I start the game at a rock solid 60 FPS, and usually stay there for the first 50 cycles and standard base expansions. The farther I go though, the worse it gets. I am currently on cycle 300 of this save with 20 dupes, and my FPS has dropped to less than 10, 100% process bound. Creatures, dupes, etc also experiencing glitchy behavior and "hanging" often with stuck animations or lack of movement orders issued. Restarting the game gets the FPS back up around 18-20, but it quickly drops again.
Things of note - I have around 300 shine bugs, but in other saves where I kept few or zero animals, the performance degradation was the same. Same goes for dupe count. The slow down does appear to correlate to the base size directly, though I am not sure it correlates to amount of machinery running. I can use debug mode to remove fog of war so that the whole map is functioning at once, and there is zero impact on game performance.
PC spec - AMD 2700x and 980ti, 16 gigs ram. Neither CPU nor GPU are anywhere near heavy load when experiencing this behavior.
Play the game for a long time.