Searching for phylogenetic trees under the frequency parsimony criterion: an approximation using generalized parsimony.

Swofford and Berlocher (1987) described a method for inferring trees from polymorphic character data that searches for trees that minimize the total amount of allelic frequency change as measured by the Manhattan metric. We provided three primary arguments for choosing our method over other parsimony methods proposed for polymorphic data: (1) it accommodates polymorphism without resorting to coding strategies that permit the existence of impossible conditions (e.g., ancestral loci for which all allele frequencies are zero); (2) it reduces the impact of sampling error (e.g., the failure to detect rare alleles in some populations or taxa; see also Rannala, 1995); and (3) it makes use of potentially useful frequency information that is lost in presence / absence coding strategies. Despite its theoretical advantages, our method has not been widely used because of its computational intensity and the inadequacy of the tree-searching algorithm used in the only existing implementation (FREQPARS; Swofford and Berlocher, 1987). Here, we propose a modification of the original method that overcomes these limitations by using an approximation to the original optimality criterion. In our original paper, we suggested that the MANAD (Manhattan distance, additivity requirement) criterion be used to select optimal trees. Tree length is defined as the sum of the branch lengths (edges), where each branch length is measured by a Manhattan distance. For a single branch bounded by nodes A and B and a single locus ;', this distance D is defined as (i) — v\ (1)