2013/12/09 by Sebastian Höhna, Höhna, Sebastian
Earth and Planetary Sciences · Biochemistry, Genetics and Molecular Biology · Environmental Science · #Evolution and Paleontology Studies #Genomics and Phylogenetic Studies #Ecology and Vegetation Dynamics Studies
paper · pdf · doi:10.48550/arxiv.1312.2392
The homogeneous reconstructed evolutionary process is a birth-death process\nwithout observed extinct lineages. Each species evolves independently with the\nsame diversification rates (speciation rate \λ(t) and extinction rate\n\μ(t)) that may change over time. The process is commonly applied to model\nspecies diversification where the data are reconstructed phylogenies, e.g.,\ntrees reconstructed from present-day molecular data, and used to infer\ndiversification rates.\n In the present paper I develop the general probability density of a\nreconstructed tree under any time-dependent birth-death process. I elaborate on\nhow to adapt this probability density if conditioned on survival of one or two\ninitial lineages, or having sampled n species and show how to transform\nbetween the probability density of a reconstructed and the probability density\nof the speciation times.\n I demonstrate the use of the general time-dependent probability density\nfunctions by deriving the probability density of a reconstructed tree under a\nbirth-death-shift model with explicit mass-extinction events. I enrich this\ncompendium by providing and discussing several special cases, including: the\npure birth process, the pure death process, the birth-death process and the\ncritical branching process. Thus, I provide here most of the commonly used\nbirth-death models in a unified framework (e.g., same condition and same data)\nwith common notation.\n