Bayesian Support for Evolution: Detecting Phylogenetic Signal in a Subset of the Primate Family

Abstract

The theory of evolution states that the diversity of species can be explained by descent with modification. Therefore, all living beings are related through a common ancestor. This evolutionary process must have left traces in our molecular composition. In this work, we present a randomization procedure in order to determine if a group of five species of the primate family, namely, macaque, guereza, orangutan, chimpanzee, and human, has retained these traces in its molecules. First, we present the randomization methodology through two toy examples, which allow to understand its logic. We then carry out a DNA data analysis to assess if the group of primates contains phylogenetic information which links them in a joint evolutionary history. This is carried out by monitoring a Bayesian measure, called marginal likelihood, which we estimate by using nested sampling. We found that it would be unusual to get the relationship observed in the data among these primate species if they had not shared a common ancestor. The results are in total agreement with the theory of evolution.

Appendices

Appendix 1

We analyze the dataset assuming a $\mathrm{GTR}+\varGamma _4$ model and consider the following prior distributions on the parameters involved in the analysis:

• Branch lengths: $t_i|\mu \sim$ Exp$(1/\mu )$, for $i =1,\ldots ,8,$ with $\mu \sim$ Inverse-Gamma(3,0.2).

• Relative rates: $q_i|\phi \sim$ Exp$(\phi )$, for $i =1,\ldots ,5,$ with $\phi \sim$ Exp(1).

• Base frequencies: $\pi \sim$ Dirichlet(1,1,1,1).

• Gamma shape parameter: $\lambda \sim$ Gamma(0.5,1).

For more information about the parameters involved in the phylogenetic analysis, see [9].

Appendix 2

Nested sampling [8] is a Bayesian algorithm to estimate mainly the marginal likelihood. It requires a tunning parameter called active points. The precision of the estimate depends on the number of active points. The higher it is, the more accurate the estimate and the higher the computational cost are.

To estimate the observed marginal likelihood, we use 100 active points. This yields a standard deviation of 0.73 of the log-marginal likelihood estimate. For the 1000 randomized datasets, we use five active points in order to get a quick picture of their log-marginal likelihood distribution.