Evolutionary reconstruction of Indo-European gender

Evolutionary reconstruction of gender in Indo-European is a highly interesting field. The subject is a perfect testbed for how well evolutionary methods generally work. The core issue is that the system that we reconstruct to Proto-Indo-European, a system with a commune/neuter distinction, which has developed into a sexus-based system (masculine/feminine/neuter) in most daughter branches, is preserved only in Anatolian (Hittite, Luwian), the oldest attested Indo-European branch. However, in Scandinavian and Dutch/Frisian, a commune/neuter system has re-emerged as a merger of a previous three-gender system. Therefore, on the surface, Anatolian and Scandinavian are similar, as we see from the MCA plot above, which indicates the synchronic similarities of Indo-European gender systems based on attested languages. However, the similarity between Scandinavian, Frisian/Dutch and Hittite/Luwian is an illusion, or - to use evolutionary terminology -  an example of homoplasy. The background and the functionality of the different systems are completely different. How can we make evolutionary methods account for this difference in the reconstruction reconstruct?
This is where we can test how well different models perform. Experiments (performed by our colleagues Chundra Cathcart, Harald Hammarström, and Marc Tang) indicate that the result of an evolutionary reconstruction are similar to the model of a comparative reconstruction (even if the the method, of course, is completely different). What we want the evolutionary reconstruciton to produce is a high probability of masculine/neuter at the root (i.e., Proto-Indo-European) and a lower probability of a feminine.
In experimenting with the data and different models, we find that the most important thing is the shape of the tree. For Indo-European, we get different results if we use a branched vs non-branched tree, if we use Indo-Anatolian vs non-Indo-Anatolian, if we use ancestry constraints vs. non-ancestry-constraints (ancestral languages are situated on the branches of trees, not 'cousins' to the living language). As for the model, we get different results depending on if we us an Markov Chain Monte Carlo model, which is basically constructing a chain that has a desired distribution as its equilibrium distribution, where one can obtain a sample of the desired distribution by recording states from the chain. A Dollo model has as its precondition that a system never returns exactly to its previous state, but it keeps trace of intermediate stages through which it passes. A Dollo model with and Indo-Anatolian tree produces a reconstruction which looks almost similar to Anatolian. However, more experimenting needs to be performed: obviously, it is necessary to have a correct tree of a family before an evolutionary reconstruction can be performed. But different models of reconstruction may be better than others, depending on how they deal with the problem of homoplasy and parallel drift.