The following heuristic hypothesis has been proposed: if an excess of a protein in several animal organs was experimentally identified as a physiological marker of increased aggressiveness, and if a single nucleotide polymorphism (SNP) can cause the overexpression of a human gene homologous to the animal gene encoding this protein, then this polymorphism can be a candidate SNP marker of social dominance. In turn, a deficient expression would correspond to subordinate behavior. Within this hypothesis, we analyzed 21 human genes, ADORA2A, BDNF, CC2D1A, CC2D1B, ESR2, FEV, FOS, GH1, GLTSCR2, GRIN1, HTR1B, HTR1A, HTR2A, HTR2C, LGI4, LEP, MAOA, SLC17A7, SLC6A3, SNCA, and TH, which determine the functions of the proteins known as the physiological markers of aggressive behavior in animals. These genes encode for hormones and their receptors, biosynthetic enzymes, receptors of neurotransmitters, and transcription and neurotrophic factors. These proteins have been postulated to play important roles in determining the hierarchical relationships in social animals. Using our previously developed Web-service SNP_TATA_Comparator (http://beehive.bionet.nsc.ru/cgi-bin/mgs/tatascan/start.pl), we analyzed 381 SNPs within the [–70;–20] region preceding the start of the protein-coding transcripts, obtained from the database dbSNP, v.147. This is the region for all the known TATA-binding protein (TBP) binding sites. As a result, we found 45 and 47 candidate SNP markers of dominance and subordination, respectively (e.g., rs373600960 and rs747572588). Within the proposed heuristic hypotheses and dbSNP database v.147, we found statistically significant (α < 10–5) evidence of the effects of natural selection against the deficient expression of genes, which can affect the predisposition to dominate. We also obtained evidence favoring the hypothesis that both subordinate and dominant behavior can be the norm of reaction of aggressiveness (difference not significant: α > 0.35). The proposed hypothesis, the candidate SNP markers obtained on its basis, and the observed regularities of the effects of their natural selection on the human genome are discussed in comparison with the published data with respect to whether these markers can have an effect on the expression of social dominance in human society. We conclude that our candidate SNPs, identified with a computational model, require further experimental verification.