Phylogenetic Invariants and Markov Invariants

“Phylogenetics” is the systematic study of reconstructing the past evolutionary history of extant species or taxa, based on present-day data, such as morphologies or molecular information (sequence data). This evolutionary history or phylogeny is ideally represented as a binary tree. In the method of “phylogenetic invariants,” a pivotal role is played by certain master functions (the so-called invariants, which give the method its name). The aim is to use the observed data as input for their evaluation, and dependent on the answers, to infer essential features of phylogenetic history without the need for parameter estimation. We compare and contrast “phylogenetic invariants” with “Markov invariants,” closely related quantities which we have recently introduced in phylogenetics.