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 Phylogenetic Comparative Methods and the Evolution of Multivariate Phenotypes

2019 ◽  
Vol 50 (1) ◽  
pp. 405-425 ◽  
Author(s):  
Dean C. Adams ◽  
Michael L. Collyer
Keyword(s):  
Phylogenetic Analysis ◽  
Evolutionary Biology ◽  
Generalized Least Squares ◽  
Comparative Methods ◽  
High Dimensional ◽  
Phenotypic Integration ◽  
Phylogenetic Comparative Methods ◽  
Evolutionary Trends ◽  
Phenotype Space ◽  
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.

scholarly journals Correlated evolution of sternal keel length and ilium length in birds

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e3622 ◽  
Author(s):  
Tao Zhao ◽  
Di Liu ◽  
Zhiheng Li
Keyword(s):  
Muscle Mass ◽  
Empirical Studies ◽  
Comparative Methods ◽  
Phylogenetic Comparative Methods ◽  
Pectoral Girdle ◽  
Correlated Evolution ◽  
Avian Evolution ◽  
Terrestrial Locomotion ◽  
Moment Arms ◽  
New Evidence

The interplay between the pectoral module (the pectoral girdle and limbs) and the pelvic module (the pelvic girdle and limbs) plays a key role in shaping avian evolution, but prior empirical studies on trait covariation between the two modules are limited. Here we empirically test whether (size-corrected) sternal keel length and ilium length are correlated during avian evolution using phylogenetic comparative methods. Our analyses on extant birds and Mesozoic birds both recover a significantly positive correlation. The results provide new evidence regarding the integration between the pelvic and pectoral modules. The correlated evolution of sternal keel length and ilium length may serve as a mechanism to cope with the effect on performance caused by a tradeoff in muscle mass between the pectoral and pelvic modules, via changing moment arms of muscles that function in flight and in terrestrial locomotion.

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 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 Is horizontal transmission really a problem for phylogenetic comparative methods? A simulation study using continuous cultural traits

2010 ◽  
Vol 365 (1559) ◽  
pp. 3903-3912 ◽  
Author(s):  
Thomas E. Currie ◽  
Simon J. Greenhill ◽  
Ruth Mace
Keyword(s):  
Cultural Evolution ◽  
Horizontal Transmission ◽  
Comparative Methods ◽  
Phylogenetic Comparative Methods ◽  
Ancestral State ◽  
Regression Analyses ◽  
Trait Evolution ◽  
Phylogenetic Methods ◽  
Cultural Traits ◽  
Future Work

Phylogenetic comparative methods (PCMs) provide a potentially powerful toolkit for testing hypotheses about cultural evolution. Here, we build on previous simulation work to assess the effect horizontal transmission between cultures has on the ability of both phylogenetic and non-phylogenetic methods to make inferences about trait evolution. We found that the mode of horizontal transmission of traits has important consequences for both methods. Where traits were horizontally transmitted separately , PCMs accurately reported when trait evolution was not correlated even at the highest levels of horizontal transmission. By contrast, linear regression analyses often incorrectly concluded that traits were correlated. Where simulated trait evolution was not correlated and traits were horizontally transmitted as a pair , both methods inferred increased levels of positive correlation with increasing horizontal transmission. Where simulated trait evolution was correlated, increasing rates of separate horizontal transmission led to decreasing levels of inferred correlation for both methods, but increasing rates of paired horizontal transmission did not. Furthermore, the PCM was also able to make accurate inferences about the ancestral state of traits. These results suggest that under certain conditions, PCMs can be robust to the effects of horizontal transmission. We discuss ways that future work can investigate the mode and tempo of horizontal transmission of cultural traits.

scholarly journals Trait Evolution with Jumps: Illusionary Normality

2017 ◽  
Author(s):  
Krzysztof Bartoszek
Keyword(s):  
Stochastic Process ◽  
Weak Convergence ◽  
Comparative Methods ◽  
The Other ◽  
Phylogenetic Comparative Methods ◽  
Evolutionary Models ◽  
Trait Evolution ◽  
Other Hand ◽  
Extinction Component

ABSTRACTPhylogenetic comparative methods for real-valued traits usually make use of stochastic process whose trajectories are continuous. This is despite biological intuition that evolution is rather punctuated than gradual. On the other hand, there has been a number of recent proposals of evolutionary models with jump components. However, as we are only beginning to understand the behaviour of branching Ornstein–Uhlenbeck (OU) processes the asymptotics of branching OU processes with jumps is an even greater unknown. In this work we build up on a previous study concerning OU with jumps evolution on a pure birth tree. We introduce an extinction component and explore via simulations, its effects on the weak convergence of such a process. We furthermore, also use this work to illustrate the simulation and graphic generation possibilities of the mvSLOUCH package.

