title: A simple mathematical model of gradual Darwinian evolution: emergence of a Gaussian trait distribution in adaptation along a fitness gradient.
abstract: We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.
authors.affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, North Park Road, Exeter, EX4 4QF, UK, v.n.biktashev@exeter.ac.uk.
authors.forename: Vadim N
authors.initials: VN
authors.lastname: Biktashev
mesh_terms: D000222:Adaptation, Physiological / Q000235:genetics*; D005075:Biological Evolution; D005828:Genetics, Population; D008957:Models, Genetic; D016011:Normal Distribution; D040641:Quantitative Trait Loci / Q000235:genetics*; D012641:Selection, Genetic / Q000235:genetics*
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