Application of the Mixing Partial Order to Genes

The partial order that describes “mixedness” of sets of objects is applied to distributions of codons that make up genes. Because partial order usually implies incomparability, the method provides a new characterization of the relationship among genes, namely, their incomparability with one another in a genome. A randomly selected group of 15 genes from the rainbow trout (Oncorhynchus mykiss) is treated to demonstrate the methodology used to determine incomparability among them and to compute their “mixing character.” Of the 15 genes studied, the androgen receptor alpha and beta genes are found to be the most mixed.