Cambrian not so fast that we can see new forms evolving. But before that there must have been a great flowering of diversity, coming perhaps from the first multicelled animals. This could have arisen in two ways 1. So any old strategy would probably work. We might picture the new, multicellular organisms proliferating quickly, then the rate of change slowing as the less efficient forms came into competition with others for the first time.
Competition provides the regulator.
The drawback to this theory was that the barrel has been nearly emptied on other occasions since then, by great climatic changes for instance. We know about these, we know what expanded to fill the nearly empty earth - and it wasn't a new set of phyla. Perhaps the lack of new phyla after the initial burst was due to genetic ageing or genetic or physiological constraint. Perhaps our ideas about classification are wrong. One explanation is that the phyla that exist outside the Burgess shale are in fact part of a continuum, and those that exist in the shales form the missing parts of this continuum, the intermediate animals that were less successful and didn't stay the course.