You searched for: “biophilia
biophilia (s) (noun) (no pl)
1. An natural bond or association between mankind and all living things: Biophilia is considered by some to be the connections humans subconsciously seek with the rest of life.
2. A conviction that there is an emotional connection between humans and other forms of life: Biophilia can include the respect for oneself and the fair and loving treatment of animals.

This word could also apply to the term, "zoophilia", et al.