Biology subjects

Bartoszek, K.

Publications and source records attributed to Bartoszek, K..

3 recordsLinked to original sources

bioRxiv2018

Limit distribution of the quartet balance index for Aldous’s β ≥ 0–model

This paper builds up on T. Martinez-Coronado, A. Mir, F. Rossello and G. Valientes work \"A balance index for phylogenetic trees based on quartets\", introducing a new balance index for trees. We show here that this balance index, in the case of Aldouss {beta} [≥] 0-model, convergences weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.

evolutionary biology↗

bioRxiv2017

Trait evolution with jumps: illusionary normality

Phylogenetic 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 biology↗

bioRxiv2017

Exact and approximate limit behaviour of the Yule tree’s cophenetic index

In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on n contemporary tips. We show that this normalized phylogenetic balance index is a submartingale that converges almost surely and in L2. We link our work with studies on trees without branch lengths and show that in this case the limit distribution is a contraction-type distribution, similar to the Quicksort limit distribution. In the continuous branch case we suggest approximations to the limit distribution. We propose heuristic methods of simulating from these distributions and it may be observed that these algorithms result in reasonable tails. Therefore, we propose a way based on the quantiles of the derived distributions for hypothesis testing, whether an observed phylogenetic tree is consistent with the pure-birth process. Simulating a sample by the proposed heuristics is rapid, while exact simulation (simulating the tree and then calculating the index) is a time-consuming procedure. We conduct a power study to investigate how well the cophenetic indices detect deviations from the Yule tree and apply the methodology to empirical phylogenies.

evolutionary biology↗