Detection of adaptive shifts on phylogenies by using shifted stochastic processes on a tree

Diversification of social complexity following a major evolutionary transition in bees

How social complexity evolved remains a long-standing enigma. In most animal groups, social complexity is typically classified into a few discrete classes. This approach is oversimplified and constrains our inference of social evolution to a narrow trajectory consisting of transitions between classes. Such categorical classifications also limit quantitative studies on the molecular and environmental drivers of social complexity. The recent accumulation of relevant quantitative data has set the stage to overcome these limitations. Here, we propose a data-driven, high-dimensional approach for studying the full diversity of social phenotypes. We curated and analyzed a comprehensive dataset encompassing 17 social traits across 80 species and studied the evolution of social complexity in bees. We found that honey bees, stingless bees, and bumble bees underwent a major evolutionary transition ∼80 mya, inconsistent with the stepwise progression of the social ladder conceptual framework. This major evolutionary transition was followed by a phase of substantial phenotypic diversification of social complexity. Other bee lineages display a continuum of social complexity, ranging from solitary to simple societies, but do not reach the levels of social complexity seen in honey bees, stingless bees, and bumble bees. Bee evolution, therefore, provides a remarkable demonstration of a macroevolutionary process in which a major transition removed biological constraints and opened novel evolutionary opportunities, driving the exploration of the landscape of social phenotypes. Our approach can be extended to incorporate additional data types and readily applied to illuminate the evolution of social complexity in other animal groups.

Extended phenotype affects somatic phenotype in spiders: web builders have lower estimated biting forces than free hunters

Reciprocal selection between extended and somatic phenotypes is an active area of investigation. Recent research on the influence of web-building on somatic evolution in spiders has produced conflicting results, with some finding no effect of web use on somatic evolution and others showing significant effects. These studies differed in focus, with the former surveying general anatomical traits and the latter concentrating on somatic systems with significant functional roles in prey capture. Here we propose and test the hypothesis that prey immobilization by webs is broadly synergistic with cheliceral biting force and that web builders have lower cheliceral forces compared to free hunters. Our analysis focused on the intercheliceral (IC) sclerite and muscles, a newly characterized system that is synapomorphic and ubiquitously distributed in spiders. Using µCT scans, we quantify IC sclerite shape and model IC muscle function. Statistical analyses show that inferred size-corrected isometric muscle force is lower in web-builders than in free hunters. No such association was found for IC sclerite shape. In the investigation of reciprocal selective effects between extended and somatic phenotypes, our results highlight the importance that these traits be functionally linked and adaptive.

The evolution of gestation length in eutherian mammals

Eutherian mammals exhibit considerable variation in their gestation lengths, which has traditionally been linked to variation in other traits, including body mass and lifespan. To understand how gestation length variation, including its association with body mass and lifespan variation, changed over mammalian evolution, we conducted phylogeny-informed analyses of 845 representative extant species. We found that gestation length substantially differed in both whether and how strongly it was associated with body mass and lifespan across mammals. For example, gestation length was not associated with lifespan or body mass in Chiroptera and Cetacea but was strongly associated only with body mass in Carnivora. We also identified 52 evolutionary shifts in gestation length variation across the mammal phylogeny and 14 shifts when we jointly considered variation of all three traits; six shifts were shared. Notably, two of these shifts, both positive, occurred at the roots of Cetacea and Pinnipedia, respectively, coinciding with the transition of these clades to the marine environment, whereas a negative shift occurred at the root of Chiroptera, coinciding with the evolution of flight in this clade. These results suggest that the relationship between gestation length and the two other traits has varied substantially across mammalian phylogeny.

Clockor2: Inferring Global and Local Strict Molecular Clocks Using Root-to-Tip Regression

Molecular sequence data from rapidly evolving organisms are often sampled at different points in time. Sampling times can then be used for molecular clock calibration. The root-to-tip (RTT) regression is an essential tool to assess the degree to which the data behave in a clock-like fashion. Here, we introduce Clockor2, a client-side web application for conducting RTT regression. Clockor2 allows users to quickly fit local and global molecular clocks, thus handling the increasing complexity of genomic datasets that sample beyond the assumption of homogeneous host populations. Clockor2 is efficient, handling trees of up to the order of 104 tips, with significant speed increases compared with other RTT regression applications. Although clockor2 is written as a web application, all data processing happens on the client-side, meaning that data never leave the user's computer. Clockor2 is freely available at https://clockor2.github.io/.

