Probing the limits of predictability: data assimilation of chaotic dynamics in complex food webs

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.

Near-term phytoplankton forecasts reveal the effects of model time step and forecast horizon on predictability

As climate and land use increase the variability of many ecosystems, forecasts of ecological variables are needed to inform management and use of ecosystem services. In particular, forecasts of phytoplankton would be especially useful for drinking water management, as phytoplankton populations are exhibiting greater fluctuations due to human activities. While phytoplankton forecasts are increasing in number, many questions remain regarding the optimal model time step (the temporal frequency of the forecast model output), time horizon (the length of time into the future a prediction is made) for maximizing forecast performance, as well as what factors contribute to uncertainty in forecasts and their scalability among sites. To answer these questions, we developed near-term, iterative forecasts of phytoplankton 1-14 days into the future using forecast models with three different time steps (daily, weekly, fortnightly), that included a full uncertainty partitioning analysis at two drinking water reservoirs. We found that forecast accuracy varies with model time step and forecast horizon, and that forecast models can outperform null estimates under most conditions. Weekly and fortnightly forecasts consistently outperformed daily forecasts at 7-day and 14-day horizons, a trend that increased up to the 14-day forecast horizon. Importantly, our work suggests that forecast accuracy can be increased by matching the forecast model time step to the forecast horizon for which predictions are needed. We found that model process uncertainty was the primary source of uncertainty in our phytoplankton forecasts over the forecast period, but parameter uncertainty increased during phytoplankton blooms and when scaling the forecast model to a new site. Overall, our scalability analysis shows promising results that simple models can be transferred to produce forecasts at additional sites. Altogether, our study advances our understanding of how forecast model time step and forecast horizon influence the forecastability of phytoplankton dynamics in aquatic systems and adds to the growing body of work regarding the predictability of ecological systems broadly.

Using near-term forecasts and uncertainty partitioning to inform prediction of oligotrophic lake cyanobacterial density

Near-term ecological forecasts provide resource managers advance notice of changes in ecosystem services, such as fisheries stocks, timber yields, or water quality. Importantly, ecological forecasts can identify where there is uncertainty in the forecasting system, which is necessary to improve forecast skill and guide interpretation of forecast results. Uncertainty partitioning identifies the relative contributions to total forecast variance introduced by different sources, including specification of the model structure, errors in driver data, and estimation of current states (initial conditions). Uncertainty partitioning could be particularly useful in improving forecasts of highly variable cyanobacterial densities, which are difficult to predict and present a persistent challenge for lake managers. As cyanobacteria can produce toxic and unsightly surface scums, advance warning when cyanobacterial densities are increasing could help managers mitigate water quality issues. Here, we fit 13 Bayesian state-space models to evaluate different hypotheses about cyanobacterial densities in a low nutrient lake that experiences sporadic surface scums of the toxin-producing cyanobacterium, Gloeotrichia echinulata. We used data from several summers of weekly cyanobacteria samples to identify dominant sources of uncertainty for near-term (1- to 4-week) forecasts of G. echinulata densities. Water temperature was an important predictor of cyanobacterial densities during model fitting and at the 4-week forecast horizon. However, no physical covariates improved model performance over a simple model including the previous week's densities in 1-week-ahead forecasts. Even the best fit models exhibited large variance in forecasted cyanobacterial densities and did not capture rare peak occurrences, indicating that significant explanatory variables when fitting models to historical data are not always effective for forecasting. Uncertainty partitioning revealed that model process specification and initial conditions dominated forecast uncertainty. These findings indicate that long-term studies of different cyanobacterial life stages and movement in the water column as well as measurements of drivers relevant to different life stages could improve model process representation of cyanobacteria abundance. In addition, improved observation protocols could better define initial conditions and reduce spatial misalignment of environmental data and cyanobacteria observations. Our results emphasize the importance of ecological forecasting principles and uncertainty partitioning to refine and understand predictive capacity across ecosystems.

