On formal limitations of causal ecological networks.

Causal multivariate time-series analysis, combined with network theory, provide a powerful tool for studying complex ecological interactions. However, these methods have limitations often underestimated when used in graphical modelling of ecological systems. In this opinion article, I examine the relationship between formal logic methods used to describe causal networks and their inherent statistical and epistemological limitations. I argue that while these methods offer valuable insights, they are restricted by axiomatic assumptions, statistical constraints and the incompleteness of our knowledge. To prove that, I first consider causal networks as formal systems, define causality and formalize their axioms in terms of modal logic and use ecological counterexamples to question the axioms. I also highlight the statistical limitations when using multivariate time-series analysis and Granger causality to develop ecological networks, including the potential for spurious correlations among other data characteristics. Finally, I draw upon Gödel's incompleteness theorems to highlight the inherent limits of fully understanding complex networks as formal systems and conclude that causal ecological networks are subject to initial rules and data characteristics and, as any formal system, will never fully capture the intricate complexities of the systems they represent. This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'.