Critically evaluating the theory and performance of Bayesian analysis of macroevolutionary mixtures

Abstract

Bayesian analysis of macroevolutionary mixtures (BAMM) has recently taken the study of lineage diversification by storm. BAMM estimates the diversification-rate parameters (speciation and extinction) for every branch of a study phylogeny and infers the number and location of diversification-rate shifts across branches of a tree. Our evaluation of BAMM reveals two major theoretical errors: (i) the likelihood function (which estimates the model parameters from the data) is incorrect, and (ii) the compound Poisson process prior model (which describes the prior distribution of diversification-rate shifts across branches) is incoherent. Using simulation, we demonstrate that these theoretical issues cause statistical pathologies; posterior estimates of the number of diversification-rate shifts are strongly influenced by the assumed prior, and estimates of diversificationrate parameters are unreliable. Moreover, the inability to correctly compute the likelihood or to correctly specify the prior for rate-variable trees precludes the use of Bayesian approaches for testing hypotheses regarding the number and location of diversification-rate shifts using BAMM.volutionary biologists have long sought to detect patterns and understand the causes of variation in rates of lineage diversification (speciation − extinction). This has motivated the development of several statistical methods for detecting whether (and where) diversification rates have changed across the branches of a phylogeny (1-4). A recent approach-Bayesian analysis of macroevolutionary mixtures (BAMM) (5)-promises to greatly enhance our ability to study this problem.This important new method offers several key advantages. (i) BAMM is based on an explicit model that describes how diversification rates shift across the branches of a tree. (ii) The underlying branching process is more complex (and presumably more realistic) than those used in previous methods. Specifically, BAMM not only includes parameters for the rate of speciation and extinction, but also accommodates possible time-dependent effects (where the age of a lineage may affect its diversification rate). This is intended to approximate the phenomenon of diversity-dependent diversification (where the number of species in a lineage may affect its diversification rate), which is believed to be a prevalent feature of empirical phylogenies (6). (iii) By virtue of developing this method in a Bayesian statistical framework, BAMM allows us to gauge the uncertainty in our inferences by providing marginal posterior probability densities rather than point estimates of parameters. (iv) By averaging inferences over any number of diversification-rate shifts, BAMM both accommodates uncertainty in the choice of model and avoids potential complications associated with model selection.BAMM provides estimates of the number and location of diversification-rate shifts across the branches of a tree and also estimates the diversification-rate parameters-speciation, extinction, and time dependence-on each branch of the tree. ...

Seed size and its rate of evolution correlate with species diversification across angiosperms

“…As the correlations with speciation and extinction were in the same direction and of comparable magnitude, and estimates of extinction rates were relatively variable (Fig 2E), net diversification rates did not change with seed size (ρ = −0.12, p-value = 0.077; Fig 2F). Generally, the observed correlations arose from many phenotypically fast-evolving clades distributed across the phylogeny (S1 Fig) and were robust to prior choice in the BAMM analyses ( S2 Fig). Given recent discussion on the reliability of BAMM for estimating diversification rates ( [21], but see [22]), we tested the robustness of our results by using alternative methodologies to infer macroevolutionary dynamics across clades at different timescales. Ten, 2 million yearwide time slices from the present up to 20 million years (myr) ago were defined.…”

“…The initial 30 million generations were discarded as burn-in. We analysed BAMM prior sensitivity following recent concerns ( [45], but see [22]) by rerunning both the diversification and the trait evolution analyses for the 13,577 species dataset with different settings for the expectedNumberOfShifts parameter of either 25, 50, 100, or 250. These analyses confirmed a low prior sensitivity for the posterior of the number of expected rate shifts (S2 Fig). Finally, we obtained clade-based measures of diversification and seed size evolution across the species-level tree.…”

Are Historical Biogeographical Events Able to Promote Biological Diversification?

“…These methods also allow us to identify shifts in macroevolutionary regimes (i.e., shifts in diversification process; e.g., bayesian analysis of macroevolutionary mixtures (BAMM) approach developed by [53]; but see Ref. [42] for a criticism about the statistical power). However, these phylogenetic methods are not integrated fully with methods of historical biogeographic inference.…”

“…The next step is to develop increasingly statistical robust methods to detect shifts in diversification dynamics and evaluate whether these shifts coincide with past dispersal or vicariance events and are not confounded by the emergence of hidden innovation key traits [53,75]. Although there is a current debate about the power of these methods to detect these shifts [42,53,55], the BAMM approach ( [53]) seems promising to detect these shifts in diversification dynamics across a phylogenetic tree with high confidence. BAMM allows us not only to detect shifts in speciation rates but shifts in the diversification dynamics itself.…”

The roles of diet, speciation and extinction on the diversification of birds, and on the assembly of frugivory networks

“…This overwhelming rock evidence of extinction contrasts with: (i) the phylogenetic perspective of diversification that usually suggests extremely low extinction rates (Quental and Marshall, 2010); (ii) a similar signature (at least when using a simple metric) between clades on equilibrium and clades experiencing diversity decline (Quental and Marshall, 2011); (iii) the view that extinction rates should not be estimated from molecular phylogenies (Rabosky, 2010). Although the development of new methods (Morlon et al, 2011;Rabosky, 2014) allow diversity decline to be estimated in principle, the question of whether extinction dynamics can be properly estimated from molecular phylogenies remains contentious Rabosky, 2010;Quental and Marshall, 2010;Morlon et al, 2011;Beaulieu and O'Meara, 2015;Rabosky, 2016, Moore et al, 2016Rabosky et al, 2017). By the virtue of knowing the true dynamics, simulation studies should be very valuable on investigating our ability to detect negative diversification rates based solely on molecular phylogenies, but to date only one exist that apply recently developed methods to a wide range of parameter space (Morlon et al, 2011).…”