I'm not sure how you can say there's no science to back this up. Livestock are accounted for as contributing nearly 15% of greenhouse gas emissions. And since so much pasture is cleared by razing old growth forest the cost may be even higher. And aside from their primary contribution, livestock place a lot of strain on water resources which are dwindling due to climate change. I'm not anyone has bothered computing the result of a world without livestock because it's so improbable but it would certainly be very significant.