uu.seUppsala University Publications

Please wait ... |

Link to record
http://uu.diva-portal.org/smash/person.jsf?pid=authority-person:20122 $(function(){PrimeFaces.cw("InputTextarea","widget_formSmash_upper_j_idt122_recordDirectLink",{id:"formSmash:upper:j_idt122:recordDirectLink",widgetVar:"widget_formSmash_upper_j_idt122_recordDirectLink",autoResize:true});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt122_j_idt124",{id:"formSmash:upper:j_idt122:j_idt124",widgetVar:"widget_formSmash_upper_j_idt122_j_idt124",target:"formSmash:upper:j_idt122:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Permanent link

Direct link

Bartoszek, Krzysztoforcid.org/0000-0002-5816-4345

Open this publication in new window or tab >>Weak Stability of Centred Quadratic Stochastic Operators### Bartoszek, Krzysztof

### Domsta, Joachim

### Pulka, Malgorzata

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, no 4, p. 1813-1830Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

MALAYSIAN MATHEMATICAL SCIENCES SOC, 2019
##### Keywords

Asymptotic stability, Dyadic stability, Infinite divisible distributions, Quadratic stochastic operators, Weak convergence
##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:uu:diva-390084 (URN)10.1007/s40840-017-0575-8 (DOI)000471896200032 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_j_idt359",{id:"formSmash:j_idt184:0:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_j_idt365",{id:"formSmash:j_idt184:0:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_j_idt371",{id:"formSmash:j_idt184:0:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_j_idt371",multiple:true});
#####

##### Funder

Knut and Alice Wallenberg FoundationSwedish Institute, 11142/2013Swedish Institute, 19826/2014Swedish Institute, 00507/2012
Available from: 2019-08-06 Created: 2019-08-06 Last updated: 2019-08-06Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Linkoping Univ, Dept Comp & Informat Sci, S-58183 Linkoping, Sweden.

State Univ Appl Sci Elblag, Krzysztof Brzeski Inst Appl Informat, Ul Wojska Polskiego 1, PL-82300 Elblag, Poland.

Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland.

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 offspring's 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.

Open this publication in new window or tab >>Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1### Bartoszek, Krzysztof

### Pułka, Małgorzata

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, Vol. 41, no 1, p. 159-173Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Quadratic stochastic operators, Nonhomogeneous Markov operators, Baire category, Mixing nonlinear Markov process
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:uu:diva-283630 (URN)10.1007/s40840-015-0245-7 (DOI)000419716700010 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_j_idt359",{id:"formSmash:j_idt184:1:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_j_idt365",{id:"formSmash:j_idt184:1:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_j_idt371",{id:"formSmash:j_idt184:1:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_j_idt371",multiple:true});
#####

##### Funder

Swedish Institute, 00507/2012, 11142/2013, 19826/2014
Available from: 2016-04-13 Created: 2016-04-13 Last updated: 2018-02-26Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.

Gdansk University of Technology.

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.

Open this publication in new window or tab >>A Noether theorem for stochastic operators on Schatten classes### Bartoszek, Krzysztof

### Bartoszek, Wojciech

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, no 2, p. 1395-1412Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Schatten classes, Markov operator, Noether property
##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:uu:diva-322500 (URN)10.1016/j.jmaa.2017.03.068 (DOI)000400224400039 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_j_idt359",{id:"formSmash:j_idt184:2:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_j_idt365",{id:"formSmash:j_idt184:2:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_j_idt371",{id:"formSmash:j_idt184:2:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_j_idt371",multiple:true});
#####

##### Funder

Swedish Institute, 00507/2012Swedish Institute, 11142/2013Swedish Institute, 19826/2014
Available from: 2017-05-30 Created: 2017-05-30 Last updated: 2017-05-30Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.

Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland..

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.

Open this publication in new window or tab >>The impact of the Polish mass breast cancer screening program on prognosis in the Pomeranian Province### Woniacki, Piotr

### Skokowskil, Jarostaw

### Bartoszek, Krzysztof

### Kosowskal, Anna

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); ### Kalinowski, Leszek

### JaSkiewicz, Janusz

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_3_j_idt188_j_idt202",{id:"formSmash:j_idt184:3:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2017 (English)In: Archives of Medical Science, ISSN 1734-1922, E-ISSN 1896-9151, Vol. 13, no 2, p. 441-447Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

TERMEDIA PUBLISHING HOUSE LTD, 2017
##### Keywords

breast cancer, screening, mass screening, prognostic factors, MCC staging, prognosis
##### National Category

