mv morph : an r package for fitting multivariate evolutionary models to morphometric data

Convergent evolution of olfactory and thermoregulatory capacities in small amphibious mammals

Olfaction and thermoregulation are key functions for mammals. The former is critical to feeding, mating, and predator avoidance behaviors, while the latter is essential for homeothermy. Aquatic and amphibious mammals face olfactory and thermoregulatory challenges not generally encountered by terrestrial species. In mammals, the nasal cavity houses a bony system supporting soft tissues and sensory organs implicated in either olfactory or thermoregulatory functions. It is hypothesized that to cope with aquatic environments, amphibious mammals have expanded their thermoregulatory capacity at the expense of their olfactory system. We investigated the evolutionary history of this potential trade-off using a comparative dataset of three-dimensional (3D) CT scans of 189 skulls, capturing 17 independent transitions from a strictly terrestrial to an amphibious lifestyle across small mammals (Afrosoricida, Eulipotyphla, and Rodentia). We identified rapid and repeated loss of olfactory capacities synchronously associated with gains in thermoregulatory capacity in amphibious taxa sampled from across mammalian phylogenetic diversity. Evolutionary models further reveal that these convergences result from faster rates of turbinal bone evolution and release of selective constraints on the thermoregulatory-olfaction trade-off in amphibious species. Lastly, we demonstrated that traits related to vital functions evolved faster to the optimum compared to traits that are not related to vital functions.

Modularity and evolution of flower shape: the role of function, development, and spandrels in Erica

Flowers have been hypothesized to contain either modules of attraction and reproduction, functional modules (pollination-effecting parts) or developmental modules (organ-specific). Do pollination specialization and syndromes influence floral modularity? In order to test these hypotheses and answer this question, we focused on the genus Erica: we gathered 3D data from flowers of 19 species with diverse syndromes via computed tomography, and for the first time tested the above-mentioned hypotheses via 3D geometric morphometrics. To provide an evolutionary framework for our results, we tested the evolutionary mode of floral shape, size and integration under the syndromes regime, and - for the first time - reconstructed the high-dimensional floral shape of their most recent common ancestor. We demonstrate that the modularity of the 3D shape of generalist flowers depends on development and that of specialists is linked to function: modules of pollen deposition and receipt in bird syndrome, and access-restriction to the floral reward in long-proboscid fly syndrome. Only size and shape principal component 1 showed multiple-optima selection, suggesting that they were co-opted during evolution to adapt flowers to novel pollinators. Whole floral shape followed an Ornstein-Uhlenbeck (selection-driven) evolutionary model, and differentiated relatively late. Flower shape modularity thus crucially depends on pollinator specialization and syndrome.

Evolution of ecological structure of anole communities in tropical rain forests from north-western South America

The coexistence of several anoles in the same place is attributed to differential partitioning of resources. Although several mainland and island communities show a similar structure, differences in life-history traits, absence of niche complementarity, higher food supply and higher numbers of predators in mainland environments support the idea that predation, rather than competition, is a more important structuring force in mainland than in island anole communities. To analyse the pattern of ecological structure in mainland anole communities, we studied communities in three tropical rain forests of north-western South America to obtain data about the use of resources on three niche axes [spatial, thermal and morphological (as a proxy of diet)] for 17 species of anoles. We analysed the patterns of niche overlap for each axis and found that overlap on the dietary axis was less than the overlap on the other axes, indicating that species using similar spatial or thermal resources diverge strongly in their diet. In addition, we identified a niche complementarity among niche axes, suggesting that intraspecific competition is also an important process in those communities. Finally, this study revealed a similar ecological structure in different communities of mainland rain-forest anoles, which share seven ecomorphs, suggesting ecological adaptation and convergence in mainland anoles.

Characterizing and Comparing Phylogenetic Trait Data from Their Normalized Laplacian Spectrum

The dissection of the mode and tempo of phenotypic evolution is integral to our understanding of global biodiversity. Our ability to infer patterns of phenotypes across phylogenetic clades is essential to how we infer the macroevolutionary processes governing those patterns. Many methods are already available for fitting models of phenotypic evolution to data. However, there is currently no comprehensive nonparametric framework for characterizing and comparing patterns of phenotypic evolution. Here, we build on a recently introduced approach for using the phylogenetic spectral density profile (SDP) to compare and characterize patterns of phylogenetic diversification, in order to provide a framework for nonparametric analysis of phylogenetic trait data. We show how to construct the SDP of trait data on a phylogenetic tree from the normalized graph Laplacian. We demonstrate on simulated data the utility of the SDP to successfully cluster phylogenetic trait data into meaningful groups and to characterize the phenotypic patterning within those groups. We furthermore demonstrate how the SDP is a powerful tool for visualizing phenotypic space across traits and for assessing whether distinct trait evolution models are distinguishable on a given empirical phylogeny. We illustrate the approach in two empirical data sets: a comprehensive data set of traits involved in song, plumage, and resource-use in tanagers, and a high-dimensional data set of endocranial landmarks in New World monkeys. Considering the proliferation of morphometric and molecular data collected across the tree of life, we expect this approach will benefit big data analyses requiring a comprehensive and intuitive framework.

Reliable Phylogenetic Regressions for Multivariate Comparative Data: Illustration with the MANOVA and Application to the Effect of Diet on Mandible Morphology in Phyllostomid Bats

Understanding what shapes species phenotypes over macroevolutionary timescales from comparative data often requires studying the relationship between phenotypes and putative explanatory factors or testing for differences in phenotypes across species groups. In phyllostomid bats for example, is mandible morphology associated to diet preferences? Performing such analyses depends upon reliable phylogenetic regression techniques and associated tests (e.g., phylogenetic Generalized Least Squares, pGLS, and phylogenetic analyses of variance and covariance, pANOVA, pANCOVA). While these tools are well established for univariate data, their multivariate counterparts are lagging behind. This is particularly true for high-dimensional phenotypic data, such as morphometric data. Here, we implement much-needed likelihood-based multivariate pGLS, pMANOVA, and pMANCOVA, and use a recently developed penalized-likelihood framework to extend their application to the difficult case when the number of traits $p$ approaches or exceeds the number of species $n$. We then focus on the pMANOVA and use intensive simulations to assess the performance of the approach as $p$ increases, under various levels of phylogenetic signal and correlations between the traits, phylogenetic structure in the predictors, and under various types of phenotypic differences across species groups. We show that our approach outperforms available alternatives under all circumstances, with greater power to detect phenotypic differences across species group when they exist, and a lower risk of improperly detecting nonexistent differences. Finally, we provide an empirical illustration of our pMANOVA on a geometric-morphometric data set describing mandible morphology in phyllostomid bats along with data on their diet preferences. Overall our results show significant differences between ecological groups. Our approach, implemented in the R package mvMORPH and illustrated in a tutorial for end-users, provides efficient multivariate phylogenetic regression tools for understanding what shapes phenotypic differences across species. [Generalized least squares; high-dimensional data sets; multivariate phylogenetic comparative methods; penalized likelihood; phenomics; phyllostomid bats; phylogenetic MANOVA; phylogenetic regression.]

