"Given the pervasive pattern of 'sudden appearance' and 'stasis' in the fossil record, does science need a Theory of Stasis or Theory of Conservation to better explain how nature actually functions. Explain.
Response 1 -
Punctuated equilibrium is the very "theory" you are looking for. However, even with that, the fossils cannot tell us anything about a mechanism. So all the fossil record can tell us is that organisms that no longer exist existed at one time. The fossil record doesn't say anything about how those organisms came to be the way they were. Science needs to focus on the extant in order to explain the extinct. We need to determine if there is a limit to evolutionary processes, as the evidence and observations seem to suggest.
And in my honest opinion the mere existence of a fossil record is evidence for Intelligent Design for the mere fact there isn't any other viable explanation for the existence of the organisms that were fossilized. Even given starting populations of prokaryotes and/ or archaea, there isn't a known non-telic mechanism capable of producing eukaryotes, let alone metazoans.