What are the p01sum and p0prop parameters in godon?

Question

When using branch-site model in Godon, model optimization results include the following parameters: p01sum and p0prop. What are those and how do they relate to p0 and p1 in the branch-site model?

Answer 1

Disclaimer: I'm the author of godon. The question above comes from the real communication with a software user.

In the godon implementation of the branch-site model I performed the following reparametrization:

$p_{01sum} = p_0 + p_1$

$p_{0prop} = \frac{p_0}{p_0 + p_1}$.

This has the following advantages:

• Both parameters have a well defined range $(0, 1)$.
• There is less dependency between the two. E.g., $p_2=1-p_0-p_1$ (proportion of sites under positivie selection) does not depend on $p_{0prop}$.
• Both properties are very helpful for both likelihood maximization and MCMC.

In case you are interested in $p_0$ and $p_1$ there is a straightforward way to go back to the original parameters:

$p_0=p_{0prop}*p_{01sum}$

$p_1=p_{01sum}-p_0$.

P.S. I also added this information to the tutorial.