AあってのB says that B exists only because of A: take A away and there is no B. あっての goes straight after the first noun, with no particle, and a second noun follows it, usually closing the sentence with だ or です.
The thing everything rests on comes first. Swap the nouns and the claim turns round.
あっての is formal and a little literary. You hear it in speeches, interviews and company mottos, where someone credits what made a success possible. In conversation, say it with から or おかげ instead.
いのち命あってのものだね物種 is a proverb built on the pattern: you have to be alive before anything else counts, so don't risk your life.