Phylogenetic confidence intervals for the optimal trait value

Bartoszek, Krzysztof; Sagitov, Serik

doi:10.1017/s0021900200113117

Cited by 3 publications

(22 citation statements)

References 46 publications

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“…In the work here we can observe the (well known) competition between the tree's speciation and OU's adaptation (drift) rates, resulting in a phase transition when the latter is half the former (the same as in the no jumps case Adamczak and Miło s [2,3] , An e et al [4] , Bartoszek and Sagitov [12] ). We show here that if variability in jump occurrences disappears with time or the model is in the critical regime (plus a bound assumption on the jumps' magnitude and chances of occurring), then the contemporary sample mean will be asymptotically normally distributed.…”

Section: Introductionmentioning

confidence: 59%

“…where X t À=þ ð Þ means the value of X(t) respectively just before and after time t, Z is a binary random variable with probability p of being 1 (i.e., jump occurs) and f $ N 0, r 2 c À Á : The parameters p and r 2 c can, in particular, differ between speciation events. Taking p ¼ 0 or r 2 c ¼ 0 we recover the YOU without jumps model and results (described by Bartoszek and Sagitov [12] ).…”

Section: Phenotype Modelmentioning

confidence: 65%

“…In this work we build up on previous results (Bartoszek [10] , Bartoszek and Sagitov [12] ) and study in detail the asymptotic behavior of the average of the tip values of a branching OU process, with jumps at speciation points, evolving on a pure birth tree. To the best of our knowledge the work here is one of the first to consider the effect of jumps on a branching OU process in a phylogenetic context (but also look at Bastide et al [15] ).…”

Section: Introductionmentioning

confidence: 89%

“…In this work we consider a fundamental model of phylogenetic tree growth the conditioned on number of tip species pure birth process (Yule tree). We first make the notation from Section 2 more intuitive, illustrating it also in Figures 1 and 5 (see also Bartoszek [10] , Bartoszek and Sagitov [12] , Sagitov and Bartoszek [49] ). We consider a tree that has n tip species.…”

Section: The Branching Phenotypementioning

confidence: 99%

“…Large sample size distributional approximations will allow for choosing seeds for numerical maximum likelihood procedures and sanity checks if the results of numerical procedures make sense. For example in the one-dimensional OU case it is known that (for a Yule tree) the sample average is a consistent estimator of the long term mean and the sample variance of the OU process' stationary variance (Bartoszek and Sagitov [12] ). In the BM (Yule tree) case one can have a consistent estimator of the diffusion coefficient.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Central Limit Theorem for punctuated equilibrium

Bartoszek

2020

Stochastic Models

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Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated-the phenotype can jump. Such a jump could especially occur at speciation, i.e., dramatic change occurs that drives the species apart. Here we derive a Central Limit Theorem for punctuated equilibrium. We show that, if adaptation is fast, for weak convergence to normality to hold, the variability in the occurrence of change has to disappear with time.

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Section: Introductionmentioning

confidence: 59%

Section: Phenotype Modelmentioning

confidence: 65%

Section: Introductionmentioning

confidence: 89%

Section: The Branching Phenotypementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Central Limit Theorem for punctuated equilibrium

Bartoszek

2020

Stochastic Models

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Phase transition on the convergence rate of parameter estimation under an Ornstein–Uhlenbeck diffusion on a tree

Ané

Roch

2016

J. Math. Biol.

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Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges because of the intrinsic correlation between the observations produced by the shared evolutionary history, thus violating the standard independence assumption of large-sample theory. For instance Ho and Ané [18] recently proved that the mean (also known in this context as selection optimum) of an OrnsteinUhlenbeck process on a tree cannot be estimated consistently from an increasing number of tip observations if the tree height is bounded. Here, using a fruitful connection to the so-called reconstruction problem in probability theory, we study the convergence rate of parameter estimation in the unbounded height case. For the mean of the process, we provide a necessary and sufficient condition for the consistency of the maximum likelihood estimator (MLE) and establish a phase transition on its convergence rate in terms of the growth of the tree. In particular we show that a loss of √ n-consistency (i.e., the variance of the MLE becomes Ω(n −1 ), where n is the number of tips) occurs when the tree growth is larger than a threshold related to the phase transition of the reconstruction problem. For the covariance parameters, we give a novel, efficient estimation method which achieves √ n-consistency under natural assumptions on the tree. Our theoretical results provide practical suggestions for the design of comparative data collection.

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Fast and accurate detection of evolutionary shifts in Ornstein–Uhlenbeck models

et al. 2016

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1. The detection of evolutionary shifts in trait evolution from extant taxa is motivated by the study of convergent evolution, or to correlate shifts in traits with habitat changes or with changes in other phenotypes. 2. We propose here a phylogenetic lasso method to study trait evolution from comparative data and detect past changes in the expected mean trait values. We use the Ornstein-Uhlenbeck process, which can model a changing adaptive landscape over time and over lineages. 3. Our method is very fast, running in minutes for hundreds of species, and can handle multiple traits. We also propose a phylogenetic Bayesian information criterion that accounts for the phylogenetic correlation between species, as well as for the complexity of estimating an unknown number of shifts at unknown locations in the phylogeny. This criterion does not suffer model overfitting and has high precision, so it offers a conservative alternative to other information criteria. 4. Our re-analysis of Anolis lizard data suggests a more conservative scenario of morphological adaptation and convergence than previously proposed. Software is available on GitHub.

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Phylogenetic confidence intervals for the optimal trait value

Cited by 3 publications

References 46 publications

A Central Limit Theorem for punctuated equilibrium

A Central Limit Theorem for punctuated equilibrium

Phase transition on the convergence rate of parameter estimation under an Ornstein–Uhlenbeck diffusion on a tree

Fast and accurate detection of evolutionary shifts in Ornstein–Uhlenbeck models

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