# BAMBE

## Bayesian Analysis in Molecular Biology and Evolution

### Version 2.03 beta, January 2001

© Copyright 2000, 2001, Donald Simon & Bret Larget, Department of Mathematics and Computer Science, Duquesne University.

### Likelihood models of nucleotide base substitution

The most general model implemented in BAMBE is TN93 (Tamura and Nei, 1993). This model has both HKY85 (Hasegawa, Kishino, and Yano, 1985) and F84 (Felsenstein's PHYLIP since 1984) as special cases. Added flexibility is available with up to ten different site categories with different parameters in each.

We parameterize the instantaneous rate matrix as:

+-                                              -+
|  -()      K pi_G   pi_C           pi_T         |
|						  |
|  K pi_A   -()      pi_C           pi_T	  |
theta  |						  |
|  pi_A     pi_G     -()            K gamma pi_T |
|						  |
|  pi_A     pi_G     K gamma pi_C   -()          |
+-                                              -+

where K = 4*ttr/(gamma+1), and we implicitly assume the order A,G,C,T for bases.

There are seven parameters, six of which are free. The model is reversible with stationary distribution given by pi_A, pi_G, pi_C, pi_T which are constrained to sum to 1. The parameter theta controls the overall mutation rate. The transition/transversion ratio is ttr and gamma is the final parameter which affects the ratio of transition/transversion rates among purines and pyrimidines.

Under HKY85 and F84, there is an additional parameter kappa, and ttr and gamma are functions of kappa and the pi's.

• HKY85
• ttr = kappa/2
• gamma = 1
• F84
• ttr = (kappa + 2*pi_r*pi_y) / (4*pi_r*pi_y)
• gamma = ((kappa + pi_y)*pi_r) / ((kappa + pi_r)*pi_y)
where pi_r = pi_a + pi_g and pi_y = pi_c + pi_t.

When the value kappa is input to F84, it is different than the transition/transversion parameter `T' that PHYLIP takes as input.