Ethan R. Deyle

Detecting causality in complex ecosystems

Cause or Correlation? Three centuries ago, Bishop Berkeleys 1710 classic “A treatise on the nature of human knowledge,” first spelled out the “correlation vs. causation” dilemma. Sugihara et al. (p. 496, published online 20 September) present an approach to this conundrum, and extend current discussions about causation to dynamic systems with weak to moderate coupling (such as ecosystems). The resulting method, convergent cross mapping can detect causal linkages between time series. A new method, based on nonlinear state space reconstruction, can distinguish causality from correlation. Identifying causal networks is important for effective policy and management recommendations on climate, epidemiology, financial regulation, and much else. We introduce a method, based on nonlinear state space reconstruction, that can distinguish causality from correlation. It extends to nonseparable weakly connected dynamic systems (cases not covered by the current Granger causality paradigm). The approach is illustrated both by simple models (where, in contrast to the real world, we know the underlying equations/relations and so can check the validity of our method) and by application to real ecological systems, including the controversial sardine-anchovy-temperature problem.

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.

Spatial convergent cross mapping to detect causal relationships from short time series

Recent developments in complex systems analysis have led to new techniques for detecting causal relationships using relatively short time series, on the order of 30 sequential observations. Although many ecological observation series are even shorter, perhaps fewer than ten sequential observations, these shorter time series are often highly replicated in space (i.e., plot replication). Here, we combine the existing techniques of convergent cross mapping (CCM) and dewdrop regression to build a novel test of causal relations that leverages spatial replication, which we call multispatial CCM. Using examples from simulated and real-world ecological data, we test the ability of multispatial CCM to detect causal relationships between processes. We find that multispatial CCM successfully detects causal relationships with as few as five sequential observations, even in the presence of process noise and observation error. Our results suggest that this technique may constitute a useful test for causality in systems where experiments are difficult to perform and long time series are not available. This new technique is available in the multispatialCCM package for the R programming language.

Distinguishing time-delayed causal interactions using convergent cross mapping

An important problem across many scientific fields is the identification of causal effects from observational data alone. Recent methods (convergent cross mapping, CCM) have made substantial progress on this problem by applying the idea of nonlinear attractor reconstruction to time series data. Here, we expand upon the technique of CCM by explicitly considering time lags. Applying this extended method to representative examples (model simulations, a laboratory predator-prey experiment, temperature and greenhouse gas reconstructions from the Vostok ice core, and long-term ecological time series collected in the Southern California Bight), we demonstrate the ability to identify different time-delayed interactions, distinguish between synchrony induced by strong unidirectional-forcing and true bidirectional causality, and resolve transitive causal chains.

Global environmental drivers of influenza.

Significance Patterns of influenza outbreak are different in the tropics than in temperate regions. Although considerable experimental progress has been made in identifying climate-related drivers of influenza, the apparent latitudinal differences in outbreak patterns raise basic questions as to how potential environmental variables combine and act across the globe. Adopting an empirical dynamic modeling framework, we clarify that absolute humidity drives influenza outbreaks across latitudes, find that the effect of absolute humidity on influenza is U-shaped, and show that this U-shaped pattern is mediated by temperature. These findings offer a unifying synthesis that explains why experiments and analyses disagree on this relationship. In temperate countries, influenza outbreaks are well correlated to seasonal changes in temperature and absolute humidity. However, tropical countries have much weaker annual climate cycles, and outbreaks show less seasonality and are more difficult to explain with environmental correlations. Here, we use convergent cross mapping, a robust test for causality that does not require correlation, to test alternative hypotheses about the global environmental drivers of influenza outbreaks from country-level epidemic time series. By moving beyond correlation, we show that despite the apparent differences in outbreak patterns between temperate and tropical countries, absolute humidity and, to a lesser extent, temperature drive influenza outbreaks globally. We also find a hypothesized U-shaped relationship between absolute humidity and influenza that is predicted by theory and experiment, but hitherto has not been documented at the population level. The balance between positive and negative effects of absolute humidity appears to be mediated by temperature, and the analysis reveals a key threshold around 75 °F. The results indicate a unified explanation for environmental drivers of influenza that applies globally.

