Final answer:
Species change gradually over time in the gradualism model, with sparser evidence for intermediate forms. Punctuated equilibrium involves rapid changes followed by long static periods, with less common but significant intermediate evidence supporting it.
Step-by-step explanation:
In the gradualism model, species change gradually over time. Evidence for intermediate changes in species' characteristics is sparser or less commonly found, potentially due to the gradual nature of the changes making each intermediate form not particularly distinct. In contrast, in the punctuated equilibrium model, changes can be rapid followed by periods without significant change. Evidence for intermediate changes in species' characteristics in the fossil record is also less common; however, when present, often reflects these rapid changes.
The gradual speciation model depicts incremental changes over vast periods, whereas the punctuated equilibrium model suggests that rapid changes occur due to a variety of factors including environmental shifts or isolation events, followed by long periods of stasis. Both models propose that speciation occurs as a form of branching, rather than in a straight line, and the fossil record supports both theories by showing periods of gradual change as well as instances of sudden, substantial shifts.