Dr Krzysztof Bartoszek, Dept. of Mathematics, Uppsala University, will give a seminar Tuesday February 18 in room 525, Naturhistoriska riksmuseet, 15:00.Welcome!
Tree-free phylogenetic comparative methods: what can we say about a species' trait without observing the phylogeny?
Abstract -- Phylogenetic comparative methods commonly assume that the evolutionary relationships between the studied species are known. With the current wealth of molecular information, this is often 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 pull) to OU processes with more and more pull.
In the OU process with a pure birth tree we show a Central Limit Theorem for the contemporary sample average. A phase transition is observed when the drift equals half the speciation rate.
The study of such a model requires knowledge of the moments of the times since speciation. This connects our work to moments of tree statistics allowing for short derivations of them.