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  • 1.
    Asadzadeh, Mohammad
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.
    Bartoszek, Krzysztof
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.
    A combined discontinuous Galerkin and finite volume scheme for multi–dimensional VPFP system2011In: AIP Conference Proceedings 1333 / [ed] Deborah A. Levin, Ingrid J. Wysong, Alejandro L. Garcia and Henry Abarbanel, American Institute of Physics (AIP), 2011, Vol. 1333, p. 57-62Conference paper (Refereed)
    Abstract [en]

    We construct a numerical scheme for the multi-dimensional Vlasov-Poisson-Fokker-Planck system based on a combined finite volume (FV) method for the Poisson equation in spatial domain and the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element in time, phase-space variables for the Vlasov-Fokker-Planck equation.

  • 2.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    A Central Limit Theorem for punctuated equilibrium2020In: Stochastic Models, ISSN 1532-6349, E-ISSN 1532-4214, Vol. 36, no 3, p. 473-517Article in journal (Refereed)
    Abstract [en]

    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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  • 3.
    Bartoszek, Krzysztof
    Gdansk University of Technology, Poland.
    A Graph – String Model of Gene Assembly in Ciliates [Grafowo-tekstowy model rekombinacji DNA u orzęsek]2006In: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej, 2006, p. 521-534Conference paper (Refereed)
    Abstract [en]

    The ciliates are a family of unicellular organisms that characterize themselves by having two types of nuclei, micro - and macronuclei. During cell mating the genetic material must change from the micronuclei to the macronuclei form. The paper summarises a formal model for this change. The model, which is described in recent works, is based on strings and graphs. It shows that inside the cell complex computational operations have to take place.

  • 4.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Exact and approximate limit behaviour of the Yule trees cophenetic index2018In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 303, p. 26-45Article in journal (Refereed)
    Abstract [en]

    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 sub-martingale that converges almost surely and in L-2. 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.

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  • 5.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Limit distribution of the quartet balance index for Aldous’s $(\beta \ge 0)$-model2020In: Applicationes Mathematicae, ISSN 1233-7234, E-ISSN 1730-6280, Vol. 6, p. 29-44Article in journal (Refereed)
    Abstract [en]

    This paper builds on T. Martínez-Coronado, A. Mir, F. Rosselló and G. Valiente’s 2018 work, introducing a new balance index for trees. We show that this balance index, in the case of Aldous’s $(\beta \ge 0)$-model, converges weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.

  • 6.
    Bartoszek, Krzysztof
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Phylogenetic effective sample size2016In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 407, p. 371-386Article in journal (Refereed)
    Abstract [en]

    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.

  • 7.
    Bartoszek, Krzysztof
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Quantifying the effects of anagenetic and cladogenetic evolution2014In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 254, p. 42-57Article in journal (Refereed)
    Abstract [en]

    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.

  • 8.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Revisiting the Nowosiółka skull with RMaCzek2023In: Mathematica Applicanda, ISSN 1730-2668, Vol. 50, no 2, p. 255-266Article in journal (Refereed)
    Abstract [en]

    One of the first fully quantitative distance matrix visualization methods was proposed by Jan Czekanowski at the beginning of the previous century. Recently, a software package, RMaCzek, was made available that allows for producing such diagrams in R. Here we reanalyze the original data that Czekanowski used for introducing his method, and in the accompanying code show how the user can specify their own custom distance functions in the package.

  • 9.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Simulating an infinite mean waiting time2019In: Mathematica Applicanda, ISSN 1730-2668, Vol. 47, no 1, p. 93-102Article in journal (Refereed)
    Abstract [en]

    We consider a hybrid method to simulate the return time to the initial state in a critical-case birth-death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the simulation approach is to directly simulate the process, unless the simulated time exceeds some threshold and if it does, draw the return time from the tail of the power law.

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    Simulating an infinite mean waiting time
  • 10.
    Bartoszek, Krzysztof
    Gdansk University of Technology, Poland.
    The Bootstrap and Other Methods of Testing Phylogenetic Trees2007In: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej, 2007, p. 103-108Conference paper (Refereed)
    Abstract [en]

    The final step of a phylogenetic analysis is the test of the generated tree. This is not a easy task for which there is an obvious methodology because we do not know the full probabilistic model of evolution. A number of methods have been proposed but there is a wide debate concerning the interpretations of the results they produce.

  • 11.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    The phylogenetic effective sample size and jumps2018In: MATHEMATICA APPLICANDA (MATEMATYKA STOSOWANA), ISSN 1730-2668, Vol. 46, no 1, p. 25-33Article in journal (Refereed)
    Abstract [en]

    The phylogenetic effective sample size is a parameter that has as its goal the quantification of the amount of independent signal in a phylogenetically correlatedsample. It was studied for Brownian motion and Ornstein-Uhlenbeck models of trait evolution. Here, we study this composite parameter when the trait is allowedto jump at speciation points of the phylogeny. Our numerical study indicates thatthere is a non-trivial limit as the effect of jumps grows. The limit depends on thevalue of the drift parameter of the Ornstein-Uhlenbeck process.

  • 12.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Trait evolution with jumps: illusionary normality2017In: Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine, 2017, p. 23-28Conference paper (Refereed)
    Abstract [en]

    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 thangradual. On the other hand, there has been a number of recent proposals of evolutionarymodels with jump components. However, as we are only beginning to understandthe behaviour of branching Ornstein-Uhlenbeck (OU) processes the asymptoticsof branching  OU processes with jumps is an even greater unknown. In thiswork 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 possibilitiesof the mvSLOUCH package.

  • 13.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Bartoszek, Wojciech
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    A Noether theorem for stochastic operators on Schatten classes2017In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, no 2, p. 1395-1412Article in journal (Refereed)
    Abstract [en]

    We show that a stochastic (Markov) operator S acting on a Schatten class C-1 satisfies the Noether condition (i.e. S' (A) = A and S' (A(2)) = A(2), where A is an element of C-infinity is a Hermitian and bounded operator on a fixed separable and complex Hilbert space (H, <.,.>)), if and only if S(E-A(G)XEA(G)) = E-A (G)S(X)E-A (G) for any state X is an element of C-1 and all Borel sets G subset of R, where E-A (G) denotes the orthogonal projection coming from the spectral resolution A = integral(sigma(A)) zE(A)(dz). Similar results are obtained for stochastic one-parameter continuous semigroups.

  • 14.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology, Poland.
    Bartoszek, Wojciech
    Gdansk University of Technology, Poland.
    On the Time Behaviour of Okazaki Fragments2006In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 43, no 2, p. 500-509Article in journal (Refereed)
    Abstract [en]

    We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.

  • 15.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Bartoszek, Wojciech
    Gdansk Univ Technol, Poland.
    Krzeminski, Michal
    Gdansk Univ Technol, Poland.
    Simple SIR models with Markovian control2021In: Japanese Journal of Statistics and Data Science, ISSN 2520-8756, Vol. 4, no 1, p. 731-762Article in journal (Refereed)
    Abstract [en]

    We consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving Markov chain. We formulate some questions and conjectures of a purely theoretical nature.

