The design when collecting Fertilizer is that it is completely by chance when feeding animals. The only guarantee is the number of fertilizers that a certain animal will produce once it's fed. (e.g. Black Leghorn Chicken = 1 Fertilizer, Boer Goat = 2 fertilizers). There are few animals in the General Store that are exempted. Meaning, they will not produce fertilizers by design. (e.g. Pink Landrace Pig, LaMancha Goat) To make sure, we can check each animal from the General Store so we would know which animals do give out fertilizer from those who doesn't.
Lastly, all Prized animals will never produce fertilizers by design as indicated in the General Store as well.