Prior hypotheses or regularization allow inference of diversification histories from extant timetrees

Abstract

Phylogenies of extant species are widely used to study past diversification dynamics. The most common approach is to formulate a set of candidate models representing evolutionary hypotheses for how and why speciation and extinction rates in a clade changed over time, and compare those models through their probability to have generated the corresponding empirical tree. Recently, Louca & Pennell reported the existence of an infinite number of ‘congruent’ models with potentially markedly different diversification dynamics, but equal likelihood, for any empirical tree (see also Lambert & Stadler). Here we explore the implications of these results, and conclude that they neither undermine the hypothesis-driven model selection procedure widely used in the field nor show that speciation and extinction dynamics cannot be investigated from extant timetrees using a data-driven procedure.

What the paper shows and why it matters

(AI-generated)

Phylogenies of living species are used to infer how speciation and extinction rates changed in the past. The most common approach is to compare a few birth-death models, each standing for an evolutionary hypothesis, and ask which explains the tree best. Louca and Pennell (2020) showed that for any such tree there are infinitely many “congruent” models with different rate histories but identical likelihood, the measure of how well a model explains the data. The paper finds this result interesting and useful, but takes on its implicit goal: to learn the rate histories from the data alone, treating all congruent models as equally admissible and leaving out hypotheses, prior knowledge and a penalty for complexity.

The paper argues that the existence of many equally likely birth-death models for one tree does not undermine inference of diversification histories from trees of living species, because hypotheses and regularisation supply the constraints. Congruent models stand for no hypothesis formulated beforehand, so a well-conducted comparison would not consider them, and, as Louca and Pennell admit, most hypotheses that biologists compare can be told apart. To estimate rates from the data, regularisation (constraining a model, for example by smoothing or Bayesian priors) can handle the fact that the data cannot single out one model, and the paper expects it to remove the cases with markedly different histories. A deliberately simplified analysis of the Madagascan vangas illustrates these points. Of four models, one with declining speciation is best supported. Congruent models derived from it with a constant extinction rate differ in detail but keep the declining trend; those with constant speciation imply negative extinction and are discarded.

**Figure 1.** Diversification of the Madagascan vangas as inferred from congruent models. From Morlon et al. (2020), *bioRxiv*, licensed under CC BY-NC-ND 4.0. Click the image to enlarge.

The paper concludes that the implications of the congruence result are largely overinterpreted in Louca and Pennell’s paper, mainly because the constraints from hypothesis-driven research, prior knowledge and penalising complexity are not considered there. It treats the result as a reminder that chosen hypotheses shape conclusions, and as a possible source of new hypotheses, not as a challenge to current practice. Two questions stay open: whether model selection picks the right hypothesis when the true model is outside the candidate set, and which regularisation methods work best. Helmstetter et al. (2022) cite the paper as a response from the community to Louca and Pennell.

References

Louca & Pennell (2020). Extant timetrees are consistent with a myriad of diversification histories. Nature 580, 502–505. doi:10.1038/s41586-020-2176-1
Helmstetter et al. (2022). Pulled Diversification Rates, Lineages-Through-Time Plots, and Modern Macroevolutionary Modeling. Systematic Biology 71, 758–773. doi:10.1093/sysbio/syab083