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.

scholarly journals Markov chains and the determination of fair premiums

1967 ◽  
Vol 4 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Stefan Vajda
Keyword(s):  
Stochastic Process ◽  
Markov Chains ◽  
Stochastic Processes ◽  
Mathematical Theory ◽  
The Other ◽  
Main Stream ◽  
Other Hand ◽  
Pure Mathematics ◽  
The University

The relationships between actuarial and pure mathematics are curious. Actuaries have contributed to the development of mathematical theory: it is sufficient to mention, as examples, Fredholm of an earlier, and Cramér of a more recent generation. Scandinavian mathematicians, in particular, have been concerned with a very special type of stochastic process, reflected in the collective theory of risk, and the work of Philipson, Ammeter and others in this field is well known to readers of this Bulletin. However, the main stream of the theory of stochastic processes has little contact with actuarial applications.On the other hand, many actuaries have studied and assimilated pure mathematics and have thrown light on actuarial matters by describing their own preoccupations in the terminology of modern, often abstract, mathematics. E. Franckx is one of their number.The Instituto di Matematica Finanziaria of the University of Trieste (Faculty of Economics and Commerce) has published a booklet entitledEssai d'une théorie opérationnelle des risques Markoviens which contains three lectures delivered by Professor Franckx in Trieste and a contribution which he presented to the 17th Congress of Actuaries, held in London in 1964.

scholarly journals Stationarity as a path property

2019 ◽  
Vol 39 (2) ◽  
pp. 403-422
Author(s):  
Yi Shen ◽  
Tony S. Wirjanto
Keyword(s):  
Stochastic Process ◽  
Stationary Process ◽  
The Other ◽  
Mild Conditions ◽  
Other Hand ◽  
Distributional Property ◽  
Shift Invariance ◽  
Stationarity Test ◽  
Path Property ◽  
Almost All

Traditionally, stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of paths, denoted by A, which corresponds to the notion of stationarity. On one hand, the set A is shown to be large enough, so that for any stationary process, almost all of its paths are in A. On the other hand, we prove that any path in A will behave in the optimal way under any stationarity test satisfying some mild conditions.

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 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 Al-Qira'ah al-Shadzah and Its Influence on Language Orientation

2018 ◽  
Vol 4 (1) ◽  
pp. 32
Author(s):  
Khairuddin Khairuddin
Keyword(s):  
Comparative Methods ◽  
The Other ◽  
Other Hand ◽  
Language Orientation

This study aims to describe Qira'ah Shadzah and its role in continuity the dialect of Arabic, especially the verses related to Qira'ah Shadzah contained in chapter Al-Imran. This study used descriptive-normative and comparative methods. The results show that Qira'ah Shadzah made an important contribution in maintaining the continuity of Arab dialect. This is derived from the observation of some Qira'ah Shadzah because there is a change of vowel, such as the transfer from fathah to dhamma, from kasrah to dhamma, from fathah to kasrah, or from dhamma to kasrah. These changes show that Arab customs differ between desert people and civilized people. Where civilized people more often use fathah and kasrah because both are symbols of meekness, while on the other hand desert people prefer to use the dhammah which is a hard and rough symbol.

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.

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.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

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