Inspired by a Moran post:
What we see in nature now is that most species either move or go extinct when their environment changes. It seems that we should apply a principle of biological uniformitarianism analogous to geological uniformitarianism, which I think then puts stasis in a different light.
Doesn't natural selection act to maintain the original overal morphology in spite of the slow changes in genome? Most species would then appear in the fossil record as more or less the same, because they are more or less well adapted. Certainly natural selection cannot continue adaptation in search of a hypothetical perfect adaptation.
When a new adaptation begins to form, because of founder effects or the slower drift due to random change, wouldn't natural selection only then act as an agent of morphological change, perfecting the adaptation? Because of back breeding of temporarily separated populations or random environmental changes reversing trends toward adaptations and the physiological constraints on adaptation, this kind of speciation driven by natural selection would be relatively uncommon. But, because of the power of natural selection, the process on a geological scale would be relatively rapid. Due to the more or less random sampling in the fossil record, the transitional forms would mostly be lost (particularly in speciation events triggered by genetic drift in founder populations,) and the appearances by a new species as it spreads would appear to be geologically sudden.
Possibly, a different situation would be radiative adaptation into a relatively empty ecosystem. Because of the lack of competition the intensity of natural selection would be minimized, resulting in a wider range of morphologies. Wouldn't the more rapid emergence of variants that could serve as new adaptations then lead natural selection to propel speciation more rapidly and more often than in the ordinary course of events? Another way of phrasing it is to say that after a mass extinction, all the environments are new, because other species are a part of the environment. And adaptation to new environments changes natural selection from a stabilizing force to a speciating force.
Also, it seems to me that a relatively unpressured population that exhibits a wide range of individual traits would have increased incidence of incompatibility between widely variant members of the species, not just in gross morphology but in more subtle changes unreflected in the fossil record. In this situation, the accidental emergence of any kind of sexual marker or isolator would be selected for, leading to more offspring between more compatible variants. Sexual selection then would also be a force for speciation.
At any rate, it seems that gross morphological changes are far commoner after mass extinctions, leading to whole new orders of species.