Robust Phylogenetic Regression

Modern comparative biology owes much to phylogenetic regression. At its conception, this technique sparked a revolution that armed biologists with phylogenetic comparative methods (PCMs) for disentangling evolutionary correlations from those arising from hierarchical phylogenetic relationships. Over the past few decades, the phylogenetic regression framework has become a paradigm of modern comparative biology that has been widely embraced as a remedy for shared ancestry. However, recent evidence has shown doubt over the efficacy of phylogenetic regression, and PCMs more generally, with the suggestion that many of these methods fail to provide an adequate defense against unreplicated evolution-the primary justification for using them in the first place. Importantly, some of the most compelling examples of biological innovation in nature result from abrupt lineage-specific evolutionary shifts, which current regression models are largely ill equipped to deal with. Here we explore a solution to this problem by applying robust linear regression to comparative trait data. We formally introduce robust phylogenetic regression to the PCM toolkit with linear estimators that are less sensitive to model violations than the standard least-squares estimator, while still retaining high power to detect true trait associations. Our analyses also highlight an ingenuity of the original algorithm for phylogenetic regression based on independent contrasts, whereby robust estimators are particularly effective. Collectively, we find that robust estimators hold promise for improving tests of trait associations and offer a path forward in scenarios where classical approaches may fail. Our study joins recent arguments for increased vigilance against unreplicated evolution and a better understanding of evolutionary model performance in challenging-yet biologically important-settings.

Analytical advances alleviate model misspecification in non-Brownian multivariate comparative methods

Adams and Collyer argue that contemporary multivariate (Gaussian) phylogenetic comparative methods are prone to favouring more complex models of evolution and sometimes rotation invariance can be an issue. Here we dissect the concept of rotation invariance and point out that, depending on the understanding, this can be an issue with any method that relies on numerical instead of analytical estimation approaches. We relate this to the ongoing discussion concerning phylogenetic principal component analysis. Contrary to what Adams and Collyer found, we do not observe a bias against the simpler Brownian motion process in simulations when we use the new, improved, likelihood evaluation algorithm employed by mvSLOUCH, which allows for studying much larger phylogenies and more complex model setups.

Rapid adaptation of cellular metabolic rate to the MicroRNA complements of mammals and its relevance to the evolution of endothermy

The metabolic efficiency of mammalian cells depends on the attenuation of intrinsic translation noise by microRNAs. We devised a metric of cellular metabolic rate (cMR), rMR/Mexp optimally fit to the number of microRNA families (mirFam), that is robust to variation in mass and sensitive to body temperature (Tb), consistent with the heat dissipation limit theory of Speakman and Król (2010). Using mirFam as predictor, an Ornstein-Uhlenbeck process of stabilizing selection, with an adaptive shift at the divergence of Boreoeutheria, accounted for 95% of the variation in cMR across mammals. Branchwise rates of evolution of cMR, mirFam and Tb concurrently increased 6- to 7-fold at the divergence of Boreoeutheria, independent of mass. Cellular MR variation across placental mammals was also predicted by the sum of model conserved microRNA-target interactions, revealing an unexpected degree of integration of the microRNA-target apparatus into the energy economy of the mammalian cell.

Evolutionary shift detection with ensemble variable selection

Abrupt environmental changes can lead to evolutionary shifts in trait evolution. Identifying these shifts is an important step in understanding the evolutionary history of phenotypes. The detection performances of different methods are influenced by many factors, including different numbers of shifts, shift sizes, where a shift occurs on a tree, and the types of phylogenetic structure. Furthermore, the model assumptions are oversimplified, so are likely to be violated in real data, which could cause the methods to fail. We perform simulations to assess the effect of these factors on the performance of shift detection methods. To make the comparisons more complete, we also propose an ensemble variable selection method (R package ELPASO) and compare it with existing methods (R packages [Formula: see text]1ou and PhylogeneticEM). The performances of methods are highly dependent on the selection criterion. [Formula: see text]1ou+pBIC is usually the most conservative method and it performs well when signal sizes are large. [Formula: see text]1ou+BIC is the least conservative method and it performs well when signal sizes are small. The ensemble method provides more balanced choices between those two methods. Moreover, the performances of all methods are heavily impacted by measurement error, tree reconstruction error and shifts in variance.

