water quality research and management.

On the forecastability of food insecurity

Food insecurity, defined as the lack of physical or economic access to safe, nutritious and sufficient food, remains one of the main challenges included in the 2030 Agenda for Sustainable Development. Near real-time data on the food insecurity situation collected by international organizations such as the World Food Programme can be crucial to monitor and forecast time trends of insufficient food consumption levels in countries at risk. Here, using food consumption observations in combination with secondary data on conflict, extreme weather events and economic shocks, we build a forecasting model based on gradient boosted regression trees to create predictions on the evolution of insufficient food consumption trends up to 30 days in to the future in 6 countries (Burkina Faso, Cameroon, Mali, Nigeria, Syria and Yemen). Results show that the number of available historical observations is a key element for the forecasting model performance. Among the 6 countries studied in this work, for those with the longest food insecurity time series, that is Syria and Yemen, the proposed forecasting model allows to forecast the prevalence of people with insufficient food consumption up to 30 days into the future with higher accuracy than a naive approach based on the last measured prevalence only. The framework developed in this work could provide decision makers with a tool to assess how the food insecurity situation will evolve in the near future in countries at risk. Results clearly point to the added value of continuous near real-time data collection at sub-national level.

Hydrological changes caused by the construction of dams and reservoirs: The CECP analysis

We investigated the influence of the construction of cascade dams and reservoirs on the predictability and complexity of the streamflow of the São Francisco River, Brazil, by using complexity entropy causality plane (CECP) in its standard and weighted form. We analyzed daily streamflow time series recorded in three fluviometric stations: São Francisco (upstream of cascade dams), Juazeiro (downstream of Sobradinho dam), and Pão de Açúcar station (downstream of Sobradinho and Xingó dams). By comparing the values of CECP information quantifiers (permutation entropy and statistical complexity) for the periods before and after the construction of Sobradinho (1979) and Xingó (1994) dams, we found that the reservoirs' operations changed the temporal variability of streamflow series toward the less predictable regime as indicated by higher entropy (lower complexity) values. Weighted CECP provides some finer details in the predictability of streamflow due to the inclusion of amplitude information in the probability distribution of ordinal patterns. The time evolution of streamflow predictability was analyzed by applying CECP in 2 year sliding windows that revealed the influence of the Paulo Alfonso complex (located between Sobradinho and Xingó dams), construction of which started in the 1950s and was identified through the increased streamflow entropy in the downstream Pão de Açúcar station. The other streamflow alteration unrelated to the construction of the two largest dams was identified in the upstream unimpacted São Francisco station, as an increase in the entropy around 1960s, indicating that some natural factors could also play a role in the decreased predictability of streamflow dynamics.

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.

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.

Precipitation predictability affects intra- and trans-generational plasticity and causes differential selection on root traits of Papaver rhoeas

Climate forecasts show that in many regions the temporal distribution of precipitation events will become less predictable. Root traits may play key roles in dealing with changes in precipitation predictability, but their functional plastic responses, including transgenerational processes, are scarcely known. We investigated root trait plasticity of Papaver rhoeas with respect to higher versus lower intra-seasonal and inter-seasonal precipitation predictability (i.e., the degree of temporal autocorrelation among precipitation events) during a four-year outdoor multi-generation experiment. We first tested how the simulated predictability regimes affected intra-generational plasticity of root traits and allocation strategies of the ancestors, and investigated the selective forces acting on them. Second, we exposed three descendant generations to the same predictability regime experienced by their mothers or to a different one. We then investigated whether high inter-generational predictability causes root trait differentiation, whether transgenerational root plasticity existed and whether it was affected by the different predictability treatments. We found that the number of secondary roots, root biomass and root allocation strategies of ancestors were affected by changes in precipitation predictability, in line with intra-generational plasticity. Lower predictability induced a root response, possibly reflecting a fast-acquisitive strategy that increases water absorbance from shallow soil layers. Ancestors' root traits were generally under selection, and the predictability treatments did neither affect the strength nor the direction of selection. Transgenerational effects were detected in root biomass and root weight ratio (RWR). In presence of lower predictability, descendants significantly reduced RWR compared to ancestors, leading to an increase in performance. This points to a change in root allocation in order to maintain or increase the descendants' fitness. Moreover, transgenerational plasticity existed in maximum rooting depth and root biomass, and the less predictable treatment promoted the lowest coefficient of variation among descendants' treatments in five out of six root traits. This shows that the level of maternal predictability determines the variation in the descendants' responses, and suggests that lower phenotypic plasticity evolves in less predictable environments. Overall, our findings show that roots are functional plastic traits that rapidly respond to differences in precipitation predictability, and that the plasticity and adaptation of root traits may crucially determine how climate change will affect plants.

