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. 2025 Feb 13;380(1919):20230317.
doi: 10.1098/rstb.2023.0317. Epub 2025 Feb 20.

Speciation completion rates have limited impact on macroevolutionary diversification

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Speciation completion rates have limited impact on macroevolutionary diversification

Pierre Veron et al. Philos Trans R Soc Lond B Biol Sci. .

Abstract

Standard birth-death (BD) processes used in macroevolutionary studies assume instantaneous speciation, an unrealistic premise that limits the interpretation of speciation and extinction rates. The protracted birth-death (PBD) model instead assumes that speciation involves two steps: initiation and completion. In order to understand their respective influence on macroevolutionary speciation rates, we compute a standard time-varying BD scenario that is 'equivalent' to the PBD model in terms of speciation and extinction probabilities. First, we find a sharp decline in the equivalent birth rate near the present, indicating that rates estimated at the tips of phylogenies may not accurately reflect the underlying speciation process. Second, the completion rate controls the timing of the decay rather than the asymptotic equivalent rates. The equivalent birth rate in the past scales with the speciation initiation rate, with a scaling factor depending mostly on the population extinction rate. Our results suggest that the rates of population formation and extinction may often play a larger role than the speed of accumulation of reproductive isolation in modulating speciation rates. Our study establishes a theoretical framework for understanding how microevolutionary processes combine to explain the diversification of species on macroevolutionary time scales.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

Keywords: macroevolution; microevolution; phylogeny; speciation.

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Conflict of interest statement

We declare we have no competing interests.

Figures

The birth–death (BD) and protracted birth–death (PBD) models
Figure 1.
The BD and PBD models. (a, b) Illustrations of the rates involved in the BD model (a), and the PBD model (b). (c, d) Possible outcomes of the PBD process in a fixed time horizon, starting from a good lineage (c) or an incipient lineage (d); non-exhaustive examples of events leading to these outcomes are shown.
Alternative scenarios by which main outcomes occur in the protracted BD model.
Figure 2.
Alternative scenarios by which main outcomes occur in the PBD model. Upper panels: starting from an incipient lineage at time 0, decomposition of the possible exclusive ways of extinction (left) and no completion (right) before a given time t. Bottom panels: starting from a good lineage at time 0, decomposition of the possible exclusive ways of extinction (left) and speciation (right) before a given time t. Dotted lines represent incipient lineages, solid lines represent good lineages. Triangles summarize the subtrees containing the potential descendants of an ancestor lineage, with the condition that all of them go extinct within the remaining time (indicated by a cross), or that one of them completes speciation (indicated by a blue dot), or that none of these events occur. The probabilities written under the triangles correspond to the probability of the described event.
Influence of the parameters of the protracted birth–death (PBD) process on equivalent birth–death (BD) rates.
Figure 3.
Influence of the parameters of the PBD process on equivalent BD rates. Solid lines represent equivalent BD rates derived from (2.1) and (2.2) as a function of time for different values of PBD rates. Dotted lines represent constant equivalent BD rates derived analytically from (2.7) for the same PBD parameters. In the top/middle/bottom row, the initiation/completion/extinction rates vary, with the other rates constant (default values are λ1=λ3=0.3,λ2=0.4,μ1=μ2=0.1). In electronic supplementary material, figures S2 and S3, we calculated the same rates with the five parameters varying independently. t=30 corresponds to the present, t=0 to the past.
Relative influence of the parameters of the PBD model on the equivalent constant birth rate.
Figure 4.
Relative influence of the parameters of the PBD model on the equivalent constant birth rate. Colours indicate which of the PBD processes among initiation, completion and population extinction limits the equivalent constant birth rate λ~ most, as a function of (a) the initiation and completion rates and (b) the population extinction and completion rates, with the colour code explained in the triangle on the right. A yellow region (e.g. 1 or 2) indicates a combination of parameters where the most influential parameter on the birth rate is the rate of initiation. A blue region (e.g. 3) indicates a combination of parameters where the most influential parameter is the rate of completion λ2. An orange region (e.g. 4 or 5) indicates a combination of parameters where both population extinction and speciation initiation are influential. Green regions (e.g. 6 or 7) indicate situations where both speciation initiation and completion have a similar influence on the birth rate. In all cases, the rates of initiation and completion have a positive influence on the birth rate and the rate of population extinction has a negative influence. The detailed methods are explained in appendix F and the values of the relative influence are provided in electronic supplementary material, figure S5. When they do not vary, the default values of the parameters are 0.1.
Statistics of trees generated under the protracted birth–death (PBD) process and its equivalent birth–death (BD) processes.
Figure 5.
Statistics of trees generated under the PBD process and its equivalent BD processes. By row: species richness SR, γ shape statistic and stairs2 balance index for trees generated under the three models (PBD, equivalent constant-rate BD (BD) and equivalent time-varying rate BD (varBD)) for different values of the parameters of the PBD model. In each column, only one of the PBD parameters varies, with the others held constant (default λ1=0.5,λ2=1.0,λ3=0.4,μ1=0.2,μ2=0.2). For each set of parameters of the PBD model, BD and varBD trees were generated under equivalent birth and death rates computed using equations (2.1), (2.2) and (2.7), respectively. The lines correspond to the medians of statistics across all 200 replicates, the shaded areas indicate the first and last quartiles of the statistics. The sizes of the dots indicate the number of valid data for which the statistics could be calculated.

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