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.

Comparative Analyses of Phenotypic Sequences Using Phylogenetic Trees

Phenotypic sequences are a type of multivariate trait organized structurally, such as teeth distributed along the dental arch, or temporally, such as the stages of an ontogenetic series. Unlike other multivariate traits, the elements of a phenotypic sequence are distributed along an ordered set, which allows for distinct evolutionary patterns between neighboring and distant positions. In fact, sequence traits share many characteristics with molecular sequences, although important distinctions pose challenges to current comparative methods. We implement an approach to estimate rates of trait evolution that explicitly incorporates the sequence organization of traits. We apply models to study the temporal pattern evolution of cricket calling songs. We test whether neighboring positions along a phenotypic sequence have correlated rates of evolution or whether rate variation is independent of sequence position. Our results show that cricket song evolution is strongly autocorrelated and that models perform well when used with sequence phenotypes even under small sample sizes. Our approach is flexible and can be applied to any multivariate trait with discrete units organized in a sequence-like structure.

The association between morphological and ecological characters across a global passerine radiation

Strong relationships between morphological and ecological characters are commonly predicted to reflect the association between form and function, with this hypothesis being well supported in restricted taxonomic and geographical contexts. Conversely, among broader sets of species, ecological variables have been shown to have limited power to explain morphological variation. To understand these apparent discrepancies, for a large and globally distributed passerine radiation, we test whether (a) the character states of four ecological variables (foraging mode, diet, strata and habitat) have different morphological optima, (b) ecological variables explain substantial variance in morphology and (c) ecological character states can be accurately predicted from morphology. We collected 10 linear morphological measurements for 782 species of corvoid passerines, and assessed (a) the fit of models of continuous trait evolution with different morphological optima for each ecological character state, (b) variation in morphological traits among ecological character states using phylogenetically corrected regressions and (c) the accuracy of morphological traits in predicting species-level membership of ecological character states using linear discriminant analysis (LDA). Models of morphological evolution with different ecological optima were well supported across numerous morphological axes, corresponding with significant differences in trait distributions among ecological character states. LDA also showed that membership of the ecological categories can be predicted with relatively high accuracy by morphology. In contrast to these findings, ecological variables explain limited amounts of variation in morphological traits. For a global radiation of passerine birds, we confirm that the generation of morphological variation is generally consistent with ecological selection pressures, but that ecological characters are of limited utility in explaining morphological differences among species. Although selection towards different optima means that membership of ecological character states tend to be well predicted by morphology, the overall morphospace of individual ecological character states tend to be broad, implying that morphology can evolve in multiple ways in response to similar selection pressures. Extensive variation in morphological adaptations among similar ecological strategies is likely to be a widespread phenomenon across the tree of life.

Variation in limb loading magnitude and timing in tetrapods

Comparative analyses of locomotion in tetrapods reveal two patterns of stride cycle variability. Tachymetabolic tetrapods (birds and mammals) have lower inter-cycle variation in stride duration than bradymetabolic tetrapods (amphibians, lizards, turtles and crocodilians). This pattern has been linked to the fact that birds and mammals share enlarged cerebella, relatively enlarged and heavily myelinated Ia afferents, and γ-motoneurons to their muscle spindles. Both tachymetabolic tetrapod lineages also possess an encapsulated Golgi tendon morphology, thought to provide more spatially precise information on muscle tension. The functional consequence of this derived Golgi tendon morphology has never been tested. We hypothesized that one advantage of precise information on muscle tension would be lower and more predictable limb bone stresses, achieved in tachymetabolic tetrapods by having less variable substrate reaction forces than bradymetabolic tetrapods. To test this hypothesis, we analyzed hindlimb substrate reaction forces during locomotion of 55 tetrapod species in a phylogenetic comparative framework. Variation in species means of limb loading magnitude and timing confirm that, for most of the variables analyzed, variance in hindlimb loading and timing is significantly lower in species with encapsulated versus unencapsulated Golgi tendon organs. These findings suggest that maintaining predictable limb loading provides a selective advantage for birds and mammals by allowing energy savings during locomotion, lower limb bone safety factors and quicker recovery from perturbations. The importance of variation in other biomechanical variables in explaining these patterns, such as posture, effective mechanical advantage and center-of-mass mechanics, remains to be clarified.

Rates of ecomorphological trait evolution in passerine bird clades are independent of age

Although the links between species richness and diversification rates with clade age have been studied extensively, few studies have investigated the relationship between the rates of trait evolution and clade age. The rate of morphological trait evolution has repeatedly been shown to vary through time, as expected, for example, for adaptive radiations, but the strength and sources of this variation are not well understood. We compare the relationship between the rates of trait evolution and clade age across eight monophyletic clades of passerine birds by investigating ecomorphological traits, i.e. morphological traits that influence the ecology of the species directly. We study the ecomorphological divergence pattern using analyses of the disparity through time and determine the best-fitting model of evolution for each trait in each clade. We find no support for a consistent dependence of evolutionary rates on clade age across wing, tail, tarsus and beak shape in our eight clades and also show that early burst models of trait evolution are rarely the best-fitting models within these clades. These results suggest that key innovations or adaptive radiations might be less common evolutionary patterns and processes than generally thought or might depend on the taxonomic level investigated.

Beyond Brownian Motion and the Ornstein-Uhlenbeck Process: Stochastic Diffusion Models for the Evolution of Quantitative Characters

Gaussian processes, such as Brownian motion and the Ornstein-Uhlenbeck process, have been popular models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. However, they have drawbacks that limit their utility. Here we describe new, non-Gaussian stochastic differential equation (diffusion) models of quantitative trait evolution. We present general methods for deriving new diffusion models and develop new software for fitting non-Gaussian evolutionary models to trait data. The theory of stochastic processes provides a mathematical framework for understanding the properties of current and future phylogenetic comparative methods. Attention to the mathematical details of models of trait evolution and diversification may help avoid some pitfalls when using stochastic processes to model macroevolution.

