# Non-parametric inference of causal interactions from geological records

### Abstract

Quantification of drive-response relationships from geological records is challenged both by the complexity of the interactions and by indirect and uncertain proxy data. Here I demonstrate the use of information-theoretic techniques to detect causal relationships directly from incomplete and noisy time series. A non-parametric estimate of information transfer (IT) is used to quantify (1) the relative strength of statistical dependence among three variables, including nonlinear relationships, and (2) the directionality of coupling between two variables, compared to surrogate time series. Surrogates preserve the amplitudes and frequencies of the original data, and allow causation to be distinguished from correlation. Simple data pre-processing helps overcome biases related to non-stationarity. Causal inference involves a combination of the two IT calculations, and the method is sufficiently robust to sparse, irregular sampling to have geological applicability. Two case studies highlight some of the possibilities and limitations: (1) IT analysis of oxygen isotope records from Chinese speleothems against ice cores from Greenland and Antarctica suggests time-varying relative influence of the two hemispheres on monsoon intensity over the interval 40 to 10 Ka. IT from the Greenland record dominates except in the deep glacial phase, during which IT from the Antarctic record is more prominent. (2) IT analyses of Phanerozoic seawater isotope ratios capture long-term coupling between temperature ($\delta^{18}$O) and carbon cycling ($\delta^{13}$C), and between the cycling of carbon ($\delta^{13}$C) and sulfur ($\delta^{34}$S). Results suggest that the $\delta^{34}$S record contains an important signal for understanding Phanerozoic Earth system evolution. Although directional IT between proxies cannot be equated with direct causality, the method holds some promise as a data-driven approach to inferring causal interactions from geological records.

Type
Publication
American Journal of Science 311: 315-334