Chih-hao Hsieh

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.

Why fishing magnifies fluctuations in fish abundance

It is now clear that fished populations can fluctuate more than unharvested stocks. However, it is not clear why. Here we distinguish among three major competing mechanisms for this phenomenon, by using the 50-year California Cooperative Oceanic Fisheries Investigations (CalCOFI) larval fish record. First, variable fishing pressure directly increases variability in exploited populations. Second, commercial fishing can decrease the average body size and age of a stock, causing the truncated population to track environmental fluctuations directly. Third, age-truncated or juvenescent populations have increasingly unstable population dynamics because of changing demographic parameters such as intrinsic growth rates. We find no evidence for the first hypothesis, limited evidence for the second and strong evidence for the third. Therefore, in California Current fisheries, increased temporal variability in the population does not arise from variable exploitation, nor does it reflect direct environmental tracking. More fundamentally, it arises from increased instability in dynamics. This finding has implications for resource management as an empirical example of how selective harvesting can alter the basic dynamics of exploited populations, and lead to unstable booms and busts that can precede systematic declines in stock levels.

Fishing elevates variability in the abundance of exploited species

The separation of the effects of environmental variability from the impacts of fishing has been elusive, but is essential for sound fisheries management. We distinguish environmental effects from fishing effects by comparing the temporal variability of exploited versus unexploited fish stocks living in the same environments. Using the unique suite of 50-year-long larval fish surveys from the California Cooperative Oceanic Fisheries Investigations we analyse fishing as a treatment effect in a long-term ecological experiment. Here we present evidence from the marine environment that exploited species exhibit higher temporal variability in abundance than unexploited species. This remains true after accounting for life-history effects, abundance, ecological traits and phylogeny. The increased variability of exploited populations is probably caused by fishery-induced truncation of the age structure, which reduces the capacity of populations to buffer environmental events. Therefore, to avoid collapse, fisheries must be managed not only to sustain the total viable biomass but also to prevent the significant truncation of age structure. The double jeopardy of fishing to potentially deplete stock sizes and, more immediately, to amplify the peaks and valleys of population variability, calls for a precautionary management approach.

Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean.

The prospect of rapid dynamic changes in the environment is a pressing concern that has profound management and public policy implications. Worries over sudden climate change and irreversible changes in ecosystems are rooted in the potential that nonlinear systems have for complex and ‘pathological’ behaviours. Nonlinear behaviours have been shown in model systems and in some natural systems, but their occurrence in large-scale marine environments remains controversial. Here we show that time series observations of key physical variables for the North Pacific Ocean that seem to show these behaviours are not deterministically nonlinear, and are best described as linear stochastic. In contrast, we find that time series for biological variables having similar properties exhibit a low-dimensional nonlinear signature. To our knowledge, this is the first direct test for nonlinearity in large-scale physical and biological data for the marine environment. These results address a continuing debate over the origin of rapid shifts in certain key marine observations as coming from essentially stochastic processes or from dominant nonlinear mechanisms. Our measurements suggest that large-scale marine ecosystems are dynamically nonlinear, and as such have the capacity for dramatic change in response to stochastic fluctuations in basin-scale physical states.

Order in spontaneous behavior

Brains are usually described as input/output systems: they transform sensory input into motor output. However, the motor output of brains (behavior) is notoriously variable, even under identical sensory conditions. The question of whether this behavioral variability merely reflects residual deviations due to extrinsic random noise in such otherwise deterministic systems or an intrinsic, adaptive indeterminacy trait is central for the basic understanding of brain function. Instead of random noise, we find a fractal order (resembling Lévy flights) in the temporal structure of spontaneous flight maneuvers in tethered Drosophila fruit flies. Lévy-like probabilistic behavior patterns are evolutionarily conserved, suggesting a general neural mechanism underlying spontaneous behavior. Drosophila can produce these patterns endogenously, without any external cues. The flys behavior is controlled by brain circuits which operate as a nonlinear system with unstable dynamics far from equilibrium. These findings suggest that both general models of brain function and autonomous agents ought to include biologically relevant nonlinear, endogenous behavior-initiating mechanisms if they strive to realistically simulate biological brains or out-compete other agents.

