scholarly journals Fast and Robust Inference of Phylogenetic Ornstein-Uhlenbeck Models Using Parallel Likelihood Calculation

2017 ◽  
Author(s):  
Venelin Mitov ◽  
Tanja Stadler
Keyword(s):  
Brownian Motion ◽  
Bayesian Inference ◽  
Mixed Model ◽  
False Positive Rate ◽  
Comparative Methods ◽  
Neutral Evolution ◽  
Stabilizing Selection ◽  
Full Potential ◽  
Mammal Species ◽  
Trait Evolution

AbstractPhylogenetic comparative methods have been used to model trait evolution, to test selection versus neutral hypotheses, to estimate optimal trait-values, and to quantify the rate of adaptation towards these optima. Several authors have proposed algorithms calculating the likelihood for trait evolution models, such as the Ornstein-Uhlenbeck (OU) process, in time proportional to the number of tips in the tree. Combined with gradient-based optimization, these algorithms enable maximum likelihood (ML) inference within seconds, even for trees exceeding 10,000 tips. Despite its useful statistical properties, ML has been criticised for being a point estimator prone to getting stuck in local optima. As an elegant alternative, Bayesian inference explores the entire information in the data and compares it to prior knowledge but, usually, runs in much longer time, even for small trees. Here, we propose an approach to use the full potential of ML and Bayesian inference, while keeping the runtime within minutes. Our approach combines (i) a new algorithm for parallel likelihood calculation; (ii) a previously published method for adaptive Metropolis sampling. In principle, the strategy of (i) and (ii) can be applied to any likelihood calculation on a tree which proceeds in a pruning-like fashion leading to enormous speed improvements. As a showcase, we implement the phylogenetic Ornstein-Uhlenbeck mixed model (POUMM) in the form of an easy-to-use and highly configurable R-package. In addition to the above-mentioned usage of comparative methods, the POUMM allows to estimate non-heritable variance and phylogenetic heritability. Using simulations and empirical data from 487 mammal species, we show that the POUMM is far more reliable in terms of unbiased estimates and false positive rate for stabilizing selection, compared to its alternative - the non-mixed Ornstein-Uhlenbeck model, which assumes a fully heritable and perfectly measurable trait. Further, our analysis reveals that the phylogenetic mixed model (PMM), which assumes neutral evolution (Brownian motion) can be a very unstable estimator of phylogenetic heritability, even if the Brownian motion assumption is only weakly violated. Our results prove the need for a simultaneous account for selection and non-heritable variance in phylogenetic evolutionary models and challenge stabilizing selection hypotheses stated in numerous macro-evolutionary studies.

scholarly journals Beyond Brownian motion and the Ornstein-Uhlenbeck process: Stochastic diffusion models for the evolution of quantitative characters

2016 ◽  
Author(s):  
Simon Phillip Blomberg
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Comparative Methods ◽  
Diffusion Models ◽  
Mathematical Framework ◽  
Phylogenetic Comparative Methods ◽  
Uhlenbeck Process ◽  
Trait Evolution ◽  
Ornstein Uhlenbeck Process ◽  
Non Gaussian

AbstractGaussian 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 which limit their utility. Here I describe new, non-Gaussian stochastic differential equation (diffusion) models of quantitative trait evolution. I present general methods for deriving new diffusion models, and discuss possible schemes for fitting non-Gaussian evolutionary models to trait data. The theory of stochastic processes provides a mathematical framework for understanding the properties of current, new 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.

