Relaxed random walk (RRW) models of trait evolution introduce branch-specific rate multipliers to modulate the variance of a standard Brownian diffusion process along a phylogeny and more accurately model overdispersed biological data. Increased taxonomic sampling challenges inference under RRWs as the number of unknown parameters grows with the number of taxa. To solve this problem, we present a scalable method to efficiently fit RRWs and infer this branch-specific variation in a Bayesian framework. We develop a Hamiltonian Monte Carlo (HMC) sampler to approximate the high-dimensional, correlated posterior that exploits a closed-form evaluation of the gradient of the trait data log-likelihood with respect to all branch-rate multipliers simultaneously. Our gradient calculation achieves computational complexity that scales only linearly with the number of taxa under study. We compare the efficiency of our HMC sampler to the previously standard univariable Metropolis-Hastings approach while studying the spatial emergence of the West Nile virus in North America in the early 2000s. Our method achieves at least a 6-fold speed increase over the univariable approach. Additionally, we demonstrate the scalability of our method by applying the RRW to study the correlation between five mammalian life history traits in a phylogenetic tree with $3650$ tips.[Bayesian inference; BEAST; Hamiltonian Monte Carlo; life history; phylodynamics, relaxed random walk.].

Erratum in Syst Biol. 2021 Jun 16;70(4):862.

The analysis of time-resolved phylogenies (timetrees) and geographic location data allows estimation of dispersal rates, for example, for invasive species and infectious diseases. Many estimation methods are based on the Brownian Motion model for diffusive dispersal on a 2D plane; however, the accuracy of these methods deteriorates substantially when dispersal occurs at global scales because spherical Brownian motion (SBM) differs from planar Brownian motion. No statistical method exists for estimating SBM diffusion coefficients from a given timetree and tip coordinates, and no method exists for simulating SBM along a given timetree. Here, I present new methods for simulating SBM along a given timetree, and for estimating SBM diffusivity from a given timetree and tip coordinates using a modification of Felsenstein's independent contrasts and maximum likelihood. My simulation and fitting methods can accommodate arbitrary time-dependent diffusivities and scale efficiently to trees with millions of tips, thus enabling new analyses even in cases where planar BM would be a sufficient approximation. I demonstrate these methods using a timetree of marine and terrestrial Cyanobacterial genomes, as well as timetrees of two globally circulating Influenza B clades. My methods are implemented in the R package "castor." [Independent contrasts; phylogenetic; random walk; simulation; spherical Brownian motion.].

The branching patterns of molecular phylogenies are generally assumed to contain information on rates of the underlying speciation and extinction processes. Simple birth-death models with constant, time-varying, or diversity-dependent rates have been invoked to explain these patterns. They have one assumption in common: all lineages have the same set of diversification rates at a given point in time. It seems likely, however, that there is variability in diversification rates across subclades in a phylogenetic tree. This has inspired the construction of models that allow multiple rate regimes across the phylogeny, with instantaneous shifts between these regimes. Several methods exist for calculating the likelihood of a phylogeny under a specified mapping of diversification regimes and for performing inference on the most likely diversification history that gave rise to a particular phylogenetic tree. Here, we show that the likelihood computation of these methods is not correct. We provide a new framework to compute the likelihood correctly and show, with simulations of a single shift, that the correct likelihood indeed leads to parameter estimates that are on average in much better agreement with the generating parameters than the incorrect likelihood. Moreover, we show that our corrected likelihood can be extended to multiple rate shifts in time-dependent and diversity-dependent models. We argue that identifying shifts in diversification rates is a nontrivial model selection exercise where one has to choose whether shifts in now-extinct lineages are taken into account or not. Hence, our framework also resolves the recent debate on such unobserved shifts. [Diversification; macroevolution; phylogeny; speciation].

Sequence alignment is essential for phylogenetic and molecular evolution inference, as well as in many other areas of bioinformatics and evolutionary biology. Inaccurate alignments can lead to severe biases in most downstream statistical analyses. Statistical alignment based on probabilistic models of sequence evolution addresses these issues by replacing heuristic score functions with evolutionary model-based probabilities. However, score-based aligners and fixed-alignment phylogenetic approaches are still more prevalent than methods based on evolutionary indel models, mostly due to computational convenience. Here, I present new techniques for improving the accuracy and speed of statistical evolutionary alignment. The "cumulative indel model" approximates realistic evolutionary indel dynamics using differential equations. "Adaptive banding" reduces the computational demand of most alignment algorithms without requiring prior knowledge of divergence levels or pseudo-optimal alignments. Using simulations, I show that these methods lead to fast and accurate pairwise alignment inference. Also, I show that it is possible, with these methods, to align and infer evolutionary parameters from a single long synteny block ($\approx$530 kbp) between the human and chimp genomes. The cumulative indel model and adaptive banding can therefore improve the performance of alignment and phylogenetic methods. [Evolutionary alignment; pairHMM; sequence evolution; statistical alignment; statistical genetics.].

