A Central Limit Theorem for punctuated equilibrium

Bartoszek, Krzysztof

doi:10.1080/15326349.2020.1752242

Cited by 3 publications

(14 citation statements)

References 49 publications

(119 reference statements)

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“…However, if the drift is slow, then the dependencies induced by common ancestry persist and statements about the limit are more involved. The above was shown for the YOU model in [10], while the YOU model with normally distributed jumps was considered in [8]. In the slow drift regime one can show L 2 convergence (see e.g.…”

Section: Introductionmentioning

confidence: 87%

“…There are two key random components to consider: the height of the tree (U n ) and the time from the present backwards to the coalescence of a random pair (out of n 2 possible pairs) of tip species (τ (n) ). These random variables are illustrated in Figure 2, but see also Figure A.8 in [7] and Figures 1 and 5 in [8].…”

Section: The Yule-ornstein-uhlenbeck Modelmentioning

confidence: 99%

“…In Sections 3 and 4 of the present paper, we extend the central limit theorems for X n by giving bounds for the Kolmogorov and Wasserstein distances between the distribution of X n and properly chosen normal distributions (Theorems 3.1, 3.2, 4.1, and 4.2), which converge weakly to the limiting normal distributions of [10] and [8] as n → ∞. The key observation is that conditional on the tree (and the locations of jumps), X n is a linear combination of normally distributed random variables, which makes it possible to apply Theorems 2.1 and 2.2.…”

Section: Introductionmentioning

confidence: 98%

“…In the slow drift regime one can show L 2 convergence (see e.g. [1], [8], [10]). However, so far there is no complete characterization of the limit in this case.…”

Section: Introductionmentioning

confidence: 98%

“…The key observation is that conditional on the tree (and the locations of jumps), X n is a linear combination of normally distributed random variables, which makes it possible to apply Theorems 2.1 and 2.2. One needs to compute the first two moments of the conditional expectation and variance of X n , which requires a careful analysis of the random quantities involved, e.g., the heights in the tree and speciation events along lineages, but a considerable part of this work was done in [10] and [8] and can be reused here.…”

Section: Introductionmentioning

confidence: 99%

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Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

Bartoszek

Erhardsson

2021

Adv. Appl. Probab.

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Explicit bounds are given for the Kolmogorov and Wasserstein distances between a mixture of normal distributions, by which we mean that the conditional distribution given some $\sigma$ -algebra is normal, and a normal distribution with properly chosen parameter values. The bounds depend only on the first two moments of the first two conditional moments given the $\sigma$ -algebra. The proof is based on Stein’s method. As an application, we consider the Yule–Ornstein–Uhlenbeck model, used in the field of phylogenetic comparative methods. We obtain bounds for both distances between the distribution of the average value of a phenotypic trait over n related species, and a normal distribution. The bounds imply and extend earlier limit theorems by Bartoszek and Sagitov.

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Section: Introductionmentioning

confidence: 87%

Section: The Yule-ornstein-uhlenbeck Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

“…In the slow drift regime one can show L 2 convergence (see e.g. [1], [8], [10]). However, so far there is no complete characterization of the limit in this case.…”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

Bartoszek

Erhardsson

2021

Adv. Appl. Probab.

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How Important Is Budding Speciation for Comparative Studies?

Caetano,

Quental

2023

Systematic Biology

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The acknowledgment of evolutionary dependence among species has fundamentally changed how we ask biological questions. Phylogenetic models became the standard approach for studies with three or more lineages, in particular those using extant species. Most phylogenetic comparative methods (PCMs) translate relatedness into covariance, meaning that evolutionary changes before lineages split should be interpreted together whereas after the split lineages are expected to change independently. This clever realization has shaped decades of research. Here we discuss one element of the comparative method often ignored or assumed as unimportant: if nodes of a phylogeny represent the dissolution of the ancestral lineage into two new ones or if the ancestral lineage can survive speciation events (i.e., budding). Budding speciation is often reported in paleontological studies, due to the nature of the evidence for budding in the fossil record, but it is surprisingly absent in comparative methods. Here we show that many PCMs assume that divergence happens as a symmetric split, even if these methods don’t explicitly mention this assumption. We discuss the properties of trait evolution models for continuous and discrete traits and their adequacy under a scenario of budding speciation. We discuss the effects of budding speciation under a series of plausible evolutionary scenarios and show when and how these can influence our estimates. We also propose that long-lived lineages that have survived through a series of budding speciation events and given birth to multiple new lineages can produce evolutionary patterns that challenge our intuition about the most parsimonious history of trait changes in a clade. We hope our discussion can help bridge comparative approaches in paleontology and neontology as well as foster awareness about the assumptions we make when we use phylogenetic trees.

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How important is budding speciation for comparative studies?

Caetano

Quental

2022

Preprint

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The acknowledgment of evolutionary dependence among species has changed how we ask biological questions in a fundamental way. Phylogenetic models became the standard approach for studies with three or more lineages, in particular those using extant species. Most phylogenetic comparative methods (PCMs) translate relatedness into covariance, meaning that evolutionary changes before lineages split should be interpreted together whereas after the split lineages are expected to change independently. This clever realization has shaped decades of research. Here we investigate one element of the comparative method often ignored or assumed as unimportant: if nodes of a phylogeny represent the dissolution of the ancestral lineage into two new ones or if the ancestral lineage can survive speciation events (i.e., budding). Budding speciation is reported in paleontological studies, due to the nature of the evidence for budding in the fossil record, but it is surprisingly absent in comparative methods. Here we show that many PCMs assume that divergence happens as a symmetric split, even if these methods don't explicitly mention this assumption. We discuss the properties of trait evolution models for continuous and discrete traits and their adequacy under a scenario of budding speciation. We test the effects of budding speciation under a series of plausible evolutionary scenarios and show when and how these can influence our estimates. We also propose that long-lived lineages that have survived through a series of budding speciation events and given birth to multiple new lineages (here called "progenitor lineages") can produce evolutionary patterns that challenge our intuition about the most parsimonious history of trait changes in a clade. We hope our discussion can help bridge comparative approaches in paleontology and neontology as well as foster awareness about the assumptions we make when we use phylogenetic trees.

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A Central Limit Theorem for punctuated equilibrium

Cited by 3 publications

References 49 publications

Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

How Important Is Budding Speciation for Comparative Studies?

How important is budding speciation for comparative studies?

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