Fast likelihood calculation for multivariate Gaussian phylogenetic models with shifts

Phylogenetic comparative methods (PCMs) have been used to study the evolution of quantitative traits in various groups of organisms, ranging from micro-organisms to animal and plant species. A common approach has been to assume a Gaussian phylogenetic model for the trait evolution along the tree, such as a branching Brownian motion (BM) or an Ornstein-Uhlenbeck (OU) process. Then, the parameters of the process have been inferred based on a given tree and trait data for the sampled species. At the heart of this inference lie multiple calculations of the model likelihood, that is, the probability density of the observed trait data, conditional on the model parameters and the tree. With the increasing availability of big phylogenetic trees, spanning hundreds to several thousand sampled species, this approach is facing a two-fold challenge. First, the assumption of a single Gaussian process governing the entire tree is not adequate in the presence of heterogeneous evolutionary forces acting in different parts of the tree. Second, big trees present a computational challenge, due to the time and memory complexity of the model likelihood calculation. Here, we explore a sub-family, denoted G_LInv, of the Gaussian phylogenetic models, with the transition density exhibiting the properties that the expectation depends Linearly on the ancestral trait value and the variance is Invariant with respect to the ancestral value. We show that G_LInv contains the vast majority of Gaussian models currently used in PCMs, while supporting an efficient (linear in the number of nodes) algorithm for the likelihood calculation. The algorithm supports scenarios with missing data, as well as different types of trees, including trees with polytomies and non-ultrametric trees. To account for the heterogeneity in the evolutionary forces, the algorithm supports models with "shifts" occurring at specific points in the tree. Such shifts can include changes in some or all parameters, as well as the type of the model, provided that the model remains within the G_LInv family. This contrasts with most of the current implementations where, due to slow likelihood calculation, the shifts are restricted to specific parameters in a single type of model, such as the long-term selection optima of an OU process, assuming that all of its other parameters, such as evolutionary rate and selection strength, are global for the entire tree. We provide an implementation of this likelihood calculation algorithm in an accompanying R-package called PCMBase. The package has been designed as a generic library that can be integrated with existing or novel maximum likelihood or Bayesian inference tools.

Stepwise shifts underlie evolutionary trends in morphological complexity of the mammalian vertebral column

A fundamental concept in evolutionary biology is that life tends to become more complex through geologic time, but empirical examples of this phenomenon are controversial. One debate is whether increasing complexity is the result of random variations, or if there are evolutionary processes which actively drive its acquisition, and if these processes act uniformly across clades. The mammalian vertebral column provides an opportunity to test these hypotheses because it is composed of serially-repeating vertebrae for which complexity can be readily measured. Here we test seven competing hypotheses for the evolution of vertebral complexity by incorporating fossil data from the mammal stem lineage into evolutionary models. Based on these data, we reject Brownian motion (a random walk) and uniform increasing trends in favor of stepwise shifts for explaining increasing complexity. We hypothesize that increased aerobic capacity in non-mammalian cynodonts may have provided impetus for increasing vertebral complexity in mammals.

Phylogenetic Comparative Methods and the Evolution of Multivariate Phenotypes

Evolutionary biology is multivariate, and advances in phylogenetic comparative methods for multivariate phenotypes have surged to accommodate this fact. Evolutionary trends in multivariate phenotypes are derived from distances and directions between species in a multivariate phenotype space. For these patterns to be interpretable, phenotypes should be characterized by traits in commensurate units and scale. Visualizing such trends, as is achieved with phylomorphospaces, should continue to play a prominent role in macroevolutionary analyses. Evaluating phylogenetic generalized least squares (PGLS) models (e.g., phylogenetic analysis of variance and regression) is valuable, but using parametric procedures is limited to only a few phenotypic variables. In contrast, nonparametric, permutation-based PGLS methods provide a flexible alternative and are thus preferred for high-dimensional multivariate phenotypes. Permutation-based methods for evaluating covariation within multivariate phenotypes are also well established and can test evolutionary trends in phenotypic integration. However, comparing evolutionary rates and modes in multivariate phenotypes remains an important area of future development.

The Evolutionary Radiation of Hominids: a Phylogenetic Comparative Study

Over the last 150 years the diversity and phylogenetic relationships of the hominoids have been one of the main focuses in biological and anthropological research. Despite this, the study of factors involved in their evolutionary radiation and the origin of the hominin clade, a key subject for the further understanding of human evolution, remained mostly unexplored. Here we quantitatively approach these events using phylogenetic comparative methods and craniofacial morphometric data from extant and fossil hominoid species. Specifically, we explore alternative evolutionary models that allow us to gain new insights into this clade diversification process. Our results show a complex and variable scenario involving different evolutionary regimes through the hominid evolutionary radiation –modeled by Ornstein-Uhlenbeck multi-selective regime and Brownian motion multi-rate scenarios–. These different evolutionary regimes might relate to distinct ecological and cultural factors previously suggested to explain hominid evolution at different evolutionary scales along the last 10 million years.

Weighing homoplasy against alternative scenarios with the help of macroevolutionary modeling: A case study on limb bones of fossorial sciuromorph rodents

Homoplasy is a strong indicator of a phenotypic trait's adaptive significance when it can be linked to a similar function. We assessed homoplasy in functionally relevant scapular and femoral traits of Marmotini and Xerini, two sciuromorph rodent clades that independently acquired a fossorial lifestyle from an arboreal ancestor. We studied 125 species in the scapular dataset and 123 species in the femoral dataset. Pairwise evolutionary model comparison was used to evaluate whether homoplasy of trait optima is more likely than other plausible scenarios. The most likely trend of trait evolution among all traits was assessed via likelihood scoring of all considered models. The homoplasy hypothesis could never be confirmed as the single most likely model. Regarding likelihood scoring, scapular traits most frequently did not differ among Marmotini, Xerini, and arboreal species. For the majority of femoral traits, results indicate that Marmotini, but not Xerini, evolved away from the ancestral arboreal condition. We conclude on the basis of the scapular results that the forelimbs of fossorial and arboreal sciuromorphs share mostly similar functional demands, whereas the results on the femur indicate that the hind limb morphology is less constrained, perhaps depending on the specific fossorial habitat.

Evolution of the vomer and its implications for cranial kinesis in Paraves

Most living birds exhibit cranial kinesis-movement between the rostrum and braincase-in which force is transferred through the palatal and jugal bars. The palate alone distinguishes the Paleognathae from the Neognathae, with cranial kinesis more developed in neognaths. Most previous palatal studies were based on 2D data and rarely incorporated data from stem birds despite great interest in their kinetic abilities. Here we reconstruct the vomer of the Early Cretaceous stem bird Sapeornis and the troodontid Sinovenator, taxa spanning the dinosaur-bird transition. A 3D shape analysis including these paravians and an extensive sampling of neornithines reveals their strong similarity to paleognaths and indicates that morphological differences in the vomer between paleognaths and neognaths are intimately related to their different kinetic abilities. These results suggest the skull of Mesozoic paravians lacked the kinetic abilities observed in neognaths, a conclusion also supported by our identification of an ectopterygoid in Sapeornis here. We conclude that cranial kinesis evolved relatively late, likely an innovation of the Neognathae, and is linked to the transformation of the vomer. This transformation increased palatal mobility, enabling the evolution of a diversity of kinetic mechanisms and ultimately contributing to the extraordinary evolutionary success of this clade.

