| Summary: | Animal breeding theory is based on the assumption that traits are controlled by many genes each having small effect, however, genes with a large effect have been identified in favourable circumstances. Where major genes can be identified, and individual animals genotyped, exploitation of the genetic variation can be optimised. Segregation analysis has been proposed as a suitable method for detecting major genes. It involves maximising and comparing the likelihood of the data under different genetic models to ascertain the most likely genetic structure. To identify a major gene the likelihood of the data under a polygenic model is maximised and compared with the maximum likelihood under the mixed model (i.e. containing a major gene and polygenic component). A significant improvement in the likelihood obtained by incorporating the major gene gives evidence for its existence. Equations for the exact mixed model and polygenic likelihoods can be obtained, however the mixed model likelihood involves the integration of a complex function. Several approximations to this likelihood have been investigated. The first effectively retains the integration and approximates crossproduct terms involving the major gene and the polygenic component. The second (Herm) approximates the integration with a summation using the Hermite polynomial. The likelihood has been maximised using a quasi-Newton algorithm. The third and fourth methods are extensions of mixed model methods (in the statistical sense, i.e. including fixed and random effects), which are already familiar to animal breeders. One replaces the integration with a single estimate of the mode of each sire's transmitting ability distribution (ME1), the other estimates three modes one for each possible major genotype of the sire (ME3). These have been implemented using an expectation-maximisation algorithm. The first approximation was thought too complex to extend to include, for example, fixed effects. The operational characteristics of the other three methods have been investigated using simulated data. The Monte-Carlo simulation program uses Boolean algebra to describe the genotype of individuals at each locus and the inheritance of the alleles. Different genetic models have been considered and the data was analysed twice, firstly assuming that the polygenic heritability was known and fixing it at the expected value, secondly estimating the heritability from the data. For all the analyses the simulated data contained 50 sires each with 20 half-sib offspring. Segregation analysis is capable of detecting a major gene segregating in a population and accurately estimating its effect and frequency. Approximations to the mixed model likelihood make the method feasible for large data sets.
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