Evolutionary Sample Size and Consilience in Phylogenetic Comparative Analysis

2021 ◽  
Author(s):  
Jacob D Gardner ◽  
Chris L Organ
Keyword(s):  
Sample Size ◽  
A Priori ◽  
Class Imbalance ◽  
Comparative Methods ◽  
Character State ◽  
Phylogenetic Comparative Methods ◽  
Sample Sizes ◽  
Correlated Evolution ◽  
Evolutionary Transitions ◽  
Discrete Traits

Abstract Phylogenetic comparative methods (PCMs) are commonly used to study evolution and adaptation. However, frequently used PCMs for discrete traits mishandle single evolutionary transitions. They erroneously detect correlated evolution in these situations. For example, hair and mammary glands cannot be said to have evolved in a correlated fashion because each evolved only once in mammals, but a commonly used model (Pagel’s Discrete) statistically supports correlated (dependent) evolution. Using simulations, we find that rate parameter estimation, which is central for model selection, is poor in these scenarios due to small effective (evolutionary) sample sizes of independent character state change. Pagel’s Discrete model also tends to favor dependent evolution in these scenarios, in part, because it forces evolution through state combinations unobserved in the tip data. This model prohibits simultaneous dual transitions along branches. Models with underlying continuous data distributions (e.g., Threshold and GLMM) are less prone to favor correlated evolution but are still susceptible when evolutionary sample sizes are small. We provide three general recommendations for researchers who encounter these common situations: i) create study designs that evaluate a priori hypotheses and maximize evolutionary sample sizes; ii) assess the suitability of evolutionary models—for discrete traits, we introduce the phylogenetic imbalance ratio; and iii) evaluate evolutionary hypotheses with a consilience of evidence from disparate fields, like biogeography and developmental biology. Consilience plays a central role in hypothesis testing within the historical sciences where experiments are difficult or impossible to conduct, such as many hypotheses about correlated evolution. These recommendations are useful for investigations that employ any type of PCM. [Class imbalance; consilience; correlated evolution; evolutionary sample size; phylogenetic comparative methods.]

scholarly journals Realistic scenarios of missing taxa in phylogenetic comparative methods and their effects on model selection and parameter estimation

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e7917 ◽  
Author(s):  
Rafael S. Marcondes
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Phylogenetic Signal ◽  
Comparative Methods ◽  
Phylogenetic Comparative Methods ◽  
Trait Evolution ◽  
Continuous Trait ◽  
Starting Point ◽  
Almost All ◽  
Future Work

Model-based analyses of continuous trait evolution enable rich evolutionary insight. These analyses require a phylogenetic tree and a vector of trait values for the tree’s terminal taxa, but rarely do a tree and dataset include all taxa within a clade. Because the probability that a taxon is included in a dataset depends on ecological traits that have phylogenetic signal, missing taxa in real datasets should be expected to be phylogenetically clumped or correlated to the modelled trait. I examined whether those types of missing taxa represent a problem for model selection and parameter estimation. I simulated univariate traits under a suite of Brownian Motion and Ornstein-Uhlenbeck models, and assessed the performance of model selection and parameter estimation under absent, random, clumped or correlated missing taxa. I found that those analyses perform well under almost all scenarios, including situations with very sparsely sampled phylogenies. The only notable biases I detected were in parameter estimation under a very high percentage (90%) of correlated missing taxa. My results offer a degree of reassurance for studies of continuous trait evolution with missing taxa, but the problem of missing taxa in phylogenetic comparative methods still demands much further investigation. The framework I have described here might provide a starting point for future work.

scholarly journals Do extra-group fertilizations increase the potential for sexual selection in male mammals?

2017 ◽  
Vol 13 (10) ◽  
pp. 20170313 ◽  
Author(s):  
Kavita Isvaran ◽  
Sumithra Sankaran
Keyword(s):  
Sexual Selection ◽  
Mating System ◽  
Uniform Distribution ◽  
Mating Systems ◽  
Fertilization Success ◽  
Comparative Methods ◽  
Phylogenetic Comparative Methods ◽  
Trait Evolution ◽  
The Social ◽  
Measures Of Inequality

Fertilizations by males outside the social breeding group (extra-group paternity, EGP) are widespread in birds and mammals. EGP is generally proposed to increase male reproductive skew and thereby increase the potential for sexual selection, but the generality of this relationship is unclear. We extracted data from 27 mammals in seven orders and used phylogenetic comparative methods to investigate the influence of EGP and social mating system on measures of inequality in male fertilization success, which are indices of the potential for sexual selection. We find that EGP and social mating system can predict the potential for sexual selection in mammalian populations, but only when considered jointly and not individually. EGP appears to increase the potential for sexual selection but only when the degree of social polygyny is relatively low. When social polygyny is high, EGP appears to result in a more uniform distribution of reproduction and a decrease in the potential for sexual selection. A possible explanation to be investigated is that the phenotype of extra-group fathers differs systematically across social mating systems. Our findings have implications for the use of EGP and social mating system as indices of sexual selection in comparative analyses of trait evolution under sexual selection.

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