 In many statistical situations where GLS (or, ordinary least squares [OLS]) is used residual errors "ε" are assumed to be independent and identically distributed random variables that are assumed to be normal
whereas in PGLS the errors are assumed to be distributed as
where "V" is a matrix of expected variance and covariance of the residuals given an evolutionary model and a phylogenetic tree.Therefore, it is the structure of residuals and not the variables themselves that show phylogenetic signal.This has long been a source of confusion in the scientific literature.