Causal discovery from ecological time-series with one timestamp and multiple observations

Ecologists frequently seek to establish causal relations between entities of an ecological system, such as species interactions, ecosystem functions or ecosystem services, using observational data. Despite this, many studies still primarily rely on correlation-based methods, which lack the capability for causal interpretation. Recently, causal discovery methods have gained traction in analysing ecological time-series. However, the scarcity of ecological time-series data presents a challenge due to the demanding and time-consuming nature of collecting consistent measurements over extended periods. In this paper, we delve into the applicability of causal discovery methods when applied to point-in-time (or snapshot-like) observational data obtained from ecological dynamic systems. Specifically, we examine the PC algorithm, which holds theoretical validity assuming the causal Markov condition, faithfulness and causal sufficiency. Additionally, we explore the FCI algorithm, an extension of the PC algorithm designed to handle cases where causal sufficiency is violated. Through a combination of theoretical reasoning and simulation experiments, we elucidate the scenarios in which both algorithms are expected to yield meaningful results. We demonstrate that even in situations where causal sufficiency is not satisfied, the PC algorithm - characterized by its comparatively simpler interpretability - can still deduce specific types of relationships between ecological entities. Furthermore, we illustrate our theoretical findings on simulated data as well as on real data containing records of the abundance of various bird species as well as climatic and land-cover conditions.