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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. 

Abstract Climate change interacts with local processes to threaten biodiversity by disrupting the complex network of ecological interactions. While changes in network interactions drastically affect ecosystems, how ecological networks respond to climate change, in particular warming and nutrient supply fluctuations, is largely unknown. Here, using an equation-free modelling approach on monthly plankton community data in ten Swiss lakes, we show that the number and strength of plankton community interactions fluctuate and respond nonlinearly to water temperature and phosphorus. While lakes show system-specific responses, warming generally reduces network interactions, particularly under high phosphate levels. This network reorganization shifts trophic control of food webs, leading to consumers being controlled by resources. Small grazers and cyanobacteria emerge as sensitive indicators of changes in plankton networks. By exposing the outcomes of a complex interplay between environmental drivers, our results provide tools for studying and advancing our understanding of how climate change impacts entire ecological communities. 

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. 

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 different 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.