I would think that the idea of a "mitzvah sichlis" as you call it is that such mitzvos have obvious benefit to man even without any concept of religion. Specifically, these are the mitzvos which form the framework of a functioning society, and indeed most (if not all) societies, even non-religious ones, have laws about murder, theft, adultery, etc.
The idea, then, is that man can logically arrive at the conclusion that certain actions (e.g. murder) impede the proper function of society and are therefore inherently "bad". Not necessarily "bad" as in a moral judgement, but "bad" in a practical framework.
As such there would be no reason for a parallel construct with animals and fish. Animals and fish can't contemplate the sophisticated ideas involved in determining what would lead to a functional or dysfunctional society, they don't actually have "society" in the sense that humans have, and even to whatever extent that they do have "society" it is not for the most part impeded by preying on other groups of animals (much like human society is not much impeded by preying on animals).