The term “gradual” can mean different things. For some writers, it means “very smooth”, but another meaning is “stepwise”. We can see this in e.g. the terms graduation, graduated cylinder, etc. – these are referring to discrete steps. Similarly “gradations”. Considering that the raw material of evolution is mutations, at some level, everyone should agree that evolution is fundamentally a stepwise process, not perfectly smooth. The interesting argument, then, is more about how big are the steps.
If one reads Darwin’s works carefully, you will often see this “stepwise” interpretation is the better one, even if the steps are small. And even “large/small” is a relative thing. E.g. long before the Origin of Species, Darwin discusses seeing an earthquake in Chile that lifted the coast a meter (or several meters, I forget). He then assembles evidence that this process has, “gradually”, raised up the Andes so they are thousands of meters high. Most people wouldn’t think of earthquakes as a “gradual” process, but from a deep-time perspective, they are.
Punk eek isnt really opposed to gradualism. It’s just Mayr’s allopatric speciation applied to the fossil record. It’s not about big changes. A lot of the time it takes an expert to tell the changes apart. Stasis is a real phenomenon and its relatively well understood. Things like population size, body size, and stabilizing selection can all contribute to it. I know some people will point to Prothero’s work on the La Brea tar pits and stabilizing selection and say this rules this out but he only looked at a timespan of 40ky. Among other difficulties. Also, the extent of stasis is also overblown as well. We should expect the pattern we see. If everything happened in a phyletic gradualistic way, life wouldve went extinct a long time ago