Various genetic distance (GDist) formulas have been proposed for formalizing and quantifying the concept of genetic difference (GDiff), so that heterosis phenotypes, for different choices of parents that are crossed, can be compared quantitatively. Biologically, GDist formulas, such as that of Jaccard, Nei and Nei and Li, are defined in terms of the proportional presences, in the paternal and maternal parents, of trigger point regions (TPRs) assumed to be driving the associated genetics, such as transposable elements in promoters. However, such formulas do not allow the relative importance biologically of the proportional presences to be taken into account. Here, a parametric formula is proposed, analysed and validated, where the value of the parameter can be chosen to take account of the perceived relative biological performance of the individual proportional presences. The validation is based on the fact that, for particular choices of the parameter, some of the traditional formulas, such as Jaccard and Nei, are recovered which in turn highlight how such formulas are giving different weightings to the proportional presences. Mathematical and stochastic aspect associated with the study and modelling of heterosis are discussed.
This is joint work with Ming-Bo Wang, CSIRO Agriculture and Food, and Mark Westcott, CSIRO Data61.
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