19 Dubious Ways to Compute the Marginal Likelihood of a Phylogenetic Tree Topology.

The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the normalizing constant for the posterior density, obtained by integrating the product of the likelihood and the prior with respect to model parameters. Thus, the computational burden of computing the marginal likelihood scales with the dimension of the parameter space. In phylogenetics, where we work with tree topologies that are high-dimensional models, standard approaches to computing marginal likelihoods are very slow. Here, we study methods to quickly compute the marginal likelihood of a single fixed tree topology. We benchmark the speed and accuracy of 19 different methods to compute the marginal likelihood of phylogenetic topologies on a suite of real data sets under the JC69 model. These methods include several new ones that we develop explicitly to solve this problem, as well as existing algorithms that we apply to phylogenetic models for the first time. Altogether, our results show that the accuracy of these methods varies widely, and that accuracy does not necessarily correlate with computational burden. Our newly developed methods are orders of magnitude faster than standard approaches, and in some cases, their accuracy rivals the best established estimators.

Phylogeny and source climate impact seed dormancy and germination of restoration-relevant forb species.

For many species and seed sources used in restoration activities, specific seed germination requirements are often unknown. Because seed dormancy and germination traits can be constrained by phylogenetic history, related species are often assumed to have similar traits. However, significant variation in these traits is also present within species as a result of adaptation to local climatic conditions. A growing number of studies have attempted to disentangle how phylogeny and climate influence seed dormancy and germination traits, but they have focused primarily on species-level effects, ignoring potential population-level variation. We examined the relationships between phylogeny, climate, and seed dormancy and germination traits for 24 populations of eight native, restoration-relevant forb species found in a wide range of climatic conditions in the Southwest United States. The seeds were exposed to eight temperature and stratification length regimes designed to mimic regional climatic conditions. Phylogenetic relatedness, overall climatic conditions, and temperature conditions at the site were all significantly correlated with final germination response, with significant among-population variation in germination response across incubation treatments for seven of our eight study species. Notably, germination during stratification was significantly predicted by precipitation seasonality and differed significantly among populations for seven species. While previous studies have not examined germination during stratification as a potential trait influencing overall germination response, our results suggest that this trait should be included in germination studies as well as seed sourcing decisions. Results of this study deepen our understanding of the relationships between source climate, species identity, and germination, leading to improved seed sourcing decisions for restorations.