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  • 16.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Coronado, Tomas M.
    Univ Balearic Isl, Spain; Balearic Isl Hlth Res Inst IdISBa, Spain.
    Mir, Arnau
    Univ Balearic Isl, Spain; Balearic Isl Hlth Res Inst IdISBa, Spain.
    Rossello, Francesc
    Univ Balearic Isl, Spain; Balearic Isl Hlth Res Inst IdISBa, Spain.
    Squaring within the Colless index yields a better balance index2021In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 331, article id 108503Article in journal (Refereed)
    Abstract [en]

    The Colless index for bifurcating phylogenetic trees, introduced by Colless (1982), is defined as the sum, over all internal nodes v of the tree, of the absolute value of the difference of the sizes of the clades defined by the children of v. It is one of the most popular phylogenetic balance indices, because, in addition to measuring the balance of a tree in a very simple and intuitive way, it turns out to be one of the most powerful and discriminating phylogenetic shape indices. But it has some drawbacks. On the one hand, although its minimum value is reached at the so-called maximally balanced trees, it is almost always reached also at trees that are not maximally balanced. On the other hand, its definition as a sum of absolute values of differences makes it difficult to study analytically its distribution under probabilistic models of bifurcating phylogenetic trees. In this paper we show that if we replace in its definition the absolute values of the differences of Glade sizes by the squares of these differences, all these drawbacks are overcome and the resulting index is still more powerful and discriminating than the original Colless index.

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  • 17.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Domsta, Joachim
    State Univ Appl Sci Elblag, Krzysztof Brzeski Inst Appl Informat, Ul Wojska Polskiego 1, PL-82300 Elblag, Poland.
    Pulka, Malgorzata
    Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland.
    Weak Stability of Centred Quadratic Stochastic Operators2019In: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, no 4, p. 1813-1830Article in journal (Refereed)
    Abstract [en]

    We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offsprings trait is equal to an additively perturbed arithmetic mean of the parents traits. It is shown that for the existence of a weak limit, it is sufficient that the distributions of the trait and the perturbation have a finite variance or have tails controlled by a suitable power function. In particular, probability distributions from the domain of attraction of stable distributions have found an application, although in general the limit is not stable.

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    Weak Stability of Centred Quadratic Stochastic Operators
  • 18.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Erhardsson, Torkel
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    NORMAL APPROXIMATION FOR MIXTURES OF NORMAL DISTRIBUTIONS AND THE EVOLUTION OF PHENOTYPIC TRAITS2021In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 53, no 1, p. 162-188Article in journal (Refereed)
    Abstract [en]

    Explicit bounds are given for the Kolmogorov andWasserstein 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 Steins 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.

  • 19.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Fuentes Gonzalez, Jesualdo
    Florida International University, Miami, USA..
    Mitov, Venelin
    IntiQuan GmbH, Basel, Switzerland..
    Pienaar, Jason
    Florida International University, Miami, USA..
    Piwczyński, Marcin
    Nicolaus Copernicus University, Toruń, Poland..
    Puchałka, Radosław,
    Nicolaus Copernicus University, Toruń, Poland..
    Spalik, Krzysztof
    University of Warsaw, Warszawa, Poland..
    Voje, Kjetil
    University of Oslo, Oslo, Norway..
    Fast mvSLOUCH: Model comparison for multivariate Ornstein--Uhlenbeck-based models of trait evolution on large phylogenies2023Data set
    Abstract [en]

    These are the Supplementary Material, R scripts and numerical results accompanying Bartoszek, Fuentes Gonzalez, Mitov, Pienaar, Piwczyński, Puchałka, Spalik and Voje "Model Selection Performance in Phylogenetic Comparative Methods under multivariate Ornstein–Uhlenbeck Models of Trait Evolution".

    The four data files concern two datasets. Ungulates: measurements of muzzle width, unworn lower third molar crown height, unworn lower third molar crown width and feeding style and their phylogeny; Ferula: measurements of ratio of canals, periderm thickness, wing area, wing thickness,  and fruit mass, and their phylogeny.

    Methods

    Ungulates

    The compiled ungulate dataset involves two key components: phenotypic data (Data.csv) and phylogenetic tree (Tree.tre), which consist on the following (full references for the citations presented below are provided in the paper linked to this repository, which also provides further details on the compiled dataset):The phenotypic data includes three continuous variables and one categorical variable. The continuous variables (MZW: muzzle width; HM3: unworn lower third molar crown height; WM3: unworn lower third molar crown width), measured in cm, come from Mendoza et al. (2002; J. Zool.). The categorical variable (FS, i.e. feeding style: B=browsers, G=grazers, M=mixed feeders) is based on Pérez–Barbería and Gordon (2001; Proc. R. Soc. B: Biol. Sci.). Taxonomic mismatches between these two sources were resolved based on Wilson and Reeder (2005; Johns Hopkins University Press). Only taxa with full entries for all these variables were included (i.e. no missing data allowed).

    The phylogenetic tree is pruned from the unsmoothed mammalian timetree of Hedges et al. (2015; MBE) to only include the 104 ungulate species for which there is complete phenotypic data available. Wilson and Reeder (2005; Johns Hopkins University Press) was used again to resolve taxonomic mismatches with the phenotypic data. The branch lengths of the tree are scaled to unit height and thus informative of relative time.

    Ferula

    1) The phenotypic data are divided into two data sets: first containing five continuous variables (no_ME) measured on mericarps (the dispersal unit of fruit in Apiaceae), whereas the second having the same variables together with measurement error (ME; see paper for computational details) for 75 species of Ferula and three species of Leutea. Three continuous variables were measured on anatomical cross sections (ratio_canals_ln – the proportion of oil ducts covering the space between median and lateral ribs [dimensionless], mean_gr_peri_ln_um – periderm (fruit wall) thickness [μm], thick_wings_ln_um – wing thickness [μm]); the remaining two on whole mericarps (Wings_area_ln_mm – wings area [mm2], Seed_mass_ln_mg – seed mass [mg])

    2) The phylogenetic tree was pruned from the tree obtained from the recent taxonomic revision of the genus (Panahi et al. 2018) to only include the 78 species for which the phenotypic data were generated. This tree and the associated alignment, composed of one nuclear and three plastid markers (Panahi et al. 2018), constituted an input to mcmctree software (Yang 2007) to obtain dated tree using a secondary calibration point for the root based on Banasiak et al.’s (2013) work. The branch lengths of the final tree (Ferula_fruits_tree.txt) were scaled to unit height and thus informative of relative time.

    The R setup for the manuscript was as follows:

    R version 3.6.1 (2019-09-12) Platform: x86_64-pc-linux-gnu (64-bit) Running under: openSUSE Leap 42.3

    The exact output can depend on the random seed. However, in the script we have the option of rerunning the analyses as it was in the manuscript, i.e.the random seeds that were used to generate the results are saved, included and can be read in.

    The code is divided into several directories with scripts, random seeds and result files.

    1) LikelihoodTestingDirectory contains the script test_rotation_invariance_mvSLOUCH.R that demonstrates that mvSLOUCH's likelihood calculations are rotation invariant.        

    2) Carnivorans

    Directory contains files connected to the Carnivrons' vignette in mvSLOUCH.       

    2.1) Carnivora_mvSLOUCH_objects_Full.RData

    Full output of  running the R code in the vignette.With mvSLOUCH is a very bare-minimum subset of this file that allows for the creation of the vignette.           

     2.2) Carnivora_mvSLOUCH_objects.RData              

    Reduced objects from Carnivora_mvSLOUCH_objects_Full.RData that are included with mvSLOUCH's vignette.                            