Ultraconserved genomic elements (UCEs) are generally treated as independent loci in phylogenetic analyses. The identification pipeline for UCE probes does not require prior knowledge of genetic identity, only selecting loci that are highly conserved, single copy, without repeats, and of a particular length. Here, we characterized UCEs from 11 phylogenomic studies across the animal tree of life, from birds to marine invertebrates. We found that within vertebrate lineages, UCEs are mostly intronic and intergenic, while in invertebrates, the majority are in exons. We then curated four different sets of UCE markers by genomic category from five different studies including: birds, mammals, fish, Hymenoptera (ants, wasps, and bees), and Coleoptera (beetles). Of genes captured by UCEs, we find that many are represented by two or more UCEs, corresponding to nonoverlapping segments of a single gene. We considered these UCEs to be nonindependent, merged all UCEs that belonged to a particular gene, constructed gene and species trees, and then evaluated the subsequent effect of merging cogenic UCEs on gene and species tree reconstruction. Average bootstrap support for merged UCE gene trees was significantly improved across all data sets apparently driven by the increase in loci length. Additionally, we conducted simulations and found that gene trees generated from merged UCEs were more accurate than those generated by unmerged UCEs. As loci length improves gene tree accuracy, this modest degree of UCE characterization and curation impacts downstream analyses and demonstrates the advantages of incorporating basic genomic characterizations into phylogenomic analyses. [Anchored hybrid enrichment; ants; ASTRAL; bait capture; carangimorph; Coleoptera; conserved nonexonic elements; exon capture; gene tree; Hymenoptera; mammal; phylogenomic markers; songbird; species tree; ultraconserved elements; weevils.].

Current phylogenetic comparative methods modeling quantitative trait evolution generally assume that, during speciation, phenotypes are inherited identically between the two daughter species. This, however, neglects the fact that species consist of a set of individuals, each bearing its own trait value. Indeed, because descendent populations after speciation are samples of a parent population, we can expect their mean phenotypes to randomly differ from one another potentially generating a "jump" of mean phenotypes due to asymmetrical trait inheritance at cladogenesis. Here, we aim to clarify the effect of asymmetrical trait inheritance at speciation on macroevolutionary analyses, focusing on model testing and parameter estimation using some of the most common models of quantitative trait evolution. We developed an individual-based simulation framework in which the evolution of phenotypes is determined by trait changes at the individual level accumulating across generations, and cladogenesis occurs then by separation of subsets of the individuals into new lineages. Through simulations, we assess the magnitude of phenotypic jumps at cladogenesis under different modes of trait inheritance at speciation. We show that even small jumps can strongly alter both the results of model selection and parameter estimations, potentially affecting the biological interpretation of the estimated mode of evolution of a trait. Our results call for caution when interpreting analyses of trait evolution, while highlighting the importance of testing a wide range of alternative models. In the light of our findings, we propose that future methodological advances in comparative methods should more explicitly model the intraspecific variability around species mean phenotypes and how it is inherited at speciation.

The incorporation of stratigraphic data into phylogenetic analysis has a long history of debate but is not currently standard practice for paleontologists. Bayesian tip-dated (or morphological clock) phylogenetic methods have returned these arguments to the spotlight, but how tip dating affects the recovery of evolutionary relationships has yet to be fully explored. Here I show, through analysis of several data sets with multiple phylogenetic methods, that topologies produced by tip dating are outliers as compared to topologies produced by parsimony and undated Bayesian methods, which retrieve broadly similar trees. Unsurprisingly, trees recovered by tip dating have better fit to stratigraphy than trees recovered by other methods under both the Gap Excess Ratio (GER) and the Stratigraphic Completeness Index (SCI). This is because trees with better stratigraphic fit are assigned a higher likelihood by the fossilized birth-death tree model. However, the degree to which the tree model favors tree topologies with high stratigraphic fit metrics is modulated by the diversification dynamics of the group under investigation. In particular, when net diversification rate is low, the tree model favors trees with a higher GER compared to when net diversification rate is high. Differences in stratigraphic fit and tree topology between tip dating and other methods are concentrated in parts of the tree with weaker character signal, as shown by successive deletion of the most incomplete taxa from two data sets. These results show that tip dating incorporates stratigraphic data in an intuitive way, with good stratigraphic fit an expectation that can be overturned by strong evidence from character data. [fossilized birth-death; fossils; missing data; morphological clock; morphology; parsimony; phylogenetics.].