The Cauchy Process on Phylogenies: A Tractable Model for Pulsed Evolution

Phylogenetic comparative methods use random processes, such as the Brownian Motion, to model the evolution of continuous traits on phylogenetic trees. Growing evidence for non-gradual evolution motivated the development of complex models, often based on Lévy processes. However, their statistical inference is computationally intensive and currently relies on approximations, high-dimensional sampling, or numerical integration. We consider here the Cauchy Process (CP), a particular pure-jump Lévy process in which the trait increment along each branch follows a centered Cauchy distribution with a dispersion proportional to its length. In this work, we derive an exact algorithm to compute both the joint probability density of the tip trait values of a phylogeny under a CP and the ancestral trait values and branch increments posterior densities in quadratic time. A simulation study shows that the CP generates patterns in comparative data that are distinct from any Gaussian process, and that restricted maximum likelihood parameter estimates and root trait reconstruction are unbiased and accurate for trees with 200 tips or less. The CP has only two parameters but is rich enough to capture complex-pulsed evolution. It can reconstruct posterior ancestral trait distributions that are multimodal, reflecting the uncertainty associated with the inference of the evolutionary history of a trait from extant taxa only. Applied on empirical datasets taken from the Evolutionary Ecology and Virology literature, the CP suggests nuanced scenarios for the body size evolution of Greater Antilles Lizards and for the geographical spread of the West Nile Virus epidemics in North America, both consistent with previous studies using more complex models. The method is efficiently implemented in C with an R interface in package cauphy, which is open source and freely available online.

The evolution of Ericaceae flowers and their pollination syndromes at a global scale

PREMISE

Floral evolution in large clades is difficult to study not only because of the number of species involved, but also because they often are geographically widespread and include a diversity of outcrossing pollination systems. The cosmopolitan blueberry family (Ericaceae) is one such example, most notably pollinated by bees and multiple clades of nectarivorous birds.

METHODS

We combined data on floral traits, pollination ecology, and geography with a comprehensive phylogeny to examine the structuring of floral diversity across pollination systems and continents. We focused on ornithophilous systems to test the hypothesis that some Old World Ericaceae were pollinated by now-extinct hummingbirds.

RESULTS

Despite some support for floral differentiation at a continental scale, we found a large amount of variability within and among landmasses, due to both phylogenetic conservatism and parallel evolution. We found support for floral differentiation in anther and corolla traits across pollination systems, including among different ornithophilous systems. Corolla traits show inconclusive evidence that some Old World Ericaceae were pollinated by hummingbirds, while anther traits show stronger evidence. Some major shifts in floral traits are associated with changes in pollination system, but shifts within bee systems are likely also important.

CONCLUSIONS

Studying the floral evolution of large, morphologically diverse, and widespread clades is feasible. We demonstrate that continent-specific radiations have led to widespread parallel evolution of floral morphology. We show that traits outside of the perianth may hold important clues to the ecological history of lineages.

Defining plant ecological specialists and generalists: Building a framework for identification and classification

Specialization is a widespread but highly ambiguous and context-dependent ecological concept. This quality makes comparisons across related studies difficult and makes associated terms such as "specialist" and "generalist" scientifically obscure. Here, we present a metric-based framework to quantify specialization in 141 Quercus species using functional traits, biogeography, and species interactions. Rankings of specialization based on five metrics were used to answer questions about how specialization is used colloquially (i.e., individual species assessment by experts) and influenced by phylogenetics (Ancestral Character State Reconstruction, Automatic Shift Detection), biogeography (patterns of clustering by region and with climate), and species threat level (IUCN Red List). Metric-based ranking can be representative of specialization in a consistent and practical manner, correlating with IUCN Red List data, and the mean scores of individual expert assessments. Specialization is shown to be highly correlated with precipitation seasonality and only moderately influenced by evolutionary history. Data-deficient species were more likely to be highly specialized, and higher specialization was positively correlated with greater IUCN threat level. Frameworks for characterizing specialization and generalization can be done using metric ranking and can turn concepts that are often unclear into a definitive system. Metric-based rankings of specialization can also be used to reveal interesting insights about a clade's evolutionary history and geographic distribution when paired with the related phylogenetic and geographic data. Metric-based rankings can be applied to other systems and be a valuable tool for identifying species at risk and in need of conservation.

Complex adaptive landscape for a "Simple" structure: The role of trade-offs in the evolutionary dynamics of mandibular shape in ground squirrels

Trade-offs are inherent features of many biomechanical systems and are often seen as evolutionary constraints. Structural decoupling may provide a way to escape those limits in some systems but not for structures that transmit large forces, such as mammalian mandibles. For such structures to evolve in multiple directions on a complex adaptive landscape, different regions must change shape while maintaining structural integrity. We evaluated the complexity of the adaptive landscape for mandibular shape in Marmotini, a lineage of ground squirrels that varies in the proportions of seeds and foliage in their diets, by comparing the fit of models based on traits that predict changes in mandibular loading. The adaptive landscape was more complex than predicted by a two-peak model with a single dietary shift. The large number of adaptive peaks reflects a high diversity of directions of shape evolution. The number of adaptive peaks also reflects a multiplicity of functional trade-offs posed by the conflicting demands of processing foods with various combinations of material properties. The ability to balance trade-offs for diets with different proportions of the same foods may account for diversification and disparity of lineages in heterogeneous environments. Rather than constraints, trade-offs may be the impetus of evolutionary change.

