This is an idea that was introduced in 1972 by Donald Campbell. But it seems to me that it's been much ignored by both philosophers of science and also by scientists themselves in the years since then. The one place in science where downward or top-down causation does get a lot of attention, I think, is in psychology.
Campbell's claim was that bottom-up accounts in biology are necessary but they're not sufficient, they are only partial. In addition to the bottom-up account in terms of biochemistry, you also need a top-down account to complement it. Here's his example:
He raises the question: How do you explain the fact that the jaws of worker ants or termites are so beautifully designed to do the kind of work that termites do, gnawing wood or the ants carrying seeds. He says from an engineering view they're optimally designed; you could hardly do any better job if you were--with those materials--if you set out to design it yourself. So how to explain that?
Well, the bottom-up account, the termites' genes give instructions for protein formation and the proteins make up the jaw structure. But this explanation is incomplete. How come the lucky termite has that particular DNA instead of some of the countless other possible forms that it could have? How did it come to have the instructions for such useful jaws?
The answer, of course, is natural selection. Though it has been, in the past, random production of lots and lots of variants, and only the useful ones have survived to reproduce. So we have a bottom-up cause in terms of the macromolecules. But we also have to have a top-down cause in terms of the ecosystem in which the little bugs live and the way that that has had a differential effect on the survival and reproduction of the termites as whole organisms.
This diagram, in terms of levels of organization, is static and so it's not the best way to represent what's going on. What we really need is a feedback loop that allows us to take into account changes over time.
And so here I've got the bottom-up part of the explanation, the DNA to protein structure. But then we've also got the top-down part which is from the environment by means of the differential survival and reproduction back to the DNA. And then we start through the whole cycle again.
So downward selection is selectively wiping out a lot of the variation but it's not interfering with the laws of biology and a fortiori it's not interfering with the laws of physics.
So this is a particular example of how top-down and bottom-up causation conspire to produce the world that we've got. We have bottom-up causation that permits a vast number of varieties at all sorts of levels. And then downward selective processes determine which of those possibilities actually exist.
For example, chemistry permits something like 10 to the 200th power of different proteins--a rough estimate. Somebody could probably give me a better number on that but I just want to give you a ballpark figure of what a vast number of possibilities there are for large complex molecules. But not all of those exist.
In order to explain why the certain ones that do exist in the world exist, we have to know how those large complicated molecules fit into biological organisms and biological processes.
So, in sum, life brings new sorts of causal interactions into the world. These are consistent with physics but they're not predictable by physics.
Consider for a silly example the difference between shining a flashlight beam on a pound of hamburger versus shining a flashlight beam on a live animal. The hamburger is not affected appreciably by the light striking it but the animal might jump up and run. The physics of the light beam is the same in both cases but the effect is vastly different.
So the non-reductionist says when you have these more complex structures it's not that there are new causal forces--psychic forces or vital forces or whatever. Instead, the causal forces of physics will enter into vastly more complex interactions. The laws of physics don't predict rabbits but rabbits and their behavior do not violate the laws of physics.