Phylogenetic comparative methods commonly assume that the evolutionary relationships between the studied species are known. With the current wealth of molecular information this most often can be the case, but does not always need to be so. Especially amongst the lower orders we are lacking phylogenies, we might be studying fossil data where the DNA signal has degraded and in fact we are still discovering new species (even among the higher orders).
We consider a birth-death process conditioned on the number of tip species. The univariate trait evolving on top of it is modelled by a Brownian motion or Ornstein-Uhlenbeck process. We introduce the concept of the interspecies correlation coefficient which describes how quickly the tip species lose shared ancestral signal as we proceed from a Brownian motion (no drift) to OU processes with more and more drift. In the OU process with a pure birth tree we present a Central Limit Theorem for the contemporary sample average. A phase transition is observed when the drift equals half the speciation rate.

Tree-free phylogenetic comparative methods; Branching Ornstein-Uhlenbeck process, Yule tree