Foundations of a mathematical theory of darwinism.

This paper pursues the 'formal darwinism' project of Grafen, whose aim is to construct formal links between dynamics of gene frequencies and optimization programmes, in very abstract settings with general implications for biologically relevant situations. A major outcome is the definition,...

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Autors principals: Batty, C, Crewe, P, Grafen, A, Gratwick, R
Format: Journal article
Idioma:English
Publicat: 2014
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author Batty, C
Crewe, P
Grafen, A
Gratwick, R
author_facet Batty, C
Crewe, P
Grafen, A
Gratwick, R
author_sort Batty, C
collection OXFORD
description This paper pursues the 'formal darwinism' project of Grafen, whose aim is to construct formal links between dynamics of gene frequencies and optimization programmes, in very abstract settings with general implications for biologically relevant situations. A major outcome is the definition, within wide assumptions, of the ubiquitous but problematic concept of 'fitness'. This paper is the first to present the project for mathematicians. Within the framework of overlapping generations in discrete time and no social interactions, the current model shows links between fitness maximization and gene frequency change in a class-structured population, with individual-level uncertainty but no uncertainty in the class projection operator, where individuals are permitted to observe and condition their behaviour on arbitrary parts of the uncertainty. The results hold with arbitrary numbers of loci and alleles, arbitrary dominance and epistasis, and make no assumptions about linkage, linkage disequilibrium or mating system. An explicit derivation is given of Fisher's Fundamental Theorem of Natural Selection in its full generality.
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spelling oxford-uuid:62c48ce3-7b05-48d0-bb08-82efb77d15d42022-03-26T18:08:23ZFoundations of a mathematical theory of darwinism.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:62c48ce3-7b05-48d0-bb08-82efb77d15d4EnglishSymplectic Elements at Oxford2014Batty, CCrewe, PGrafen, AGratwick, RThis paper pursues the 'formal darwinism' project of Grafen, whose aim is to construct formal links between dynamics of gene frequencies and optimization programmes, in very abstract settings with general implications for biologically relevant situations. A major outcome is the definition, within wide assumptions, of the ubiquitous but problematic concept of 'fitness'. This paper is the first to present the project for mathematicians. Within the framework of overlapping generations in discrete time and no social interactions, the current model shows links between fitness maximization and gene frequency change in a class-structured population, with individual-level uncertainty but no uncertainty in the class projection operator, where individuals are permitted to observe and condition their behaviour on arbitrary parts of the uncertainty. The results hold with arbitrary numbers of loci and alleles, arbitrary dominance and epistasis, and make no assumptions about linkage, linkage disequilibrium or mating system. An explicit derivation is given of Fisher's Fundamental Theorem of Natural Selection in its full generality.
spellingShingle Batty, C
Crewe, P
Grafen, A
Gratwick, R
Foundations of a mathematical theory of darwinism.
title Foundations of a mathematical theory of darwinism.
title_full Foundations of a mathematical theory of darwinism.
title_fullStr Foundations of a mathematical theory of darwinism.
title_full_unstemmed Foundations of a mathematical theory of darwinism.
title_short Foundations of a mathematical theory of darwinism.
title_sort foundations of a mathematical theory of darwinism
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