The Expected Behaviors of Posterior Predictive Tests and Their Unexpected Interpretation.

Poor fit between models of sequence or trait evolution and empirical data is known to cause biases and lead to spurious conclusions about evolutionary patterns and processes. Bayesian posterior prediction is a flexible and intuitive approach for detecting such cases of poor fit. However, the expected behavior of posterior predictive tests has never been characterized for evolutionary models, which is critical for their proper interpretation. Here, we show that the expected distribution of posterior predictive P-values is generally not uniform, in contrast to frequentist P-values used for hypothesis testing, and extreme posterior predictive P-values often provide more evidence of poor fit than typically appreciated. Posterior prediction assesses model adequacy under highly favorable circumstances, because the model is fitted to the data, which leads to expected distributions that are often concentrated around intermediate values. Nonuniform expected distributions of P-values do not pose a problem for the application of these tests, however, and posterior predictive P-values can be interpreted as the posterior probability that the fitted model would predict a dataset with a test statistic value as extreme as the value calculated from the observed data.

Stochastic Modeling and Simulation of Viral Evolution.

RNA viruses comprise vast populations of closely related, but highly genetically diverse, entities known as quasispecies. Understanding the mechanisms by which this extreme diversity is generated and maintained is fundamental when approaching viral persistence and pathobiology in infected hosts. In this paper, we access quasispecies theory through a mathematical model based on the theory of multitype branching processes, to better understand the roles of mechanisms resulting in viral diversity, persistence and extinction. We accomplish this understanding by a combination of computational simulations and the theoretical analysis of the model. In order to perform the simulations, we have implemented the mathematical model into a computational platform capable of running simulations and presenting the results in a graphical format in real time. Among other things, we show that the establishment of virus populations may display four distinct regimes from its introduction into new hosts until achieving equilibrium or undergoing extinction. Also, we were able to simulate different fitness distributions representing distinct environments within a host which could either be favorable or hostile to the viral success. We addressed the most used mechanisms for explaining the extinction of RNA virus populations called lethal mutagenesis and mutational meltdown. We were able to demonstrate a correspondence between these two mechanisms implying the existence of a unifying principle leading to the extinction of RNA viruses.