    2.3) Carnivora_mvSLOUCH_objects_remove_script.R               

    R script to reduce Carnivora_mvSLOUCH_objects_Full.RData to Carnivora_mvSLOUCH_objects.RData.     

    2.4) mvSLOUCH_Carnivorans.Rmd               

    The vignette itself.           

    2.5) refs_mvSLOUCH.bib               

    Bib file for the vignette.           

    2.6) ScaledTree.png, ScaledTree2.png, ScaledTree3.png, ScaledTree4.png   

    Plots of phylogenetic trees for vignette.

    3) SimulationStudy

    Directory contains all the output of the simulation study presented in the manuscript and scripts that allow for replication (the random number generator seeds are also provided) or running ones own simulation study, and scripts to generate graphs, and model comparison summary. This study was done using version 2.6.2 of mvSLOUCH. If one reruns using mvSLOUCH >= 2.7, then one will obtain different (corrected) values of R2 and an additional R2 version.    

    4) Ungulates

    Directory contains files connected to the "Feeding styles and oral morphology in ungulates" analyses performed for the manuscript.       

    4.1) Data.csv       

    The phenotypic data includes three continuous variables and one categorical variable. Continuous variables (MZW: muzzle width; HM3: unworn lower third molar crown height; WM3: unworn lower third molar crown width) from Mendoza et al. (2002), measured in cm. Categorical variable (FS, i.e. feeding style: B=browsers, G=grazers, M=mixed feeders) based on Pérez–Barbería and Gordon (2001). Phylogeny pruned from Hedges et al. (2015).

    Taxonomic mismatches among these sources were resolved based on Wilson and Reeder (2005). Hedges, S. B., J. Marin, M. Suleski, M. Paymer, and S. Kumar. 2015. Tree of life reveals clock-like speciation and diversification. Molecular Biology and Evolution 32:835-845. Mendoza, M., C. M. Janis, and P. Palmqvist. 2002. Characterizing complex craniodental patterns related to feeding behaviour in ungulates:a multivariate approach. Journal of Zoology 258:223-246 Pérez–Barbería, F. J., and I. J. Gordon. 2001. Relationships between oral morphology and feeding style in the Ungulata: a phylogenetically controlled evaluation. Proceedings of the Royal Society of London. Series B: Biological Sciences 268:1023-1032. Wilson, D. E., and D. M. Reeder. 2005. Mammal species of the world: A taxonomic and geographic reference. Johns Hopkins University Press, Baltimore, Maryland.                

    4.2) Tree.tre       

    Ungulates' phylogeny, extracted from the mammalian phylogeny of Hedges, S. B., J. Marin, M. Suleski, M. Paymer, and S. Kumar. 2015. Tree of life reveals clock–like speciation and diversification. Mol. Biol. Evol. 32:835–845.           

    4.3) OUB.R, OUF.R, OUG.R       

    R scripts for the analyses performed in the manuscript. Different files correspond to different regime setups of the feeding style variable.           

    4.4) OU1.txt, OUB.txt, OUF.txt, OUG.txt       

    Outputs of the model comparison conducted under the R scripts presented above (4.3). Different files correspond to different regime setups of the feeding style variable.        

    5) Ferula analyses

    In the models_ME directory there are input and output files from the mvSLOUCH analyzes of Ferula data with measurement error included, while in the models_no_ME directory the analyzes of data without measurement error. In each directory, one can find the following files:

    - input files: Data_ME.csv (with mesurment error) or Data_no_ME.csv (without measurement error) and tree file in Newick format (Ferula_fruits_tree.txt); the trait names in data files are abbreviated as follows: ration_canals – the proportion of oil ducts covering the space between median and lateral ribs, mean_gr_peri – periderm thickness, wings_area – wing area, thick_wings – wing thickness and seed_mass – seed mass,

    - the results for 8 analyzed models (see Fig. 2 in the main text), each in separate directory named model1, model2 and so on,

    - each model directory comprises the following files: two R scripts (for analyzes with diagonal and with upper triangular matrix Σyy; each model was run 1000 times), two csv files included information such as number of repetition (i), seed for preliminary analyzes generating starting point (seed_start_point), seed for the main analyses (seed) and AIC, AICc, SIC, BIC, R2 and loglik for each model run (these csv files are sorted according to AICc values), two directories containing results for 1000 analyzes, and two files extracted from these directories showing parameter estimation for the best models (with UpperTri and Diagonal matrix Σyy)

  • 20.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Fuentes-Gonzalez, Jesualdo
    Florida Int Univ, FL USA; Florida Int Univ, FL USA.
    Mitov, Venelin
    IntiQuan GmbH, Switzerland.
    Pienaar, Jason
    Florida Int Univ, FL USA; Florida Int Univ, FL USA.
    Piwczynski, Marcin
    Nicolaus Copernicus Univ Torun, Poland.
    Puchalka, Radoslaw
    Nicolaus Copernicus Univ Torun, Poland.
    Spalik, Krzysztof
    Univ Warsaw, Poland.
    Voje, Kjetil Lysne
    Univ Oslo, Norway.
    Analytical advances alleviate model misspecification in non-Brownian multivariate comparative methods2023In: Evolution, ISSN 0014-3820, E-ISSN 1558-5646Article in journal (Refereed)
    Abstract [en]

    Adams and Collyer argue that contemporary multivariate (Gaussian) phylogenetic comparative methods are prone to favouring more complex models of evolution and sometimes rotation invariance can be an issue. Here we dissect the concept of rotation invariance and point out that, depending on the understanding, this can be an issue with any method that relies on numerical instead of analytical estimation approaches. We relate this to the ongoing discussion concerning phylogenetic principal component analysis. Contrary to what Adams and Collyer found, we do not observe a bias against the simpler Brownian motion process in simulations when we use the new, improved, likelihood evaluation algorithm employed by mvSLOUCH, which allows for studying much larger phylogenies and more complex model setups.

  • 21.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Uppsala University, Sweden.
    Glemin, Sylvain
    Uppsala University, Sweden; CNRS University of Montpellier IRD EPHE, France.
    Kaj, Ingemar
    Uppsala University, Sweden.
    Lascoux, Martin
    Uppsala University, Sweden.
    Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations2017In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 429, p. 35-45Article in journal (Refereed)
    Abstract [en]

    The Ornstein-Uhlenbeck (OU) process plays a major role in the analysis of the evolution of phenotypic traits along phylogenies. The standard OU process includes random perturbations and stabilizing selection and assumes that species evolve independently. However, evolving species may interact through various ecological process and also exchange genes especially in plants. This is particularly true if we want to study phenotypic evolution among diverging populations within species. In this work we present a straightforward statistical approach with analytical solutions that allows for the inclusion of adaptation and migration in a common phylogenetic framework, which can also be useful for studying local adaptation among populations within the same species. We furthermore present a detailed simulation study that clearly indicates the adverse effects of ignoring migration. Similarity between species due to migration could be misinterpreted as very strong convergent evolution without proper correction for these additional dependencies. Finally, we show that our model can be interpreted in terms of ecological interactions between species, providing a general framework for the evolution of traits between "interacting" species or populations.(C) 2017 Elsevier Ltd. All rights reserved.

