Statistical Applications in Genetics and Molecular Biology

Abstract Approaches based upon sequence weights, to construct a position weight matrix ofnucleotides from aligned inputs, are popular but little effort has been expended to measure theirquality.We derive optimal sequence weights that minimize the sum of the variances of the estimatorsof base frequency parameters for sequences related by a phylogenetic tree. Using these we findthat approaches based upon sequence weights can perform very poorly in comparison toapproaches based upon a theoretically optimal maximum-likelihood method in the inference of theparameters of a position-weight matrix. Specifically, we find that among a collection of primatesequences, even an optimal sequences-weights approach is only 51% as efficient as the maximum-likelihood approach in inferences of base frequency parameters.We also show how to employ the variance estimators to obtain a greedy ordering of speciesfor sequencing. Application of this ordering for the weighted estimators to a primate collectionyields a curve with a long plateau that is not observed with maximum-likelihood estimators. Thisplateau indicates that the use of weighted estimators on these data seriously limits the utility ofobtaining the sequences of more than two or three additional species.