Likelihood approximations of implied weights parsimony can be selected over the Mk model by the Akaike information criterion.

A likelihood method that approximates the behaviour of implied weighting is described. This approach provides a likelihood perspective on several aspects of implied weighting, such as guidance for the choice of concavity values, a justification to use different concavities for different numbers of taxa, and a natural basis for extended implied weighting. In this approach, the number of free parameters in the estimation depends on C, the number of characters (in contrast to the standard Mk model, which estimates 2T-3 parameters for T taxa). Depending on the characteristics of the dataset, the likelihood obtained with this approach may in some cases be similar or superior to that of the Mk model, but with fewer parameters being adjusted. Because of that tradeoff, testing against the Mk model by means of the Akaike information criterion on a set of 182 morphological datasets indicated many cases (36) in which the likelihood approximation to implied weighting is the best method, from an information-theoretic point of view. Given that it is expected to produce (almost) the same results as this maximum-likelihood approximation, implied weighting can therefore be seen as a valid alternative to the Mk model often used for morphological datasets, on the basis of a criterion for model fit widely advocated by likelihoodists.