Phylo-comparative analyses reveal the dual role of drift and selection in reproductive character displacement

When incipient species meet in secondary contact, natural selection can rapidly reduce costly reproductive interactions by directly targeting reproductive traits. This process, called reproductive character displacement (RCD), leaves a characteristic pattern of geographic variation where divergence of traits between species is greater in sympatry than allopatry. However, because other forces can also cause similar patterns, care must be given in separating pattern from process. Here we show how the phylo-comparative method together with genomic data can be used to evaluate evolutionary processes at the population level in closely related species. Using this framework, we test the role of RCD in speciation of two cricket species endemic to Anatolian mountains by quantifying patterns of character displacement, rates of evolution and adaptive divergence. Our results show differing patterns of character displacement between species for reproductive vs. non-reproductive characters and strong patterns of asymmetric divergence. We demonstrate diversification results from rapid divergence of reproductive traits towards multiple optima under the dual influence of strong drift and selection. These results present the first solid evidence for RCD in Anatolian mountains, quantify the amount of drift and selection necessary for RCD to lead to speciation, and demonstrate the utility of phylo-comparative methods for quantifying evolutionary parameters at the population level.

Automatic generation of evolutionary hypotheses using mixed Gaussian phylogenetic models

Phylogenetic comparative methods are widely used to understand and quantify the evolution of phenotypic traits, based on phylogenetic trees and trait measurements of extant species. Such analyses depend crucially on the underlying model. Gaussian phylogenetic models like Brownian motion and Ornstein-Uhlenbeck processes are the workhorses of modeling continuous-trait evolution. However, these models fit poorly to big trees, because they neglect the heterogeneity of the evolutionary process in different lineages of the tree. Previous works have addressed this issue by introducing shifts in the evolutionary model occurring at inferred points in the tree. However, for computational reasons, in all current implementations, these shifts are "intramodel," meaning that they allow jumps in 1 or 2 model parameters, keeping all other parameters "global" for the entire tree. There is no biological reason to restrict a shift to a single model parameter or, even, to a single type of model. Mixed Gaussian phylogenetic models (MGPMs) incorporate the idea of jointly inferring different types of Gaussian models associated with different parts of the tree. Here, we propose an approximate maximum-likelihood method for fitting MGPMs to comparative data comprising possibly incomplete measurements for several traits from extant and extinct phylogenetically linked species. We applied the method to the largest published tree of mammal species with body- and brain-mass measurements, showing strong statistical support for an MGPM with 12 distinct evolutionary regimes. Based on this result, we state a hypothesis for the evolution of the brain-body-mass allometry over the past 160 million y.

The multi-peak adaptive landscape of crocodylomorph body size evolution

BACKGROUND

Little is known about the long-term patterns of body size evolution in Crocodylomorpha, the > 200-million-year-old group that includes living crocodylians and their extinct relatives. Extant crocodylians are mostly large-bodied (3-7 m) predators. However, extinct crocodylomorphs exhibit a wider range of phenotypes, and many of the earliest taxa were much smaller (< 1.2 m). This suggests a pattern of size increase through time that could be caused by multi-lineage evolutionary trends of size increase or by selective extinction of small-bodied species. Here, we characterise patterns of crocodylomorph body size evolution using a model fitting-approach (with cranial measurements serving as proxies). We also estimate body size disparity through time and quantitatively test hypotheses of biotic and abiotic factors as potential drivers of crocodylomorph body size evolution.

RESULTS

Crocodylomorphs reached an early peak in body size disparity during the Late Jurassic, and underwent an essentially continual decline since then. A multi-peak Ornstein-Uhlenbeck model outperforms all other evolutionary models fitted to our data (including both uniform and non-uniform), indicating that the macroevolutionary dynamics of crocodylomorph body size are better described within the concept of an adaptive landscape, with most body size variation emerging after shifts to new macroevolutionary regimes (analogous to adaptive zones). We did not find support for a consistent evolutionary trend towards larger sizes among lineages (i.e., Cope's rule), or strong correlations of body size with climate. Instead, the intermediate to large body sizes of some crocodylomorphs are better explained by group-specific adaptations. In particular, the evolution of a more aquatic lifestyle (especially marine) correlates with increases in average body size, though not without exceptions.

CONCLUSIONS

Shifts between macroevolutionary regimes provide a better explanation of crocodylomorph body size evolution on large phylogenetic and temporal scales, suggesting a central role for lineage-specific adaptations rather than climatic forcing. Shifts leading to larger body sizes occurred in most aquatic and semi-aquatic groups. This, combined with extinctions of groups occupying smaller body size regimes (particularly during the Late Cretaceous and Cenozoic), gave rise to the upward-shifted body size distribution of extant crocodylomorphs compared to their smaller-bodied terrestrial ancestors.

Ecomorphology of Neotropical Electric Fishes: An Integrative Approach to Testing the Relationships between Form, Function, and Trophic Ecology

The relationship between form and function is thought to play an integral role in structuring broad-scale patterns of morphological evolution and resource utilization. In ecomorphological studies, mechanical performance is widely understood to constrain the evolution of form and function. However, the relationship between form, function, and resource utilization is less clear. Additionally, seasonal fluctuations in resource availability may further complicate patterns of resource use. How organisms cope with these complexities, and the effect of these factors on broadscale patterns of morphological evolution is also poorly understood. Here we use three-dimensional geometric morphometrics, biomechanics, stable isotope analysis, and gut-content analysis to study trophic evolution in a clade of riverine-adapted electric fishes from a region with high seasonal variability; the Amazon River. We find significant and phylogenetically structured relationships among measures of trophic ecology and skull shape. We also recover a significant relationship between the mechanical advantage of the mandible and trophic position, where species feeding at higher trophic levels have narrower jaws with lower mechanical advantages, and species feeding at lower trophic levels have deeper jaws with higher mechanical advantages. Our results indicate that selection is driving the evolution of mandible shape and performance toward specialization on different trophic ecologies.