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  • 22.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Gonzalez, Jesualdo Fuentes
    Department of Biological Sciences, Florida International University, Miami, Fl 33199, USA.
    Mitov, Venelin
    IntiQuan GmbH, Basel, Switzerland.
    Pienaar, Jason
    Department of Biological Sciences and the Institute of Environment, Florida International University, Miami, Fl 33199, USA.
    Piwczyński, Marcin
    Department of Ecology and Biogeography, Nicolaus Copernicus University in Toruń, Toruń, Poland.
    Puchałka, Radosław
    Department of Ecology and Biogeography, Nicolaus Copernicus University in Toruń, Toruń, Poland.
    Spalik, Krzysztof
    Institute of Evolutionary Biology, Faculty of Biology, Biological and Chemical Research Centre, University of Warsaw, Warszawa, Poland.
    Voje, Kjetil Lysne
    Natural History Museum, University of Oslo, Oslo, Norway.
    Model Selection Performance in Phylogenetic Comparative Methods Under Multivariate Ornstein–Uhlenbeck Models of Trait Evolution2023In: Systematic Biology, ISSN 1063-5157, E-ISSN 1076-836X, Vol. 72, no 2, p. 275-293Article in journal (Refereed)
    Abstract [en]

    The advent of fast computational algorithms for phylogenetic comparative methods allows for considering multiple hypotheses concerning the co-adaptation of traits and also for studying if it is possible to distinguish between such models based on contemporary species measurements. Here we demonstrate how one can perform a study with multiple competing hypotheses using mvSLOUCH by analyzing two data sets, one concerning feeding styles and oral morphology in ungulates, and the other concerning fruit evolution in Ferula (Apiaceae). We also perform simulations to determine if it is possible to distinguish between various adaptive hypotheses. We find that Akaikes information criterion corrected for small sample size has the ability to distinguish between most pairs of considered models. However, in some cases there seems to be bias towards Brownian motion or simpler Ornstein-Uhlenbeck models. We also find that measurement error and forcing the sign of the diagonal of the drift matrix for an Ornstein-Uhlenbeck process influences identifiability capabilities. It is a cliche that some models, despite being imperfect, are more useful than others. Nonetheless, having a much larger repertoire of models will surely lead to a better understanding of the natural world, as it will allow for dissecting in what ways they are wrong. [Adaptation; AICc; model selection; multivariate Ornstein-Uhlenbeck process; multivariate phylogenetic comparative methods; mvSLOUCH.]

  • 23.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Guidotti, Emanuele
    Univ Neuchatel, Switzerland.
    Iacus, Stefano Maria
    European Commiss, Italy.
    Okroj, Marcin
    Univ Gdansk, Poland; Med Univ Gdansk, Poland.
    Are official confirmed cases and fatalities counts good enough to study the COVID-19 pandemic dynamics? A critical assessment through the case of Italy2020In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 101, p. 1951-1979Article in journal (Refereed)
    Abstract [en]

    As the COVID-19 outbreak is developing the two most frequently reported statistics seem to be the raw confirmed case and case fatalities counts. Focusing on Italy, one of the hardest hit countries, we look at how these two values could be put in perspective to reflect the dynamics of the virus spread. In particular, we find that merely considering the confirmed case counts would be very misleading. The number of daily tests grows, while the daily fraction of confirmed cases to total tests has a change point. It (depending on region) generally increases with strong fluctuations till (around, depending on region) 15-22 March and then decreases linearly after. Combined with the increasing trend of daily performed tests, the raw confirmed case counts are not representative of the situation and are confounded with the sampling effort. This we observe when regressing on time the logged fraction of positive tests and for comparison the logged raw confirmed count. Hence, calibrating model parameters for this viruss dynamics should not be done based only on confirmed case counts (without rescaling by the number of tests), but take also fatalities and hospitalization count under consideration as variables not prone to be distorted by testing efforts. Furthermore, reporting statistics on the national level does not say much about the dynamics of the disease, which are taking place at the regional level. These findings are based on the official data of total death counts up to 15 April 2020 released by ISTAT and up to 10 May 2020 for the number of cases. In this work, we do not fit models but we rather investigate whether this task is possible at all. This work also informs about a new tool to collect and harmonize official statistics coming from different sources in the form of a package for the R statistical environment and presents the "COVID-19 Data Hub."

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  • 24.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology.
    Izydorek, Bartosz
    Gdansk University of Technology.
    Ratajczak, Tadeusz
    Gdansk University of Technology, Poland.
    Skokowski, Jaroslaw
    Medical University of Gdansk, Poland.
    Szwaracki, Karol
    Gdansk University of Technology, Poland.
    Tomczak, Wiktor
    Gdansk University of Technology, Poland.
    Neural Network Breast Cancer Relapse Time Prognosis2006In: ASO Summer School 2006 abstract book Ostrzyce 30.06-2.07. 2006 / [ed] J. Skokowski and K. Drucis, 2006, p. 8-10Conference paper (Other academic)
    Abstract [en]

    This paper is a result of a project at the Faculty of Electronics, Telecommunication and Computer Science (Technical University of Gdansk). The aim of the project was to create a neural network to predict the relapsetime of breast cancer. The neural network was to be trained on data collected over the past 20 years by dr. Jarosław Skokowski. The data includes 439 patient records described by about 40 parameters. For our neuralnetwork we only considered 6 medically most significant parameters the number of nodes showing evidence of cancer, size of tumour (in mm.), age, bloom score, estrogen receptors and proestrogen receptors and the relapsetime as the outcome. Our neural network was created in the MATLAB environment.

  • 25.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Jones, Graham
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden / Department of Biological and Environmental Science, University of Gothenburg, Gothenburg, Sweden.
    Oxelman, Bengt
    Department of Biological and Environmental Science, University of Gothenburg, Gothenburg, Sweden.
    Sagitov, Serik
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Time to a single hybridization event in a group of species with unknown ancestral history2013In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 322, p. 1-6Article in journal (Refereed)
    Abstract [en]

    We consider a stochastic process for the generation of species which combines a Yule process with a simple model for hybridization between pairs of co-existent species. We assume that the origin of the process, when there was one species, occurred at an unknown time in the past, and we condition the process on producing n species via the Yule process and a single hybridization event. We prove results about the distribution of the time of the hybridization event. In particular we calculate a formula for all moments, and show that under various conditions, the distribution tends to an exponential with rate twice that of the birth rate for the Yule process.

  • 26.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Sweden.
    Krzeminski, Michal
    Gdansk University of Technology.
    Critical case stochastic phylogenetic tree model via the Laplace transform2014In: Demonstratio Matematicae, ISSN 0420-1213, Vol. 47, no 2, p. 474-481Article in journal (Refereed)
    Abstract [en]

    Birth-and-death models are now a common mathematical tool to describe branching patterns observed in real-world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth-and-death model that is compatible with phylogenetic trees of both in uenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non-trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this we correct the proof of Liggett and Schinazi (2009) in the critical case.

  • 27.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.
    Krzeminski, Michal
    Gdansk University of Technology.
    Skokowski, Jaroslaw
    Medical University of Gdansk.
    Survival time prognosis under a Markov model of cancer development2010In: Proceedings of the XVI National Conference Applications of Mathematics to Biology and Medicine, Krynica, Poland, September 14–18, 2010 / [ed] M. Ziółko, M. Bodnar and E. Kutafina, 2010, p. 6-11Conference paper (Refereed)
    Abstract [en]

    In this study we look at a breast cancer data set of women from the Pomerania region collected in the year 1987- 1992 in the Medical University of Gdansk.We analyze the clinical risk factors in conjunction with a Markov model of cancer development. We evaluate Artificial Neural Network (ANN) survival time prediction (which was done on this data set in a previous study) via a simulation study.

