Sorry, I thought the bloggers on this forum would be familiar with these two experiments. You can learn about the Kishony Mega-Plate experiment here:Spatiotemporal microbial evolution on antibiotic landscapes - PMC
and you can watch a video of the experiment here:https://www.youtube.com/watch?v=Irnc6w_Gsas
Essentially, what these experimenters do is make a large petri dish. And on this petri dish, they put different levels of an antibiotic in bands on the dish. On the left and right edges of the petri dish, no antibiotic. As you move toward the middle of the petri dish, the antibiotic concentration is increased in each band. Bacteria are then inoculated on the petri dish which initially grows only in the drug-free region. But as colonies grow, variants appear which can grow in the next higher drug concentration region. In this experiment, the antibiotic is the selection pressure.
The Lenski Long Term evolution experiment is performed in a different manner. You can read about how this experiment performed here:E. coli long-term evolution experiment - Wikipedia
There many other publications based on this experiment but this link gives the essential principles. Essentially, what this experiment consists of are vials which contain 10ml of glucose growth solution for bacteria. Each day 5e6 bacteria are introduced into the solution which has sufficient nutrients to support the growth of about 5e8 bacteria (about 6-7 doublings (generations) per day). By the end of the day, the glucose is used up. 1% of the bacteria are then taken from this solution and introduced into a fresh 10ml solution for the next day's growth. Every 500 generations, the bacteria are saved, their genetic sequence determined, mutations identified. In this experiment, the selection pressure is starvation (nutrient limitation). This experiment has been carried out continuously since 1988 until it was paused recently because of the Covid episode.
If you or any members of this forum know how to correctly describe the physics and mathematics of either of these experiments or know of links that do this, please provide that information.