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## Computational Methodology

Composite interval mapping [ZengZeng1993,ZengZeng1994] combines interval mapping with multiple regression. The statistical model is defined as (3.5)

where
• is a vector of trait values
• and are the additive and dominance effects of the putative QTL being tested
• and are indicator variable vectors specifying the probabilities of an individual being in different genotypes for the putative QTL constructed by flanking makers
• is the vector of effects of other selected markers fitted in the model
• is the marker information matrix for those selected markers
• is the error vector.

Estimates of the parameters are obtained by maximum likelihood through an ECM (for Expectation/Conditional Maximization) algorithm [Meng and RubinMeng and Rubin1993]. In each E-step, the probability of an individual being in different genotypes of the putative QTL is updated. In the CM-step, the estimation of parameters and is separated from that of , and each group is estimated conditional on the others. This procedure is implemented for numerical consideration. As and are separated from , is unchanged in each iteration, and its costly recalculation is avoided.

For an population, the hypotheses for testing are and . This is performed through a likelihood ratio test procedure. In addition, it is possible to test hypotheses on and individually. For a backcross data set, dominance cannot be estimated and is dropped from Equation 3.5.

The trait will have a variance . Under the null hypothesis the sample variance of the residuals will be . For a given alternative model, say the variance of the residuals would be . With this in mind we can calculate the proportion of variance explained by a QTL at the test site. The quantity is usually called and estimated by An alternative estimate would use the total variance. Denote it by  is the proportion of the variance explained by the QTL conditioned on the background markers and any explanatory variables. is the proportion of the total variance explained by the QTL and the the background markers and any explanatory variables. Generally,      Next: Models Up: Zmapqtl Previous: Zmapqtl   Contents   Index
Christopher Basten 2002-03-27