There are considerable phylogenetic incongruencies between morphological and phylogenomic data for the deep evolution of animals. This has contributed to a heated debate over the earliest-branching lineage of the animal kingdom: the sister to all other Metazoa (SOM). Here, we use published phylogenomic data sets ($\sim $45,000-400,000 characters in size with $\sim $15-100 taxa) that focus on early metazoan phylogeny to evaluate the impact of incorporating morphological data sets ($\sim $15-275 characters). We additionally use small exemplar data sets to quantify how increased taxon sampling can help stabilize phylogenetic inferences. We apply a plethora of common methods, that is, likelihood models and their "equivalent" under parsimony: character weighting schemes. Our results are at odds with the typical view of phylogenomics, that is, that genomic-scale data sets will swamp out inferences from morphological data. Instead, weighting morphological data 2-10$\times $ in both likelihood and parsimony can in some cases "flip" which phylum is inferred to be the SOM. This typically results in the molecular hypothesis of Ctenophora as the SOM flipping to Porifera (or occasionally Placozoa). However, greater taxon sampling improves phylogenetic stability, with some of the larger molecular data sets ($>$200,000 characters and up to $\sim $100 taxa) showing node stability even with $\geqq100\times $ upweighting of morphological data. Accordingly, our analyses have three strong messages. 1) The assumption that genomic data will automatically "swamp out" morphological data is not always true for the SOM question. Morphological data have a strong influence in our analyses of combined data sets, even when outnumbered thousands of times by molecular data. Morphology therefore should not be counted out a priori. 2) We here quantify for the first time how the stability of the SOM node improves for several genomic data sets when the taxon sampling is increased. 3) The patterns of "flipping points" (i.e., the weighting of morphological data it takes to change the inferred SOM) carry information about the phylogenetic stability of matrices. The weighting space is an innovative way to assess comparability of data sets that could be developed into a new sensitivity analysis tool. [Metazoa; Morphology; Phylogenomics; Weighting.].

Mouse lemurs (Microcebus) are a radiation of morphologically cryptic primates distributed throughout Madagascar for which the number of recognized species has exploded in the past two decades. This taxonomic revision has prompted understandable concern that there has been substantial oversplitting in the mouse lemur clade. Here, we investigate mouse lemur diversity in a region in northeastern Madagascar with high levels of microendemism and predicted habitat loss. We analyzed RADseq data with multispecies coalescent (MSC) species delimitation methods for two pairs of sister lineages that include three named species and an undescribed lineage previously identified to have divergent mtDNA. Marked differences in effective population sizes, levels of gene flow, patterns of isolation-by-distance, and species delimitation results were found among the two pairs of lineages. Whereas all tests support the recognition of the presently undescribed lineage as a separate species, the species-level distinction of two previously described species, M. mittermeieri and M. lehilahytsara is not supported-a result that is particularly striking when using the genealogical discordance index (gdi). Nonsister lineages occur sympatrically in two of the localities sampled for this study, despite an estimated divergence time of less than 1 Ma. This suggests rapid evolution of reproductive isolation in the focal lineages and in the mouse lemur clade generally. The divergence time estimates reported here are based on the MSC calibrated with pedigree-based mutation rates and are considerably more recent than previously published fossil-calibrated relaxed-clock estimates. We discuss the possible explanations for this discrepancy, noting that there are theoretical justifications for preferring the MSC estimates in this case. [Cryptic species; effective population size; microendemism; multispecies coalescent; speciation; species delimitation.].