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.

Decomposing predictability to identify dominant causal drivers in complex ecosystems

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

Prediction of Microcystis Occurrences and Analysis Using Machine Learning in High-Dimension, Low-Sample-Size and Imbalanced Water Quality Data

Machine learning, Deep learning, and water quality data have been used in recent years to predict the outbreak of harmful algae, especially Microcystis, and analyze outbreak causes. However, for various reasons, water quality data are often High-Dimension, Low-Sample- Size (HDLSS), meaning the sample size is lower than the number of dimensions. Moreover, imbalance problems may arise due to bias in the occurrence frequency of Microcystis. These problems make predicting the occurrence of Microcystis and analyzing its causes with machine learning difficult. In this study, a machine learning model that applies Feature Engineering (FE) and Feature Selection (FS) algorithms are used to predict outbreaks of Microcystis and analyze the outbreak factors from imbalanced HDLSS water quality data. The prediction performance was verified with binary classification to determine whether Microcystis would occur in the future by applying three machine learning models to four data patterns. The cause analysis of Microcystis occurrence was performed by visualizing the results of applying FE and FS. For the test data, the predictive performance of FE and FS methods was significantly better than that of the conventional method, with an accuracy of .108 points and an F-value of .691 points higher than the conventional method. A prediction performance increase was observed with a smaller model capacity. Data-driven analysis suggested that total nitrogen, chemical oxygen demand, chlorophyll-a, dissolved oxygen saturation, and water temperature are associated with Microcystis occurrences. The results also indicated that basic statistics of the water quality distribution (especially mean, standard deviation, and skewness) over a year, not the concentrations of water components, are related to the occurrence of Microcystis. These are new findings not found in previous studies and are expected to contribute significantly to future studies of algae. This study provides a method for analyzing water quality data with high-dimensionality and small samples, imbalance problems, or both.

MASTREE+: Time-series of plant reproductive effort from six continents

Significant gaps remain in understanding the response of plant reproduction to environmental change. This is partly because measuring reproduction in long-lived plants requires direct observation over many years and such datasets have rarely been made publicly available. Here we introduce MASTREE+, a data set that collates reproductive time-series data from across the globe and makes these data freely available to the community. MASTREE+ includes 73,828 georeferenced observations of annual reproduction (e.g. seed and fruit counts) in perennial plant populations worldwide. These observations consist of 5971 population-level time-series from 974 species in 66 countries. The mean and median time-series length is 12.4 and 10 years respectively, and the data set includes 1122 series that extend over at least two decades (≥20 years of observations). For a subset of well-studied species, MASTREE+ includes extensive replication of time-series across geographical and climatic gradients. Here we describe the open-access data set, available as a.csv file, and we introduce an associated web-based app for data exploration. MASTREE+ will provide the basis for improved understanding of the response of long-lived plant reproduction to environmental change. Additionally, MASTREE+ will enable investigation of the ecology and evolution of reproductive strategies in perennial plants, and the role of plant reproduction as a driver of ecosystem dynamics.

A roadmap towards predicting species interaction networks (across space and time)

Networks of species interactions underpin numerous ecosystem processes, but comprehensively sampling these interactions is difficult. Interactions intrinsically vary across space and time, and given the number of species that compose ecological communities, it can be tough to distinguish between a true negative (where two species never interact) from a false negative (where two species have not been observed interacting even though they actually do). Assessing the likelihood of interactions between species is an imperative for several fields of ecology. This means that to predict interactions between species-and to describe the structure, variation, and change of the ecological networks they form-we need to rely on modelling tools. Here, we provide a proof-of-concept, where we show how a simple neural network model makes accurate predictions about species interactions given limited data. We then assess the challenges and opportunities associated with improving interaction predictions, and provide a conceptual roadmap forward towards predictive models of ecological networks that is explicitly spatial and temporal. We conclude with a brief primer on the relevant methods and tools needed to start building these models, which we hope will guide this research programme forward. This article is part of the theme issue 'Infectious disease macroecology: parasite diversity and dynamics across the globe'.

