The Fisher-Bulmer infinitesimal model is the classical mathematical model of phenotypic evolution in quantitative genetics. I show that it arises from certain population genetic models in the limit as the number of genes contributing to the phenotypic trait tends to infinity. The conditions which these population genetic models must satisfy are discussed, in particular, the restrictions which are placed on the strength and the form of linkage disequilibrium (statistical associations between variation in different genes) in the population. Other situations, where the Fisher-Bulmer model does not arise in the limit of infinitely many genes, are also considered. Alternative limiting models are investigated. One of these, here referred to as the 'rare alleles model', applies when each gene mostly occurs in only one form, with the alternative forms occurring much more rarely. A method is developed for analysing the behaviour of the rare alleles model. This is used to investigate the balance between mutation and selection against deleterious alleles, and the selection pressure which this generates on the outcrossing rate.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:649225 |
| Date | January 1994 |
| Creators | Dawson, Kevin J. |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/14750 |
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