General statistical model shows that macroevolutionary patterns and processes are consistent with Darwinian gradualism

Macroevolution posed difficulties for Darwin and later theorists because species’ phenotypes frequently change abruptly, or experience long periods of stasis, both counter to the theory of incremental change or gradualism. We introduce a statistical model that accommodates this uneven evolutionary landscape by estimating two kinds of historical change: directional changes that shift the mean phenotype along the branches of a phylogenetic tree, and evolvability changes that alter a clade’s ability to explore its trait-space. In mammals, we find that both processes make substantial independent contributions to explaining macroevolution, and are rarely linked. ‘Watershed’ moments of increased evolvability greatly outnumber reductions in evolutionary potentials, and large or abrupt phenotypic shifts are explicable statistically as biased random walks, allowing macroevolutionary theory to engage with the language and concepts of gradualist microevolution. Our findings recast macroevolutionary phenomena, illustrating the necessity of accounting for a variety of evolutionary processes simultaneously.

‘Macroevolution posed difficulties for Darwin and later theorists because species frequently change abruptly, or experience long periods of stasis, both counter to the theory of incremental change or gradualism. Here, the authors propose a macroevolutionary statistical model that accommodates this uneven evolutionary landscape, and shows how even abrupt macroevolutionary changes are compatible with gradualist microevolutionary processes.’

Hierarchical correction of p-values via an ultrametric tree running Ornstein-Uhlenbeck process

Statistical testing is classically used as an exploratory tool to search for association between a phenotype and many possible explanatory variables. This approach often leads to multiple testing under dependence. We assume a hierarchical structure between tests via an Ornstein-Uhlenbeck process on a tree. The process correlation structure is used for smoothing the p-values. We design a penalized estimation of the mean of the Ornstein-Uhlenbeck process for p-value computation. The performances of the algorithm are assessed via simulations. Its ability to discover new associations is demonstrated on a metagenomic dataset. The corresponding R package is available from https://github.com/abichat/zazou.

Complex interactions underlie the correlated evolution of floral traits and their association with pollinators in a clade with diverse pollination systems

Natural selection by pollinators is an important factor in the morphological diversity and adaptive radiation of flowering plants. Selection by similar pollinators in unrelated plants leads to convergence in floral morphology, or "floral syndromes." Previous investigations into floral syndromes have mostly studied relatively small and/or simple systems, emphasizing vertebrate pollination. Despite the importance of multiple floral traits in plant-pollinator interactions, these studies have examined few quantitative traits, so their co-variation and phenotypic integration have been underexplored. To gain better insights into pollinator-trait dynamics, we investigate the model system of the phlox family (Polemoniaceae), a clade of ∼400 species pollinated by a diversity of vectors. Using a comprehensive phylogeny and large dataset of traits and observations of pollinators, we reconstruct ancestral pollination system, accounting for the temporal history of pollinators. We conduct phylogenetically controlled analyses of trait co-variation and association with pollinators, integrating many analyses over phylogenetic uncertainty. Pollinator shifts are more heterogeneous than previously hypothesized. The evolution of floral traits is partially constrained by phylogenetic history and trait co-variation, but traits are convergent and differences are associated with different pollinators. Trait shifts are usually gradual, rather than rapid, suggesting complex genetic and ecological interactions of flowers at macroevolutionary scales.

Climate and phylogenetic history structure morphological and architectural trait variation among fine-root orders

Fine roots mediate below-ground resource acquisition, yet understanding of how fine-root functional traits vary along environmental gradients, within branching orders and across phylogenetic scales remains limited. Morphological and architectural fine-root traits were measured on individual root orders of 20 oak species (genus Quercus) from divergent climates of origin that were harvested after three growing seasons in a glasshouse. These were then compared with similar measurements obtained from a phylogenetically diverse dataset of woody species from the Fine-Root Ecology Database (FRED). For the oaks, only precipitation seasonality and growing season moisture availability were correlated to aspects of root diameter and branching. Strong correlations among root diameters and architecture of different branch orders were common, while correlations between diameter and length were weakly negative. By contrast, the FRED dataset showed strong positive correlations between diameter and length and fewer correlations between root diameter and architectural traits. Our findings suggest that seasonal patterns of water availability are more important drivers of root adaptation in oaks than annual averages in precipitation and temperature. Furthermore, contrasting patterns of trait relationships between the oak and FRED datasets suggest that branching patterns are differentially constrained at narrow vs broad phylogenetic scales.