Predictability of COVID-19 worldwide lethality using permutation-information theory quantifiers

This paper examines the predictability of COVID-19 worldwide lethality considering 43 countries. Based on the values inherent to Permutation entropy ( H s ) and Fisher information measure ( F s ), we apply the Shannon-Fisher causality plane (SFCP), which allows us to quantify the disorder an evaluate randomness present in the time series of daily death cases related to COVID-19 in each country. We also use Hs and Fs to rank the COVID-19 lethality in these countries based on the complexity hierarchy. Our results suggest that the most proactive countries implemented measures such as facemasks, social distancing, quarantine, massive population testing, and hygienic (sanitary) orientations to limit the impacts of COVID-19, which implied lower entropy (higher predictability) to the COVID-19 lethality. In contrast, the most reactive countries implementing these measures depicted higher entropy (lower predictability) to the COVID-19 lethality. Given this, our findings shed light that these preventive measures are efficient to combat the COVID-19 lethality.

Effects of intrinsic environmental predictability on intra-individual and intra-population variability of plant reproductive traits and eco-evolutionary consequences

BACKGROUND AND AIMS

It is widely accepted that changes in the environment affect mean trait expression, but little is known about how the environment shapes intra-individual and intra-population variance. Theory suggests that intra-individual variance might be plastic and under natural selection, rather than reflecting developmental noise, but evidence for this hypothesis is scarce. Here, we experimentally tested whether differences in intrinsic environmental predictability affect intra-individual and intra-population variability of different reproductive traits, and whether intra-individual variability is under selection.

METHODS

Under field conditions, we subjected Onobrychis viciifolia to more and less predictable precipitation over 4 generations and 4 years. We analysed effects on the coefficient of intra-individual variation (CVi-i) and the coefficient of intra-population variation (CVi-p), assessed whether the coefficients of intra-individual variation (CsVi-i) are under natural selection and tested for transgenerational responses (ancestor environmental effects on offspring).

KEY RESULTS

Less predictable precipitation led to higher CsVi-i and CsVi-p, consistent with plastic responses. The CsVi-i of all studied traits were under consistent stabilizing selection, and precipitation predictability affected the strength of selection and the location of the optimal CVi-i of a single trait. All CsVi-i differed from the optimal CVi-i and the maternal and offspring CsVi-i were positively correlated, showing that there was scope for change. Nevertheless, no consistent transgenerational effects were found in any of the three descendant generations, which contrasts with recent studies that detected rapid transgenerational responses in the trait means of different plant species. This suggests that changes in intra-individual variability take longer to evolve than changes in trait means, which may explain why high intra-individual variability is maintained, despite the stabilizing selection.

CONCLUSIONS

The results indicate that plastic changes of intra-individual variability are an important determinant of whether plants will be able to cope with changes in environmental predictability induced by the currently observed climatic change.

Detection of local mixing in time-series data using permutation entropy

Mixing of neighboring data points in a sequence is a common, but understudied, effect in physical experiments. This can occur in the measurement apparatus (if material from multiple time points is pulled into a measurement chamber simultaneously, for instance) or the system itself, e.g., via diffusion of isotopes in an ice sheet. We propose a model-free technique to detect this kind of local mixing in time-series data using an information-theoretic technique called permutation entropy. By varying the temporal resolution of the calculation and analyzing the patterns in the results, we can determine whether the data are mixed locally, and on what scale. This can be used by practitioners to choose appropriate lower bounds on scales at which to measure or report data. After validating this technique on several synthetic examples, we demonstrate its effectiveness on data from a chemistry experiment, methane records from Mauna Loa, and an Antarctic ice core.

Systematic bias in studies of consumer functional responses

Functional responses are a cornerstone to our understanding of consumer-resource interactions, so how to best describe them using models has been actively debated. Here we focus on the consumer dependence of functional responses to evidence systematic bias in the statistical comparison of functional-response models and the estimation of their parameters. Both forms of bias are universal to nonlinear models (irrespective of consumer dependence) and are rooted in a lack of sufficient replication. Using a large compilation of published datasets, we show that - due to the prevalence of low sample size studies - neither the overall frequency by which alternative models achieve top rank nor the frequency distribution of parameter point estimates should be treated as providing insight into the general form or central tendency of consumer interference. We call for renewed clarity in the varied purposes that motivate the study of functional responses, purposes that can compete with each other in dictating the design, analysis and interpretation of functional-response experiments.

What processes must we understand to forecast regional-scale population dynamics?

