Do any computational phylogenetic methods enable the specification of ancestral states? Various phylogenetic algorithms estimate ancestral states of a phylogenetic dataset. Is there a way in either maximum parsimony, distance-based methods, or Bayesian inference to indicate what the ancestral states of characters were?
For maximum parsimony, Fitch's method seems simple and intuitive, and can be done in the R phangorn package: Fitch, Walter M. (1971). "Toward Defining the Course of Evolution: Minimum Change for a Specific Tree Topology". Systematic Zoology. 20 (4): 406. doi:10.2307/2412116. ISSN 0039-7989. JSTOR 2412116

There are various methodological criticisms of parsimony that you can find in the literature, but its appeal is you can easily understand why the algorithm came to the conclusions it did. 

RAxML can do maximum likelihood reconstructions based on a tree and tip values, and I think Mr. Bayes can do a Bayesian version.