Power law tails in phylogenetic systems

Covariance analysis of protein sequence alignments can predict structure and function from sequence alignments alone. Current methodologies typically assume that sequences are independent, notwithstanding their phylogenetic relationships. This corruption constrains the alignments for which covariance analysis can be used. It is critically important to control for phylogeny and understand how phylogeny contaminates signal. This paper presents a mathematical analysis that argues that there is a distinctive signature of phylogeny in the covariance matrix, allowing us to identify modes that are corrupted by phylogeny. This signature is present in large protein sequence alignments, explaining recent covariance analyses, and provides an important step toward decoupling phylogenetic effects from biologically meaningful interactions.