Functional trait evolution in Sphagnum peat mosses and its relationship to niche construction

Species in the genus Sphagnum create, maintain, and dominate boreal peatlands through 'extended phenotypes' that allow these organisms to engineer peatland ecosystems and thereby impact global biogeochemical cycles. One such phenotype is the production of peat, or incompletely decomposed biomass, that accumulates when rates of growth exceed decomposition. Interspecific variation in peat production is thought to be responsible for the establishment and maintenance of ecological gradients such as the microtopographic hummock-hollow gradient, along which sympatric species sort within communities. This study investigated the mode and tempo of functional trait evolution across 15 species of Sphagnum using data from the most extensive studies of Sphagnum functional traits to date and phylogenetic comparative methods. We found evidence for phylogenetic conservatism of the niche descriptor height-above-water-table and of traits related to growth, decay and litter quality. However, we failed to detect the influence of phylogeny on interspecific variation in other traits such as shoot density and suggest that environmental context can obscure phylogenetic signal. Trait correlations indicate possible adaptive syndromes that may relate to niche and its construction. This study is the first to formally test the extent to which functional trait variation among Sphagnum species is a result of shared evolutionary history.

On trends and patterns in macroevolution: Williston's law and the branchiostegal series of extant and extinct osteichthyans

BACKGROUND

The branchiostegal series consists of an alignment of bony elements in the posterior portion of the skull of osteichthyan vertebrates. We trace the evolution of the number of elements in a comprehensive survey that includes 440 extant and 66 extinct species. Using a newly updated actinopterygian tree in combination with phylogenetic comparative analyses, we test whether osteichthyan branchiostegals follow an evolutionary trend under 'Williston's law', which postulates that osteichthyan lineages experienced a reduction of bony elements over time.

RESULTS

We detected no overall macroevolutionary trend in branchiostegal numbers, providing no support for 'Williston's law'. This result is robust to the subsampling of palaeontological data, but the estimation of the model parameters is much more ambiguous.

CONCLUSIONS

We find substantial evidence for a macroevolutionary dynamic favouring an 'early burst' of trait evolution over alternative models. Our study highlights the challenges of accurately reconstructing macroevolutionary dynamics even with large amounts of data about extant and extinct taxa.

Non-uniform evolutionary response of gecko eye size to changes in diel activity patterns

Geckos feature a large range of eye sizes, but what drives this phenotypic diversity is currently unknown. Earlier studies point towards diel activity patterns (DAPs) and locomotory mode, but phylogenetic comparative studies in support of the proposed adaptive mode of eye evolution are lacking. Here, we test the hypothesis of DAPs as the driver of eye size evolution with a dataset on 99 species of gecko. Results from phylogenetic generalized least-square analysis (PGLS) and multivariate model-fitting reveal smaller eyes in diurnal geckos consistent with different phenotypic optima. However, Bayesian analyses of selective regime shifts demonstrate that only two of nine transitions from nocturnal to diurnal activity are coupled with decreases in eye size, and two other regime shifts are not associated with DAP transitions. This non-uniform evolutionary response suggests that eye size is not the only functionally relevant variable. Evolutionary adaptations may therefore include different combinations of several traits (e.g. photoreceptors), all with the same functional outcome. Our results further demonstrate that DAP only partially explains eye size diversity in geckos. As open habitats favour the evolution of large eyes while obstructed habitats favour small eyes, the degree of habitat clutter emerges as another potential axis of eye diversification.

Evolutionary shifts in extant mustelid (Mustelidae: Carnivora) cranial shape, body size and body shape coincide with the Mid-Miocene Climate Transition

Environmental changes can lead to evolutionary shifts in phenotypic traits, which in turn facilitate the exploitation of novel adaptive landscapes and lineage diversification. The global cooling, increased aridity and expansion of open grasslands during the past 50 Myr are prime examples of new adaptive landscapes that spurred lineage and ecomorphological diversity of several mammalian lineages such as rodents and large herbivorous megafauna. However, whether these environmental changes facilitated evolutionary shifts in small- to mid-sized predator morphology is unknown. Here, I used a complete cranial and body morphological dataset to examine the timing of evolutionary shifts in cranial shape, body size and body shape within extant mustelids (martens, otters, polecats and weasels) during the climatic and environmental changes of the Cenozoic. I found that evolutionary shifts in all three traits occurred within extant mustelid subclades just after the onset of the Mid-Miocene Climate Transition. These mustelid subclades first shifted towards more elongate body plans followed by concurrent shifts towards smaller body sizes and more robust crania. I hypothesize that these cranial and body morphological shifts enabled mustelids to exploit novel adaptive zones associated with the climatic and environmental changes of the Mid to Late Miocene, which facilitated significant increases in clade carrying capacity.

When Does Form Reflect Function? Acknowledging and Supporting Ecomorphological Assumptions

Ecomorphology is the study of relationships between organismal morphology and ecology. As such, it is the only way to determine if morphometric data can be used as an informative proxy for ecological variables of interest. To achieve this goal, ecomorphology often depends on, or directly tests, assumptions about the nature of the relationships among morphology, performance, and ecology. We discuss three approaches to the study of ecomorphology: morphometry-driven, function-driven, and ecology-driven and study design choices inherent to each approach. We also identify 10 assumptions that underlie ecomorphological research: 4 of these are central to all ecomorphological studies and the remaining 6 are variably applicable to some of the specific approaches described above. We discuss how these assumptions may impact ecomorphological studies and affect the interpretation of their findings. We also point out some limitations of ecomorphological studies, and highlight some ways by which we can strengthen, validate, or eliminate systematic assumptions.

Signatures of echolocation and dietary ecology in the adaptive evolution of skull shape in bats

Morphological diversity may arise rapidly as a result of adaptation to novel ecological opportunities, but early bursts of trait evolution are rarely observed. Rather, models of discrete shifts between adaptive zones may better explain macroevolutionary dynamics across radiations. To investigate which of these processes underlie exceptional levels of morphological diversity during ecological diversification, we use modern phylogenetic tools and 3D geometric morphometric datasets to examine adaptive zone shifts in bat skull shape. Here we report that, while disparity was established early, bat skull evolution is best described by multiple adaptive zone shifts. Shifts are partially decoupled between the cranium and mandible, with cranial evolution more strongly driven by echolocation than diet. Phyllostomidae, a trophic adaptive radiation, exhibits more adaptive zone shifts than all other families combined. This pattern was potentially driven by ecological opportunity and facilitated by a shift to intermediate cranial shapes compared to oral-emitters and other nasal emitters.

What drives changes in morphological diversity? Here, Arbour et al. analyse skull 3D shape evolution across the bat radiation using µCT scan data, finding two phases of skull shape diversification, early adaptive shifts related to echolocation, and more recent shifts related to diet transitions.

