Insights into the Influence of Priors in Posterior Mapping of Discrete Morphological Characters: a Case Study in Annonaceae

Background: Posterior mapping is an increasingly popular hierarchical Bayesian based method used to infer character histories and reconstruct ancestral states at nodes of molecular phylogenies, notably of morphological characters. As for all Bayesian analyses specification of prior values is an integrative and important part of the analysis. He we provide an example of how alternative prior choices can seriously influence results and mislead interpretations.

Methods/principal Findings: For two contrasting discrete morphological characters, namely a slow and a fast evolving character found in the plant family Annonaceae, we specified a total of eight different prior distributions per character. We investigated how these prior settings affected important summary statistics. Our analyses showed that the different prior distributions had marked effects on the results in terms of average number of character state changes. These differences arise because priors play a crucial role in determining which areas of parameter space the values of the simulation will be drawn from, independent of the data at hand. However, priors seemed to fit the data better if they would result in a more even sampling of parameter space (normal posterior distribution), in which case alternative standard deviation values had little effect on the results. The most probable character history for each character was affected differently by the prior. For the slower evolving character, the same character history always had the highest posterior probability independent of the priors used. In contrast, the faster evolving character showed different most probable character histories depending on the prior. These differences could be related to the level of homoplasy exhibited by each character.

Conclusions: Although our analyses were restricted to two morphological characters within a single family, our results underline the importance of carefully choosing prior values for posterior mapping. Prior specification will be of crucial importance when interpreting the results in a meaningful way. It is hard to suggest a statistically sound method for prior specification without more detailed studies. Meanwhile, we propose that the data could be used to estimate the prior value of the gamma distribution placed on the transformation rate in posterior mapping.