The full name for FOS is fructooligosaccharides which is what AJ identifies it by. Other common ingredients that are prebiotics are inulin (chicory root) and beet pulp. Some dogs with gut issues seem to do better with FOS than inulin or beet pulp and that is why I asked about the other foods you tried.
When you see an ingredient that ends in “fermentation product” it is a probiotic. Whatever proceeds that is the particular strain of bacteria. Some foods might have 1 strain whereas others may have 5 or 6 or more. The different strains of bacteria have separate functions in the gut. Right now Atlas only has the strains of bacteria in his gut to handle what he is eating and when you add the new food that is why his poo gets soft.
I think it would help to supplement with a probiotic that contains prebiotics when you start adding new food, but not while Atlas is just eating the NB. I don’t remember if I mentioned this before or not, but when I was feeding my girls NB, one was getting probiotics everyday along with her food, but when NB discontinued the formula I was feeding, I could not add 4 kibbles of a new food without it giving her diarrhea. I ended up putting her on kefir and some fresh food in addition to the probiotic. My other girl I had to add a prebioitic/probiotic combination in addition to the new kibble with probiotics. Neither one of the girls had trouble transitioning to new foods prior to feeding the NB for several months. This is why I said that I don’t think it has the right components to build a healthy gut.
I’ll go through some ingredient lists and get back with you on the brands. I don’t know that any of the limited ingredients foods are going to be any cheaper, but I do think you need to add another food to help build his gut bacteria.