Evolutionary parallelisms of pectoral and pelvic network-anatomy from fins to limbs

Lobe-fins transformed into limbs during the Devonian period, facilitating the water-to-land transition in tetrapods. We traced the evolution of well-articulated skeletons across the fins-to-limbs transition, using a network-based approach to quantify and compare topological features of fins and limbs. We show that the topological arrangement of bones in pectoral and pelvic appendages evolved in parallel during the fins-to-limbs transition, occupying overlapping regions of the morphospace, following a directional trend, and decreasing their disparity over time. We identify the presence of digits as the morphological novelty triggering topological changes that discriminated limbs from fins. The origin of digits caused an evolutionary shift toward appendages that were less densely and heterogeneously connected, but more assortative and modular. Disparity likewise decreased for both appendages, more markedly until a time concomitant with the earliest-known tetrapod tracks. Last, we rejected the presence of a pectoral-pelvic similarity bottleneck at the origin of tetrapods.

The African ape-like foot of Ardipithecus ramidus and its implications for the origin of bipedalism

The ancestral condition from which humans evolved is critical for understanding the adaptive origin of bipedal locomotion. The 4.4 million-year-old hominin partial skeleton attributed to Ardipithecus ramidus preserves a foot that purportedly shares morphometric affinities with monkeys, but this interpretation remains controversial. Here I show that the foot of Ar. ramidus is most similar to living chimpanzee and gorilla species among a large sample of anthropoid primates. The foot morphology of Ar. ramidus suggests that the evolutionary precursor of hominin bipedalism was African ape-like terrestrial quadrupedalism and climbing. The elongation of the midfoot and phalangeal reduction in Ar. ramidus relative to the African apes is consistent with hypotheses of increased propulsive capabilities associated with an early form of bipedalism. This study provides evidence that the modern human foot was derived from an ancestral form adapted to terrestrial plantigrade quadrupedalism.

Walking on two legs is considered to be one of the first steps towards becoming human. While some animals are also able to walk on two legs, such as kangaroos, birds, and some rodents, the way they move is nevertheless quite distinct to the way humans walk.

How animals evolve traits is influenced by the characteristics of their ancestors. But what exactly was the common ancestor of humans and chimpanzees like? Most primates are suited for a life in the trees. But some also have skeletal characteristics associated with living on the ground. For example, the feet of chimpanzees and gorillas show adaptations that suit life on the ground, such as walking on the sole of the foot with a heel first foot posture. So far, it was unclear whether the ancestor of humans and chimpanzees was primarily adapted to living on the ground or in the trees.

To investigate this further, Prang studied the oldest-known fossil foot (4.4 million years) attributed to the hominin Ardipithecus ramidus. This involved using evolutionary models to evaluate the relationship between foot bone proportions and the locomotory behaviour of monkeys and apes. The results revealed that humans evolved from an ancestor that had a foot similar to living chimpanzees and gorillas. The African ape foot is uniquely suited to life on the ground, including shorter toe bones, but also shows some adaptations to life in the trees, such as an elongated, grasping big toe. Therefore, the locomotion of our common ancestor probably bore a strong resemblance to these two ape species. Moreover, if the last common ancestor already had ground-living characteristics, the first step of the evolution of human bipedalism did not involve descending from the trees to the ground, as our ancestors had already achieved this milestone in some form and frequency.

This is an important discovery. If this ancestor already had adaptations for life on the ground, why did only humans evolve to walk upright despite the retention of climbing capabilities in the earliest human relatives? A next step could be to investigate what selective pressures favored upright walking in a partly ground-living African ape. This may provide us with more insight into our own evolutionary story as well as the ways in which living primates evolve adaptations in an ecological context.

Estimating Correlated Rates of Trait Evolution with Uncertainty

Correlated evolution among traits, which can happen due to genetic constraints, ontogeny, and selection, can have an important impact on the trajectory of phenotypic evolution. For example, shifts in the pattern of evolutionary integration may allow the exploration of novel regions of the morphospace by lineages. Here, we use phylogenetic trees to study the pace of evolution of several traits and their pattern of evolutionary correlation across clades and over time. We use regimes mapped to the branches of the phylogeny to test for shifts in evolutionary integration while incorporating the uncertainty related to trait evolution and ancestral regimes with joint estimation of all parameters of the model using Bayesian Markov chain Monte Carlo. We implemented the use of summary statistics to test for regime shifts based on a series of attributes of the model that can be directly relevant to biological hypotheses. In addition, we extend Felsenstein's pruning algorithm to the case of multivariate Brownian motion models with multiple rate regimes. We performed extensive simulations to explore the performance of the method under a series of scenarios. Finally, we provide two test cases; the evolution of a novel buccal morphology in fishes of the family Centrarchidae and a shift in the trajectory of evolution of traits during the radiation of anole lizards to and from the Caribbean islands. [Anolis; Centrarchidae; comparative methods; evolutionary integration; evolutionary rates; modularity; pruning algorithm.].

Tempo and mode of mandibular shape and size evolution reveal mixed support for incumbency effects in two clades of island-endemic rodents (Muridae: Murinae)

Existing radiations in a spatially limited system such as an oceanic island may limit the ecological opportunity experienced by later colonists, resulting in lower macroevolutionary rates for secondary radiations. Additionally, potential colonists may be competitively excluded by these incumbent (resident) species, unless they are biologically distinct (biotic filtering). The extant phenotypic diversity of secondary colonists may thus be impacted by lower rates of phenotypic evolution, exclusion from certain phenotypes, and transitions to new morphotypes to escape competition from incumbent lineages. We used geometric morphometric methods to test whether the rates and patterns of mandibular evolution of the Luzon "old endemic" rodent clades, Phloeomyini and Chrotomyini, are consistent with these predictions. Each clade occupied nearly completely separate shape space and partially separate size space. We detected limited support for decelerating and clade-specific evolutionary rates for both shape and size, with strong evidence for a shift in evolutionary mode within Chrotomyini. Our results suggest that decelerating phenotypic evolutionary rates are not a necessary result of incumbency interactions; rather, incumbency effects may be more likely to determine which clades can become established in the system. Nonincumbent clades that pass a biotic filter can potentially exhibit relatively unfettered evolution.

Niche divergence and limits to expansion in the high polyploid Dianthus broteri complex

Niche evolution in plant polyploids remains controversial and evidence for alternative patterns has been reported. Using the autopolyploid Dianthus broteri complex (2×, 4×, 6× and 12×) as a model, we aimed to integrate three scenarios - competitive exclusion, recurrent origins of cytotypes and niche filling - into a single framework of polyploid niche evolution. We hypothesized that high polyploids would tend to evolve towards extreme niches when low ploidy cytotypes have nearly filled the niche space. We used several ecoinformatics and phylogenetic comparative analyses to quantify differences in the ecological niche of each cytotype and to evaluate alternative models of niche evolution. Each cytotype in this complex occupied a distinct ecological niche. The distributions were mainly constrained by soil characteristics, temperature and drought stress imposed by the Mediterranean climate. Tetraploids had the highest niche breadth and overlap due to their multiple origins, whereas the higher ploidy cytotypes were found in different, restricted, nonoverlapping niches. Niche evolution analyses suggested a scenario with one niche optimum for each ploidy, including the two independent tetraploid lineages. Our results suggest that the fate of nascent polyploids could not be predicted without accounting for phylogenetic relatedness, recurrent origins or the niche occupied by ancestors.

