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Abstract Background Rare genomic changes (RGCs) that are thought to comprise derived shared characters of individual clades are becoming an increasingly important class of markers in genome-wide phylogenetic studies. Recently, we proposed a new type of RGCs designated RGC_CAMs (after Conserved Amino acids-Multiple substitutions) that were inferred using genome-wide identification of amino acid replacements that were: i) located in unambiguously aligned regions of orthologous genes, ii) shared by two or more taxa in positions that contain a different, conserved amino acid in a much broader range of taxa, and iii) require two or three nucleotide substitutions. When applied to animal phylogeny, the RGC_CAM approach supported the coelomate clade that unites deuterostomes with arthropods as opposed to the ecdysozoan (molting animals) clade. However, a non-negligible level of homoplasy was detected. Results We provide a direct estimate of the level of homoplasy caused by parallel changes and reversals among the RGC_CAMs using 462 alignments of orthologous genes from 19 eukaryotic species. It is shown that the impact of parallel changes and reversals on the results of phylogenetic inference using RGC_CAMs cannot explain the observed support for the Coelomata clade. In contrast, the evidence in support of the Ecdysozoa clade, in large part, can be attributed to parallel changes. It is demonstrated that parallel changes are significantly more common in internal branches of different subtrees that are separated from the respective common ancestor by relatively short times than in terminal branches separated by longer time intervals. A similar but much weaker trend was detected for reversals. The observed evolutionary trend of parallel changes is explained in terms of the covarion model of molecular evolution. As the overlap between the covarion sets in orthologous genes from different lineages decreases with time after divergence, the likelihood of parallel changes decreases as well. Conclusion The level of homoplasy observed here appears to be low enough to justify the utility of RGC_CAMs and other types of RGCs for resolution of hard problems in phylogeny. Parallel changes, one of the major classes of events leading to homoplasy, occur much more often in relatively recently diverged lineages than in those separated from their last common ancestor by longer time intervals of time. This pattern seems to provide the molecular-evolutionary underpinning of Vavilov's law of homologous series and is readily interpreted within the framework of the covarion model of molecular evolution. Reviewers This article was reviewed by Alex Kondrashov, Nicolas Galtier, and Maximilian Telford and Robert Lanfear (nominated by Laurence Hurst).