## Friday, December 27, 2013

### Two sides of the same coin

One of the things that people want to do with phylogenies is to estimate parameters or test hypotheses about species diversification processes (Nee et al, 1992). The idea has been revisited recently, for testing for the presence of diversity dependence (Etienne et al 2012), or for estimating variation in speciation or extinction rates over time (Morlon et al, 2011, Stadler 2011).

In order to study diversification processes, however, one should first estimate a time-calibrated phylogeny.

Time-calibrated phylogenies are usually estimated using Bayesian methods.

However, a Bayesian method requires a prior on divergence times. The choice of the prior on divergence times has a strong impact on divergence times estimation. It will therefore potentially also have a strong impact on the outcome of the test of alternative diversification processes.

More fundamentally, some priors on divergence times have themselves an interpretation in terms of an underlying diversification process: the birth-death prior (Yang and Rannala, 1996), for instance, amounts to assuming constant speciation and extinction rates. Thus, testing diversification models based on a time-calibrated phylogeny that has itself been estimated assuming a given diversification model is either circular (if the two diversification models are identical) or contradictory (if the models are different).

So, what should we do ?

Obviously, what we could do here is, use the alternative diversification models that we want to test as alternative priors on divergence times. We can then compare the resulting alternative models, for instance using Bayes factors. By doing so, we will simultaneously (1) integrate the uncertainty about divergence times in our comparison of alternative diversification models (while avoiding the circularity issues mentioned above) and (2) infer divergence times under several diversification models, typically deciding to keep those obtained under the best fitting model.

Priors which can be interpreted in terms of macro-evolutionary processes are what I would call mechanistic priors. They are not meant to be uninformative priors, like the uniform prior on divergence times (although I am not totally sure that the uniform prior on divergence times is really uninformative), nor subjective priors.

Trying to derive mechanistic priors is, I think, an interesting and constructive answer to prior sensitivity issues. It is a risky business, because mechanistic priors tend to make strong assumptions and therefore potentially lack robustness. On the other hand, doing this is potentially more insightful in the long term.

Also, it naturally leads to an integration of different levels of macro-evolutionary studies. In the present case, what we obtain is an elegant statistical formalization of the idea that molecular dating and diversification studies are in fact two sides of the same coin.

--

Etienne, R. S., Haegeman, B., Stadler, T., Aze, T., Pearson, P. N., Purvis, A., & Phillimore, A. B. (2012). Diversity-dependence brings molecular phylogenies closer to agreement with the fossil record. Proceedings of the Royal Society B: Biological Sciences, 279:1300–1309.

Morlon, H., Parsons, T. L., & Plotkin, J. B. (2011). Reconciling molecular phylogenies with the fossil record. Proceedings of the National Academy of Sciences, 108:16327–16332.

Nee, S., Mooers, A. O., & Harvey, P. H. (1992). Tempo and mode of evolution revealed from molecular phylogenies. Proceedings of the National Academy of Sciences of the United States of America, 89:8322–8326.

Rannala, B., & Yang, Z. (1996). Probability distribution of molecular evolutionary trees: a new method of phylogenetic inference. Journal of Molecular Evolution, 43:304–311.

Stadler, T. (2011). Mammalian phylogeny reveals recent diversification rate shifts. Proceedings of the National Academy of Sciences, 108:6187–6192.