The paper under discussion provides a detailed survey of the important developments in Fréchet analysis on manifolds or on stratified sample spaces. As it appears that data is now being realized over non-Euclidean spaces, such a paper is timely as such methods are called for in modern data analysis. In this discussion we explore this in the context of computational biology in general, and in particular for microbiome data which is gaining in popularity both in the scholarly and the popular presses. We will discuss the microbiome and metagenomics as well as outline how data is collected and strategies for data analysis. Finally we tie in how the microbiome data can be analyzed within the context of Fréchet analysis.