Max-linear Bayesian Networks are a class of Directed acyclic graphical (DAG) models which are of interest to statistics and data science due to their relevance to causality and probabilistic inference, particularly of extreme events. They differ from the more extensively studied Gaussian Bayesian Networks in that the structural equations governing the model are tropical polynomials in the random variables. This difference leads to several novel challenges in the task of causal discovery, i.e. the reconstruction of the true DAG underlying a given empirical distribution. More specifically, the combinatorial criteria for separation in the graph equating to conditional independence in the distribution are such that there is no longer a well-defined notion of Markov equivalence. In this talk, we explain how the PC algorithm for causal discovery in Gaussian Bayesian Networks fails in the max-linear setting, and discuss how it may be modified such as to output a well-defined subgraph of the true DAG which encodes its most significant causal relationships. This is a joint work with Carlos Améndola and Benjamin Hollering.