One of the greatest achievements of genetics in the 20th century is D.K. Belyaev’s discovery of destabilizing selection during the domestication of animals and that this selection affects only gene expression regulation (not gene structure) and influences systems of neuroendocrine control of ontogenesis in a stressful environment. Among the experimental data generalized by Belyaev’s discovery, there are also findings about accelerated extinction of testes’ hormonal function and disrupted seasonality of reproduction of domesticated foxes in comparison with their wild congeners. To date, Belyaev’s discovery has already been repeatedly confirmed, for example, by independent observations during deer domestication, during the use of rats as laboratory animals, after the reintroduction of endangered species such as Przewalski’s horse, and during the creation of a Siberian reserve population of the Siberian grouse when it had reached an endangered status in natural habitats. A genome-wide comparison among humans, several domestic animals, and some of their wild congeners has given rise to the concept of self-domestication syndrome, which includes autism spectrum disorders. In our previous study, we created a bioinformatic model of human self-domestication syndrome using differentially expressed genes (DEGs; of domestic animals versus their wild congeners) orthologous to the human genes (mainly, nervous-system genes) whose changes in expression affect reproductive potential, i.e., growth of the number of humans in the absence of restrictions caused by limiting factors. Here, we applied this model to 68 human genes whose changes in expression alter the reproductive health of women and men and to 3080 DEGs of domestic versus wild animals. As a result, in domestic animals, we identified 16 and 4 DEGs, the expression changes of which are codirected with changes in the expression of the human orthologous genes decreasing and increasing human reproductive potential, respectively. The wild animals had 9 and 11 such DEGs, respectively. This difference between domestic and wild animals was significant according to Pearson’s χ2 test (p < 0.05) and Fisher’s exact test (p < 0.05). We discuss the results from the standpoint of restoration of endangered animal species whose natural habitats are subject to an anthropogenic impact.