What is Birth Diff Rate under Yule?

[RobinvanVelzen]

Dear all, 

I have a minor question. In Beauti 2 when I select Yule as the tree prior, this automatically creates a second prior parameter called birthRate. That makes sense as the Yule model assumes a constant birth rate. 

In addition, however, I find two additional parameters under the Yule model: Birth Diff Rate and Conditional on Root and I have no idea what they do. I also could not find any information on beast2.org/parameters/ Hovering over these parameters gives the following explanations:

Birth Diff Rate: 'birth difference rate parameter, lambda - mu in birth/death model' That makes sense for a birth/death model (because that assumes indeed two different rate parameters for birth and death which I think are lambda and mu, respectively), but I have selected the Yule model so I do not understand what it is doing there. Even more intriguingly, the default is for this parameter to be estimated... 

Conditional on Root: 'whether to condition on the root (default false)'. Again I am not sure what it means: What exactly is conditioned on the root when checking this toggle: the birthRate, Birth Diff Rate, or something else? When would you want to condition on the root, and when not? 

I am generally inclined to use default settings but I know that priors can have a huge effect on Bayesian analysis so I would feel much more comfortable if I understood what these parameters mean and what their effects are. 

If anyone could give some clarification that would be great. 

Thanks, 

Robin

[Remco Bouckaert]

Hi Robin,

The Yule model is implemented as the birth-death model with death rate fixed to 0, so you see the somewhat non-intuitive description because it the description for the birth-death model.

Cheers,

Remco

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[Robin van Velzen]

Hi Remco, 

Thanks for the explanation - that is more or less what I expected. But I am still not really clear on why the Birth Diff Rate parameter is available under Yule and why it is set to be estimated by default. What will happen if I change the value or the estimation toggle? If the death rate is zero perhaps changing these parameters does not have an effect?  But in that case why show the parameters in Beauti? 

Thanks again, Robin

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[Remco Bouckaert]

Hi Robin,

For the Yule model, the birth-diff rate should be interpreted as the birth-rate (since the death rate is zero). It is usual to estimate the birth rate for the Yule model, so that is why it is marked ‘estimated’ by default. BEAUti allows you to set the starting value, which can help in convergence, but if you leave it at the default value of 1, it will get close to the expected value eventually. If you decide to uncheck the estimate flag, the starting value does not change, and this can have a considerable effect on age estimates in the tree.

Cheers,

Remco