The time-dependent reconstructed evolutionary process with a key-role for mass-extinction events

Abstract

The homogeneous reconstructed evolutionary process is a birth-death process without observed extinct lineages. Each species evolves independently with the same diversification rate-speciation rate, λ(t), and extinction rate, µ(t)-that may change over time. The process is commonly applied to model species diversification where the data are reconstructed phylogenies, e.g., trees estimated from present-day molecular data, and used to infer diversification rates.In the present paper I develop the general probability density of a reconstructed tree under any homogeneous, time-dependent birth-death process. I demonstrate how to adapt this probability density when conditioning on the survival of one or two initial lineages, or on the process realizing n species, and also how to transform between the probability density of a reconstructed tree and the probability density of the speciation times.I demonstrate the use of the general time-dependent probability density functions by deriving the probability density of a reconstructed tree under a birth-death-shift model with explicit mass-extinction events. I extend these functions to several special cases, including the pure-birth process, the pure-death process, the birth-death process, and the critical-branching process. Thus, I specify equations for the most commonly used birth-death models in a unified framework (e.g., same condition and same data) using a common notation.

Transcriptome‐based phylogeny of endemic Lake Baikal amphipod species flock: fast speciation accompanied by frequent episodes of positive selection

“…a). Both frequently used models of changes in diversification rates with time (Rabosky & Lovette ; Höhna ) support decreasing speciation rates (Fig. S4B, Supporting information).…”

“…= 1; P < 0.001). Höhna () model, which takes into account incomplete lineage sampling, supports an exponentially decreasing speciation rate with a nonzero extinction rate with the assumption of ‘diversified’ sampling strategy. Predicted extinction rate exceeds speciation rate resulting in predicted negative diversification rate in the most recent 1/10 of the time since divergence from the common ancestor with the Caspian species (Fig.…”

“…Species were selected for sequencing with the goal to increase the number of lineages covered (i.e. additional available species redundant with respect to large clades such as Micruropus , Eulimnogammarus or Pallasea were not included into sequencing); thus, the ‘diversified’ model of phylogenetic incompleteness was assumed for diversification rate analysis (Höhna ), see below.…”

“…Branching times were estimated from the chronotree obtained by chronos function (Kim & Sanderson ) of ape r package. Diversification rates along the reconstructed phylogeny were estimated using the models of Rabosky & Lovette () and the ‘diversified’ version of Höhna (); the ‘random’ version of this model was also evaluated for comparison. Both these models suffer from a number of methodological problems and their predictions may be biased (Moore et al .…”

Stochastic character mapping of state-dependent diversification reveals the tempo of evolutionary decline in self-compatible Onagraceae lineages

“…where N 0 is the number of lineages at time 0 and d is the net diversification rate λ − µ (Nee et al 1994;Höhna 2015). Therefore, we estimated as:d…”