Performance in three shell functions predicts the phenotypic distribution of hard-shelled turtles

Adaptive landscapes have served as fruitful guides to evolutionary research for nearly a century. Current methods guided by landscape frameworks mostly utilize evolutionary modeling (e.g., fitting data to Ornstein-Uhlenbeck models) to make inferences about adaptive peaks. Recent alternative methods utilize known relationships between phenotypes and functional performance to derive information about adaptive landscapes; this information can then help explain the distribution of species in phenotypic space and help infer the relative importance of various functions for guiding diversification. Here, data on performance for three turtle shell functions-strength, hydrodynamic efficiency, and self-righting ability-are used to develop a set of predicted performance optima in shell shape space. The distribution of performance optima shows significant similarity to the distribution of existing turtle species and helps explain the absence of shells in otherwise anomalously empty regions of morphospace. The method outperforms a modeling-based approach in inferring the location of reasonable adaptive peaks and in explaining the shape of the phenotypic distributions of turtle shells. Performance surface-based methods allow researchers to more directly connect functional performance with macroevolutionary diversification, and to explain the distribution of species (including presences and absences) across phenotypic space.

Clownfishes evolution below and above the species level

The difference between rapid morphological evolutionary changes observed in populations and the long periods of stasis detected in the fossil record has raised a decade-long debate about the exact role played by intraspecific mechanisms at the interspecific level. Although they represent different scales of the same evolutionary process, micro- and macroevolution are rarely studied together and few empirical studies have compared the rates of evolution and the selective pressures between both scales. Here, we analyse morphological, genetic and ecological traits in clownfishes at different evolutionary scales and demonstrate that the tempo of molecular and morphological evolution at the species level can be, to some extent, predicted from parameters estimated below the species level, such as the effective population size or the rate of evolution within populations. We also show that similar codons in the gene of the rhodopsin RH1, a light-sensitive receptor protein, are under positive selection at the intra and interspecific scales, suggesting that similar selective pressures are acting at both levels.

The Grass was Greener: Repeated Evolution of Specialized Morphologies and Habitat Shifts in Ghost Spiders Following Grassland Expansion in South America

While grasslands, one of Earth's major biomes, are known for their close evolutionary ties with ungulate grazers, these habitats are also paramount to the origins and diversification of other animals. Within the primarily South American spider subfamily Amaurobioidinae (Anyphaenidae), several species are found living in the continent's grasslands, with some displaying putative morphological adaptations to dwelling unnoticed in the grass blades. Herein, a dated molecular phylogeny provides the backbone for analyses revealing the ecological and morphological processes behind these spiders' grassland adaptations. The multiple switches from Patagonian forests to open habitats coincide with the expansion of South America's grasslands during the Miocene, while the specialized morphology of several grass-dwelling spiders originated at least three independent times and is best described as the result of different selective regimes operating on macroevolutionary timescales. Although grass-adapted lineages evolved towards different peaks in adaptive landscape, they all share one characteristic: an anterior narrowing of the prosoma allowing spiders to extend the first two pairs of legs, thus maintaining a slender resting posture in the grass blade. By combining phylogenetic, morphological, and biogeographic perspectives we disentangle multiple factors determining the evolution of a clade of terrestrial invertebrate predators alongside their biomes.

A Penalized Likelihood Framework for High-Dimensional Phylogenetic Comparative Methods and an Application to New-World Monkeys Brain Evolution

Working with high-dimensional phylogenetic comparative data sets is challenging because likelihood-based multivariate methods suffer from low statistical performances as the number of traits $p $ approaches the number of species $n $ and because some computational complications occur when $p $ exceeds $n$. Alternative phylogenetic comparative methods have recently been proposed to deal with the large $p $ small $n $ scenario but their use and performances are limited. Herein, we develop a penalized likelihood (PL) framework to deal with high-dimensional comparative data sets. We propose various penalizations and methods for selecting the intensity of the penalties. We apply this general framework to the estimation of parameters (the evolutionary trait covariance matrix and parameters of the evolutionary model) and model comparison for the high-dimensional multivariate Brownian motion (BM), Early-burst (EB), Ornstein-Uhlenbeck (OU), and Pagel's lambda models. We show using simulations that our PL approach dramatically improves the estimation of evolutionary trait covariance matrices and model parameters when $p$ approaches $n$, and allows for their accurate estimation when $p$ equals or exceeds $n$. In addition, we show that PL models can be efficiently compared using generalized information criterion (GIC). We implement these methods, as well as the related estimation of ancestral states and the computation of phylogenetic principal component analysis in the R package RPANDA and mvMORPH. Finally, we illustrate the utility of the new proposed framework by evaluating evolutionary models fit, analyzing integration patterns, and reconstructing evolutionary trajectories for a high-dimensional 3D data set of brain shape in the New World monkeys. We find a clear support for an EB model suggesting an early diversification of brain morphology during the ecological radiation of the clade. PL offers an efficient way to deal with high-dimensional multivariate comparative data.

Post-Cretaceous bursts of evolution along the benthic-pelagic axis in marine fishes

Ecological opportunity arising in the aftermath of mass extinction events is thought to be a powerful driver of evolutionary radiations. Here, we assessed how the wake of the Cretaceous-Palaeogene (K-Pg) mass extinction shaped diversification dynamics in a clade of mostly marine fishes (Carangaria), which comprises a disparate array of benthic and pelagic dwellers including some of the most astonishing fish forms (e.g. flatfishes, billfishes, remoras, archerfishes). Analyses of lineage diversification show time-heterogeneous rates of lineage diversification in carangarians, with highest rates reached during the Palaeocene. Likewise, a remarkable proportion of Carangaria's morphological variation originated early in the history of the group and in tandem with a marked incidence of habitat shifts. Taken together, these results suggest that all major lineages and body plans in Carangaria originated in an early burst shortly after the K-Pg mass extinction, which ultimately allowed the occupation of newly released niches along the benthic-pelagic habitat axis.

