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

Language follows a distinct mode of extra-genomic evolution

As one of the most specific, yet most diverse of human behaviors, language is shaped by both genomic and extra-genomic evolution. Sharing methods and models between these modes of evolution has significantly advanced our understanding of language and inspired generalized theories of its evolution. Progress is hampered, however, by the fact that the extra-genomic evolution of languages, i.e. linguistic evolution, maps only partially to other forms of evolution. Contrasting it with the biological evolution of eukaryotes and the cultural evolution of technology as the best understood models, we show that linguistic evolution is special by yielding a stationary dynamic rather than stable solutions, and that this dynamic allows the use of language change for social differentiation while maintaining its global adaptiveness. Linguistic evolution furthermore differs from technological evolution by requiring vertical transmission, allowing the reconstruction of phylogenies; and it differs from eukaryotic biological evolution by foregoing a genotype vs phenotype distinction, allowing deliberate and biased change. Recognising these differences will improve our empirical tools and open new avenues for analyzing how linguistic, cultural, and biological evolution interacted with each other when language emerged in the hominin lineage. Importantly, our framework will help to cope with unprecedented scientific and ethical challenges that presently arise from how rapid cultural evolution impacts language, most urgently from interventional clinical tools for language disorders, potential epigenetic effects of technology on language, artificial intelligence and linguistic communicators, and global losses of linguistic diversity and identity. Beyond language, the distinctions made here allow identifying variation in other forms of biological and cultural evolution, developing new perspectives for empirical research.

The interplay between climatic niche evolution, polyploidy and reproductive traits explains plant speciation in the Mediterranean Basin: a case study in Centaurium (Gentianaceae)

Speciation and diversification patterns in angiosperms are frequently shaped by niche evolution. Centaurium Hill is a Mediterranean genus with ca. 25 species, of which 60% are polyploids (tetra- and hexaploids), distributed mainly in the Mediterranean Basin and in areas with temperate and arid climates of Asia, Europe, North-Central Africa and North America. The evolutionary history of this genus has been studied using morphological, biogeographical and molecular approaches, but its climatic niche characterization and its relation with genome evolution (chromosome number and ploidy level) has not been addressed yet. Thus, this study aims to identify the role of the evolution of climatic niche, ploidy level, life cycle and floral traits in the diversification of Centaurium. Climatic niche characterization involved estimating present climate preferences using quantitative data and reconstructing ancestral niches to evaluate climatic niche shifts. The evolution of climatic niche towards selective optima determined by ploidy level (three ploidy levels) and different binary traits (polyploidy, floral size, floral display, herkogamy and life cycle) was addressed under the Ornstein-Uhlenbeck model. Chromosome number evolution was inferred using the ChromoSSE model, testing if changes are clado- or anagenetic. Chromosome number evolution and its link with cladogenesis, life cycle and floral traits was modeled on the phylogeny. The reconstruction of the ancestral niches shows that Centaurium originated in a mild climate and diversified to both humid and cold as well as to dry and warmer climates. Niche conservatism was estimated in the climatic niche of the ancestors, while the climatic niche of the current taxa experienced transitions from their ancestors' niche. Besides, the evolution of climatic niche towards multiple selective optima determined by the studied traits was supported, life cycle optima receiving the highest support. The reconstruction of chromosome number transitions shows that the rate of speciation process resulting from chromosomal changes (chromosomal cladogenesis) is similar to that of non-chromosomal cladogenesis. Additionally, dependent evolution of floral size, floral display and herkogamy with chromosome number variation was supported. In conclusion, polyploidization is a crucial process in the Mediterranean region that assisted speciation and diversification into new areas with different climates, entailing niche shifts and evolution of reproductive strategies.

Foliar spectra accurately distinguish most temperate tree species and show strong phylogenetic signal

PREMISE

Spectroscopy is a powerful remote sensing tool for monitoring plant biodiversity over broad geographic areas. Increasing evidence suggests that foliar spectral reflectance can be used to identify trees at the species level. However, most studies have focused on only a limited number of species at a time, and few studies have explored the underlying phylogenetic structure of leaf spectra. Accurate species identifications are important for reliable estimations of biodiversity from spectral data.

