1. An apparatus to identify one or more association variables that are associated with a trait, comprising: at least one processor; at least one memory; and at least one program module, the program module stored in the memory and configurable to be executed by the processor, the program module including: instructions for determining patterns of occurrence of compound variables based on a set of mathematical interactions and patterns of occurrence of a set of biological variables of a group of life forms, wherein a pattern of occurrence of a given compound variable is determined based on a given mathematical interaction in the set of mathematical interactions and patterns of occurrence of a given pair of biological variables in the set of biological variables; instructions for calculating statistical relationships corresponding to a pattern of occurrence of the trait in the group of life forms and the patterns of occurrence of the compound variables, wherein a given statistical relationship corresponds to the pattern of occurrence of the trait in the group of life forms and the pattern of occurrence of a given compound variable, and wherein the calculating includes contributions from presence and absence information in the pattern of occurrence of the trait and the pattern of occurrence of the given compound variable; instructions for determining numbers of occurrences of biological variables that were used to determine the compound variables in at least a subset of the compound variables, wherein the subset of the compound variables have statistical relationships greater than a statistical confidence value; instructions for determining numbers of different mathematical interactions used to determine the compound variables in the subset of the compound variables for the biological variables associated with the corresponding numbers of occurrences; and instructions for identifying one or more of the biological variables in the set of biological variables as the one or more association variables based on the numbers of occurrences and the numbers of different mathematical interactions.