Cancer and Oncology
##### Identifiers

urn:nbn:se:uu:diva-320343 (URN)10.5114/aoms.2016.60387 (DOI)000395365500022 ()28261300 (PubMedID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt359",{id:"formSmash:j_idt184:3:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt365",{id:"formSmash:j_idt184:3:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt371",{id:"formSmash:j_idt184:3:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt371",multiple:true});
#####

Available from: 2017-04-19 Created: 2017-04-19 Last updated: 2017-04-19Bibliographically approved

Med Univ Gdansk, Dept Surg Oncol, 7 Debinki St, PL-80952 Gdansk, Poland..

Med Univ Gdansk, Dept Surg Oncol, 7 Debinki St, PL-80952 Gdansk, Poland..

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.

Med Univ Gdansk, Dept Surg Oncol, 7 Debinki St, PL-80952 Gdansk, Poland..

Med Univ Gdansk, Dept Med Lab Diagnost, Bank Frozen Tissues & Genet Specimens, Gdansk, Poland..

Med Univ Gdansk, Dept Surg Oncol, 7 Debinki St, PL-80952 Gdansk, Poland..

Introduction: Mammographic screening results in diagnosis of less advanced breast cancer (BC). A meta-analysis of randomized clinical trials confirmed that BC screening reduces mortality. In 2007, the National Breast Cancer Screening Program (NBCSP) was established in Poland with the crucial aim of reducing mortality from BC. The purpose of this study was to assess the impact of participation in the NBCSP on prognosis. Material and methods: A single institution, non-randomized retrospective study was undertaken. The study population comprised 643 patients with BC treated in the Department of Surgical Oncology (DSO) at the Medical University of Gdansk over a 4-year period, from 01.01.2007 until 31.12.2010. Patients were divided into two groups: group A-patients who participated in the NBCSP (n = 238, 37.0%); and group B-patients who did not participate in the NBCSP (n = 405, 63.0%). Results: Statistical analysis revealed that group A displayed a less advanced MCC stage (more patients in AJCC stage I, p = 0.002), lower tumor diameter (more patients with pT1, p = 0.006, and pT < 15 mm, p = 0.008) and a lower incidence of metastases to axillary lymph nodes (more patients with pNO, p = 0.01). From 2009 to 2010 the NBCSP revealed a statistically significant benefit significantly more patients in stage 0 + I (60.7% vs. 48.8%, p = 0.018) and with tumors pT < 15 mm (48.8% vs. 35.1%, p = 0.011) were observed in group A. Conclusions: The study results revealed the beneficial impact of the NBCSP. Superior prognostic factors and favorable staging were observed in women who participated in the NBCSP.

Open this publication in new window or tab >>Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations### Bartoszek, Krzysztof

### Glemin, Sylvain

### Kaj, Ingemar

### Lascoux, Martin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 429, p. 35-45Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Migration, Ornstein-Uhlenbeck process, Phylogenetic comparative methods, Species interactions, Trait evolution
##### National Category

Biological Sciences
##### Identifiers

urn:nbn:se:uu:diva-333740 (URN)10.1016/j.jtbi.2017.06.011 (DOI)000407873100003 ()28619246 (PubMedID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_j_idt359",{id:"formSmash:j_idt184:4:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_j_idt365",{id:"formSmash:j_idt184:4:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_j_idt371",{id:"formSmash:j_idt184:4:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt371",multiple:true});
#####

Available from: 2017-11-16 Created: 2017-11-16 Last updated: 2018-05-31Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Ecology and Genetics, Plant Ecology and Evolution. CNRS Univ Montpellier IRD EPHE, UMR ISEM 5554, Montpellier, France..

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Ecology and Genetics, Plant Ecology and Evolution.

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.

Open this publication in new window or tab >>Phylogenetic effective sample size### Bartoszek, Krzysztof

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 407, p. 371-386Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Biodiversity;Effective sample size;Measurement error;Ornstein-Uhlenbeck process;Phylogenetic comparative methods; Quantitative trait evolution
##### National Category

Probability Theory and Statistics Bioinformatics and Systems Biology Evolutionary Biology
##### Research subject

Applied Mathematics and Statistics; Bioinformatics
##### Identifiers

urn:nbn:se:uu:diva-300893 (URN)10.1016/j.jtbi.2016.06.026 (DOI)000383111800030 ()27343033 (PubMedID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_j_idt359",{id:"formSmash:j_idt184:5:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_j_idt365",{id:"formSmash:j_idt184:5:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_j_idt371",{id:"formSmash:j_idt184:5:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_j_idt371",multiple:true});
#####

##### Funder

Knut and Alice Wallenberg Foundation
Available from: 2016-08-15 Created: 2016-08-15 Last updated: 2017-11-28Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.

