Biology subjects

Krzysztof Bartoszek

Publications and source records attributed to Krzysztof Bartoszek.

5 recordsLinked to original sources

bioRxiv2016

A Central Limit Theorem for Punctuated Equilibrium

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 can 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 hold, dramatic change has to be a rare event.\n\nAMS subject classification: 60F05, 60J70, 60J85, 62P10, 92B99

Evolutionary Biology↗

bioRxiv2015

Phylogenetic effective sample size

In this paper I address the question -- how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes -- the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations.

Evolutionary Biology↗

bioRxiv2014

A Consistent Estimator of the Evolutionary Rate

We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate {lambda}, conditioned on the observed number of particles to be equal n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance {sigma}2. In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator [Formula] of the evolutionary rate{rho} 2 ={sigma}2/{lambda}. The estimator [Formula] is proportional to the sample variance [Formula] computed from n trait values. We find an approximate formula for the standard error of [Formula] based on a neat asymptotic relation for the variance of [Formula].

Evolutionary Biology↗

bioRxiv2014

Quantifying the effects of anagenetic and cladogenetic evolution

An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both types of change, quantify the effects of speciational change via the correlation between species and attribute the proportion of change to each type. I discuss results of parameter estimation of Hominoid body size in this light. I derive mathematical formulae related to this problem, the probability generating functions of the number of speciation events along a randomly drawn lineage and from the most recent common ancestor of two randomly chosen tip species for a conditioned Yule tree. Additionally I obtain in closed form the variance of the distance from the root to the most recent common ancestor of two randomly chosen tip species.

Evolutionary Biology↗

bioRxiv2014

Phylogenetic confidence intervals for the optimal trait value

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

Evolutionary Biology↗