An urgent challenge facing biologists is predicting the regional-scale population dynamics of species facing environmental change. Biologists suggest that we must move beyond predictions based on phenomenological models and instead base predictions on underlying processes. For example, population biologists, evolutionary biologists, community ecologists and ecophysiologists all argue that the respective processes they study are essential. Must our models include processes from all of these fields? We argue that answering this critical question is ultimately an empirical exercise requiring a substantial amount of data that have not been integrated for any system to date. To motivate and facilitate the necessary data collection and integration, we first review the potential importance of each mechanism for skilful prediction. We then develop a conceptual framework based on reaction norms, and propose a hierarchical Bayesian statistical framework to integrate processes affecting reaction norms at different scales. The ambitious research programme we advocate is rapidly becoming feasible due to novel collaborations, datasets and analytical tools.

Predictability limit of partially observed systems

Applications from finance to epidemiology and cyber-security require accurate forecasts of dynamic phenomena, which are often only partially observed. We demonstrate that a system's predictability degrades as a function of temporal sampling, regardless of the adopted forecasting model. We quantify the loss of predictability due to sampling, and show that it cannot be recovered by using external signals. We validate the generality of our theoretical findings in real-world partially observed systems representing infectious disease outbreaks, online discussions, and software development projects. On a variety of prediction tasks-forecasting new infections, the popularity of topics in online discussions, or interest in cryptocurrency projects-predictability irrecoverably decays as a function of sampling, unveiling predictability limits in partially observed systems.

From sequence to information

Today massive amounts of sequenced metagenomic and metatranscriptomic data from different ecological niches and environmental locations are available. Scientific progress depends critically on methods that allow extracting useful information from the various types of sequence data. Here, we will first discuss types of information contained in the various flavours of biological sequence data, and how this information can be interpreted to increase our scientific knowledge and understanding. We argue that a mechanistic understanding of biological systems analysed from different perspectives is required to consistently interpret experimental observations, and that this understanding is greatly facilitated by the generation and analysis of dynamic mathematical models. We conclude that, in order to construct mathematical models and to test mechanistic hypotheses, time-series data are of critical importance. We review diverse techniques to analyse time-series data and discuss various approaches by which time-series of biological sequence data have been successfully used to derive and test mechanistic hypotheses. Analysing the bottlenecks of current strategies in the extraction of knowledge and understanding from data, we conclude that combined experimental and theoretical efforts should be implemented as early as possible during the planning phase of individual experiments and scientific research projects.

This article is part of the theme issue ‘Integrative research perspectives on marine conservation’.

Advances in forecasting harmful algal blooms using machine learning models: A case study with Planktothrix rubescens in Lake Geneva

The development of anthropic activities during the 20th century increased the nutrient fluxes in freshwater ecosystems, leading to the eutrophication phenomenon that most often promotes harmful algal blooms (HABs). Recent years have witnessed the regular and massive development of some filamentous algae or cyanobacteria in Lake Geneva. Consequently, important blooms could result in detrimental impacts on economic issues and human health. In this study, we tried to lay the foundation of an HAB forecast model to help scientists and local stakeholders with the present and future management of this peri-alpine lake. Our forecast strategy was based on pairing two machine learning models with a long-term database built over the past 34 years. We created HAB groups via a K-means model. Then, we introduced different lag times in the input of a random forest (RF) model, using a sliding window. Finally, we used a high-frequency dataset to compare the natural mechanisms with numerical interaction using individual conditional expectation plots. We demonstrate that some HAB events can be forecasted over a year scale. The information contained in the concentration data of the cyanobacteria was synthesized in the form of four intensity groups that directly depend on the P. rubescens concentration. The categorical transformation of these data allowed us to obtain a forecast with correlation coefficients that stayed above a threshold of 0.5 until one year for the counting cells and two years for the biovolume data. Moreover, we found that the RF model predicted the best P. rubescens abundance for water temperatures around 14°C. This result is consistent with the biological processes of the toxic cyanobacterium. In this study, we found that the coupling between K-means and RF models could help in forecasting the development of the bloom-forming P. rubescens in Lake Geneva. This methodology could create a numerical decision support tool, which should be a significant advantage for lake managers.

