Abstract—The merits of alternative approaches to the inference of evolutionary trees have been much discussed, but there have been few attempts to compare inferences systematically or to pinpoint the source of differences. The two major classes of approach are via likelihood inference under an evolutionary model and estimates based upon parsimony methods. Within the general class of likelihood approaches, there are differences depending upon the particular class of models considered. This paper makes comparisons of the characteristics of inferences for the case of quantitative variation (of allele frequencies, for example), concentrating on the case of very small numbers of populations where explicit solutions are possible, but also upon features which apply as well to inferences for larger groups of populations. The parsimony method of “minimum evolution” was proposed by Edwards and Cavalli‐Sforza (1964) to provide an approximation to the likelihood solution for an intractable model. In fact, its estimated phylogenies are closest to those of a more recent model of Felsenstein (1981) which, like parsimony, produces a fundamentally unrooted tree. Likelihood estimates based upon models involving an implicit or explicit root are radically different. These differ also from each other, depending upon whether or not the root is explicitly estimated, and upon whether or not a model for the fissioning of populations is included. Some general features of the comparisons can be sum