The hypothesis of 'selfish DNA' is tested for the case of animals using the relation between genome size and conservation status of a given species. In contrast to plants, where the larger genome was previously shown to increase the likelihood of extinction, the picture is more complicated in animals. At the within-families and within-orders levels, the larger genome increases the risk of extinction only in reptiles and birds (which have the smallest genomes among tetrapods). In fishes and amphibians, the effect is caused by the higher taxonomic levels (above order). In several phylogenetic lineages of anamniotes, there is a correlation between a higher fraction of threatened species and a lower number of extant species in a lineage with the larger genome. In mammals, no effect was observed at any taxonomic level. The obtained data support the concept of hierarchical selection. It is also shown that, in plants and reptiles, the probability of being threatened increases from less than 10% to more than 80% with the increase in genome size, which can help in establishing conservation priorities.