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Abstract The foundation of Empirical dynamic modeling (EDM) is in representing time-series data as the trajectory of a dynamic system in a multidimensional state space rather than as a collection of traces of individual variables changing through time. Takens’s theorem provides a rigorous basis for adopting this state-space view of time-series data even from just a single time series, but there is considerable additional value to building out a state space with explicit covariates. Multivariate EDM case studies to-date, however, generally rely on building up understanding first from univariate to multivariate and use lag-coordinate embeddings for critical steps along the path of analysis. Here, we propose an alternative set of steps for multivariate EDM analysis when the traditional roadmap is not practicable. The general approach borrows ideas of random data projection from compressed sensing, but additional justification is described within the framework of Takens’s theorem. We then detail algorithms that implement this alternative method and validate through application to simulated model data. The model demonstrations are constructed to explicitly demonstrate the possibility for this approach to extend EDM application from time-series trajectories to effectively realizations of the underlying vector field, i.e. data sets that measure change over time with very short formal time series but are otherwise “big” in terms of number of variables and samples. 

Severe deterioration of water quality in lakes, characterized by overabundance of algae and declining dissolved oxygen in the deep lake (DO B ), was one of the ecological crises of the 20th century. Even with large reductions in phosphorus loading, termed “reoligotrophication,” DO B and chlorophyll (CHL) have often not returned to their expected pre–20th-century levels. Concurrently, management of lake health has been confounded by possible consequences of climate change, particularly since the effects of climate are not neatly separable from the effects of eutrophication. Here, using Lake Geneva as an iconic example, we demonstrate a complementary alternative to parametric models for understanding and managing lake systems. This involves establishing an empirically-driven baseline that uses supervised machine learning to capture the changing interdependencies among biogeochemical variables and then combining the empirical model with a more conventional equation-based model of lake physics to predict DO B over decadal time-scales. The hybrid model not only leads to substantially better forecasts, but also to a more actionable description of the emergent rates and processes (biogeochemical, ecological, etc.) that drive water quality. Notably, the hybrid model suggests that the impact of a moderate 3°C air temperature increase on water quality would be on the same order as the eutrophication of the previous century. The study provides a template and a practical path forward to cope with shifts in ecology to manage environmental systems for non-analogue futures. 

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 of 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. 

Abstract 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 of 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.