What is a genetic map function?

Abstract

We review the reasons that genetic map functions are studied and the way they are used. The connexions between chiasma point processes on four-stranded bivalents, crossover point processes on the single strand products of meiosis, multilocus recombination probabilities and map functions are discussed in detail, mainly, but not exclusively under the assumption of no chromatid interference. As a result of this discussion we obtain a number of inequalities constraining map functions which lead to both bound and smoothness constraints. We show that most of the functions proposed as map functions in the literature do in fact arise in association with a stationary renewal chiasma process, and we c..