Phylofactorization - theory and challenges

Data from biological communities are composed of species connected by the phylogeny. A greedy algorithm ‘phylofactorization’ - was developed to construct an isometric log-ratio transform whose balances correspond to edges along which traits arose, controlling for previously made inferences.In this paper, the general theory of phylofactorization is presented as a graph-partitioning algorithm. A special case-regression phylofactorization-chooses coordinates based on sequential maximization of objective functions from regression on “contrast” variables such as an isometric log-ratio transform. The connections between regression phylofactorization and other methods is discussed, including matrix factorization, hierarchical regression, factor analysis and latent variable models. Open challenges in the statistical analysis of phylofactorization are presented, including criteria for choosing the number of factors and approximating null-distributions of commonly used test statistics and objective functions. As a graph-partitioning algorithm, cross-validation of phylo factorization across datasets requires graph-topological considerations, such as how to deal with novel nodes and edges and whether or not to control for partition order. Overcoming these challenges can accelerate our analysis of phylogenetically-structured data and allow annotations of edges in an online tree of life.