I would argue that a species name is a proper noun, referring to a distinct and particular entity among a variety of entities, and so should be capitalised.
Of course, where this falls down is when it comes to species like Lion, Tiger, Giraffe, etc, which by that logic would never be written without a capital and that's just daft. In lists I would always capitalise, but 'one-word' species I would not in a body of text unless my meaning very specifically means the species (in which case I'd probably switch to scientific anyway). Multi-word names I almost always capitalise if they refer to a particular species or subspecies.
Of course, where this falls down is when it comes to species like Lion, Tiger, Giraffe, etc, which by that logic would never be written without a capital and that's just daft. In lists I would always capitalise, but 'one-word' species I would not in a body of text unless my meaning very specifically means the species (in which case I'd probably switch to scientific anyway). Multi-word names I almost always capitalise if they refer to a particular species or subspecies.