Structuration of Phenotypes and Genotypes through Galois Lattices and Implications

The Galois Lattice of a binary relation formalizes it as a concept system, dually ordered in "extension" / "intension". All implications between conjunctions of properties holding in it are summarized by a (recursive) canonical basis -all basis having the same cardinality (see [MR #87k:08009]). We report here how these tools structure phenotypes / genotypes in behavior genetics. On a generic viewpoint, both situations comprise two binary data sets that are paired through either a column or a row matching, which raises specific questions. If the data are small, as compared with data bases in bioinformatics, this illustrates how these abstract tools can unfold and better interpretations.