Prolonging the past counteracts the pull of the present: protracted speciation can explain observed slowdowns in diversification

Abstract

Phylogenetic trees show a remarkable slowdown in the increase of number of lineages towards the present, a phenomenon which cannot be explained by the standard birth-death model of diversification with constant speciation and extinction rates. The birth-death model instead predicts a constant or accelerating increase in the number of lineages, which has been called the pull of the present. The observed slowdown has been attributed to nonconstancy of the speciation and extinction rates due to some form of diversity dependence (i.e., species-level density dependence), but the mechanisms underlying this are still unclear. Here, we propose an alternative explanation based on the simple concept that speciation takes time to complete. We show that this idea of "protracted" speciation can be incorporated in the standard birth-death model of diversification. The protracted birth-death model predicts a realistic slowdown in the rate of increase of number of lineages in the phylogeny and provides a compelling fit to four bird phylogenies with realistic parameter values. Thus, the effect of recognizing the generally accepted fact that speciation is not an instantaneous event is significant; even if it cannot account for all the observed patterns, it certainly contributes substantially and should therefore be incorporated into future studies.

Figure 1.

The pure birth model a) with and b) without protracted speciation. Dotted lines indicate an incipient species and solid lines are good species. c) Phylogeny of the protracted pure birth process of panel b: only those lineages that have completed speciation before the present will show up in the phylogeny. Note that the branching points are at the times that the incipient species are produced, not at the times that they become good species.

Figure 2.

Expected LTT plot for the protracted pure birth model (i.e., no extinction) for various values of the speciation completion rate λ₂. The value of the speciation initiation rate λ₁ is 0.5. The curve for λ₂ = ∞ is barely visible, as it almost coincides with the curve for λ₂ = 10.

FIGURE 3.

The birth–death model with and without protracted speciation. a) A birth–death process that is extinct before the present time T, an eventuality that most analyses are conditioned against. b) A birth–death process that survives up to the present time T. c) The birth–death process of b where speciation is protracted. Dotted lines indicate an incipient species and solid lines are good species. d) Phylogeny of the protracted birth–death process of panel c. Only those lineages that have completed speciation or incipient lineages whose parent species has gone extinct before the present will show up in the phylogeny.

FIGURE 4.

Expected LTT plots for the protracted birth–death model for various values of the extinction rate μ₁ = μ₂ (upper panels) and the corresponding histograms of the slowdown statistic r (bottom panels). The lines are for different speciation completion rates λ₂. The value of the speciation initiation rate λ₁ is set at 0.5. The curve for λ₂ = ∞ is barely visible, as it almost coincides with the curve for λ₂ = 10.

FIGURE 5.

Expected LTT plots for the protracted birth–death model for various values of the incipient species extinction rate μ₂, where the extinction rate of good species is set at μ₁ = 0.4. The lines are for different speciation completion rates λ₂. The value of the speciation initiation rate λ₁ is set at 0.5.

FIGURE 6.

LTT plots (stars) of four bird phylogenies, selected from Phillimore & Price (2008) (see text for selection criteria) and the fits of the protracted birth model (gray) and the protracted birth–death model (black). The former is obtained through maximum likelihood, the latter by least squares (see text). We assumed that μ₂ = μ₁ and λ₃ = λ₁, so the fitted parameters are λ₁, λ₂, and μ₁.