It is widely recognized that different regions of a genome often have different evolutionary histories and that ignoring this variation when estimating phylogenies can be misleading. However, the extent to which this is also true for morphological data is still largely unknown. Discordance among morphological traits might plausibly arise due to either variable convergent selection pressures or else phenomena such as hemiplasy. Here, we investigate patterns of discordance among 282 morphological characters, which we scored for 50 bee species particularly targeting corbiculate bees, a group that includes the well-known eusocial honeybees and bumblebees. As a starting point for selecting the most meaningful partitions in the data, we grouped characters as morphological modules, highly integrated trait complexes that as a result of developmental constraints or coordinated selection we expect to share an evolutionary history and trajectory. In order to assess conflict and coherence across and within these morphological modules, we used recently developed approaches for computing Bayesian phylogenetic information allied with model comparisons using Bayes factors. We found that despite considerable conflict among morphological complexes, accounting for among-character and among-partition rate variation with individual gamma distributions, rate multipliers, and linked branch lengths can lead to coherent phylogenetic inference using morphological data. We suggest that evaluating information content and dissonance among partitions is a useful step in estimating phylogenies from morphological data, just as it is with molecular data. Furthermore, we argue that adopting emerging approaches for investigating dissonance in genomic datasets may provide new insights into the integration and evolution of anatomical complexes. [Apidae; entropy; morphological modules; phenotypic integration; phylogenetic information.].

Gene tree discordance in large genomic data sets can be caused by evolutionary processes such as incomplete lineage sorting and hybridization, as well as model violation, and errors in data processing, orthology inference, and gene tree estimation. Species tree methods that identify and accommodate all sources of conflict are not available, but a combination of multiple approaches can help tease apart alternative sources of conflict. Here, using a phylotranscriptomic analysis in combination with reference genomes, we test a hypothesis of ancient hybridization events within the plant family Amaranthaceae s.l. that was previously supported by morphological, ecological, and Sanger-based molecular data. The data set included seven genomes and 88 transcriptomes, 17 generated for this study. We examined gene-tree discordance using coalescent-based species trees and network inference, gene tree discordance analyses, site pattern tests of introgression, topology tests, synteny analyses, and simulations. We found that a combination of processes might have generated the high levels of gene tree discordance in the backbone of Amaranthaceae s.l. Furthermore, we found evidence that three consecutive short internal branches produce anomalous trees contributing to the discordance. Overall, our results suggest that Amaranthaceae s.l. might be a product of an ancient and rapid lineage diversification, and remains, and probably will remain, unresolved. This work highlights the potential problems of identifiability associated with the sources of gene tree discordance including, in particular, phylogenetic network methods. Our results also demonstrate the importance of thoroughly testing for multiple sources of conflict in phylogenomic analyses, especially in the context of ancient, rapid radiations. We provide several recommendations for exploring conflicting signals in such situations. [Amaranthaceae; gene tree discordance; hybridization; incomplete lineage sorting; phylogenomics; species network; species tree; transcriptomics.].

Taxon sampling is a central aspect of phylogenetic study design, but it has received limited attention in the context of total-evidence dating, a widely used dating approach that directly integrates molecular and morphological information from extant and fossil taxa. We here assess the impact of commonly employed outgroup sampling schemes and missing morphological data in extant taxa on age estimates in a total-evidence dating analysis under the uniform tree prior. Our study group is Pimpliformes, a highly diverse, rapidly radiating group of parasitoid wasps of the family Ichneumonidae. We analyze a data set comprising 201 extant and 79 fossil taxa, including the oldest fossils of the family from the Early Cretaceous and the first unequivocal representatives of extant subfamilies from the mid-Paleogene. Based on newly compiled molecular data from ten nuclear genes and a morphological matrix that includes 222 characters, we show that age estimates become both older and less precise with the inclusion of more distant and more poorly sampled outgroups. These outgroups not only lack morphological and temporal information but also sit on long terminal branches and considerably increase the evolutionary rate heterogeneity. In addition, we discover an artifact that might be detrimental for total-evidence dating: "bare-branch attraction," namely high attachment probabilities of certain fossils to terminal branches for which morphological data are missing. Using computer simulations, we confirm the generality of this phenomenon and show that a large phylogenetic distance to any of the extant taxa, rather than just older age, increases the risk of a fossil being misplaced due to bare-branch attraction. After restricting outgroup sampling and adding morphological data for the previously attracting, bare branches, we recover a Jurassic origin for Pimpliformes and Ichneumonidae. This first age estimate for the group not only suggests an older origin than previously thought but also that diversification of the crown group happened well before the Cretaceous-Paleogene boundary. Our case study demonstrates that in order to obtain robust age estimates, total-evidence dating studies need to be based on a thorough and balanced sampling of both extant and fossil taxa, with the aim of minimizing evolutionary rate heterogeneity and missing morphological information. [Bare-branch attraction; ichneumonids; fossils; morphological matrix; phylogeny; RoguePlots.].