METHODS

Using over 3500 leaf-level spectral measurements, we evaluated whether foliar reflectance spectra (400-2400 nm) can accurately differentiate most tree species from a regional species pool in eastern North America. We explored relationships between spectral, phylogenetic, and leaf functional trait variation as well as their influence on species classification using a hurdle regression model.

RESULTS

Spectral reflectance accurately differentiated tree species (κ = 0.736, ±0.005). Foliar spectra showed strong phylogenetic signal, and classification errors from foliar spectra, although present at higher taxonomic levels, were found predominantly between closely related species, often of the same genus. In addition, we find functional and phylogenetic distance broadly control the occurrence and frequency of spectral classification mistakes among species.

CONCLUSIONS

Our results further support the link between leaf spectral diversity, taxonomic hierarchy, and phylogenetic and functional diversity, and highlight the potential of spectroscopy to remotely sense plant biodiversity and vegetation response to global change.

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.

Confined modes of single-particle trajectories induced by stochastic resetting

Random trajectories of single particles in living cells contain information about the interaction between particles, as well as with the cellular environment. However, precise consideration of the underlying stochastic properties, beyond normal diffusion, remains a challenge as applied to each particle trajectory separately. In this paper, we show how positions of confined particles in living cells can obey not only the Laplace distribution, but the Linnik one. This feature is detected in experimental data for the motion of G proteins and coupled receptors in cells, and its origin is explained in terms of stochastic resetting. This resetting process generates power-law waiting times, giving rise to the Linnik statistics in confined motion, and also includes exponentially distributed times as a limit case leading to the Laplace one. The stochastic process, which is affected by the resetting, can be Brownian motion commonly found in cells. Other possible models producing similar effects are discussed.

When can we reconstruct the ancestral state? Beyond Brownian motion

Reconstructing the ancestral state of a group of species helps answer many important questions in evolutionary biology. Therefore, it is crucial to understand when we can estimate the ancestral state accurately. Previous works provide a necessary and sufficient condition, called the big bang condition, for the existence of an accurate reconstruction method under discrete trait evolution models and the Brownian motion model. In this paper, we extend this result to a wide range of continuous trait evolution models. In particular, we consider a general setting where continuous traits evolve along the tree according to stochastic processes that satisfy some regularity conditions. We verify these conditions for popular continuous trait evolution models including Ornstein-Uhlenbeck, reflected Brownian Motion, bounded Brownian Motion, and Cox-Ingersoll-Ross.

Genome size variation and polyploidy prevalence in the genus Eragrostis are associated with the global dispersal in arid area

BACKGROUND

Biologists have long debated the drivers of the genome size evolution and variation ever since Darwin. Assumptions for the adaptive or maladaptive consequences of the associations between genome sizes and environmental factors have been proposed, but the significance of these hypotheses remains controversial. Eragrostis is a large genus in the grass family and is often used as crop or forage during the dry seasons. The wide range and complex ploidy levels make Eragrostis an excellent model for investigating how the genome size variation and evolution is associated with environmental factors and how these changes can ben interpreted.

METHODS

We reconstructed the Eragrostis phylogeny and estimated genome sizes through flow cytometric analyses. Phylogenetic comparative analyses were performed to explore how genome size variation and evolution is related to their climatic niches and geographical ranges. The genome size evolution and environmental factors were examined using different models to study the phylogenetic signal, mode and tempo throughout evolutionary history.

RESULTS

Our results support the monophyly of Eragrostis. The genome sizes in Eragrostis ranged from ~0.66 pg to ~3.80 pg. We found that a moderate phylogenetic conservatism existed in terms of the genome sizes but was absent from environmental factors. In addition, phylogeny-based associations revealed close correlations between genome sizes and precipitation-related variables, indicating that the genome size variation mainly caused by polyploidization may have evolved as an adaptation to various environments in the genus Eragrostis.

CONCLUSION

This is the first study to take a global perspective on the genome size variation and evolution in the genus Eragrostis. Our results suggest that the adaptation and conservatism are manifested in the genome size variation, allowing the arid species of Eragrostis to spread the xeric area throughout the world.

Evolutionary history of hominin brain size and phylogenetic comparative methods

An absolutely and relatively large brain has traditionally been viewed as a distinctive characteristic of the Homo genus, with anatomically modern humans presented at the apex of a long line of progressive increases in encephalization. Many studies continue to focus attention on increasing brain size in the Homo genus, while excluding measures of absolute and relative brain size of more geologically recent, smaller brained, hominins such as Homo floresiensis, and Homo naledi and smaller brained Homo erectus specimens. This review discusses the benefits of using phylogenetic comparative methods to trace the diverse changes in hominin brain evolution and the drawbacks of not doing so.

