Assumptions of Diversification Rate Estimation

Choices and impact of conditions of the birth-death process

Sebastian Höhna

Last modified on March 9, 2022

Conditions of the Birth-Death Process


Five different possible conditions for our generalized fossilized-birth-death process. I) The process survives until the present. II) The process starts at the root and both descendants of the root survive until the present. III) Sampling at least one lineage. IV) The process start at the root and both descendants have at least one lineage sampled. V) The process starts at the root, both descendants have at least one lineage sampled, and the process survives until the present.

Birth-death models are often conditioned on specific events, see (Stadler 2013), (Höhna 2015) and (Magee and Höhna 2021) for some discussion on the topic. However, when there are non-contemporaneous samples in the dataset which may be ancestral to other samples, conditioning becomes somewhat complex. The key issues for conditioning are whether it is assumed that the process starts at the root or the origin, and whether the descending lineage(s) is (are) assumed to leave any sampled descendant or specifically to have a descendant sampled at the present day. Consideration of these possibilities leads to five possible conditions, though conditioning is not strictly required.

For macroevolutionary analyses of diversification rates, condition (I) is the most adequate if we have both extinct and extant taxa, condition (II) if we have only extant taxa, and condition (III) if we have only extinct taxa. For phylodynamic applications, if it can safely be assumed that there are no sampled ancestors prior to the first observed infection (which will always be true if $r(t) = 1$), condition (IV) may be used, otherwise only condition (III) is applicable. Conditioning on survival as in (I), (II), or (V) requires $\Phi_0 > 0$, and so is primarily of interest in macroevolutionary applications. Of these conditions, (II) is the strictest and requires prior knowledge that the MRCA of the extant samples is the MRCA of all samples. Condition (V) is less restrictive, requiring only that none of the fossils could be sampled ancestors prior to the first observed speciation event, which would apply if all fossils are within the crown group. We could additionally condition on the number of extant taxa $N$, as suggest by (Gernhard 2008), although there is, as of today and to our knowledge, no solution known to condition on the number of extinct taxa.

  1. Gernhard T. 2008. The conditioned reconstructed process. Journal of Theoretical Biology. 253:769–778. 10.1016/j.jtbi.2008.04.005
  2. Höhna S. 2015. The time-dependent reconstructed evolutionary process with a key-role for mass-extinction events. Journal of Theoretical Biology. 380:321–331. http://dx.doi.org/10.1016/j.jtbi.2015.06.005
  3. Magee A.F., Höhna S. 2021. Impact of K-Pg Mass Extinction Event on Crocodylomorpha Inferred from Phylogeny of Extinct and Extant Taxa. bioRxiv.:426715. 10.1101/426715
  4. Stadler T. 2013. How can we improve accuracy of macroevolutionary rate estimates? Systematic Biology. 62:321–329.