Some basic aspects of human and animal biology and evolution involve the establishment of biological uniqueness of species and individuals within their huge variety. The discrimination among closely related species occurs in their offspring at the level of chromosomal DNA sequence homology, which is required for fertility as the hallmark of species. Biological identification of individuals, i.e., of their biological "self", occurs at the level of protein sequences presented by the MHC/HLA complex as part of the immune system that discriminates non-self from self. Here, a mechanistic molecular model is presented that can explain how DNA sequence divergence and the activity of key mismatch repair proteins, MutS and MutL, lead to 1) genetic separation of closely related species (sympatric speciation) (Fitch and Ayala, Proceedings of the National Academy of Sciences, 1994, 91, 6717-6720), 2) the stability of genomes riddled by diverged repeated sequences, and 3) conservation of highly polymorphic DNA sequence blocks that constitute the immunological self. All three phenomena involve suppression of recombination between diverged homologies, resulting in prevention of gene sharing between closely related genomes (evolution of new species) as well as sequence sharing between closely related genes within a genome (e.g., evolution of immunoglobulin, MHC, and other gene families bearing conserved polymorphisms).