High predictability of direct competition between marine diatoms under different temperatures and nutrient states

The distribution of marine phytoplankton will shift alongside changes in marine environments, leading to altered species frequencies and community composition. An understanding of the response of mixed populations to abiotic changes is required to adequately predict how environmental change may affect the future composition of phytoplankton communities. This study investigated the growth and competitive ability of two marine diatoms, Phaeodactylum tricornutum and Thalassiosira pseudonana, along a temperature gradient (9-35°C) spanning the thermal niches of both species under both high-nitrogen nutrient-replete and low-nitrogen nutrient-limited conditions. Across this temperature gradient, the competitive outcome under both nutrient conditions at any assay temperature, and the critical temperature at which competitive advantage shifted from one species to the other, was well predicted by the temperature dependencies of the growth rates of the two species measured in monocultures. The temperature at which the competitive advantage switched from P. tricornutum to T. pseudonana increased from 18.8°C under replete conditions to 25.3°C under nutrient-limited conditions. Thus, P. tricornutum was a better competitor over a wider temperature range in a low N environment. Being able to determine the competitive outcomes from physiological responses of single species to environmental changes has the potential to significantly improve the predictive power of phytoplankton spatial distribution and community composition models.

Using curvature to select the time lag for delay reconstruction

We propose a curvature-based approach for choosing a good value for the time-delay parameter τ in delay reconstructions. The idea is based on the effects of the delay on the geometry of the reconstructions. If the delay is too small, the reconstructed dynamics are flattened along the main diagonal of the embedding space; too-large delays, on the other hand, can overfold the dynamics. Calculating the curvature of a two-dimensional delay reconstruction is an effective way to identify these extremes and to find a middle ground between them: both the sharp reversals at the extremes of an insufficiently unfolded reconstruction and the bends in an overfolded one create spikes in the curvature. We operationalize this observation by computing the mean Menger curvature of a trajectory segment on 2D reconstructions as a function of time delay. We show that the minimum of these values gives an effective heuristic for choosing the time delay. In addition, we show that this curvature-based heuristic is useful even in cases where the customary approach, which uses average mutual information, fails-e.g., noisy or filtered data.

Wavelet entropy-based evaluation of intrinsic predictability of time series

Intrinsic predictability is imperative to quantify inherent information contained in a time series and assists in evaluating the performance of different forecasting methods to get the best possible prediction. Model forecasting performance is the measure of the probability of success. Nevertheless, model performance or the model does not provide understanding for improvement in prediction. Intuitively, intrinsic predictability delivers the highest level of predictability for a time series and informative in unfolding whether the system is unpredictable or the chosen model is a poor choice. We introduce a novel measure, the Wavelet Entropy Energy Measure (WEEM), based on wavelet transformation and information entropy for quantification of intrinsic predictability of time series. To investigate the efficiency and reliability of the proposed measure, model forecast performance was evaluated via a wavelet networks approach. The proposed measure uses the wavelet energy distribution of a time series at different scales and compares it with the wavelet energy distribution of white noise to quantify a time series as deterministic or random. We test the WEEM using a wide variety of time series ranging from deterministic, non-stationary, and ones contaminated with white noise with different noise-signal ratios. Furthermore, a relationship is developed between the WEEM and Nash-Sutcliffe Efficiency, one of the widely known measures of forecast performance. The reliability of WEEM is demonstrated by exploring the relationship to logistic map and real-world data.

Time Series Complexities and Their Relationship to Forecasting Performance

Entropy is a key concept in the characterization of uncertainty for any given signal, and its extensions such as Spectral Entropy and Permutation Entropy. They have been used to measure the complexity of time series. However, these measures are subject to the discretization employed to study the states of the system, and identifying the relationship between complexity measures and the expected performance of the four selected forecasting methods that participate in the M4 Competition. This relationship allows the decision, in advance, of which algorithm is adequate. Therefore, in this paper, we found the relationships between entropy-based complexity framework and the forecasting error of four selected methods (Smyl, Theta, ARIMA, and ETS). Moreover, we present a framework extension based on the Emergence, Self-Organization, and Complexity paradigm. The experimentation with both synthetic and M4 Competition time series show that the feature space induced by complexities, visually constrains the forecasting method performance to specific regions; where the logarithm of its metric error is poorer, the Complexity based on the emergence and self-organization is maximal.

