Benefits and complications of maximum likelihood estimation in (composite) interval mapping methods using EM and ECM

Abstract

Normal mixtures are applied in interval mapping to model the segregation of genotypes following Mendel's Law in successive generations of crossing. Standard methods use least squares or maximum likelihood estimates. Theoretically, maximum likelihood is known to result in more efficient estimates than least squares. In the interval mapping literature, some authors state that both methods yield equivalent results, whereas other authors emphasize the higher efficiency of maximum likelihood. The present paper investigates differences of both methods more closely.

We show by example the occurrence of multiple LOD-Score profiles when applying maximum likelihood estimation methods for a basic interval mapping and composite interval mapping model. This analysis results in some peaks of the LOD-Score profile that distinctly differ from F-statistic profiles without being spurious. A spurious profile for IM and CIM was found as well. It is concluded that users of IM and CIM mapping software must be prepared for the rare occurrence of spurious solutions in LOD profiles. The example indicates that especially in sparse marker maps maximum likelihood estimation has a potential to result in non-spurious profiles that are not similar to the F-statistic profiles. However, the discrimination of spurious and non-spurious further profiles is not straightforward in applications. Until the mathematical background of this phenomenon is investigated more thoroughly and rules to ascertain the information content of these additional solutions have been developed, the simultaneous use of the least squares and ML methods may caution against the rare occurrence of spurious results.