Evidence for an evo-devo-derived hypothesis on three-dimensional flower shape modularity in a tropical orchid clade

Covarying suites of phenotypic traits, or modules, are increasingly recognized to promote morphological evolution. However, information on how modularity influences flower diversity is rare and lacking for Orchidaceae. Here, we combine high-resolution X-ray computed tomography scanning with three-dimensional geometric morphometrics and phylogenetic comparative methods to test various hypotheses about three-dimensional patterns of flower evolutionary modularity in Malagasy Bulbophyllum orchids and examine rates and modes of module evolution. Based on the four evolutionary modules identified (i.e., sepals, lateral petals, labellum + column-foot, and column-part), our data support the hypothesis that both genetic-developmental and functional adaptive factors shaped evolutionary flower trait covariation in these tropical orchids. In line with "evo-devo" studies, we also find that the labellum evolved independently from the rest of the petal whorl. Finally, we show that modules evolved with different rates, and either in a neutral fashion (only column-part) or under selective constraints, as likely imposed by pollinators. Overall, this study supports current views that modular units can enhance the range and rate of morphological evolution.

Trophic niche shifts and phenotypic trait evolution are largely decoupled in Australasian parrots

BACKGROUND

Trophic shifts from one dietary niche to another have played major roles in reshaping the evolutionary trajectories of a wide range of vertebrate groups, yet their consequences for morphological disparity and species diversity differ among groups.

METHODS

Here, we use phylogenetic comparative methods to examine whether the evolution of nectarivory and other trophic shifts have driven predictable evolutionary pathways in Australasian psittaculid parrots in terms of ecological traits such as body size, beak shape, and dispersal capacity.

RESULTS

We found no evidence for an 'early-burst' scenario of lineage or morphological diversification. The best-fitting models indicate that trait evolution in this group is characterized by abrupt phenotypic shifts (evolutionary jumps), with no sign of multiple phenotypic optima correlating with different trophic strategies. Thus, our results point to the existence of weak directional selection and suggest that lineages may be evolving randomly or slowly toward adaptive peaks they have not yet reached.

CONCLUSIONS

This study adds to a growing body of evidence indicating that the relationship between avian morphology and feeding ecology may be more complex than usually assumed and highlights the importance of adding more flexible models to the macroevolutionary toolbox.

An Evolutionary Study of Carex Subg. Psyllophorae (Cyperaceae) Sheds Light on a Strikingly Disjunct Distribution in the Southern Hemisphere, With Emphasis on Its Patagonian Diversification

Carex subgenus Psyllophorae is an engaging study group due to its early diversification compared to most Carex lineages, and its remarkable disjunct distribution in four continents corresponding to three independent sections: sect. Psyllophorae in Western Palearctic, sect. Schoenoxiphium in Afrotropical region, and sect. Junciformes in South America (SA) and SW Pacific. The latter section is mainly distributed in Patagonia and the Andes, where it is one of the few Carex groups with a significant in situ diversification. We assess the role of historical geo-climatic events in the evolutionary history of the group, particularly intercontinental colonization events and diversification processes, with an emphasis on SA. We performed an integrative study using phylogenetic (four DNA regions), divergence times, diversification rates, biogeographic reconstruction, and bioclimatic niche evolution analyses. The crown age of subg. Psyllophorae (early Miocene) supports this lineage as one of the oldest within Carex. The diversification rate probably decreased over time in the whole subgenus. Geography seems to have played a primary role in the diversification of subg. Psyllophorae. Inferred divergence times imply a diversification scenario away from primary Gondwanan vicariance hypotheses and suggest long-distance dispersal-mediated allopatric diversification. Section Junciformes remained in Northern Patagonia since its divergence until Plio-Pleistocene glaciations. Andean orogeny appears to have acted as a northward corridor, which contrasts with the general pattern of North-to-South migration for temperate-adapted organisms. A striking niche conservatism characterizes the evolution of this section. Colonization of the SW Pacific took place on a single long-distance dispersal event from SA. The little ecological changes involved in the trans-Pacific disjunction imply the preadaptation of the group prior to the colonization of the SW Pacific. The high species number of the section results from simple accumulation of morphological changes (disparification), rather than shifts in ecological niche related to increased diversification rates (radiation).

