Sebastian Höhna: Estimating non-constant species diversification rates and patterns under incomplete, systematic species sampling

The macro-evolutionary process of species diversity is commonly modeled using a birth-death branching process. Here I consider the class of processes where each species alive at time t has the same speciation rate lambda(t) and the extinction rate mu(t). The questions I aim to answer are: Did the rates change over time? How did the rates change over time? Where there times of mass-extinction and/or rapid radiations? Recent extensions include specific rate functions (e.g. exponential decreasing/increasing) and random species sampling. In this talk I will present the likelihood equations for any time-dependent rate function (e.g. with one or several modes) and systematic species sampling (e.g. one species per family). I will show the estimates of the speciation rate and extinction rate over time for the complete order of mammals. Additionally, I will present a second approach for the derivation of the likelihood which can be used for fast simulation of reconstructed phylogenetic trees for:

1. a fixed time of the process,
2. a fixed number of sampled species and
3. a fixed number of sampled species and time of the process.