 
Summary: Evaluating the Performance of a SuccessiveApproximations Approach to
Parameter Optimization in MaximumLikelihood Phylogeny Estimation
Jack Sullivan,* Zaid Abdo, ą Paul Joyce, ą and David L. Swofford§
*Department of Biological Sciences, Initiative in Bioinformatics and Evolutionary Studies and Program in Bioinformatics and
Computational Biology, and ąDepartment of Mathematics, University of Idaho; and §School of Computational Science and
Department of Biological Science, Florida State University
Almost all studies that estimate phylogenies from DNA sequence data under the maximumlikelihood (ML) criterion
employ an approximate approach. Most commonly, model parameters are estimated on some initial phylogenetic estimate
derived using a rapid method (neighborjoining or parsimony). Parameters are then held constant during a tree search, and
ideally, the procedure is repeated until convergence is achieved. However, the effectiveness of this approximation has not
been formally assessed, in part because doing so requires computationally intensive, fulloptimization analyses. Here, we
report both indirect and direct evaluations of the effectiveness of successive approximations. We obtained an indirect
evaluation by comparing the results of replicate runs on real data that use random trees to provide initial parameter esti
mates. For six real data sets taken from the literature, all replicate iterative searches converged to the same joint estimates of
topology and model parameters, suggesting that the approximation is not startingpoint dependent, as long as the heuristic
searches of tree space are rigorous. We conducted a more direct assessment using simulations in which we compared the
accuracy of phylogenies estimated using full optimization of all model parameters on each tree evaluated to the accuracy of
trees estimated via successive approximations. There is no significant difference between the accuracy of the approxima
tion searches relative to fulloptimization searches. Our results demonstrate that successive approximation is reliable and
provide reassurance that this much faster approach is safe to use for ML estimation of topology.