Evidence for selectively constrained 3D flower shape evolution in a Late Miocene clade of Malagasy Bulbophyllum orchids

Questions concerning the evolution of complex biological structures are central to the field of evolutionary biology. Yet, still little information is known about the modes and temporal dynamics of three-dimensional (3D) flower shape evolution across the history of clades. Here, we combined high-resolution X-ray computed tomography with 3D geometric morphometrics and phylogenetic comparative methods to test models of whole-flower shape evolution in the orchid family, using an early Late Miocene clade (c. 50 spp.) of Malagasy Bulbophyllum as model system. Based on landmark data of 38 species, our high-dimensional model fitting decisively rejects a purely neutral mode of evolution, suggesting instead that flower shapes evolved towards a primary adaptive optimum. Only a small number of recently evolved species/lineages attained alternative shape optima, resulting in an increased rate of phenotypic evolution. Our findings provide evidence of constrained 3D flower shape evolution in a small-sized clade of tropical orchids, resulting in low rates of phenotypic evolution and uncoupled trait-diversification rates. We hypothesise that this deep imprint of evolutionary constraint on highly complex floral structures might reflect long-term (directional and/or stabilizing) selection exerted by the group's main pollinators (flies).

A variable-rate quantitative trait evolution model using penalized-likelihood

In recent years it has become increasingly popular to use phylogenetic comparative methods to investigate heterogeneity in the rate or process of quantitative trait evolution across the branches or clades of a phylogenetic tree. Here, I present a new method for modeling variability in the rate of evolution of a continuously-valued character trait on a reconstructed phylogeny. The underlying model of evolution is stochastic diffusion (Brownian motion), but in which the instantaneous diffusion rate (σ2) also evolves by Brownian motion on a logarithmic scale. Unfortunately, it's not possible to simultaneously estimate the rates of evolution along each edge of the tree and the rate of evolution of σ2 itself using Maximum Likelihood. As such, I propose a penalized-likelihood method in which the penalty term is equal to the log-transformed probability density of the rates under a Brownian model, multiplied by a 'smoothing' coefficient, λ, selected by the user. λ determines the magnitude of penalty that's applied to rate variation between edges. Lower values of λ penalize rate variation relatively little; whereas larger λ values result in minimal rate variation among edges of the tree in the fitted model, eventually converging on a single value of σ2 for all of the branches of the tree. In addition to presenting this model here, I have also implemented it as part of my phytools R package in the function multirateBM. Using different values of the penalty coefficient, λ, I fit the model to simulated data with: Brownian rate variation among edges (the model assumption); uncorrelated rate variation; rate changes that occur in discrete places on the tree; and no rate variation at all among the branches of the phylogeny. I then compare the estimated values of σ2 to their known true values. In addition, I use the method to analyze a simple empirical dataset of body mass evolution in mammals. Finally, I discuss the relationship between the method of this article and other models from the phylogenetic comparative methods and finance literature, as well as some applications and limitations of the approach.

Repeated loss of variation in insect ovary morphology highlights the role of development in life-history evolution

The number of offspring an organism can produce is a key component of its evolutionary fitness and life history. Here we perform a test of the hypothesized trade-off between the number and size of offspring using thousands of descriptions of the number of egg-producing compartments in the insect ovary (ovarioles), a common proxy for potential offspring number in insects. We find evidence of a negative relationship between egg size and ovariole number when accounting for adult body size. However, in contrast to prior claims, we note that this relationship is not generalizable across all insect clades, and we highlight several factors that may have contributed to this size-number trade-off being stated as a general rule in previous studies. We reconstruct the evolution of the arrangement of cells that contribute nutrients and patterning information during oogenesis (nurse cells), and show that the diversification of ovariole number and egg size have both been largely independent of their presence or position within the ovariole. Instead, we show that ovariole number evolution has been shaped by a series of transitions between variable and invariant states, with multiple independent lineages evolving to have almost no variation in ovariole number. We highlight the implications of these invariant lineages on our understanding of the specification of ovariole number during development, as well as the importance of considering developmental processes in theories of life-history evolution.

