"Is it permissible for a veterinarian working in a forest to sterilize predatory animals to control their reproduction at the request of the forest owners? "

It is permissible to prevent an animal from reproducing if there is a benefit in doing so, but it is preferable to leave it as it is if there is no benefit. Among the benefits is the fear of harm that some animals may inflict on others, whether by medicines or castration, especially if it does not result in torture. Sterilization is easier than castration because it prevents reproduction without harm or injury. It is permissible to castrate an animal for a benefit, and the evidence for this is the Prophet's (peace and blessings be upon him) sacrifice of two white, castrated rams.