The term "yardwaste" makes little sense, because everything that falls in the yard is useful. Nature has been in the recycling business for a few billion years now, give or take, and has in that time figured out how to convert all its spent products back into the building blocks for new life. But nature goes beyond simply dismantling structures as quickly as possible to make something new. When one of our products, such as a TV, stops functioning, its useful days are considered over. But when a tree limb dies, it becomes a perch where birds can have a commanding view unimpeded by dense leaves. When the limb falls, it becomes cover for animals, a place for a butterfly or firefly to rest. The legacy of a tree, or parts thereof, is not only as food and fertilizer but also the structure it leaves behind.
A naturalist friend of mine, Joshua Rose, who now lives in Amherst, MA, wrote an article last winter about the utility of building a woodpile in the backyard. Though his PhD focused on dragonflies, he has gained in-depth knowledge of plants, birds, herps, and all other manner of life, to the point that he could more appropriately be called a supernaturalist. These supernatural powers allow him to perceive and convey an understanding of how woodpiles benefit the lives of a broad range of creatures, including us. The article can be found at this link: http://www.gazettenet.com/2012/01/07/brush-piles-a-backyard-bonanza-for-wildlife.