Advances in causal discovery methods for ecological time series.

Recent advances in data collection technologies (e.g. automated sensor networks, satellite remote sensing, and high-throughput sequencing) have greatly expanded the availability of ecological time series, enabling new opportunities for causal analyses in dynamic ecosystems. Granger causality (GC) and convergent cross mapping (CCM), two prominent dynamical causal discovery methods, have gained attention in ecological studies for uncovering causal relationships in nonlinear systems. GC traces its roots to economics and was later extended through the information-theoretic framework of transfer entropy (TE). On the other hand, CCM was developed from studies of chaotic time series. Both methods have provided critical insights into the dynamics of complex systems. In this review, we synthesize foundational concepts and recent developments in GC and CCM, exploring their respective strengths and limitations, while clarifying their interrelationship. We also review recent advances in temporal causal discovery methods, originally developed within the framework of statistical causal inference for non-temporal data, and highlight their applicability to ecological data sets. Despite these advances, such approaches remain largely unfamiliar to ecologists. We argue that a rigorous framework of time-series-based causal inference, together with an appreciation of their diverse methodological developments to date, will not only raise awareness of unresolved challenges but also create new research opportunities in ecology. By offering an integrated perspective, we encourage the application and development of cutting-edge methods in ecology to help foster a deeper understanding of ecosystem dynamics.