Tracking and forecasting ecosystem interactions in real time

Evidence shows that species interactions are not constant but change as the ecosystem shifts to new states. Although controlled experiments and model investigations demonstrate how nonlinear interactions can arise in principle, empirical tools to track and predict them in nature are lacking. Here we present a practical method, using available time-series data, to measure and forecast changing interactions in real systems, and identify the underlying mechanisms. The method is illustrated with model data from a marine mesocosm experiment and limnologic field data from Sparkling Lake, WI, USA. From simple to complex, these examples demonstrate the feasibility of quantifying, predicting and understanding state-dependent, nonlinear interactions as they occur in situ and in real time—a requirement for managing resources in a nonlinear, non-equilibrium world.

Are exploited fish populations stable

Shelton and Mangel (1) examined patterns of variability in fish populations and concluded that the higher stock variability observed in exploited species results from heightened effects of stochastic forcing in the supposed absence of nonlinear dynamics. In contrast, Anderson et al. (2) found that higher variability in these stocks is attributable to amplified nonlinear behavior in noisy ecological systems under exploitation. Here, we reconcile these apparently conflicting views and demonstrate that stochasticity of demographic parameters directly enhances nonlinearity (2–4), thus challenging assessments of stability based on statistical fits to noise-free models.

Dynamical evidence for causality between galactic cosmic rays and interannual variation in global temperature

Significance Here we use newly available methods to examine the dynamical association between cosmic rays (CR) and global temperature (GT) in the 20th-century observational record. We find no measurable evidence of a causal effect linking CR to the overall 20th-century warming trend; however, on short interannual timescales, we find a significant, although modest, causal effect of CR on short-term, year-to-year variability in GT. Thus, although CR clearly do not contribute measurably to the 20th-century global warming trend, they do appear as a nontraditional forcing in the climate system on short interannual timescales, providing another interesting piece of the puzzle in our understanding of factors influencing climate variability. As early as 1959, it was hypothesized that an indirect link between solar activity and climate could be mediated by mechanisms controlling the flux of galactic cosmic rays (CR) [Ney ER (1959) Nature 183:451–452]. Although the connection between CR and climate remains controversial, a significant body of laboratory evidence has emerged at the European Organization for Nuclear Research [Duplissy J, et al. (2010) Atmos Chem Phys 10:1635–1647; Kirkby J, et al. (2011) Nature 476(7361):429–433] and elsewhere [Svensmark H, Pedersen JOP, Marsh ND, Enghoff MB, Uggerhøj UI (2007) Proc R Soc A 463:385–396; Enghoff MB, Pedersen JOP, Uggerhoj UI, Paling SM, Svensmark H (2011) Geophys Res Lett 38:L09805], demonstrating the theoretical mechanism of this link. In this article, we present an analysis based on convergent cross mapping, which uses observational time series data to directly examine the causal link between CR and year-to-year changes in global temperature. Despite a gross correlation, we find no measurable evidence of a causal effect linking CR to the overall 20th-century warming trend. However, on short interannual timescales, we find a significant, although modest, causal effect between CR and short-term, year-to-year variability in global temperature that is consistent with the presence of nonlinearities internal to the system. Thus, although CR do not contribute measurably to the 20th-century global warming trend, they do appear as a nontraditional forcing in the climate system on short interannual timescales.

Reply to Luo et al.: Robustness of causal effects of galactic cosmic rays on interannual variation in global temperature

Tsonis et al. (1) recently used convergent cross mapping (CCM) (2) to identify a causal relationship between cosmic rays (CRs) and interannual variation in global temperature (ΔGT). Subsequently, Luo et al. (3) questioned this finding using the Clark implementation of CCM (version 1.0 of the multispatial CCM package).* This version of the CCM code, which has since been debugged by Clark, unfortunately contains errors that are not in the original rEDM software package that Tsonis et al. used.† Thus, though well-intentioned, the Luo et al. (3) analysis is incorrect.

Reply to Baskerville and Cobey: Misconceptions about causation with synchrony and seasonal drivers

Baskerville and Cobey (1) caution against convergent cross-mapping (CCM) as a test for causation. However, their argument is based on an incorrect application of CCM arising from misconceptions about causation with synchrony. As stated in Deyle et al. (2), it is widely believed that there is synchrony between flu incidence and seasonal environmental drivers such as absolute humidity (AH). Synchrony is a well-studied phenomenon that can result from strong coupling or dynamic resonance. In unidirectionally driven systems synchrony can arise when the affected variable becomes effectively enslaved to the driving variable so that their dynamics become indistinguishable. As explained in Sugihara et al. (3), this leads to the false appearance of bidirectional causality (one direction being nonsensical). … [↵][1]1To whom correspondence should be addressed. Email: gsugihara{at}ucsd.edu. [1]: #xref-corresp-1-1