zoism

from The Century Dictionary.

• noun The doctrine that the phenomena of life depend upon a peculiar vital principle; any vitalistic theory.

from the GNU version of the Collaborative International Dictionary of English.

• noun Reverence for animal life or belief in animal powers and influences, as among savages.
• noun (Biol.) A doctrine, now discarded, that the phenomena of life are due to a peculiar vital principle; the theory of vital force.