I'm no expert but there's not really a definitive transition from one era to the next. If you want to trace back to the modern equivalent of what we know as standup today, you'll need to research vaudeville. Performers such as Charley Chase and Frank Fay are considered among the first to perform in tune with what we could call standup, albeit still not directly comparable to today. Some historians argue Charley Chase was the first you could call a standup comedian, others argue it was Frank Fay.

At the end of the day I suppose it depends on the context of your research. If we're talking specifically about modern standup, I'd say vaudeville from the 1809s opened that door. Vaudeville originated in France. But what led to vaudeville? Vaudeville evolved from earlier forms of song and satire from the preceding centuries.

So, basically the history of modern comedy is a big can of worms, and you can go back as far as you want to try and find correlations, but the evolution of comedy isn't definite in the way I believe you're trying to discern.