QSAR of ecotoxicological data on the basis of data-driven if-then-rules

A rather small data matrix of seven chemicals and 17 different ecotoxicological end points is examined by methods of Discrete Mathematics. Especially, the lattice theory and its variant, the Formal Concept Analysis may be an attractive tool to analyze Quantitative Structure Activity Relationships, when a numerical functional approach is not at hand. The central item is the so called concept, which is a pair of subsets: A subset of molecules and a subset of properties which correspond to each other. The concepts are partially ordered due to a subset relation. From this subset relation, if-then-rules are derived, which aim to relate the structure of molecules with their ecotoxicological properties. For example, the following chemical rule is found: Cl --> (2A,2C,2M). That means, all substances considered here having a "-Cl" as structural code have a medium ecotoxicological effect on Daphnia magna, Orconectes immunisare (Crustacea) and on Photobacterium phosphoreum, at least within the training set.