It appears there is no word in English for the German artgerecht. My phone's dictionary says:
artgerecht: ensuring animal welfare by satisfying the specific requirements of the species held
Google translate is not bad by translating it literally:
Leo shows the mess of the English language. It has several translations for artgerechte Tierhaltung:
animal welfare adequate animal housing species-appropriate animal husbandry welfare oriented animal husbandry ethical husbandry humane husbandry
Alright, so there are options.
Why did I look into this? Oftentimes the concepts of sustainability and species-appropriate husbandry are mixed together. In my opinion it is better to clearly separate them. Not that I think you should, but you could sustainably and in an environmentally friendly manner keep slaves or torture animals.
Mixing the concepts leads to unclear thinking. When mixing the terms, you need to tease out the baggage that the other concept brings, and people will wonder, what is this nonsense so-called sustainability? A word that poorly describes your cause does a disservice to furthering the ideal of sustainability, ethical manufacturing, and species-appropriate animal husbandry.
Another comment on the English language: Why so complicated? We should be able to use the same word for ethical manufacturing and species-appropriate animal husbandry. In the first case, I measn to apply it to humans, in the second case to any animal. Is there a better way to phrase this?