Monte Carlo algorithms for Brownian phylogenetic models

The diffused evolutionary dynamics of morphological novelty

Rates of evolution are fundamental to understand the processes that shaped the history of life. The predominant view holds that high rates of phenotypic evolution result from lineage transitions across peaks in an adaptive landscape, with subsequent slow-downs, but evidence remains debated. I developed a phylogenetic "diffused Brownian motion" model that characterizes nuanced variations in evolutionary rates and use it to comprehensively assess body size evolution and its underlying rates for 2,950 extinct and 792 extant species that span over 450 Mys of evolution. I find that evolutionary rates do not conform to expectations from adaptive landscape theory, but rather have been stable, unaffected by the accumulation of phenotypic disparity. Long-term evolutionary trends, such as several net increases in clade-average body size, result both from sustained evolution at the lineage level and the sorting of species phenotypes and their underlying evolutionary rates at the clade level, sometimes acting in opposite directions. These findings substantiate an active role of species in shaping their environment that generate continuous novelty of life forms.

Imbalanced speciation pulses sustain the radiation of mammals

The evolutionary histories of major clades, including mammals, often comprise changes in their diversification dynamics, but how these changes occur remains debated. We combined comprehensive phylogenetic and fossil information in a new "birth-death diffusion" model that provides a detailed characterization of variation in diversification rates in mammals. We found an early rising and sustained diversification scenario, wherein speciation rates increased before and during the Cretaceous-Paleogene (K-Pg) boundary. The K-Pg mass extinction event filtered out more slowly speciating lineages and was followed by a subsequent slowing in speciation rates rather than rebounds. These dynamics arose from an imbalanced speciation process, with separate lineages giving rise to many, less speciation-prone descendants. Diversity seems to have been brought about by these isolated, fast-speciating lineages, rather than by a few punctuated innovations.

Inferring long-term effective population size with Mutation-Selection Models

Mutation–selection phylogenetic codon models are grounded on population genetics first principles and represent a principled approach for investigating the intricate interplay between mutation, selection, and drift. In their current form, mutation–selection codon models are entirely characterized by the collection of site-specific amino-acid fitness profiles. However, thus far, they have relied on the assumption of a constant genetic drift, translating into a unique effective population size (Ne) across the phylogeny, clearly an unrealistic assumption. This assumption can be alleviated by introducing variation in Ne between lineages. In addition to Ne, the mutation rate (μ) is susceptible to vary between lineages, and both should covary with life-history traits (LHTs). This suggests that the model should more globally account for the joint evolutionary process followed by all of these lineage-specific variables (Ne, μ, and LHTs). In this direction, we introduce an extended mutation–selection model jointly reconstructing in a Bayesian Monte Carlo framework the fitness landscape across sites and long-term trends in Ne, μ, and LHTs along the phylogeny, from an alignment of DNA coding sequences and a matrix of observed LHTs in extant species. The model was tested against simulated data and applied to empirical data in mammals, isopods, and primates. The reconstructed history of Ne in these groups appears to correlate with LHTs or ecological variables in a way that suggests that the reconstruction is reasonable, at least in its global trends. On the other hand, the range of variation in Ne inferred across species is surprisingly narrow. This last point suggests that some of the assumptions of the model, in particular concerning the assumed absence of epistatic interactions between sites, are potentially problematic.

Differential Genome Size and Repetitive DNA Evolution in Diploid Species of Melampodium sect. Melampodium (Asteraceae)

Plant genomes vary greatly in composition and size mainly due to the diversity of repetitive DNAs and the inherent propensity for their amplification and removal from the host genome. Most studies addressing repeatome dynamics focus on model organisms, whereas few provide comprehensive investigations across the genomes of related taxa. Herein, we analyze the evolution of repeats of the 13 species in Melampodium sect. Melampodium, representing all but two of its diploid taxa, in a phylogenetic context. The investigated genomes range in size from 0.49 to 2.27 pg/1C (ca. 4.5-fold variation), despite having the same base chromosome number (x = 10) and very strong phylogenetic affinities. Phylogenetic analysis performed in BEAST and ancestral genome size reconstruction revealed mixed patterns of genome size increases and decreases across the group. High-throughput genome skimming and the RepeatExplorer pipeline were utilized to determine the repeat families responsible for the differences in observed genome sizes. Patterns of repeat evolution were found to be highly correlated with phylogenetic position, namely taxonomic series circumscription. Major differences found were in the abundances of the SIRE (Ty1-copia), Athila (Ty3-gypsy), and CACTA (DNA transposon) lineages. Additionally, several satellite DNA families were found to be highly group-specific, although their overall contribution to genome size variation was relatively small. Evolutionary changes in repetitive DNA composition and genome size were complex, with independent patterns of genome up- and downsizing throughout the evolution of the analyzed diploids. A model-based analysis of genome size and repetitive DNA composition revealed evidence for strong phylogenetic signal and differential evolutionary rates of major lineages of repeats in the diploid genomes.

