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   About the program                                                             
                                                                                 
   MrBayes is a program for the Bayesian estimation of phylogeny. Bayesian       
   inference of phylogeny is based upon the posterior probability distribution   
   of trees. Trees are labelled T1, T2, ..., Tn, where n is the number of        
   possible trees. The posterior probability of the i-th tree is calculated      
   using Bayes's formula as                                                     
                                                                                 
      Pr[Ti | X] = Pr[X | Ti] X Pr[Ti] / Pr[X]                                   
                                                                                 
   where X is a character matrix. Here, "Pr[Ti | X]" is the posterior          
   probability of the i-th tree, "Pr[X | Ti]" is the likelihood of the         
   i-th tree, and "Pr[Ti]" is the prior probability of the i-th tree. The      
   denominator of Bayes's formula ("Pr[X]") is a normalizing constant that    
   involves a summation over all possible trees. The likelihood, as described    
   above, cannot be calculated with knowledge of only the tree's topology. You  
   also need to have information on the lenths of the branches and on the        
   mechanism of character change. Hence, the likelihood ("Pr[X | Ti]")         
   involves a multidimensional integral over all possible combinations of        
   branch lengths and substitution model parameters.                             
                                                                                 
   In practice, it is impossible to calculate the posterior probability dist-    
   ribution of trees analytically. Instead, the posterior probability            
   of trees must be approximated. MrBayes uses a method called Markov chain      
   Monte Carlo (MCMC) to approximate the posterior probability of trees.         
   The object of MCMC is to construct a Markov chain that has as its state       
   space the parameters of the phylogenetic model and a stationary distribution  
   that is the posterior probability distribution of trees. MCMC takes valid,    
   albeit dependent, samples from the posterior probability distribution of      
   trees. The fraction of the time any tree appears in this sample is a          
   valid approximation of the posterior probability of the tree. MrBayes keeps   
   track of all the parameters of the phylogenetic model. The trees (with branch 
   lengths) that were sampled by the MCMC procedure are saved in one file        
   (a file with a ".t" extension) whereas the parameters of the model of       
   character change are saved in another file (a file with a ".p" ext-         
   ension). You can summarize the results in the ".t" and ".p" files         
   using the "sumt" and "sump" commands, respectively.                       
                                                                                 
   MrBayes is cowritten by John Huelsenbeck and Fredrik Ronquist. It is          
   rather unusual to find a program of this sort that has multiple authors.      
   However, each author brings unique strengths to the development of the        
   program. Originally, the program was started by JH in August of               
   2000 and was intended to be distributed to a small number of people.          
   In March of 2001, Fredrik started making contributions to the program.        
   The contributions were of such a significant nature that he was made          
   a coauthor of the program. In particular, FR improved the speed of the        
   likelihood functions of the program and included new proposal mechanisms      
   for changing trees. The newest version of the program, v3.1, is a              
   completely rewritten version of the earlier program, and has more             
   integrally included FR's contributions.                                          
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