Algebraic relations among DNA site-pattern frequencies have proven useful for inferring phylogenetic relationships between species. Often, these algebraic relations can be expressed as rank conditions on certain matrices constructed from phylogenetic data. In this talk, we will discuss how certain rank conditions for phylogenetic sequence data can be interpreted as conditional independence statements that give evidence of the evolutionary tree that produced the sequences. We will also present some new results that generalize the classic phylogenetic rank conditions to coalescent models of evolution. We show that rank-based reconstruction methods based on these results are robust to violations of model assumptions and perform well even in the presence of gene flow.