Random steps in evolution and point processes

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Title: Random steps in evolution and point processes
Author: Service, Robert
Contributor: University of Helsinki, Faculty of Science, Department of Mathematics and Statistics
Publisher: Helsingin yliopisto
Date: 2012-10-11
Language: en
URI: http://urn.fi/URN:ISBN:978-952-10-8287-0
Thesis level: Doctoral dissertation (article-based)
Abstract: The thesis consists of four papers in the area of mathematical biology and probability theory. Mathematical biology is an field of research which seeks understanding of biological phenomena through the application of existing and new mathematical methods. The motivating biological problem addressed in the first two papers of the thesis falls into the area of the mathematical theory of evolution, where an ecological model described by a dynamical system is equipped with a further mechanism, under which one (or more) of the species represented in the model is able to undergo evolution through mutation and natural selection. The present work examines when the possibility of displacement of a resident phenotype by a mutant of another phenotype is described in simple terms by a so-called optimisation principle. An optimisation principle is a numerical function, defined for phenotypes, that allows one to compare the potential to invade all potential environments set by some currently present phenotype simultaneously. The main result of the first paper gives a set of necessary and sufficient conditions for when an optimization principle exists. The third and fourth papers in the thesis deal from different viewpoints with topics connected to Poisson point processes.Väitöskirja koostuu neljästä artikkelista matemaattisen biologian ja todennäköisyysteorian aloilta. Matemaattinen biologia on tutkimusala, joka tähtää biologisten ilmiöiden ymmärrykseen olemassaolevien ja uusien matemaattisten menetelmien avulla. Kaksi ensimmäistä väitöskirjan artikkelia käsittelevät matemaattista evoluutioteoriaa. Päätulos antaa välttämättömät ja riittävät ehdot evoluution kulkua määräävän optimointntiperiaatteen olemassaololle. Kaksi jälkimmäistä artikkelia käsittelee eri näkökulmista aiheita, jotka liittyvät Poissonin pisteprosessien teoriaan.
Subject: matematiikka
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