  • 28.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Lio, Pietro
    Univ Cambridge, England.
    MODELLING TRAIT-DEPENDENT SPECIATION WITH APPROXIMATE BAYESIAN COMPUTATION2019In: ACTA PHYSICA POLONICA B PROCEEDINGS SUPPLEMENT, JAGIELLONIAN UNIV , 2019, Vol. 12, no 1, p. 25-47Conference paper (Refereed)
    Abstract [en]

    Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The fields progression is hampered by the lack of robust software to estimate the numerous parameters of the speciation process. In this work, we present an R package, pcmabc, publicly available on CRAN, based on Approximate Bayesian Computations, that implements three novel phylogenetic algorithms for trait-dependent speciation modelling. Our phylogenetic comparative methodology takes into account both the simulated traits and phylogeny, attempting to estimate the parameters of the processes generating the phenotype and the trait. The user is not restricted to a predefined set of models and can specify a variety of evolutionary and branching models. We illustrate the software with a simulation-reestimation study focused around the branching Ornstein-Uhlenbeck process, where the branching rate depends non-linearly on the value of the driving Ornstein-Uhlenbeck process. Included in this work is a tutorial on how to use the software.

  • 29.
    Bartoszek, Krzysztof
    et al.
    Mathematical Statistics, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.
    Liò, Pietro
    Computer Laboratory, University of Cambridge Cambridge, United Kingdom.
    Sorathiya, Anil
    Computer Laboratory, University of Cambridge Cambridge, United Kingdom.
    Influenza differentiation and evolution2010In: Acta Physica Polonica B Proceedings Supplement, 2010, Vol. 3, p. 417-452, article id 2Conference paper (Refereed)
    Abstract [en]

    The aim of the study is to do a very wide analysis of HA, NA and M influenza gene segments to find short nucleotide regions,which differentiate between strains (i.e. H1, H2, ... e.t.c.), hosts, geographic regions, time when sequence was found and combination of time and region using a simple methodology. Finding regions  differentiating between strains has as its goal the construction of a Luminex microarray which will allow quick and efficient strain recognition. Discovery for the other splitting factors could shed lighton structures significant for host specificity and on the history of influenza evolution. A large number of places in the HA, NA and M gene segments were found that can differentiate between hosts, regions, time and combination of time and region. Also very good differentiation between different Hx strains can be seen.We link one of our findings to a proposed stochastic model of creation of viral phylogenetic trees.

  • 30.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Uppsala Univ, Sweden.
    Majchrzak, Marta
    Polish Acad Sci, Poland.
    Sakowski, Sebastian
    Univ Lodz, Poland.
    Kubiak-Szeligowska, Anna B.
    Polish Acad Sci, Poland.
    Kaj, Ingemar
    Uppsala Univ, Sweden.
    Parniewski, Pawel
    Polish Acad Sci, Poland.
    Predicting pathogenicity behavior in Escherichia coli population through a state dependent model and TRS profiling2018In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 14, no 1, article id e1005931Article in journal (Refereed)
    Abstract [en]

    The Binary State Speciation and Extinction (BiSSE) model is a branching process based model that allows the diversification rates to be controlled by a binary trait. We develop a general approach, based on the BiSSE model, for predicting pathogenicity in bacterial populations from microsatellites profiling data. A comprehensive approach for predicting pathogenicity in E. coli populations is proposed using the state-dependent branching process model combined with microsatellites TRS-PCR profiling. Additionally, we have evaluated the possibility of using the BiSSE model for estimating parameters from genetic data. We analyzed a real dataset (from 251 E. coli strains) and confirmed previous biological observations demonstrating a prevalence of some virulence traits in specific bacterial sub-groups. The method may be used to predict pathogenicity of other bacterial taxa.

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  • 31.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Okroj, Marcin
    Univ Gdansk, Poland; Med Univ Gdansk, Poland.
    Controversies around the statistical presentation of data on mRNA-COVID 19 vaccine safety in pregnant women2022In: Journal of Reproductive Immunology, ISSN 0165-0378, E-ISSN 1872-7603, Vol. 151, article id 103503Article in journal (Refereed)
    Abstract [en]

    The work entitled "Preliminary Findings of mRNA Covid-19 Vaccine Safety in Pregnant Persons" published on April 21, 2021, in The New England Journal of Medicine, presented data collected from American surveillance systems and registries. However, problems with an unanimous interpretation of those results appeared in the public debate and citing articles. Some stated that the risk of miscarriage in vaccinated women was similar to historical values reported before the vaccines approval. The others stated that risk was highly above-normative in women vaccinated during the first and second trimesters. We found several problems with the statistical treatment/interpretation of the originally presented values: a substantial percentage (up to 95.6%) of missing data, an incorrect denominator used for risk estimation, and too short follow-up that disabled the evaluation of the studys endpoint in numerous participants. Eventually, the Authors published a corrigendum on September 8, 2021, and pointed to updated data. Herein, we explain the statistical controversies raised by the original presentation and stress that analyzing the trade-off between knowledge and confusion brought by the release of incomplete results of such a high social interest, should aid in solving the dilemma of whether to publish preliminary data or none.

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  • 32.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Pienaar, Jason
    Department of Genetics, University of Pretoria, Pretoria 0002, South Africa.
    Mostad, Petter
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Andersson, Staffan
    Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden.
    Hansen, Thomas F.
    CEES, Department of Biology, University of Oslo, Oslo, Norway.
    A phylogenetic comparative method for studying multivariate adaptation2012In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 314, p. 204-215Article in journal (Refereed)
    Abstract [en]

    Phylogenetic comparative methods have been limited in the way they model adaptation. Although some progress has been made, there are still no methods that can fully account for coadaptationbetween traits. Based on Ornstein-Uhlenbeck (OU) models of adaptive evolution, we present a method,with R implementation, in which multiple traits evolve both in response to each other and, as inprevious OU models, to fixed or randomly evolving predictor variables. We present the interpretation ofthe model parameters in terms of evolutionary and optimal regressions enabling the study of allometric and adaptive relationships between traits. To illustrate the method we reanalyze a data set of antlerand body-size evolution in deer (Cervidae).

  • 33.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pietro, Lio'
    Computer Laboratory , University of Cambridge, Cambridge, Un ited Kingdom.
    A novel algorithm to reconstruct phylogenies using gene sequences and expression data2014In: International Proceedings of Chemical, Biological & Environmental Engineering; Environment, Energy and Biotechnology III, 2014, Vol. 70, p. 8-12Conference paper (Refereed)
    Abstract [en]

    Phylogenies based on single loci should be viewed with caution and the best approach for obtaining robust trees is to examine numerous loci across the genome. It often happens that for the same set of species trees derived from different genes are in conflict between each other. There are several methods that combine information from different genes in order to infer the species tree. One novel approach is to use informationfrom different -omics. Here we describe a phylogenetic method based on an Ornstein–Uhlenbeck process that combines sequence and gene expression data. We test our method on genes belonging to the histidine biosynthetic operon. We found that the method provides interesting insights into selection pressures and adaptive hypotheses concerning gene expression levels.

