Branch length heterogeneity leads to nonindependent branch length estimates and can decrease the efficiency of methods of phylogenetic inference

Branch length estimates play a central role in maximum-likelihood (ML) and minimum-evolution (ME) methods of phylogenetic inference. For various reaso ns, branch length estimates are not statistically independent under ML or M E. We studied the response of correlations among branch length estimates to the degree of among-branch length heterogeneity (BLH) in the model (true) tree. The frequency and magnitude of (especially negative) correlations amo ng branch length estimates were both shown to increase as BLH increases und er simulation and analytically. For ML, we used the correct model (Jukes-Ca ntor). For ME, we employed ordinary least-squares (OLS) branch lengths esti mated under both simple p-distances and Jukes-Cantor distances, analyzed wi th and without an among-site rate heterogeneity parameter. The efficiency o f ME and ML was also shown to decrease in response to increased BLH. We not e that the shape of the re tree will in part determine BLH and represents a critical factor in the probability of recovering the correct topology. An important finding suggests that researchers cannot expect that different br anches that were in fact the same length will have the same probability of being accurately reconstructed when BLH exists in the overall tree. We conc lude that methods designed to minimize the interdependencies of branch leng th estimates (BLEs) may (1) reduce both the variance and the covariance ass ociated with the estimates and (2) increase the efficiency of model-based o ptimality criteria. We speculate on possible ways to reduce the nonindepend ence of BLEs under OLS and ML.