  We derive a general statistical model of interactions, starting from
probabilistic principles and elementary requirements. Prevailing interaction
models in biomedical researches diverge both mathematically and practically. In
particular, genetic interaction inquiries are formulated without an obvious
mathematical unity. Our model reveals theoretical properties unnoticed so far,
particularly valuable for genetic interaction mapping, where mechanistic
details are mostly unknown, distribution of gene variants differ between
populations, and genetic susceptibilities are spuriously propagated by linkage
disequilibrium. When applied to data of the largest interaction mapping
experiment on Saccharomyces Cerevisiae to date, our results imply less aversion
to positive interactions, detection of well-documented hubs and partial
remapping of functional regions of the currently known genetic interaction
landscape. Assessment of divergent annotations across functional categories
further suggests that positive interactions have a more important role on
ribosome biogenesis than previously realized. The unity of arguments elaborated
here enables the analysis of dissimilar interaction models and experimental
data with a common framework.
