I can't find something that tells me which skill is used to interact with wild animals, such as wolves, bears, moles, etc.
Am I missing something in the BRP rulebook or is there a supplement that explains it?
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Interactions with animals is not handled by Basic Roleplaying/Call of Cthulhu core rules. The only rules are on the Riding skill to handle riding, caring, equipping and maneuvering animals, such as horses, camels, giant lizards and similar beasts.
Something similar to the way that D&D or Pathfinder uses animal handling is simply missing from the core rules of BRP/CoC, but that doesn't mean it's impossible. The usual settings simply have little interaction with animals, unlike what happens in medieval fantasy games. There are no examples of someone who is a pet professional or something like that.
However, the Natural History skill handles knowledge about animals in general, what they like, what they fear, how dangerous they are, etc. The skill is described in modern settings (1890–1920) as the academic study of animals and plant life, but in any older setting it could mean the knowledge of wilderness in general. Persuade on the other hand, does not restrict itself to people or humanoids, and with a penalty, you could use it on creatures that do not understand your language.
If you take the sample professions from CoC 7th edition, you will see that certain professions commonly have to deal with animals do have Natural History:
Farmer / Forester
Craft, Electrical Repair, First Aid, Mechanical Repair, Natural History, Operate Heavy Machine, Track, any one other skills as a personal or era specialty.
Bargain, Listen, Natural History, Occult, Spot Hidden, Swim, Throw, any one other skills as a personal or era specialty.
However, the BRP/CoC skill system is not exhaustive; the Keeper can create new skills to better suit their settings if necessary. So, if rearing and training animals is common in your setting, you could create a new skill for that. We have the Anthropology skill to understand human cultures and other humanoid civilizations, so creating a new skill to understand wild animals (like Wildlife) or a skill for training wild animals (like Animal Training) is not absurd.
This freedom of changing the system can be seen in several of CoC's supplements. For example, the Dark Ages (a historical medieval setting) has the skill Drive Horses or Oxen, which is a very specific variation of the driving skill, and has the Natural World skill instead of Natural History:
Natural World (10%)
Compared to Science, the focus of this skill is on personal experience and hearsay. It encompasses general knowledge concerning animals, plants, sea life, and climate in an environment familiar to the investigator. The keeper should halve this skill in unfamiliar lands. Also use this skill for knowledge and care of domestic plants and animals.