Recent experimental data from proteomics and genomics are interpreted here in ways that challenge the predominant viewpoint in biology according to which the four evolutionary processes, including mutation, recombination, natural selection and genetic drift, are sufficient to explain the origination of species. The predominant viewpoint appears incompatible with the finding that the sequenced genome of each species contains hundreds, or even thousands, of unique genes - the genes that are not shared with any other species. These unique genes and proteins, (...) singletons, define the very character of every species. Moreover, the distribution of protein families from the sequenced genomes indicates that the complexity of genomes grows in a manner different from that of self-organizing networks: the dominance of singletons leads to the conclusion that in living organisms a most unlikely phenomenon can be the most common one. In order to provide proper rationale for these conclusions related to the singletons, the paper first treats the frequency of functional proteins among random sequences, followed by a discussion on the protein structure space, and it ends by questioning the idea that protein domains represent conserved units of evolution. (shrink)