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

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11997
Author(s):  
Liam J. Revell
Keyword(s):  
Brownian Motion ◽  
Quantitative Trait ◽  
Penalized Likelihood ◽  
Comparative Methods ◽  
Character Trait ◽  
Likelihood Method ◽  
Rate Variation ◽  
Phylogenetic Comparative Methods ◽  
Trait Evolution ◽  
Rate Of Evolution

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.

scholarly journals A Phylogenetic Independent Contrast Method under the Ornstein-Uhlenbeck Model and its Applications in Correlated Evolution

2021 ◽  
Author(s):  
Cong Liang ◽  
Yingjun Deng
Keyword(s):  
Least Squares ◽  
Generalized Least Squares ◽  
Comparative Methods ◽  
Stabilizing Selection ◽  
Type I ◽  
Phylogenetic Comparative Methods ◽  
Trait Evolution ◽  
Correlated Evolution ◽  
Independent Contrast ◽  
Pic Method

Phylogenetic comparative methods are essential in studying the evolution of traits across a phylogeny. Felsenstein's phylogenetic independent contrast (PIC) method and the generalized least squares (GLS) regression were often utilized to study whether evolutionary changes between traits were correlated. However, a neutral Brownian model is assumed in the PIC method, which impacts the performance of the PIC method when the trait is subject to adaptation. In recent years, the Ornstein-Uhlenbeck (OU) model has attracted increasing attention in studying the evolution of traits with stabilizing selection. In this study, we extended Felsenstein's PIC method under the OU model, which we termed OU-PIC. We simulated trait evolution under the OU model on phylogenetic trees with 8, 10, and 55 species. Compared to the PIC method, the OU-PIC method with correct stabilizing selection parameters achieved an appropriate type I error rate, the highest test power, and the lowest mean squared error. We presented a concise proof of the intrinsic connection between the OU-PIC and the generalized least squares (GLS) regression method in evaluating correlated evolution under the OU model. The OU-PIC method has a broad range of applications when trait evolution could be sufficiently modeled by the OU process. Compared with other phylogenetic comparative methods, OU-PIC avoids the inverse of the covariance matrix and would facilitate the analysis of correlated evolution on large phylogenies.

scholarly journals Detecting selection with a genetic cross

2020 ◽  
Vol 117 (36) ◽  
pp. 22323-22330
Author(s):  
Hunter B. Fraser
Keyword(s):  
Skin Color ◽  
Evolutionary Biology ◽  
Neutral Evolution ◽  
Sign Test ◽  
Stabilizing Selection ◽  
Mrna Levels ◽  
Effective Population ◽  
Phenotypic Data ◽  
Genetic Cross ◽  
Selected Traits

Distinguishing which traits have evolved under natural selection, as opposed to neutral evolution, is a major goal of evolutionary biology. Several tests have been proposed to accomplish this, but these either rely on false assumptions or suffer from low power. Here, I introduce an approach to detecting selection that makes minimal assumptions and only requires phenotypic data from ∼10 individuals. The test compares the phenotypic difference between two populations to what would be expected by chance under neutral evolution, which can be estimated from the phenotypic distribution of an F2cross between those populations. Simulations show that the test is robust to variation in the number of loci affecting the trait, the distribution of locus effect sizes, heritability, dominance, and epistasis. Comparing its performance to the QTL sign test—an existing test of selection that requires both genotype and phenotype data—the new test achieves comparable power with 50- to 100-fold fewer individuals (and no genotype data). Applying the test to empirical data spanning over a century shows strong directional selection in many crops, as well as on naturally selected traits such as head shape in HawaiianDrosophilaand skin color in humans. Applied to gene expression data, the test reveals that the strength of stabilizing selection acting on mRNA levels in a species is strongly associated with that species’ effective population size. In sum, this test is applicable to phenotypic data from almost any genetic cross, allowing selection to be detected more easily and powerfully than previously possible.

scholarly journals The relative impact of evolving pleiotropy and mutational correlation on trait divergence

2019 ◽  
Author(s):  
Jobran Chebib ◽  
Frédéric Guillaume
Keyword(s):  
Stochastic Model ◽  
Directional Selection ◽  
Population Variation ◽  
The Other ◽  
Common Mechanism ◽  
Stabilizing Selection ◽  
Relative Impact ◽  
Relative Importance ◽  
Trait Evolution ◽  
Trait Divergence

