A hybrid empirical and parametric approach for managing ecosystem complexity: Water quality in Lake Geneva under nonstationary futures

Temperatures and hypolimnetic oxygen in German lakes: Observations, future trends and adaptation potential

We investigated trends in temperature, stratification, and hypolimnetic oxygen concentration of German lakes under climate change using observational data and hydrodynamic modelling. Observations from 46 lakes revealed that annually averaged surface temperatures increased by + 0.5 °C between 1990 and 2020 while bottom temperatures remained almost constant. Modelling of 12 lakes predicted further increases in surface temperatures by 0.3 °C/decade until the year 2099 in the most pessimistic emission scenario RCP 8.5 (RCP 4.5: + 0.18 °C/decade; RCP 2.6: + 0.04 °C/decade). Again, bottom temperatures increased much less while summer stratification extended by up to 38 days. Using a simplified oxygen model, we showed that hypolimnetic oxygen concentrations decreased by 0.7-1.9 mg L-1 in response to the extended stratification period. However, model runs assuming lower productivity (e. g. through nutrient reduction) resulted in increased oxygen concentrations even in the most pessimistic emission scenario. Our results suggest that the negative effects of climate change on the oxygen budget of lakes can be efficiently mitigated by nutrient control.

Combined Earth observations reveal the sequence of conditions leading to a large algal bloom in Lake Geneva

Freshwater algae exhibit complex dynamics, particularly in meso-oligotrophic lakes with sudden and dramatic increases in algal biomass following long periods of low background concentration. While the fundamental prerequisites for algal blooms, namely light and nutrient availability, are well-known, their specific causation involves an intricate chain of conditions. Here we examine a recent massive Uroglena bloom in Lake Geneva (Switzerland/France). We show that a certain sequence of meteorological conditions triggered this specific algal bloom event: heavy rainfall promoting excessive organic matter and nutrients loading, followed by wind-induced coastal upwelling, and a prolonged period of warm, calm weather. The combination of satellite remote sensing, in-situ measurements, ad-hoc biogeochemical analyses, and three-dimensional modeling proved invaluable in unraveling the complex dynamics of algal blooms highlighting the substantial role of littoral-pelagic connectivities in large low-nutrient lakes. These findings underscore the advantages of state-of-the-art multidisciplinary approaches for an improved understanding of dynamic systems as a whole.

Explaining empirical dynamic modelling using verbal, graphical and mathematical approaches

Empirical dynamic modelling (EDM) is becoming an increasingly popular method for understanding the dynamics of ecosystems. It has been applied to laboratory, terrestrial, freshwater and marine systems, used to forecast natural populations and has addressed fundamental ecological questions. Despite its increasing use, we have not found full explanations of EDM in the ecological literature, limiting understanding and reproducibility. Here we expand upon existing work by providing a detailed introduction to EDM. We use three progressively more complex approaches. A short verbal explanation of EDM is then explicitly demonstrated by graphically working through a simple example. We then introduce a full mathematical description of the steps involved. Conceptually, EDM translates a time series of data into a path through a multi-dimensional space, whose axes are lagged values of the time series. A time step is chosen from which to make a prediction. The state of the system at that time step corresponds to a 'focal point' in the multi-dimensional space. The set (called the library) of candidate nearest neighbours to the focal point is constructed, to determine the nearest neighbours that are then used to make the prediction. Our mathematical explanation explicitly documents which points in the multi-dimensional space should not be considered as focal points. We suggest a new option for excluding points from the library that may be useful for short-term time series that are often found in ecology. We focus on the core simplex and S-map algorithms of EDM. Our new R package, pbsEDM, enhances understanding (by outputting intermediate calculations), reproduces our results and can be applied to new data. Our work improves the clarity of the inner workings of EDM, a prerequisite for EDM to reach its full potential in ecology and have wide uptake in the provision of advice to managers of natural resources.

Constraining nonlinear time series modeling with the metabolic theory of ecology

Forecasting the response of ecological systems to environmental change is a critical challenge for sustainable management. The metabolic theory of ecology (MTE) posits scaling of biological rates with temperature, but it has had limited application to population dynamic forecasting. Here we use the temperature dependence of the MTE to constrain empirical dynamic modeling (EDM), an equation-free nonlinear machine learning approach for forecasting. By rescaling time with temperature and modeling dynamics on a "metabolic time step," our method (MTE-EDM) improved forecast accuracy in 18 of 19 empirical ectotherm time series (by 19% on average), with the largest gains in more seasonal environments. MTE-EDM assumes that temperature affects only the rate, rather than the form, of population dynamics, and that interacting species have approximately similar temperature dependence. A review of laboratory studies suggests these assumptions are reasonable, at least approximately, though not for all ecological systems. Our approach highlights how to combine modern data-driven forecasting techniques with ecological theory and mechanistic understanding to predict the response of complex ecosystems to temperature variability and trends.