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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. 

Abstract While it is commonly accepted that ecosystem dynamics are nonlinear, what is often not acknowledged is that nonlinearity implies scale-dependence. With the increasing availability of high-resolution ecological time series, there is a growing need to understand how scale and resolution in the data affect the construction and interpretation of causal networks—specifically, networks mapping how changes in one variable drive changes in others as part of a shared dynamic system (“dynamic causation”). We use Convergent Cross Mapping (CCM), a method specifically designed to measure dynamic causation, to study the effects of varying temporal and taxonomic/functional resolution in data when constructing ecological causal networks. As the system is viewed at different scales relationships will appear and disappear. The relationship between data resolution and interaction presence is not random: the temporal scale at which a relationship is uncovered identifies a biologically relevant scale that drives changes in population abundance. Further, causal relationships between taxonomic aggregates (low-resolution) are shown to be influenced by the number of interactions between their component species (high-resolution). Because no single level of resolution captures all the causal links in a system, a more complete understanding requires multiple levels when constructing causal networks. 

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. 

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 equilibrium 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. 

Abstract The systematic substitution of direct observational data with synthesized data derived from models during the stock assessment process has emerged as a low-cost alternative to direct data collection efforts. What is not widely appreciated, however, is how the use of such synthesized data can overestimate predictive skill when forecasting recruitment is part of the assessment process. Using a global database of stock assessments, we show that Standard Fisheries Models (SFMs) can successfully predict synthesized data based on presumed stock-recruitment relationships, however, they are generally less skillful at predicting observational data that are either raw or minimally filtered (denoised without using explicit stock-recruitment models). Additionally, we find that an equation-free approach that does not presume a specific stock-recruitment relationship is better than SFMs at predicting synthesized data, and moreover it can also predict observational recruitment data very well. Thus, while synthesized datasets are cheaper in the short term, they carry costs that can limit their utility in predicting real world recruitment. 

Abstract The stock–recruitment relationship is the basis of any stock prediction and thus fundamental for fishery management. Traditional parametric stock–recruitment models often poorly fit empirical data, nevertheless they are still the rule in fish stock assessment procedures. We here apply a multi-model approach to predict recruitment of 20 Atlantic cod (Gadus morhua) stocks as a function of adult biomass and environmental variables. We compare the traditional Ricker model with two non-parametric approaches: (i) the stochastic cusp model from catastrophe theory and (ii) multivariate simplex projections, based on attractor state-space reconstruction. We show that the performance of each model is contingent on the historical dynamics of individual stocks, and that stocks which experienced abrupt and state-dependent dynamics are best modelled using non-parametric approaches. These dynamics are pervasive in Western stocks highlighting a geographical distinction between cod stocks, which have implications for their recovery potential. Furthermore, the addition of environmental variables always improved the models’ predictive power indicating that they should be considered in stock assessment and management routines. Using our multi-model approach, we demonstrate that we should be more flexible when modelling recruitment and tailor our approaches to the dynamical properties of each individual stock.