Mathematical analysis of laboratory microbial experiments demonstrating deterministic chaotic dynamics

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

Atmospheric Rivers and Precipitation in the Middle East and North Africa (MENA)

This study investigates the historical climatology and future projected change of atmospheric rivers (ARs) and precipitation for the Middle East and North Africa (MENA) region. We use a suite of models from the Coupled Model Intercomparison Project Phase 5 (CMIP5, historical and RCP8.5 scenarios) and other observations to estimate AR frequency and mean daily precipitation. Despite its arid-to-semi-arid climate, parts of the MENA region experience strong ARs, which contribute a large fraction of the annual precipitation, such as in the mountainous areas of Turkey and Iran. This study shows that by the end of this century, AR frequency is projected to increase (~20–40%) for the North Africa and Mediterranean areas (including any region with higher latitudes than 35 N). However, for these regions, mean daily precipitation (i.e., regardless of the presence of ARs) is projected to decrease (~15–30%). For the rest of the MENA region, including the Arabian Peninsula and the Horn of Africa, minor changes in AR frequency (±10%) are expected, yet mean precipitation is projected to increase (~50%) for these regions. Overall, the projected sign of change in AR frequency is opposite to the projected sign of change in mean daily precipitation for most areas within the MENA region.

Forecasting unprecedented ecological fluctuations

Forecasting 'Black Swan' events in ecosystems is an important but challenging task. Many ecosystems display aperiodic fluctuations in species abundance spanning orders of magnitude in scale, which have vast environmental and economic impact. Empirical evidence and theoretical analyses suggest that these dynamics are in a regime where system nonlinearities limit accurate forecasting of unprecedented events due to poor extrapolation of historical data to unsampled states. Leveraging increasingly available long-term high-frequency ecological tracking data, we analyze multiple natural and experimental ecosystems (marine plankton, intertidal mollusks, and deciduous forest), and recover hidden linearity embedded in universal 'scaling laws' of species dynamics. We then develop a method using these scaling laws to reduce data dependence in ecological forecasting and accurately predict extreme events beyond the span of historical observations in diverse ecosystems.

Neutral competition boosts cycles and chaos in simulated food webs

Similarity of competitors has been proposed to facilitate coexistence of species because it slows down competitive exclusion, thus making it easier for equalizing mechanisms to maintain diverse communities. On the other hand, previous studies suggest that chaotic ecosystems can have a higher biodiversity. Here, we link these two previously unrelated findings, by analysing the dynamics of food web models. We show that near-neutrality of competition of prey, in the presence of predators, increases the chance of developing chaotic dynamics. Moreover, we confirm that chaotic dynamics correlate with a higher biodiversity.

Forecasting semi-arid biome shifts in the Anthropocene

Shrub encroachment, forest decline and wildfires have caused large-scale changes in semi-arid vegetation over the past 50 years. Climate is a primary determinant of plant growth in semi-arid ecosystems, yet it remains difficult to forecast large-scale vegetation shifts (i.e. biome shifts) in response to climate change. We highlight recent advances from four conceptual perspectives that are improving forecasts of semi-arid biome shifts. Moving from small to large scales, first, tree-level models that simulate the carbon costs of drought-induced plant hydraulic failure are improving predictions of delayed-mortality responses to drought. Second, tracer-informed water flow models are improving predictions of species coexistence as a function of climate. Third, new applications of ecohydrological models are beginning to simulate small-scale water movement processes at large scales. Fourth, remotely-sensed measurements of plant traits such as relative canopy moisture are providing early-warning signals that predict forest mortality more than a year in advance. We suggest that a community of researchers using modeling approaches (e.g. machine learning) that can integrate these perspectives will rapidly improve forecasts of semi-arid biome shifts. Better forecasts can be expected to help prevent catastrophic changes in vegetation states by identifying improved monitoring approaches and by prioritizing high-risk areas for management.

Parasite associations predict infection risk: incorporating co-infections in predictive models for neglected tropical diseases

BACKGROUND

Schistosomiasis and infection by soil-transmitted helminths are some of the world's most prevalent neglected tropical diseases. Infection by more than one parasite (co-infection) is common and can contribute to clinical morbidity in children. Geostatistical analyses of parasite infection data are key for developing mass drug administration strategies, yet most methods ignore co-infections when estimating risk. Infection status for multiple parasites can act as a useful proxy for data-poor individual-level or environmental risk factors while avoiding regression dilution bias. Conditional random fields (CRF) is a multivariate graphical network method that opens new doors in parasite risk mapping by (i) predicting co-infections with high accuracy; (ii) isolating associations among parasites; and (iii) quantifying how these associations change across landscapes.

METHODS

We built a spatial CRF to estimate infection risks for Ascaris lumbricoides, Trichuris trichiura, hookworms (Ancylostoma duodenale and Necator americanus) and Schistosoma mansoni using data from a national survey of Rwandan schoolchildren. We used an ensemble learning approach to generate spatial predictions by simulating from the CRF's posterior distribution with a multivariate boosted regression tree that captured non-linear relationships between predictors and covariance in infection risks. This CRF ensemble was compared against single parasite gradient boosted machines to assess each model's performance and prediction uncertainty.