  • 34.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Sweden.
    Pulka, Malgorzata
    Department of Probability and Biomathematics, Gdánsk University of Technology, Gdánsk, Poland.
    Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait2013In: Proceedings of the 19th National Conference on Applications of Mathematics in Biology and Medicine / [ed] Katarzyna D. Lewandowska and Piotr Bogús, 2013, p. 19-24Conference paper (Refereed)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introducedand studied recently. In the present work we discuss biological interpretations that can be attributedto them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.

  • 35.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pulka, Malgorzta
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    Asymptotic properties of quadratic stochastic operators acting on the L1 space2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, p. 26-39Article in journal (Refereed)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the l1 space. It turns out that inprinciple most of the results can be carried over to the L1 space. However, due to topologicalproperties of this space one has to restrict in some situations to kernel quadratic stochasticoperators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L1 space in terms of convergence of the associated (linear)nonhomogeneous Markov chains.

  • 36.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pułka, Małgorzata
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    Prevalence Problem in the Set of Quadratic StochasticOperators Acting on L12018In: Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, Vol. 41, no 1, p. 159-173Article in journal (Refereed)
    Abstract [en]

    This paper is devoted to the study of the problem of prevalence in the classof quadratic stochastic operators acting on the L1 space for the uniform topology.We obtain that the set of norm quasi-mixing quadratic stochastic operators is a denseand open set in the topology induced by a very natural metric. This shows the typicallong-term behaviour of iterates of quadratic stochastic operators.

  • 37.
    Bartoszek, Krzysztof
    et al.
    Uppsala universitet, Tillämpad matematik och statistik.
    Sagitov, Serik
    A consistent estimator of the evolutionary rate2015In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, p. 69-78Article in journal (Refereed)
    Abstract [en]

    We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate 2, conditioned on the observed number of particles to be equal to 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 4 of the evolutionary rate rho(2) - sigma(2)/lambda. The estimator R-n(2) is proportional to the sample variance S-n(2) computed from n trait values. We find an approximate formula for the standard error of R-n(2), based on a neat asymptotic relation for the variance of S-n(2). (C) 2015 Elsevier Ltd. All rights reserved.

  • 38.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Sagitov, Serik
    Chalmers University of Technology and the Unversity of Gothenburg, Sweden.
    Phylogenetic confidence intervals for the optimal trait value2015In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, p. 1115-1132Article in journal (Refereed)
    Abstract [en]

    We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree ismodelled 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 samplemean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean isapproximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

  • 39.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology, Poland.
    Signerska, Justyna
    Gdansk University of Technology, Poland.
    Moments of the Distribution of Okazaki Fragments2006In: Rose–Hulman Undergraduate Mathematics Journal, Vol. 7, no 2, p. 1-5Article in journal (Refereed)
    Abstract [en]

    This paper is a continuation of Bartoszek & Bartoszek (2006) who provide formulae for the probability distributions of the number of Okazaki fragments at time t during the process of DNA replication. Given the expressions for the moments of the probability distribution of the number of Okazaki fragments at time t in the recursive form, we evaluated formulae for the third and fourth moments, using Mathematica, and obtained results in explicit form. Having done this, we calculated the distribution’s skewness and kurtosis.

  • 40.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Gdansk University of Technology, Gdansk, Poland.
    Signerska, Justyna
    Department of Mathematics, Gdansk University of Technology, Gdansk, Poland.
    The Fundamental Group, Covering Spaces and Topology in Biology2006In: Conference materials 9th International Workshop for Young Mathematicians "Topology", 2006, p. 19-29Conference paper (Other academic)
    Abstract [en]

    Abstract. We give a short introduction to homotopy theory. We pass to the concepts of a pointed space (X, x0), the fundamental group of X, a simply connected space (with the example of the space contractible to a point), introduce basic concepts of covering spaces (e.g. covering map/space, fiber over x, Path lifting Theorem). With the use of the exponential map and the idea of the index of a loop, we show that the fundamental group of the circle S1 is isomorphic to the integers Z with addition. We mention some other interesting fundamental groups (e.g. the fundamental group of a torus or of thefigure eight). We also present some very interesting applications of topological concepts in Molecular Biology.

  • 41.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.
    Stokowska, Anna
    University of Gothenburg.
    Performance of pseudo-likelihood estimator in modelling cells' proliferation with noisy measurements2010In: Conference proceedings from the 12th International Workshop for Young Mathematicians "Probability and Statistics", Krakow, Poland, 20th till 26th September 2009, 2010, p. 21-42Conference paper (Other academic)
    Abstract [en]

    Branching processes are widely used to describe cell development and proliferation. Currently parameter estimation is studied in mathematical models describing the dynamics of cell cultures where we can get very accurate measurements of cell counts. In vivo samples we will not have this accuracy, here the noise levels can be very significant. We will study a newly proposed pseudo-likelihood estimator of a multitype Bellman-Harris process modelling cell development and see how it performs under noisy measurements of cell counts.

  • 42.
    Bartoszek, Krzysztof
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Västerlund, Albin
    Linköping University, Department of Computer and Information Science. Linköping University, Faculty of Science & Engineering.
    “Old Techniques for New Times”: the RMaCzek package for producing Czekanowski’s diagrams2020In: Biometrical Letters, E-ISSN 1896-3811, Vol. 57, no 2, p. 89-118Article in journal (Refereed)
    Abstract [en]

    Inspired by the MaCzek Visual Basic program we provide an R package, RMaCzek, that produces Czekanowski’s diagrams. Our package permits any seriation and distance method the user provides. In this paper we focus on the "OLO" and "QAP_2SUM" methods from the seriation package. We illustrate the possibilities of our package with three anthropological studies, one socioeconomic study and a phylogenetically motivated simulation study.

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  • 43.
    Bravo, Gustavo A.
    et al.
    Harvard Univ, MA 02138 USA.
    Antonelli, Alexandre
    Harvard Univ, MA 02138 USA; Gothenburg Global Biodivers Ctr, Sweden; Univ Gothenburg, Sweden; Gothenburg Bot Garden, Sweden.
    Bacon, Christine D.
    Gothenburg Global Biodivers Ctr, Sweden; Univ Gothenburg, Sweden.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Blom, Mozes P. K.
    Swedish Museum Nat Hist, Sweden.
    Huynh, Stella
    Univ Neuchatel, Switzerland.
    Jones, Graham
    Univ Gothenburg, Sweden.
    Knowles, L. Lacey
    Univ Michigan, MI 48109 USA.
    Lamichhaney, Sangeet
    Harvard Univ, MA 02138 USA.
    Marcussen, Thomas
    Univ Oslo, Norway.
    Morlon, Helene
    Ecole Normale Super Paris, France.
    Nakhleh, Luay K.
    Rice Univ, TX USA.
    Oxelman, Bengt
    Gothenburg Global Biodivers Ctr, Sweden; Univ Gothenburg, Sweden.
    Pfeil, Bernard
    Univ Gothenburg, Sweden.
    Schliep, Alexander
    Chalmers Univ Technol, Sweden; Univ Gothenburg, Sweden.
    Wahlberg, Niklas
    Lund Univ, Sweden.
    Werneck, Fernanda P.
    Inst Nacl de Pesquisas da Amazonia, Brazil.
    Wiedenhoeft, John
    Chalmers Univ Technol, Sweden; Univ Gothenburg, Sweden; Rutgers State Univ, NJ USA.
    Willows-Munro, Sandi
    Univ Kwazulu Natal, South Africa.
    Edwards, Scott V
    Harvard Univ, MA 02138 USA; Univ Gothenburg, Sweden; Chalmers Univ Technol, Sweden.
    Embracing heterogeneity: coalescing the Tree of Life and the future of phylogenomics2019In: PeerJ, E-ISSN 2167-8359, Vol. 7, article id e6399Article in journal (Refereed)
    Abstract [en]

