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We have presented some arguments to substantiate the usefulness of neuralreplicator analysis (NRA) for constructing variants of the natural binomialclassification of virus genomes based only on knowledge of their completegenomic sequences, without involving other data on the phenotype, functions,encoded proteins, etc., and also without the need of genomic sequencesalignment. Perhaps this will make sense when processing metagenomic data. Thismakes it possible to construct the binomial classification accepted for theviruses themselves. We restrict ourselves to three families of viruses havingdsDNA circular genomes (Papillomaviridae, Polyomaviridae and Caulimoviridae)and partly to the family Geminiviridae having ssDNA genomes though the approachpresented can be also applied to genomes of other dsDNA, ssDNA and ssRNAviruses, including linear ones (some results for Mitoviridae are alsopresented). It is argued that binomial classification of virus genomes which isdifficult to apply in all cases can nevertheless be informative tool ofrevealing virus properties, areal of hosts, forms of diseases and can also showthe connections of the viruses belonging to different families and even todifferent kingdoms.

Neural Replicator Analysis for virus genomes binomial systematics in metagenomics