But the domestication of large mammals was almost over from 4,500 years ago. By then, all of the 148 species of large mammals that could be domesticated candidates had been tested countless times, eventually only a handful had passed, and there were no more. Bea Arthur Bea Safe. There are species that can be domesticated but not domesticated. There is also a fourth type of evidence that proves why some mammals are more suitable for domestication than others, that different regions domesticated the same species at other times. each other and independently of each other.