Missing Data and Interval Mapping

Abstract

In the preceding chapters we have assumed that all marker genotypes are known exactly. In practice there are often missing genotypes; and even when the genotypes of actual markers are not missing, one can regard the positions between actual markers as potential markers, the genotypes of which are missing. One can then make an attempt to reconstruct the missing information by statistical means. For important reasons that will become apparent in Chap. 9, problems of missing information are even more acute in outbred populations, and in particular humans. In this chapter we introduce, in the relatively simple situation of crosses between inbred strains, some basic techniques that are particularly useful for dealing with different kinds of missing information that arise in problems of gene mapping. In later chapters we will discuss more general approaches that can handle more complex situations. Regarding positions between markers as missing and applying statistical tools in order to reconstruct genotypes of these imaginary markers from the observed genotypes is called interval mapping in the genetic literature. A large part of this chapter discusses the statistical properties of interval mapping. In particular, we present approximations that extend the approximations presented in Chaps. 5 and 6 to the case of interval mapping. We also use this opportunity to outline, in the context of interval mapping, some of the considerations that are applied in the development of the mathematical theory for gene mapping. Instead of mathematical proofs, we investigate, using simulations , the validity of some critical steps in the approximations. These investigations , which are discussed in the star-marked Sect. 7.2.1, involve more time-consuming simulations. They are not essential for the understanding of the statistical properties of interval mapping and may be skipped by readers who have less interest in this more technical issue.