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  1. Free, publicly-accessible full text available June 1, 2023
  2. Abstract Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated from available observations. Since observational data are frequently sampled with noise, it is possible that noise can corrupt the state-space representation degrading analytical performance. Here, we evaluate the synthesis of empirical mode decomposition with empirical dynamic modeling, which we term empirical mode modeling, to increase the information content of state-space representations in the presence of noise. Evaluation of a mathematical, and, an ecologically important geophysical application across three differentmore »state-space representations suggests that empirical mode modeling may be a useful technique for data-driven, model-free, state-space analysis in the presence of noise.« less
    Free, publicly-accessible full text available May 1, 2023
  3. Stephens, Greg J (Ed.)
    Behavioral phenotyping of model organisms has played an important role in unravelling the complexities of animal behavior. Techniques for classifying behavior often rely on easily identified changes in posture and motion. However, such approaches are likely to miss complex behaviors that cannot be readily distinguished by eye (e.g., behaviors produced by high dimensional dynamics). To explore this issue, we focus on the model organism Caenorhabditis elegans , where behaviors have been extensively recorded and classified. Using a dynamical systems lens, we identify high dimensional, nonlinear causal relationships between four basic shapes that describe worm motion (eigenmodes, also called “eigenworms”). Wemore »find relationships between all pairs of eigenmodes, but the timescales of the interactions vary between pairs and across individuals. Using these varying timescales, we create “interaction profiles” to represent an individual’s behavioral dynamics. As desired, these profiles are able to distinguish well-known behavioral states: i.e., the profiles for foraging individuals are distinct from those of individuals exhibiting an escape response. More importantly, we find that interaction profiles can distinguish high dimensional behaviors among divergent mutant strains that were previously classified as phenotypically similar. Specifically, we find it is able to detect phenotypic behavioral differences not previously identified in strains related to dysfunction of hermaphrodite-specific neurons.« less
  4. Doi, Hideyuki (Ed.)
    A central tenant of the Comprehensive Everglades Restoration Plan (CERP) is nutrient reduction to levels supportive of ecosystem health. A particular focus is phosphorus. We examine links between agricultural production and phosphorus concentration in the Everglades headwaters: Kissimmee River basin and Lake Okeechobee, considered an important source of water for restoration efforts. Over a span of 47 years we find strong correspondence between milk production in Florida and total phosphate in the lake, and, over the last decade, evidence that phosphorus concentrations in the lake water column may have initiated a long-anticipated decline.
  5. Experiments and models suggest that climate affects mosquito-borne disease transmission. However, disease transmission involves complex nonlinear interactions between climate and population dynamics, which makes detecting climate drivers at the population level challenging. By analysing incidence data, estimated susceptible population size, and climate data with methods based on nonlinear time series analysis (collectively referred to as empirical dynamic modelling), we identified drivers and their interactive effects on dengue dynamics in San Juan, Puerto Rico. Climatic forcing arose only when susceptible availability was high: temperature and rainfall had net positive and negative effects respectively. By capturing mechanistic, nonlinear and context-dependent effects ofmore »population susceptibility, temperature and rainfall on dengue transmission empirically, our model improves forecast skill over recent, state-of-the-art models for dengue incidence. Together, these results provide empirical evidence that the interdependence of host population susceptibility and climate drives dengue dynamics in a nonlinear and complex, yet predictable way.« less
  6. Gilestro, Giorgio F (Ed.)
    Automated analysis of video can now generate extensive time series of pose and motion in freely-moving organisms. This requires new quantitative tools to characterise behavioural dynamics. For the model roundworm Caenorhabditis elegans , body pose can be accurately quantified from video as coordinates in a single low-dimensional space. We focus on this well-established case as an illustrative example and propose a method to reveal subtle variations in behaviour at high time resolution. Our data-driven method, based on empirical dynamic modeling, quantifies behavioural change as prediction error with respect to a time-delay-embedded ‘attractor’ of behavioural dynamics. Because this attractor is constructedmore »from a user-specified reference data set, the approach can be tailored to specific behaviours of interest at the individual or group level. We validate the approach by detecting small changes in the movement dynamics of C. elegans at the initiation and completion of delta turns. We then examine an escape response initiated by an aversive stimulus and find that the method can track return to baseline behaviour in individual worms and reveal variations in the escape response between worms. We suggest that this general approach—defining dynamic behaviours using reference attractors and quantifying dynamic changes using prediction error—may be of broad interest and relevance to behavioural researchers working with video-derived time series.« less
  7. Small pelagic fish support some of the largest fisheries globally, yet there is an ongoing debate about the magnitude of the impacts of environmental processes and fishing activities on target species. We use a nonparametric, nonlinear approach to quantify these effects on the Pacific sardine (Sardinops sagax) in the Gulf of California. We show that the effect of fishing pressure and environmental variability are comparable. Furthermore, when predicting total catches, the best models account for both drivers. By using empirical dynamic programming with average environmental conditions, we calculated optimal policies to ensure long-term sustainable fisheries. The first policy, the equilibriummore »maximum sustainable yield, suggests that the fishery could sustain an annual catch of ∼2.16 × 10 5 tonnes. The second policy with dynamic optimal effort, reveals that the effort from 2 to 4 years ago impacts the current maximum sustainable effort. Consecutive years of high effort require a reduction to let the stock recover. Our work highlights a new framework that embraces the complex processes that drive fisheries population dynamics yet produces simple and robust advice to ensure long-term sustainable fisheries.« less
  8. null (Ed.)
    How can social and health researchers study complex dynamic systems that function in nonlinear and even chaotic ways? Common methods, such as experiments and equation-based models, may be ill-suited to this task. To address the limitations of existing methods and offer nonparametric tools for characterizing and testing causality in nonlinear dynamic systems, we introduce the edm command in Stata. This command implements three key empirical dynamic modeling (EDM) methods for time series and panel data: 1) simplex projection, which characterizes the dimensionality of a system and the degree to which it appears to function deterministically; 2) S-maps, which quantify themore »degree of nonlinearity in a system; and 3) convergent cross-mapping, which offers a nonparametric approach to modeling causal effects. We illustrate these methods using simulated data on daily Chicago temperature and crime, showing an effect of temperature on crime but not the reverse. We conclude by discussing how EDM allows checking the assumptions of traditional model-based methods, such as residual autocorrelation tests, and we advocate for EDM because it does not assume linearity, stability, or equilibrium.« less
  9. Belgrano, Andrea (Ed.)
    We found a startling correlation (Pearson ρ > 0.97) between a single event in daily sea surface temperatures each spring, and peak fish egg abundance measurements the following summer, in 7 years of approximately weekly fish egg abundance data collected at Scripps Pier in La Jolla California. Even more surprising was that this event-based result persisted despite the large and variable number of fish species involved (up to 46), and the large and variable time interval between trigger and response (up to ~3 months). To mitigate potential over-fitting, we made an out-of-sample prediction beyond the publication process for the peakmore »summer egg abundance observed at Scripps Pier in 2020 (available on bioRxiv). During peer-review, the prediction failed, and while it would be tempting to explain this away as a result of the record-breaking toxic algal bloom that occurred during the spring (9x higher concentration of dinoflagellates than ever previously recorded), a re-examination of our methodology revealed a potential source of over-fitting that had not been evaluated for robustness. This cautionary tale highlights the importance of testable true out-of-sample predictions of future values that cannot (even accidentally) be used in model fitting, and that can therefore catch model assumptions that may otherwise escape notice. We believe that this example can benefit the current push towards ecology as a predictive science and support the notion that predictions should live and die in the public domain, along with the models that made them.« less