    Building the Tree of Life (ToL) is a major challenge of modern biology, requiring advances in cyberinfrastructure, data collection, theory, and more. Here, we argue that phylogenomics stands to benefit by embracing the many heterogeneous genomic signals emerging from the first decade of large-scale phylogenetic analysis spawned by high-throughput sequencing (HTS). Such signals include those most commonly encountered in phylogenomic datasets, such as incomplete lineage sorting, but also those reticulate processes emerging with greater frequency, such as recombination and introgression. Here we focus specifically on how phylogenetic methods can accommodate the heterogeneity incurred by such population genetic processes; we do not discuss phylogenetic methods that ignore such processes, such as concatenation or supermatrix approaches or supertrees. We suggest that methods of data acquisition and the types of markers used in phylogenomics will remain restricted until a posteriori methods of marker choice are made possible with routine whole-genome sequencing of taxa of interest. We discuss limitations and potential extensions of a model supporting innovation in phylogenomics today, the multispecies coalescent model (MSC). Macroevolutionary models that use phylogenies, such as character mapping, often ignore the heterogeneity on which building phylogenies increasingly rely and suggest that assimilating such heterogeneity is an important goal moving forward. Finally, we argue that an integrative cyberinfrastructure linking all steps of the process of building the ToL, from specimen acquisition in the field to publication and tracking of phylogenomic data, as well as a culture that values contributors at each step, are essential for progress.

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  • 44.
    Hansen, Thomas F.
    et al.
    Department of Biology, Centre for Ecological and Evolutionary Synthesis, University of Oslo, Norway.
    Bartoszek, Krzysztof
    Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Interpreting the evolutionary regression: The interplay between observational and biological errors in phylogenetic comparative studies2012In: Systematic Biology, ISSN 1063-5157, E-ISSN 1076-836X, Vol. 61, no 3, p. 413-425Article in journal (Refereed)
    Abstract [en]

    Regressions of biological variables across species are rarely perfect. Usually, there are residual deviations fromthe estimated model relationship, and such deviations commonly show a pattern of phylogenetic correlations indicatingthat they have biological causes. We discuss the origins and effects of phylogenetically correlated biological variation inregression studies. In particular, we discuss the interplay of biological deviations with deviations due to observationalor measurement errors, which are also important in comparative studies based on estimated species means. We showhow bias in estimated evolutionary regressions can arise from several sources, including phylogenetic inertia and eitherobservational or biological error in the predictor variables. We show how all these biases can be estimated and correctedfor in the presence of phylogenetic correlations.We present general formulas for incorporating measurement error in linearmodels with correlated data. We also show how alternative regression models, such as major axis and reduced major axisregression, which are often recommended when there is error in predictor variables, are strongly biased when there isbiological variation in any part of the model.We argue that such methods should never be used to estimate evolutionary orallometric regression slopes.

  • 45.
    Kiang, Hao Chi
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Sakowski, Sebastian
    Univ Lodz, Poland.
    Iacus, Stefano Maria
    Harvard Univ, MA USA.
    Vespe, Michele
    European Commiss, Italy.
    Summarizing Global SARS-CoV-2 Geographical Spread by Phylogenetic Multitype Branching Models2022In: COMPUTATIONAL INTELLIGENCE METHODS FOR BIOINFORMATICS AND BIOSTATISTICS, CIBB 2021, SPRINGER INTERNATIONAL PUBLISHING AG , 2022, Vol. 13483, p. 170-184Conference paper (Refereed)
    Abstract [en]

    Using available phylogeographical data of 3585 SARS–CoV–2 genomes we attempt at providing a global picture of the virus’s dynamics in terms of directly interpretable parameters. To this end we fit a hidden state multistate speciation and extinction model to a pre-estimated phylogenetic tree with information on the place of sampling of each strain. We find that even with such coarse–grained data the dominating transition rates exhibit weak similarities with the most popular, continent–level aggregated, airline passenger flight routes.

  • 46.
    Kiang, Hao Chi
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Sakowski, Sebastian
    University of Lodz, Faculty of Mathematics and Computer Science, Lodz, Poland.
    Iacus, Stefano
    Institute of Quantitative Social Sciences, Harvard University, Cambridge (MA), USA.
    Vespe, Michele
    European Commission, Joint Research Centre, Ispra, Italy.
    Data and Materials : Summarizing Global SARS-CoV-2 Geographical Spread by Phylogenetic Multitype Branching Models2022Data set
    Abstract [en]

    Raw numerical results, phylogeny, and related data for the conference proceeding article "Summarizing Global SARS-CoV-2 Geographical Spread by Phylogenetic Multitype Branching Models".

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  • 47.
    Mioduchowska, Monika
    et al.
    Univ Gdansk, Poland; Univ Lodz, Poland; Univ Gdansk, Poland.
    Konecka, Edyta
    Adam Mickiewicz Univ, Poland.
    Goldyn, Bartlomiej
    Adam Mickiewicz Univ, Poland.
    Pinceel, Tom
    Katholieke Univ Leuven, Belgium; Univ Free State, South Africa; Vrije Univ Brussel VUB, Belgium.
    Brendonck, Luc
    Katholieke Univ Leuven, Belgium; North West Univ, South Africa.
    Lukic, Dunja
    CSIC, Spain.
    Kaczmarek, Lukasz
    Adam Mickiewicz Univ, Poland.
    Namiotko, Tadeusz
    Univ Gdansk, Poland.
    Zajac, Katarzyna
    Polish Acad Sci, Poland.
    Zajac, Tadeusz
    Polish Acad Sci, Poland.
    Jastrzebski, Jan P.
    Univ Warm & Mazury Olsztyn, Poland; Univ Warm & Mazury Olsztyn, Poland.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Playing Peekaboo with a Master Manipulator: Metagenetic Detection and Phylogenetic Analysis of Wolbachia Supergroups in Freshwater Invertebrates2023In: International Journal of Molecular Sciences, ISSN 1661-6596, E-ISSN 1422-0067, Vol. 24, no 11, article id 9400Article in journal (Refereed)
    Abstract [en]

    The infamous "master manipulators"-intracellular bacteria of the genus Wolbachia-infect a broad range of phylogenetically diverse invertebrate hosts in terrestrial ecosystems. Wolbachia has an important impact on the ecology and evolution of their host with documented effects including induced parthenogenesis, male killing, feminization, and cytoplasmic incompatibility. Nonetheless, data on Wolbachia infections in non-terrestrial invertebrates are scarce. Sampling bias and methodological limitations are some of the reasons limiting the detection of these bacteria in aquatic organisms. In this study, we present a new metagenetic method for detecting the co-occurrence of different Wolbachia strains in freshwater invertebrates host species, i.e., freshwater Arthropoda (Crustacea), Mollusca (Bivalvia), and water bears (Tardigrada) by applying NGS primers designed by us and a Python script that allows the identification of Wolbachia target sequences from the microbiome communities. We also compare the results obtained using the commonly applied NGS primers and the Sanger sequencing approach. Finally, we describe three supergroups of Wolbachia: (i) a new supergroup V identified in Crustacea and Bivalvia hosts; (ii) supergroup A identified in Crustacea, Bivalvia, and Eutardigrada hosts, and (iii) supergroup E infection in the Crustacea host microbiome community.