Convergent evolution of an extreme dietary specialisation, the olfactory system of worm-eating rodents

Turbinal bones are key components of the mammalian rostrum that contribute to three critical functions: (1) homeothermy, (2) water conservation and (3) olfaction. With over 700 extant species, murine rodents (Murinae) are the most species-rich mammalian subfamily, with most of that diversity residing in the Indo-Australian Archipelago. Their evolutionary history includes several cases of putative, but untested ecomorphological convergence, especially with traits related to diet. Among the most spectacular rodent ecomorphs are the vermivores which independently evolved in several island systems. We used 3D CT-scans (N = 87) of murine turbinal bones to quantify olfactory capacities as well as heat or water conservation adaptations. We obtained similar results from an existing 2D complexity method and two new 3D methodologies that quantify bone complexity. Using comparative phylogenetic methods, we identified a significant convergent signal in the rostral morphology within the highly specialised vermivores. Vermivorous species have significantly larger and more complex olfactory turbinals than do carnivores and omnivores. Increased olfactory capacities may be a major adaptive feature facilitating rats' capacity to prey on elusive earthworms. The narrow snout that characterises vermivores exhibits significantly reduced respiratory turbinals, which may reduce their heat and water conservation capacities.

Multi-omic analysis of signalling factors in inflammatory comorbidities

BACKGROUND

Inflammation is a core element of many different, systemic and chronic diseases that usually involve an important autoimmune component. The clinical phase of inflammatory diseases is often the culmination of a long series of pathologic events that started years before. The systemic characteristics and related mechanisms could be investigated through the multi-omic comparative analysis of many inflammatory diseases. Therefore, it is important to use molecular data to study the genesis of the diseases. Here we propose a new methodology to study the relationships between inflammatory diseases and signalling molecules whose dysregulation at molecular levels could lead to systemic pathological events observed in inflammatory diseases.

RESULTS

We first perform an exploratory analysis of gene expression data of a number of diseases that involve a strong inflammatory component. The comparison of gene expression between disease and healthy samples reveals the importance of members of gene families coding for signalling factors. Next, we focus on interested signalling gene families and a subset of inflammation related diseases with multi-omic features including both gene expression and DNA methylation. We introduce a phylogenetic-based multi-omic method to study the relationships between multi-omic features of inflammation related diseases by integrating gene expression, DNA methylation through sequence based phylogeny of the signalling gene families. The models of adaptations between gene expression and DNA methylation can be inferred from pre-estimated evolutionary relationship of a gene family. Members of the gene family whose expression or methylation levels significantly deviate from the model are considered as the potential disease associated genes.

CONCLUSIONS

Applying the methodology to four gene families (the chemokine receptor family, the TNF receptor family, the TGF- β gene family, the IL-17 gene family) in nine inflammation related diseases, we identify disease associated genes which exhibit significant dysregulation in gene expression or DNA methylation in the inflammation related diseases, which provides clues for functional associations between the diseases.

Inference of Adaptive Shifts for Multivariate Correlated Traits

To study the evolution of several quantitative traits, the classical phylogenetic comparative framework consists of a multivariate random process running along the branches of a phylogenetic tree. The Ornstein-Uhlenbeck (OU) process is sometimes preferred to the simple Brownian motion (BM) as it models stabilizing selection toward an optimum. The optimum for each trait is likely to be changing over the long periods of time spanned by large modern phylogenies. Our goal is to automatically detect the position of these shifts on a phylogenetic tree, while accounting for correlations between traits, which might exist because of structural or evolutionary constraints. We show that, in the presence of shifts, phylogenetic Principal Component Analysis fails to decorrelate traits efficiently, so that any method aiming at finding shifts needs to deal with correlation simultaneously. We introduce here a simplification of the full multivariate OU model, named scalar OU, which allows for noncausal correlations and is still computationally tractable. We extend the equivalence between the OU and a BM on a rescaled tree to our multivariate framework. We describe an Expectation-Maximization (EM) algorithm that allows for a maximum likelihood estimation of the shift positions, associated with a new model selection criterion, accounting for the identifiability issues for the shift localization on the tree. The method, freely available as an R-package (PhylogeneticEM) is fast, and can deal with missing values. We demonstrate its efficiency and accuracy compared to another state-of-the-art method ($\ell$1ou) on a wide range of simulated scenarios and use this new framework to reanalyze recently gathered data sets on New World Monkeys and Anolis lizards.

Phylogenetic Comparative Methods on Phylogenetic Networks with Reticulations

The goal of phylogenetic comparative methods (PCMs) is to study the distribution of quantitative traits among related species. The observed traits are often seen as the result of a Brownian Motion (BM) along the branches of a phylogenetic tree. Reticulation events such as hybridization, gene flow or horizontal gene transfer, can substantially affect a species' traits, but are not modeled by a tree. Phylogenetic networks have been designed to represent reticulate evolution. As they become available for downstream analyses, new models of trait evolution are needed, applicable to networks. We develop here an efficient recursive algorithm to compute the phylogenetic variance matrix of a trait on a network, in only one preorder traversal of the network. We then extend the standard PCM tools to this new framework, including phylogenetic regression with covariates (or phylogenetic ANOVA), ancestral trait reconstruction, and Pagel's $\lambda$ test of phylogenetic signal. The trait of a hybrid is sometimes outside of the range of its two parents, for instance because of hybrid vigor or hybrid depression. These two phenomena are rather commonly observed in present-day hybrids. Transgressive evolution can be modeled as a shift in the trait value following a reticulation point. We develop a general framework to handle such shifts and take advantage of the phylogenetic regression view of the problem to design statistical tests for ancestral transgressive evolution in the evolutionary history of a group of species. We study the power of these tests in several scenarios and show that recent events have indeed the strongest impact on the trait distribution of present-day taxa. We apply those methods to a data set of Xiphophorus fishes, to confirm and complete previous analysis in this group. All the methods developed here are available in the Julia package PhyloNetworks.

Phylogenetic Factor Analysis

Phylogenetic comparative methods explore the relationships between quantitative traits adjusting for shared evolutionary history. This adjustment often occurs through a Brownian diffusion process along the branches of the phylogeny that generates model residuals or the traits themselves. For high-dimensional traits, inferring all pair-wise correlations within the multivariate diffusion is limiting. To circumvent this problem, we propose phylogenetic factor analysis (PFA) that assumes a small unknown number of independent evolutionary factors arise along the phylogeny and these factors generate clusters of dependent traits. Set in a Bayesian framework, PFA provides measures of uncertainty on the factor number and groupings, combines both continuous and discrete traits, integrates over missing measurements and incorporates phylogenetic uncertainty with the help of molecular sequences. We develop Gibbs samplers based on dynamic programming to estimate the PFA posterior distribution, over 3-fold faster than for multivariate diffusion and a further order-of-magnitude more efficiently in the presence of latent traits. We further propose a novel marginal likelihood estimator for previously impractical models with discrete data and find that PFA also provides a better fit than multivariate diffusion in evolutionary questions in columbine flower development, placental reproduction transitions and triggerfish fin morphometry.