AbstractBoth pleiotropic connectivity and mutational correlations can restrict the divergence of traits under directional selection, but it is unknown which is more important in trait evolution. In order to address this question, we create a model that permits within-population variation in both pleiotropic connectivity and mutational correlation, and compare their relative importance to trait evolution. Specifically, we developed an individual-based, stochastic model where mutations can affect whether a locus affects a trait and the extent of mutational correlations in a population. We find that traits can diverge whether there is evolution in pleiotropic connectivity or mutational correlation but when both can evolve then evolution in pleiotropic connectivity is more likely to allow for divergence to occur. The most common genotype found in this case is characterized by having one locus that maintains connectivity to all traits and another that loses connectivity to the traits under stabilizing selection (subfunctionalization). This genotype is favoured because it allows the subfunctionalized locus to accumulate greater effect size alleles, contributing to increasingly divergent trait values in the traits under directional selection without changing the trait values of the other traits (genetic modularization). These results provide evidence that partial subfunctionalization of pleiotropic loci may be a common mechanism of trait divergence under regimes of corridor selection.

scholarly journals Phylogenomics of Monitor Lizards and the Role of Competition in Dictating Body Size Disparity

2020 ◽  
Vol 70 (1) ◽  
pp. 120-132 ◽  
Author(s):  
Ian G Brennan ◽  
Alan R Lemmon ◽  
Emily Moriarty Lemmon ◽  
Daniel M Portik ◽  
Valter Weijola ◽  
...  
Keyword(s):  
Size Variation ◽  
Biotic Interactions ◽  
Character Displacement ◽  
Comparative Methods ◽  
Morphological Data ◽  
Trait Evolution ◽  
Biogeographic History ◽  
Size Disparity ◽  
Multiple Orders ◽  
Monitor Lizards

Abstract Organismal interactions drive the accumulation of diversity by influencing species ranges, morphology, and behavior. Interactions vary from agonistic to cooperative and should result in predictable patterns in trait and range evolution. However, despite a conceptual understanding of these processes, they have been difficult to model, particularly on macroevolutionary timescales and across broad geographic spaces. Here, we investigate the influence of biotic interactions on trait evolution and community assembly in monitor lizards (Varanus). Monitors are an iconic radiation with a cosmopolitan distribution and the greatest size disparity of any living terrestrial vertebrate genus. Between the colossal Komodo dragon Varanus komodoensis and the smallest Australian dwarf goannas, Varanus length and mass vary by multiple orders of magnitude. To test the hypothesis that size variation in this genus was driven by character displacement, we extended existing phylogenetic comparative methods which consider lineage interactions to account for dynamic biogeographic history and apply these methods to Australian monitors and marsupial predators. Incorporating both exon-capture molecular and morphological data sets we use a combined evidence approach to estimate the relationships among living and extinct varaniform lizards. Our results suggest that communities of Australian Varanus show high functional diversity as a result of continent-wide interspecific competition among monitors but not with faunivorous marsupials. We demonstrate that patterns of trait evolution resulting from character displacement on continental scales are recoverable from comparative data and highlight that these macroevolutionary patterns may develop in parallel across widely distributed sympatric groups.[Character displacement; comparative methods; phylogenetics; trait evolution; Varanus.]

Bayesian inference for fractional Oscillating Brownian motion

2021 ◽  
Author(s):  
Héctor Araya ◽  
Meryem Slaoui ◽  
Soledad Torres
Keyword(s):  
Brownian Motion ◽  
Bayesian Inference

scholarly journals On the effect of asymmetrical trait inheritance on models of trait evolution

2019 ◽  
Author(s):  
Pablo Duchen ◽  
Michael L. Alfaro ◽  
Jonathan Rolland ◽  
Nicolas Salamin ◽  
Daniele Silvestro
Keyword(s):  
Quantitative Trait ◽  
Comparative Methods ◽  
Simulation Framework ◽  
Trait Evolution ◽  
Individual Level ◽  
Parameter Estimations ◽  
Wide Range ◽  
Biological Interpretation ◽  
Individual Based Simulation ◽  
The Individual