Rapid evolution of the primate larynx?

Tissue vibrations in the larynx produce most sounds that comprise vocal communication in mammals. Larynx morphology is thus predicted to be a key target for selection, particularly in species with highly developed vocal communication systems. Here, we present a novel database of digitally modeled scanned larynges from 55 different mammalian species, representing a wide range of body sizes in the primate and carnivoran orders. Using phylogenetic comparative methods, we demonstrate that the primate larynx has evolved more rapidly than the carnivoran larynx, resulting in a pattern of larger size and increased deviation from expected allometry with body size. These results imply fundamental differences between primates and carnivorans in the balance of selective forces that constrain larynx size and highlight an evolutionary flexibility in primates that may help explain why we have developed complex and diverse uses of the vocal organ for communication.

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.

Distinct Patterns of Hippocampal and Neocortical Evolution in Primates

Because of the central role of the hippocampus in representing spatial and temporal details of experience, comparative studies of its volume and structure are relevant to understanding the evolution of representational memory across species. The hippocampal formation, however, is organized into separate anatomical subregions with distinct functions, and little is known about the evolutionary diversification of these subregions. We investigate relative volumetric changes in hippocampal subregions across a large sample of primate species. We then compare the evolution of the hippocampal formation to the neocortex. Results across hippocampal subregions indicate that, compared to strepsirrhines, the anthropoid lineage displays a decrease in relative CA3, fascia dentata, subiculum, and rhinal cortex volume in tandem with an increase in relative neocortical volume. These findings indicate that hippocampal function in anthropoids might be substantially augmented by the executive decision-making functions of the neocortex. Humans are found to have a unique cerebral organization combining increased relative CA3, subiculum, and rhinal cortex with increased relative neocortical volumes, suggesting that these regions may play a role in behaviors that are uniquely specialized in humans.

Timing and ecological priority shaped the diversification of sedges in the Himalayas

BACKGROUND

Diversification patterns in the Himalayas have been important to our understanding of global biodiversity. Despite recent broad-scale studies, the most diverse angiosperm genus of the temperate zone-Carex L. (Cyperaceae), with ca. 2100 species worldwide-has not yet been studied in the Himalayas, which contains 189 Carex species. Here the timing and phylogenetic pattern of lineage and ecological diversification were inferred in this ecologically significant genus. We particularly investigated whether priority, adaptation to ecological conditions, or both explain the highly successful radiation of the Kobresia clade (ca. 60 species, of which around 40 are present in the Himalayas) of Himalayan Carex.

METHODS

Phylogenetic relationships were inferred using maximum likelihood analysis of two nuclear ribosomal DNA (nrDNA) regions (ITS and ETS) and one plastid gene (matK); the resulting tree was time-calibrated using penalized likelihood and a fossil calibration at the root of the tree. Biogeographical reconstruction for estimation of historical events and ancestral ranges was performed using the dispersal-extinction-cladogenesis (DEC) model, and reciprocal effects between biogeography and diversification were inferred using the geographic state speciation and extinction (GeoSSE) model. Climatic envelopes for all species for which mapped specimen data available were estimated using climatic data from WORLDCLIM, and climatic niche evolution was inferred using a combination of Ornstein-Uhlenbeck models of shifting adaptive optima and maximum likelihood inference of ancestral character states under a Brownian motion model.

RESULTS

The Himalayan Carex flora represents three of the five major Carex clades, each represented by multiple origins within the Himalayas. The oldest Carex radiation in the region, dating to ca. 20 Ma, near the time of Himalayan orogeny, gave rise to the now abundant Kobresia clade via long-distance dispersal from the Nearctic. The Himalayan Carex flora comprises a heterogeneous sample of diversifications drawn from throughout the cosmopolitan, but mostly temperate, Carex radiation. Most radiations are relatively recent, but the widespread and diverse Himalayan Kobresia radiation arose at the early Miocene. The timing and predominance of Kobresia in high-elevation Himalayan meadows suggests that Kobresia may have excluded other Carex lineages: the success of Kobresia in the Himalayas, in other words, appears to be a consequence largely of priority, competitive exclusion and historical contingency.

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.