Decreased Precipitation Predictability Negatively Affects Population Growth through Differences in Adult Survival

Global climate change is leading to decreased climatic predictability. Theoretical work indicates that changes in the climate's intrinsic predictability will affect population dynamics and extinction, but experimental evidence is scarce. Here, we experimentally tested whether differences in intrinsic precipitation predictability affect population dynamics of the European common lizard (Zootoca vivipara) by simulating more predictable (MP) and less predictable (LP) precipitation in 12 seminatural populations over 3 years and measuring different vital rates. A seasonal age-structured matrix model was parametrized to assess treatment effects on vital rates and asymptotic population growth (λ). There was a nonsignificant trend for survival being higher in MP than in LP precipitation, and no differences existed in reproductive rates. Small nonsignificant survival differences in adults explained changes in λ, and survival differences among age classes were in line with predictions from cohort resonance. As a result, λ was significantly higher in MP than in LP precipitation. This experimentally shows that small effects have major consequences on λ, that forecasted decreases in precipitation predictability are likely to exacerbate the current rate of population decline and extinction, and that stage-structured matrix models are required to unravel the aftermath of climate change.

Rapid and positive responses of plants to lower precipitation predictability

Current climate change is characterized by an increase in weather variability, which includes altered means, variance and predictability of weather parameters, and which may affect an organism's ecology and evolution. Few studies have experimentally manipulated the variability of weather parameters, and very little is known about the effects of changes in the intrinsic predictability of weather parameters on living organisms. Here, we experimentally tested the effects of differences in intrinsic precipitation-predictability on two herbaceous plants (Onobrychis viciifolia and Papaver rhoeas). Lower precipitation-predictability led to phenological advance and to an increase in reproductive success, and population growth. Both species exhibited rapid transgenerational responses in phenology and fitness-related traits across four generations that mitigated most effects of precipitation-predictability on fitness proxies of ancestors. Transgenerational responses appeared to be the result of changes in phenotypic plasticity rather than local adaptation. They mainly existed with respect to conditions prevailing during early, but not during late growth, suggesting that responses to differences in predictability during late growth might be more difficult. The results show that lower short-term predictability of precipitation positively affected fitness, rapid transgenerational responses existed and different time scales of predictability (short-term, seasonal and transgenerational predictability) may affect organisms differently. This shows that the time scale of predictability should be considered in evolutionary and ecological theories, and in assessments of the consequences of climate change.

An information-theoretic approach to extracting climate signals from deep polar ice cores

Paleoclimate records are rich sources of information about the past history of the Earth system. Information theory provides a new means for studying these records. We demonstrate that weighted permutation entropy of water-isotope data from the West Antarctica Ice Sheet (WAIS) Divide ice core reveals meaningful climate signals in this record. We find that this measure correlates with accumulation (meters of ice equivalent per year) and may record the influence of geothermal heating effects in the deepest parts of the core. Dansgaard-Oeschger and Antarctic Isotope Maxima events, however, do not appear to leave strong signatures in the information record, suggesting that these abrupt warming events may actually be predictable features of the climate's dynamics. While the potential power of information theory in paleoclimatology is significant, the associated methods require well-dated and high-resolution data. The WAIS Divide core is the first paleoclimate record that can support this kind of analysis. As more high-resolution records become available, information theory could become a powerful forensic tool in paleoclimate science.

Complexity and entropy representation for machine component diagnostics

The Complexity-entropy causality plane (CECP) is a parsimonious representation space for time series. It has only two dimensions: normalized permutation entropy (HS) and Jensen-Shannon complexity (CJS) of a time series. This two-dimensional representation allows for detection of slow or rapid drifts in the condition of mechanical components monitored through sensor measurements. The CECP representation can be used for both predictive analytics and visual monitoring of changes in component condition. This method requires minimal pre-processing of raw signals. Furthermore, it is insensitive to noise, stationarity, and trends. These desirable properties make CECP a good candidate for machine condition monitoring and fault diagnostics. In this work we study the effectiveness of CECP on three rotary component condition assessment applications. We use CECP representation of vibration signals to differentiate various machine component health conditions for rotary machine components, namely roller bearing and gears. The results confirm that the CECP representation is able to detect, with high accuracy, changes in underlying dynamics of machine component degradation states. From class separability perspective, the CECP representation is able to generate linearly separable classes for the classification of different fault states. This classification performance improves with increasing signal length. For signal length of 16,384 data points, the fault classification accuracy varies from 90% to 100% for bearing applications, and from 85% to 100% for gear applications. We observed that the optimum parameter for CECP representatino depends on the application. For bearing applications we found that embedding dimension D = 4, 5, 6, and embedding delay τ = 1, 2, 3 are suitable for good fault classification. For gear applications we find that embedding dimension D = 4, 5, and embedding delay τ = 1, 5 are suitable for fault classification.