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

scholarly journals THE SELECTIVE VALUE OF ALLELES UNDERLYING POLYGENIC TRAITS

Genetics ◽  
1984 ◽  
Vol 108 (4) ◽  
pp. 1021-1033
Author(s):  
Michael Lynch
Keyword(s):  
Molecular Evolution ◽  
Genetic Drift ◽  
Genetic Variance ◽  
Neutral Theory ◽  
Mechanistic Explanation ◽  
Neutral Evolution ◽  
Stabilizing Selection ◽  
Average Effect ◽  
Absolute Value ◽  
The Mean

ABSTRACT To define the genetic and ecological circumstances that are conductive to evolution via genetic drift at the allelic level, the selection coefficient for a constituent allele of arbitrary effect is derived for a polygenic character exposed to stabilizing selection. Under virtually all possible conditions, alleles within the class for which the absolute value of the average effect is <10-2 phenotypic standard deviations are neutral with respect to each other. In addition, when the mean phenotype is at the optimum and the genetic variance is in selection-drift-mutation equilibrium, a considerable amount of neutral evolution is expected in the class of alleles with intermediate effects on the phenotype. These results help clarify how molecular evolution via genetic drift may occur at a locus despite intense selection and provide a potential mechanistic explanation for the neutral theory of molecular evolution.

Development of a Third Trimester Contingent Prognostic Prediction Scheme for Suspected Early-Onset Pre-Eclampsia

2021 ◽  
pp. 1-9
Author(s):  
Enric Sabrià ◽  
Paula Lafuente-Ganuza ◽  
Paloma Lequerica-Fernández ◽  
Ana Isabel Escudero ◽  
Eduardo Martínez-Morillo ◽  
...  
Keyword(s):  
Early Onset ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
False Positive Rate ◽  
Area Under The Curve ◽  
Prediction Tool ◽  
Model Based ◽  
Prognostic Prediction ◽  
Short Term Prediction ◽  
Plgf Ratio

<b><i>Introduction:</i></b> Short-term prediction of pre-eclampsia (PE) using soluble FMS-like tyrosine kinase-1 (sFlt-1)/ placental growth factor (PlGF) ratio has high false-positive rate. Therefore, we developed a prognostic prediction tool that predicts early-onset PE leading to delivery within 1 week on pregnancies with an sFlt-1/PlGF ratio above 38 and compared it with an analogous model based on sFlt-1/PlGF ratio and with the 655 sFlt-1/PlGF ratio cutoff. <b><i>Methods:</i></b> Cohort study of 363 singleton pregnancies with clinical suspicion of PE before 34 weeks of gestation, allowing repeated assessments (522). 213 samples with an sFlt-1/PlGF ratio above 38 were assessed to construct and identify the best-fit linear mixed model. N-terminal pro-B-type natriuretic peptide (NT-proBNP), sFlt-1 MoM, PlGF MoM, and sFlt-1/PlGF ratio combined with gestational age (GA) were assessed. <b><i>Results:</i></b> None of the pregnancies with an sFlt-1/PlGF ratio of 38 or below developed early-onset PE (309 samples from 240 pregnancies). Conversely, 47 women of 213 assessments (22.1%) with an sFlt-1/PlGF ratio above 38 developed the assessed outcome. The selected model included sFlt-1 MoM, NT-proBNP, and GA. Differences in area under the curve were observed between the selected model and the GA + sFlt-1/PlGF model (<i>p</i> = 0.04). At an sFlt-1/PlGF ratio cutoff of 655, detection rate was 31.9% (15/47), while the selected model detection was 55.3% (26/47) (<i>p</i> = 0.008). <b><i>Discussion:</i></b> Considering repeated assessments, the sFlt-1/PlGF ratio of 38 or below adequately ruled out early-onset PE, leading to delivery within 1 week. However, when sFlt-1/PlGF ratio is above 38, the prediction tool derived from linear mixed model based on GA, NT-proBNP, and sFlt-1 MoM, provided a better prognosis prediction than the sFlt-1/PlGF ratio.

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