Hierarchical Modelling of Haplotype Effects on a Phylogeny

We introduce a hierarchical model to estimate haplotype effects based on phylogenetic relationships between haplotypes and their association with observed phenotypes. In a population there are many, but not all possible, distinct haplotypes and few observations per haplotype. Further, haplotype frequencies tend to vary substantially. Such data structure challenge estimation of haplotype effects. However, haplotypes often differ only due to few mutations, and leveraging similarities can improve the estimation of effects. We build on extensive literature and develop an autoregressive model of order one that models haplotype effects by leveraging phylogenetic relationships described with a directed acyclic graph. The phylogenetic relationships can be either in a form of a tree or a network, and we refer to the model as the haplotype network model. The model can be included as a component in a phenotype model to estimate associations between haplotypes and phenotypes. Our key contribution is that we obtain a sparse model, and by using hierarchical autoregression, the flow of information between similar haplotypes is estimated from the data. A simulation study shows that the hierarchical model can improve estimates of haplotype effects compared to an independent haplotype model, especially with few observations for a specific haplotype. We also compared it to a mutation model and observed comparable performance, though the haplotype model has the potential to capture background specific effects. We demonstrate the model with a study of mitochondrial haplotype effects on milk yield in cattle. We provide R code to fit the model with the INLA package.

The comparative method is not macroevolution: across-species evidence for within-species process

It is common for studies that employ the comparative method for the study of adaptation, i.e. documentation of potentially adaptive across-species patterns of trait-environment or trait-trait correlation, to be designated as "macroevolutionary." Authors are justified in using "macroevolution" in this way by appeal to definitions such as "evolution above the species level." I argue that regarding the comparative method as "macroevolutionary" is harmful because it hides in serious ways the true causal content of hypotheses tested with the comparative method. The comparative method is a means of testing hypotheses of adaptation and their alternatives. Adaptation is a population level phenomenon, involving heritable interindividual variation that is associated with fitness differences. For example, given heritable intrapopulational variation, more streamlined individuals in populations of fast-moving aquatic animals have higher locomotory efficiency and thus better survivorship and more resources directed to reproduction than less streamlined ones. Direct evidence consistent with this population-level scenario includes the observation that many unrelated species of fast-moving aquatic animals have similar streamlined shapes, an example of the comparative method. Crucial to note in this example is that although the data are observed across species, the comparative method for studying adaptation tests hypotheses regarding standard population-level natural selection with no content that can be construed as "macro." Even less "macro," individual-level developmental dynamics can limit or bias the range of variants available for selection. Calling any of these studies "macroevolutionary" implies that some additional process is at work, shrouding the need to test adaptation hypotheses and study the range of variants that can be produced in development.

The complex effects of mass extinctions on morphological disparity

Studies of biodiversity through deep time have been a staple for biologists and paleontologists for over 60 years. Investigations of species richness (diversity) revealed that at least five mass extinctions punctuated the last half billion years, each seeing the rapid demise of a large proportion of contemporary taxa. In contrast to diversity, the response of morphological diversity (disparity) to mass extinctions is unclear. Generally, diversity and disparity are decoupled, such that diversity may decline as morphological disparity increases, and vice versa. Here, we develop simulations to model disparity changes across mass extinctions using continuous traits and birth-death trees. We find no simple null for disparity change following a mass extinction but do observe general patterns. The range of trait values decreases following either random or trait-selective mass extinctions, whereas variance and the density of morphospace occupation only decline following trait-selective events. General trends may differentiate random and trait-selective mass extinctions, but methods struggle to identify trait selectivity. Long-term effects of mass extinction trait selectivity change support for phylogenetic comparative methods away from the simulated Brownian motion toward Ornstein-Uhlenbeck and Early Burst models. We find that morphological change over mass extinction is best studied by quantifying multiple aspects of morphospace occupation.

Disparities in the analysis of morphological disparity

Analyses of morphological disparity have been used to characterize and investigate the evolution of variation in the anatomy, function and ecology of organisms since the 1980s. While a diversity of methods have been employed, it is unclear whether they provide equivalent insights. Here, we review the most commonly used approaches for characterizing and analysing morphological disparity, all of which have associated limitations that, if ignored, can lead to misinterpretation. We propose best practice guidelines for disparity analyses, while noting that there can be no 'one-size-fits-all' approach. The available tools should always be used in the context of a specific biological question that will determine data and method selection at every stage of the analysis.