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 AIC_{c} 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.

Open this publication in new window or tab >>A consistent estimator of the evolutionary rate### Bartoszek, Krzysztof

### Sagitov, Serik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, p. 69-78Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Branching Brownian motion, Conditioned branching process, Tree-free phylogenetic comparative method, Quantitative trait evolution, Yule process
##### National Category

Evolutionary Biology Probability Theory and Statistics
##### Identifiers

urn:nbn:se:uu:diva-252680 (URN)10.1016/j.jtbi.2015.01.019 (DOI)000353011200006 ()25636492 (PubMedID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_j_idt359",{id:"formSmash:j_idt184:6:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_j_idt365",{id:"formSmash:j_idt184:6:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_j_idt371",{id:"formSmash:j_idt184:6:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_j_idt371",multiple:true});
#####

##### Funder

Swedish Research Council, 621-2010-5623The Royal Swedish Academy of Sciences
Available from: 2015-05-26 Created: 2015-05-11 Last updated: 2017-12-04Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.

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.

Open this publication in new window or tab >>A consistent estimator of the evolutionary rate### Bartoszek, Krzysztof

### Sagitov, Serik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, p. 69-78Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Branching Brownian motion; Conditioned branching process; Tree-free phylogenetic comparative method; Quantitative trait evolution; Yule process
##### National Category

Probability Theory and Statistics Evolutionary Biology
##### Research subject

Statistics; Mathematical Statistics; Biology
##### Identifiers

urn:nbn:se:uu:diva-246249 (URN)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_j_idt359",{id:"formSmash:j_idt184:7:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_j_idt365",{id:"formSmash:j_idt184:7:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_j_idt371",{id:"formSmash:j_idt184:7:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_j_idt371",multiple:true});
#####

Available from: 2015-03-04 Created: 2015-03-04 Last updated: 2017-12-04

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.

Chalmers University of Technology and the University of Gothenburg.

We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate *λ*, 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 *σ*^{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 *R*_{n}^{2} of the evolutionary rate ρ^{2}=σ^{2}/λ. 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}.

Open this publication in new window or tab >>Asymptotic properties of quadratic stochastic operators acting on the L1 space### Bartoszek, Krzysztof

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.### Pulka, Malgorzta

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, p. 26-39Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Quadratic stochastic operators, Nonhomogeneous Markov operators, Mixing nonlinear Markov process
##### National Category

Mathematical Analysis Probability Theory and Statistics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:uu:diva-241868 (URN)10.1016/j.na.2014.10.032 (DOI)000348041700004 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_j_idt359",{id:"formSmash:j_idt184:8:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_j_idt365",{id:"formSmash:j_idt184:8:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_j_idt371",{id:"formSmash:j_idt184:8:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt371",multiple:true});
#####

##### Funder

Swedish Institute
##### Note

Gdansk University of Technology.

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.

Svenska institutet supported this work through their Östersjösamarbetet scholarship program.

Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2017-12-05Bibliographically approvedOpen this publication in new window or tab >>Phylogenetic confidence intervals for the optimal trait value### Bartoszek, Krzysztof

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.### Sagitov, Serik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, p. 1115-1132Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Central limit theorem; conditioned Yule process; macroevolution; martingales; Ornstein–Uhlenbeck process; phylogenetics
##### National Category

Probability Theory and Statistics Evolutionary Biology
##### Research subject

Mathematical Statistics; Statistics
##### Identifiers

urn:nbn:se:uu:diva-241872 (URN)10.1239/jap/1450802756 (DOI)000368467600014 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt359",{id:"formSmash:j_idt184:9:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt365",{id:"formSmash:j_idt184:9:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt371",{id:"formSmash:j_idt184:9:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt371",multiple:true});
#####

##### Funder

Swedish Research Council, 621-2010-5623The Foundation for Baltic and East European StudiesKnut and Alice Wallenberg FoundationThe Royal Swedish Academy of Sciences
Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2017-12-05Bibliographically approved

Chalmers University of Technology and the Unversity of Gothenburg.

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.