On the Matrix Condition of Phylogenetic Tree

Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each element cij in C represents the affinity between extant species i and extant species j. This matrix C is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model. However, if the matrix is ill-conditioned (ie, if κ, defined by the ratio of the maximum eigenvalue of C to the minimum eigenvalue of C, is too high), this inversion may not be stable, and thus neither will be the calculation of the likelihood or parameter estimates that are based on optimizing the likelihood. We investigate this potential issue and propose several methods to attempt to remedy this issue.

Interdependent Phenotypic and Biogeographic Evolution Driven by Biotic Interactions

Biotic interactions are hypothesized to be one of the main processes shaping trait and biogeographic evolution during lineage diversification. Theoretical and empirical evidence suggests that species with similar ecological requirements either spatially exclude each other, by preventing the colonization of competitors or by driving coexisting populations to extinction, or show niche divergence when in sympatry. However, the extent and generality of the effect of interspecific competition in trait and biogeographic evolution has been limited by a dearth of appropriate process-generating models to directly test the effect of biotic interactions. Here, we formulate a phylogenetic parametric model that allows interdependence between trait and biogeographic evolution, thus enabling a direct test of central hypotheses on how biotic interactions shape these evolutionary processes. We adopt a Bayesian data augmentation approach to estimate the joint posterior distribution of trait histories, range histories, and coevolutionary process parameters under this analytically intractable model. Through simulations, we show that our model is capable of distinguishing alternative scenarios of biotic interactions. We apply our model to the radiation of Darwin’s finches—a classic example of adaptive divergence—and find limited support for in situ trait divergence in beak size, but stronger evidence for convergence in traits such as beak shape and tarsus length and for competitive exclusion throughout their evolutionary history. These findings are more consistent with presympatric, rather than postsympatric, niche divergence. Our modeling framework opens new possibilities for testing more complex hypotheses about the processes underlying lineage diversification. More generally, it provides a robust probabilistic methodology to model correlated evolution of continuous and discrete characters. [Bayesian; biotic interactions; competition; data augmentation; historical biogeography; trait evolution.]

A mixed relaxed clock model

Over recent years, several alternative relaxed clock models have been proposed in the context of Bayesian dating. These models fall in two distinct categories: uncorrelated and autocorrelated across branches. The choice between these two classes of relaxed clocks is still an open question. More fundamentally, the true process of rate variation may have both long-term trends and short-term fluctuations, suggesting that more sophisticated clock models unfolding over multiple time scales should ultimately be developed. Here, a mixed relaxed clock model is introduced, which can be mechanistically interpreted as a rate variation process undergoing short-term fluctuations on the top of Brownian long-term trends. Statistically, this mixed clock represents an alternative solution to the problem of choosing between autocorrelated and uncorrelated relaxed clocks, by proposing instead to combine their respective merits. Fitting this model on a dataset of 105 placental mammals, using both node-dating and tip-dating approaches, suggests that the two pure clocks, Brownian and white noise, are rejected in favour of a mixed model with approximately equal contributions for its uncorrelated and autocorrelated components. The tip-dating analysis is particularly sensitive to the choice of the relaxed clock model. In this context, the classical pure Brownian relaxed clock appears to be overly rigid, leading to biases in divergence time estimation. By contrast, the use of a mixed clock leads to more recent and more reasonable estimates for the crown ages of placental orders and superorders. Altogether, the mixed clock introduced here represents a first step towards empirically more adequate models of the patterns of rate variation across phylogenetic trees.This article is part of the themed issue 'Dating species divergences using rocks and clocks'.