Local description of phylogenetic group-based models

Marta Casanellas, Jesús Fernández-Sánchez, Mateusz Michałek
(Submitted on 27 Feb 2014)

Motivated by phylogenetics, our aim is to obtain a system of equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G, we provide an explicit construction of codimX phylogenetic invariants (polynomial equations) of degree at most |G| that define the variety X on a Zariski open set U. The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model. In particular, our main result confirms a conjecture by the third author and, on the set U, a couple of conjectures by Bernd Sturmfels and Seth Sullivant.

Implications of uniformly distributed, empirically informed priors for phylogeographical model selection: A reply to Hickerson et al

Jamie R. Oaks, Charles W. Linkem, Jeet Sukumaran
(Submitted on 26 Feb 2014)

Biogeographers often seek to explain speciation on geographical phenomena. Establishing that a set of population splitting events occurred at the same time can be a persuasive argument that a set of taxa were affected by the same geographic events. Huang et al. (2011) introduced an approximate Bayesian approach (implemented in the software msBayes) to estimate the probabilities of models in which multiple sets of taxa diverge simultaneously. Oaks et al. (2013) used this model-choice framework to study 22 pairs of vertebrates distributed across the Philippines; they also studied the behavior of the approach using simulations. Oaks et al. (2013) found the model was very sensitive to the prior and had low power to detect variation in divergences times. This was not surprising in light of a rich statistical literature showing the marginal likelihood of a model is sensitive to vague priors. Because this sensitivity to prior assumptions affects the crucial insights a researcher who employs msBayes seeks to gain, Oaks et al. (2013) recommended users of the approach carefully assess the robustness of their conclusions to different priors. According to Hickerson et al. (2014), the lack of robustness was due to broad priors leading to inadequate numbers of simulations. They proposed a model-averaging approach using narrow, empirically informed uniform priors. Here, we demonstrate their approach is dangerous in the sense that the empirically-derived priors often exclude the true values of the parameters. We question the value of adopting an empirical-Bayesian stance for this problem, because it can mislead model posterior probabilities. The robust approach of conducting analyses under a variety of priors can reveal sensitivity and communicate assumptions underlying inference. Furthermore, simulations provide insight into the temporal resolution of the method and guide interpretation of results.