Extended applicability of causal inference to compositional data by reciprocal logarithmic ratio transformation

Understanding state transition caused by several intrinsic and extrinsic factors such as environmental change and increased stress of human activities has been a significant focus in ecological studies. Analysis of time-series data is indispensable to identify a causal relationship between the possible factors and community change. Among several time-series analysis, a nonlinear time series analysis method called empirical dynamic modeling (EDM) has been recently applied to infer causality of community change that arose from intraspecies interactions. EDM allows model-free analysis to estimate the degree of action strength of intraspecific and interspecific interactions at the population level. Convergent cross-mapping (CCM) is an empirical dynamic analysis method used to suggest the existence of causality by reconstructing the state space of a dynamical system from a time series of observations without assuming any explicit mathematical equations. Although CCM allows for inferring directional interpretation of causal relationships from multivariate time series data, one of the major challenges is its non-applicability to compositional data, a common representation of next generation sequencing data such as microbiome. This study aimed to explore a practical approach applied explicitly to compositional data analysis. More specifically, we propose a heuristic but useful transformation that enables CCM to be applied to compositional data. The proposed transformation has demonstrated its applicability to compositional data equivalent to the conventional CCM to untransformed data. Application of the proposed transformation to sequence-based microbial community profiling data provides reasonable implication to the possible causal relationship during state transition. Author summary Several types of ecological studies such as trophic changes in lakes, marine plankton communities, forest ecosystems, terrestrial ecosystems, and interactions between plants and soils have employed time-series analyses for identifying the factors that might cause state changes. With the rise of next-generation sequencing, our understanding of these ecosystems is expanding to analyze sequence data. A nonlinear time series analysis method, termed empirical dynamic modeling, has been recently applied for analyzing time-series data. Among different empirical dynamic modeling methods, convergent cross-mapping (CCM) is frequently used to infer a causal relationship. Although CCM enables the directional interpretation of causal relationships, it cannot be applied to compositional data analysis. This study proposes a novel type of transformation, Reciprocal Logarithmic Ratio (RLR) transformation, that enables CCM to be applied to compositional data. With RLR-transformation, CCM results for compositional data are comparable to those for absolute data, and it is confirmed that the transformation is applicable to sequence data as well. The RLR-transformation is expected to provide a better understanding of ecological interactions by estimating causal relationships in compositional data. ### Competing Interest Statement The authors have declared no competing interest.