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I'm mapping states (geographic regions) onto a phylogeny to estimate the number of transmissions between countries.

I'm using two methods, stochastic character mapping implemented in Phytools and parsimony implemented in Mesquite.

I was expecting parsimony to give lower results than stochastic character mapping, as it doesn't attempt any simulation along branches. This is generally true, and the number of transitions between states is generally lower estimated by parsimony. However, in a couple of cases, the number of transitions estimated by parsimony is higher than by stochastic character mapping.

I'm still developing an intuition in this type of analysis, so could someone tell me if this is feasible, or should I be looking for a technical problem somewhere?

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If the number of taxa is large enough, an exhaustive search is not possible, and parsimony methods use heuristics to explore the tree space. It is therefore not guaranteed that the most parsimonious tree will be encountered.

This might explain your observation if your tree has a high number of taxa (> 20).

According to wikipedia:

However, although it is easy to score a phylogenetic tree (by counting the number of character-state changes), there is no algorithm to quickly generate the most-parsimonious tree. Instead, the most-parsimonious tree must be found in "tree space" (i.e., amongst all possible trees). For a small number of taxa (i.e., fewer than nine) it is possible to do an exhaustive search, in which every possible tree is scored, and the best one is selected. For nine to twenty taxa, it will generally be preferable to use branch-and-bound, which is also guaranteed to return the best tree. For greater numbers of taxa, a heuristic search must be performed.

How many taxa do you have?

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