Predicting coastal algal blooms in southern California.

The irregular appearance of planktonic algae blooms off the coast of southern California has been a source of wonder for over a century. Although large algal blooms can have significant negative impacts on ecosystems and human health, a predictive understanding of these events has eluded science, and many have come to regard them as ultimately random phenomena. However, the highly nonlinear nature of ecological dynamics can give the appearance of randomness and stress traditional methods-such as model fitting or analysis of variance-to the point of breaking. The intractability of this problem from a classical linear standpoint can thus give the impression that algal blooms are fundamentally unpredictable. Here, we use an exceptional time series study of coastal phytoplankton dynamics at La Jolla, CA, with an equation-free modeling approach, to show that these phenomena are not random, but can be understood as nonlinear population dynamics forced by external stochastic drivers (so-called "stochastic chaos"). The combination of this modeling approach with an extensive dataset allows us to not only describe historical behavior and clarify existing hypotheses about the mechanisms, but also make out-of-sample predictions of recent algal blooms at La Jolla that were not included in the model development.

On estimating the reliability of ecological forecasts.

Recent work has highlighted the utility of nonparametric forecasting methods for predicting ecological time series (Perretti et al., 2013. Proc. Natl. Acad. Sci. U.S.A. 110, 5253-5257). However, one topic that has received considerably less attention is the quantification of uncertainty in nonparametric forecasts. This important topic was brought to the forefront in the recent work by Jabot (2014. J. Theor. Biol.). Here, we add to this emerging discussion by reviewing the available methods for quantifying forecast uncertainty in nonparametric models. We conclude with a demonstration of one such method using the simulation model of Jabot (2014. J. Theor. Biol.). We find that nonparametric forecast error is accurately estimated with as few as 10 observations in the time series.

Predicting climate effects on Pacific sardine.

For many marine species and habitats, climate change and overfishing present a double threat. To manage marine resources effectively, it is necessary to adapt management to changes in the physical environment. Simple relationships between environmental conditions and fish abundance have long been used in both fisheries and fishery management. In many cases, however, physical, biological, and human variables feed back on each other. For these systems, associations between variables can change as the system evolves in time. This can obscure relationships between population dynamics and environmental variability, undermining our ability to forecast changes in populations tied to physical processes. Here we present a methodology for identifying physical forcing variables based on nonlinear forecasting and show how the method provides a predictive understanding of the influence of physical forcing on Pacific sardine.

Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data.

Accurate predictions of species abundance remain one of the most vexing challenges in ecology. This observation is perhaps unsurprising, because population dynamics are often strongly forced and highly nonlinear. Recently, however, numerous statistical techniques have been proposed for fitting highly parameterized mechanistic models to complex time series, potentially providing the machinery necessary for generating useful predictions. Alternatively, there is a wide variety of comparatively simple model-free forecasting methods that could be used to predict abundance. Here we pose a rather conservative challenge and ask whether a correctly specified mechanistic model, fit with commonly used statistical techniques, can provide better forecasts than simple model-free methods for ecological systems with noisy nonlinear dynamics. Using four different control models and seven experimental time series of flour beetles, we found that Markov chain Monte Carlo procedures for fitting mechanistic models often converged on best-fit parameterizations far different from the known parameters. As a result, the correctly specified models provided inaccurate forecasts and incorrect inferences. In contrast, a model-free method based on state-space reconstruction gave the most accurate short-term forecasts, even while using only a single time series from the multivariate system. Considering the recent push for ecosystem-based management and the increasing call for ecological predictions, our results suggest that a flexible model-free approach may be the most promising way forward.

Regime shift indicators fail under noise levels commonly observed in ecological systems.

Ecological regime shifts are rapid, potentially devastating changes in ecosystem state that last for extended periods of time. Previous theoretical work has generated numerous early-warning indicators of regime shifts, some of which have been empirically demonstrated in closed ecological systems. Here we evaluated a suite of indicators using a previously studied three-species model under conditions likely to be observed in field studies of open ecological systems. Simulations included large correlated fluctuations in extrinsic noise and a rapidly changing driving variable, while indicators were calculated using sparsely sampled time series. All indicators performed poorly under these conditions, particularly during the beginning of the regime shift. Overall, the best performing indicator was a rise in variance. Future research should focus on methods for setting benchmark values of early warning indicators and for identifying indicators that work for sparsely sampled data sets.