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  • 48.
    Mioduchowska, Monika
    et al.
    Univ Gdansk, Poland.
    Zajac, Katarzyna
    Polish Acad Sci, Poland.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Madanecki, Piotr
    Med Univ Gdansk, Poland.
    Kur, Jaroslaw
    Empty Spaces Res, Poland.
    Zajac, Tadeusz
    Polish Acad Sci, Poland.
    16S rRNAgene-based metagenomic analysis of the gut microbial community associated with the DUI species Unio crassus (Bivalvia: Unionidae)2020In: Journal of Zoological Systematics and Evolutionary Research, ISSN 0947-5745, E-ISSN 1439-0469, Vol. 58, no 2, p. 615-623Article in journal (Refereed)
    Abstract [en]

    What factors determine biome richness: genetic or environmental? Sex, phylogeny, and tolerance indicated by other symbionts (e.g., endosymbionts) or simply is it related to local habitat, especially if the gut biome is considered? To answer these questions, we investigated the gut microbial profile of both sexes of three Unio crassus populations, species with unique system of mitochondrial DNA inheritance called doubly uniparental inheritance (DUI), living in different ecological conditions. High-throughput sequencing of the V3-V4 hypervariable regions in the bacterial 16S rRNA gene fragment was performed, which resulted in a total of 1,051,647 reads, with 58,424 reads/65 OTUs (operational taxonomic units) per sample on average. We identified a core microbiome, with all individual mussels sharing 69 OTUs (representing 23% of the total number of OTUs). Proteobacteria was the dominant phylum in all samples, followed by Firmicutes, Actinobacteria, and Bacteroidetes. There were no significant differences in gut microbiome compositions between the two sexes of this species; however, we observed different phyla in geographically isolated populations. A non-metric multidimensional scaling plot and dendrogram showed that the bacterial profile complies with the genetic structure of populations. Although we found differences in microbiomes between populations, their genetic structure suggests that the microbiome is weakly related to habitat, and more strongly to phylogeography (on both F and M mitotypes). We found no significant differences in beta diversity between the individuals of the bacterial communities measured using the Bray-Curtis index. Finally, we also examined whether OTUs were represented by symbiotic bacteria that enable cellulose digestion and by endosymbiotic bacteria that play important functions in the biology of their hosts and also affect microevolutionary processes and population phenomena. With regard to the endosymbionts, however, there was no relation to sex of the studied individuals, which suggests that there are no straightforward relations between DUI and microbiome.

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  • 49.
    Mitov, Venelin
    et al.
    Swiss Fed Inst Technol, Switzerland; Swiss Inst Bioinformat, Switzerland.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Asimomitis, Georgios
    Swiss Fed Inst Technol, Switzerland.
    Stadler, Tanja
    Swiss Fed Inst Technol, Switzerland; Swiss Inst Bioinformat, Switzerland.
    Fast likelihood calculation for multivariate Gaussian phylogenetic models with shifts2020In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 131, p. 66-78Article in journal (Refereed)
    Abstract [en]

    Phylogenetic comparative methods (PCMs) have been used to study the evolution of quantitative traits in various groups of organisms, ranging from micro-organisms to animal and plant species. A common approach has been to assume a Gaussian phylogenetic model for the trait evolution along the tree, such as a branching Brownian motion (BM) or an Ornstein-Uhlenbeck (OU) process. Then, the parameters of the process have been inferred based on a given tree and trait data for the sampled species. At the heart of this inference lie multiple calculations of the model likelihood, that is, the probability density of the observed trait data, conditional on the model parameters and the tree. With the increasing availability of big phylogenetic trees, spanning hundreds to several thousand sampled species, this approach is facing a two-fold challenge. First, the assumption of a single Gaussian process governing the entire tree is not adequate in the presence of heterogeneous evolutionary forces acting in different parts of the tree. Second, big trees present a computational challenge, due to the time and memory complexity of the model likelihood calculation. Here, we explore a sub-family, denoted G(LInv) , of the Gaussian phylogenetic models, with the transition density exhibiting the properties that the expectation depends Linearly on the ancestral trait value and the variance is Invariant with respect to the ancestral value. We show that G(LInv), contains the vast majority of Gaussian models currently used in PCMs, while supporting an efficient (linear in the number of nodes) algorithm for the likelihood calculation. The algorithm supports scenarios with missing data, as well as different types of trees, including trees with polytomies and non-ultrametric trees. To account for the heterogeneity in the evolutionary forces, the algorithm supports models with "shifts" occurring at specific points in the tree. Such shifts can include changes in some or all parameters, as well as the type of the model, provided that the model remains within the G(LInv) family. This contrasts with most of the current implementations where, due to slow likelihood calculation, the shifts are restricted to specific parameters in a single type of model, such as the long-term selection optima of an OU process, assuming that all of its other parameters, such as evolutionary rate and selection strength, are global for the entire tree. We provide an implementation of this likelihood calculation algorithm in an accompanying R-package called PCMBase. The package has been designed as a generic library that can be integrated with existing or novel maximum likelihood or Bayesian inference tools. (C) 2019 The Author(s). Published by Elsevier Inc.

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  • 50.
    Mitov, Venelin
    et al.
    Swiss Fed Inst Technol, Switzerland; Swiss Inst Bioinformat SIB, Switzerland.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Stadler, Tanja
    Swiss Fed Inst Technol, Switzerland; Swiss Inst Bioinformat SIB, Switzerland.
    Automatic generation of evolutionary hypotheses using mixed Gaussian phylogenetic models2019In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 116, no 34, p. 16921-16926Article in journal (Refereed)
    Abstract [en]

    Phylogenetic comparative methods are widely used to understand and quantify the evolution of phenotypic traits, based on phylogenetic trees and trait measurements of extant species. Such analyses depend crucially on the underlying model. Gaussian phylogenetic models like Brownian motion and Ornstein-Uhlenbeck processes are the workhorses of modeling continuous-trait evolution. However, these models fit poorly to big trees, because they neglect the heterogeneity of the evolutionary process in different lineages of the tree. Previous works have addressed this issue by introducing shifts in the evolutionary model occurring at inferred points in the tree. However, for computational reasons, in all current implementations, these shifts are "intramodel," meaning that they allow jumps in 1 or 2 model parameters, keeping all other parameters "global" for the entire tree. There is no biological reason to restrict a shift to a single model parameter or, even, to a single type of model. Mixed Gaussian phylogenetic models (MGPMs) incorporate the idea of jointly inferring different types of Gaussian models associated with different parts of the tree. Here, we propose an approximate maximum-likelihood method for fitting MGPMs to comparative data comprising possibly incomplete measurements for several traits from extant and extinct phylogenetically linked species. We applied the method to the largest published tree of mammal species with body-and brain-mass measurements, showing strong statistical support for an MGPM with 12 distinct evolutionary regimes. Based on this result, we state a hypothesis for the evolution of the brain-body-mass allometry over the past 160 million y.

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