RESULTS

Parasite co-infections were common, with 19.57% of children infected with at least two parasites. The CRF ensemble achieved higher predictive power than single-parasite models by improving estimates of co-infection prevalence at the individual level and classifying schools into World Health Organization treatment categories with greater accuracy. The CRF uncovered important environmental and demographic predictors of parasite infection probabilities. Yet even after capturing demographic and environmental risk factors, the presences or absences of other parasites were strong predictors of individual-level infection risk. Spatial predictions delineated high-risk regions in need of anthelminthic treatment interventions, including areas with higher than expected co-infection prevalence.

CONCLUSIONS

Monitoring studies routinely screen for multiple parasites, yet statistical models generally ignore this multivariate data when assessing risk factors and designing treatment guidelines. Multivariate approaches can be instrumental in the global effort to reduce and eventually eliminate neglected helminth infections in developing countries.

Perspective: Advancing the research agenda for improving understanding of cyanobacteria in a future of global change

Harmful cyanobacterial blooms (=cyanoHABs) are an increasing feature of many waterbodies throughout the world. Many bloom-forming species produce toxins, making them of particular concern for drinking water supplies, recreation and fisheries in waterbodies along the freshwater to marine continuum. Global changes resulting from human impacts, such as climate change, over-enrichment and hydrological alterations of waterways, are major drivers of cyanoHAB proliferation and persistence. This review advocates that to better predict and manage cyanoHABs in a changing world, researchers need to leverage studies undertaken to date, but adopt a more complex and definitive suite of experiments, observations, and models which can effectively capture the temporal scales of processes driven by eutrophication and a changing climate. Better integration of laboratory culture and field experiments, as well as whole system and multiple-system studies are needed to improve confidence in models predicting impacts of climate change and anthropogenic over-enrichment and hydrological modifications. Recent studies examining adaptation of species and strains to long-term perturbations, e.g. temperature and carbon dioxide (CO₂) levels, as well as incorporating multi-species and multi-stressor approaches emphasize the limitations of approaches focused on single stressors and individual species. There are also emerging species of concern, such as toxic benthic cyanobacteria, for which the effects of global change are less well understood, and require more detailed study. This review provides approaches and examples of studies tackling the challenging issue of understanding how global changes will affect cyanoHABs, and identifies critical information needs for effective prediction and management.

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

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

Chaotic parameters extracted from fluorescence spectra to quantify sheep cheese whey in natural bodies of water

Sheep cheese whey (SCW) is a by-product from the dairy industry, and due to its composition, it is very hazardous for natural bodies of water. However, illegal discharges of this product have been commonly reported in watercourses and reservoirs. To prevent this type of actions, a simple and affordable sensor has been designed and validated using diverse water samples from different sources containing SCW, such as water from two Spanish reservoirs and two Spanish rivers located in the province of Madrid. Using these waters, different SCW solutions (lower than 20% in weight) have been prepared and measured. The equipment used to sense the samples is based on combining fluorescence measurements, obtained with light emitting diodes (LEDs), and algorithms which rely on chaotic parameters. Every sample was measured by six different types of LEDs possessing distinct emission wavelengths (blue, orange, green, pink, white, and UV), leading to 1786 fluorescence spectra that were employed during the modeling phase. After the mathematical analysis, the dataset that generates the best statistical results was from the blue LED. This approach was dually validated via leave-one-out cross-validation as well as externally validation, and the results were very promising (error around 6.5% and 8% quantification error, respectively). Additionally, it is important to note that the sensor used has been designed and developed by a 3D printer and has the potential of being applied in situ for real-time and cost-effective analysis of natural bodies of water.

Projecting groundwater storage changes in California's Central Valley

Accurate and detailed knowledge of California’s groundwater is of paramount importance for statewide water resources planning and management, and to sustain a multi-billion-dollar agriculture industry during prolonged droughts. In this study, we use water supply and demand information from California’s Department of Water Resources to develop an aggregate groundwater storage model for California’s Central Valley. The model is evaluated against 34 years of historic estimates of changes in groundwater storage derived from the United States Geological Survey’s Central Valley Hydrologic Model (USGS CVHM) and NASA’s Gravity Recovery and Climate Experiment (NASA GRACE) satellites. The calibrated model is then applied to predict future changes in groundwater storage for the years 2015–2050 under various precipitation scenarios from downscaled climate projections. We also discuss and project potential management strategies across different annual supply and demand variables and how they affect changes in groundwater storage. All simulations support the need for collective statewide management intervention to prevent continued depletion of groundwater availability.