The Yule prior (as we use it) is proportional to
\lambda^n exp(-\lambda H)
where n is the number of species and H is the sum of heights. Throwing on the 1/lambda prior we can integrate analytically:
\int_0^\infty \lambda^n exp(-\lambda H) 1/\lambda d \lambda
= (n-1)! / H^n
The Yule prior (as we use it) is proportional to \lambda^n exp(-\lambda H) where n is the number of species and H is the sum of heights. Throwing on the 1/lambda prior we can integrate analytically: \int_0^\infty \lambda^n exp(-\lambda H) 1/\lambda d \lambda = (n-1)! / H^n
It seems we should just use this as our prior.