Fishing effects on age and spatial structures undermine population stability of fishes

Overfishing has caused dramatic changes in structures of exploited populations as well as ecosystems. In this article, we focus on fishing effects on age (size) and spatial structures of exploited fishes. Accumulating evidence has shown that large and experienced spawning individuals are able to produce higher quality and quantity of eggs, known as maternal effects, and that individuals of different age classes tend to spawn in different locations and times. These behaviors are associated with a healthy age structure and contribute to bet-hedging capacity that is important in smoothing out short-term environmental variability. Here, we document a widespread phenomenon of age (size)-truncation of exploited populations driven by size-selective fishery removals. Such size-selective fishing may have evolutionary consequence and may be difficult to reverse. In addition, fishing often reduces population spatial heterogeneity that also contributes importantly to bet-hedging. We review studies showing that the effects of age truncation and reduction of spatial heterogeneity have reduced resilience and elevated the fluctuation amplitude of exploited populations facing a changing environment. Recent analyses indicated that fish populations often exhibit nonlinear nature and have potential to shift dramatically in a short time. All the evidence suggests that fishing, by altering age or spatial structures, may make exploited fishes, more prone to catastrophic shifts. Therefore, to achieve sustainable fisheries, management should conserve the age and spatial structure in addition to viable spawning biomass.

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.

Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling

Significance The conventional parametric approach to modeling relies on hypothesized equations to approximate mechanistic processes. Although there are known limitations in using an assumed set of equations, parametric models remain widely used to test for interactions, make predictions, and guide management decisions. Here, we show that these objectives are better addressed using an alternative equation-free approach, empirical dynamic modeling (EDM). Applied to Fraser River sockeye salmon, EDM models (i) recover the mechanistic relationship between the environment and population biology that fisheries models dismiss as insignificant, (ii) produce significantly better forecasts compared with contemporary fisheries models, and (iii) explicitly link control parameters (spawning abundance) and ecosystem objectives (future recruitment), producing models that are suitable for current management frameworks. It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner–recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts.

Extending Nonlinear Analysis to Short Ecological Time Series

Nonlinearity is important and ubiquitous in ecology. Though detectable in principle, nonlinear behavior is often difficult to characterize, analyze, and incorporate mechanistically into models of ecosystem function. One obvious reason is that quantitative nonlinear analysis tools are data intensive (require long time series), and time series in ecology are generally short. Here we demonstrate a useful method that circumvents data limitation and reduces sampling error by combining ecologically similar multispecies time series into one long time series. With this technique, individual ecological time series containing as few as 20 data points can be mined for such important information as (1) significantly improved forecast ability, (2) the presence and location of nonlinearity, and (3) the effective dimensionality (the number of relevant variables) of an ecological system.

Evaluation of Multi-Scale Climate Effects on Annual Recruitment Levels of the Japanese Eel, Anguilla japonica, to Taiwan

Long-term (1967–2008) glass eel catches were used to investigate climatic effects on the annual recruitment of Japanese eel to Taiwan. Specifically, three prevailing hypotheses that potentially explain the annual recruitment were evaluated. Hypothesis 1: high precipitation shifts the salinity front northward, resulting in favorable spawning locations. Hypothesis 2: a southward shift of the position of the North Equatorial Current (NEC) bifurcation provides a favorable larval transport route. Hypothesis 3: ocean conditions (eddy activities and productivity) along the larval migration route influence larval survival. Results of time series regression and wavelet analyses suggest that Hypothesis 1 is not supported, as the glass eel catches exhibited a negative relationship with precipitation. Hypothesis 2 is plausible. However, the catches are correlated with the NEC bifurcation with a one-year lag. Considering the time needed for larval transport (only four to six months), the one-year lag correlation does not support the direct transport hypothesis. Hypothesis 3 is supported indirectly by the results. Significant correlations were found between catches and climate indices that affect ocean productivity and eddy activities, such as the Quasi Biennial Oscillation (QBO), North Pacific Gyre Oscillation (NPGO), Pacific Decadal Oscillation (PDO), and Western Pacific Oscillation (WPO). Wavelet analysis reveals three periodicities of eel catches: 2.7, 5.4, and 10.3 years. The interannual coherence with QBO and the Niño 3.4 region suggests that the shorter-term climate variability is modulated zonally by equatorial dynamics. The low-frequency coherence with WPO, PDO, and NPGO demonstrates the decadal modulation of meridional teleconnection via ocean–atmosphere interactions. Furthermore, WPO and QBO are linked to solar activities. These results imply that the Japanese eel recruitment may be influenced by multi-timescale climate variability. Our findings call for investigation of extra-tropical ocean dynamics that affect survival of eels during transport, in addition to the existing efforts to study the equatorial system.