It is perilous to predict the future progress of science. Nonetheless, I will offer a few suggestions that I think might be productive avenues for work in comparative methods.
First, I think comparative methods can and should do a better job of integrating diverse data into a coherent framework. For example, despite clear connections, neither fossils nor contemporary data on the tempo and genetics of speciation typically can be integrated with phylogenetic studies of diversification (Rabosky and Matute 2013). Research projects with the same goal, like estimating when and why a lineage undergoes speciation, are better integrated than separate. There are a few hints about how to proceed: first, speciation models that we fit to both phylogenetic and fossil data must be better connected to the process of speciation; and second, analyses need to consider both paleontological and phylogenetic data simultaneously.
Second, it is absolutely essential to fully deal with uncertainty through entire pipelines of comparative analysis, from tree building to model fitting. The easiest way to do this is through a single integrated Bayesian framework, although using each step’s posterior as a prior is nearly as good. Even if one is not a Bayesian, I think it is critical to test how tree uncertainty might affect the results of our comparative analyses.
Third, comparative methods require a more diverse set of models that are better linked to biological processes. Current models like Brownian motion and OU have, at best, a weak and many-to-one connection to microevolutionary models. Other models are even more abstract; nothing we can measure about an evolving lineage from one generation to the next, for example, can inform us about the meaning of the lambda parameter from a PGLS analysis. This can be fine statistically, but I think we can do better. The easiest connections to make are between comparative methods and quantitative genetics. In this book I explore only the most basic aspects of this connection. More could, and should, be done. For example, no trait models that I know of deal with differences in abundance and range size among species, even though these vary tremendously among even very close relatives and are almost certain to affect the tempo and mode of trait evolution. Here we can look to other fields like ecology for inspiration.