Birth rate rate prior

The Yule skyline model is a pure-birth model where each epoch is associated with a birth rate. This model is useful when all tips are sampled at the same time. The birth rate of each epoch is sampled from a Gamma(α β) distribution where α is the shape and β is the rate. Here, we provide a guide for selecting a prior distribution for the birth rate rate β. Also see the Yule sklyline blog post.

Step 1: Estimate uncertainty in birth rate λ

Estimate the uncertainty behind the birth rate λ under the standard 1-epoch Yule model using this Step 1 & 2 for the Yule birth rate prior.

Step 2: Parameterise a distribution

Here, λ will be drawn from a Gamma(α, β) distribution. By default, α=2. Here, we must select β such that the 95% credible interval of the Gamma distribution is equal to the upper and lower 95% HPD intervals of λ. This can be achieved using R.

Alternative: specify root age prior.

Since the effective birth rate and root age are linked through the Yule Skyline prior, setting a prior on the root age can keep the birth rate in check, even with improper priors. See root age prior for details.

References

Bouckaert, RR. An efficient coalescent epoch model for Bayesian phylogenetic inference. Sys Bio, syac015, 2022 doi:10.1093/sysbio/syac015