In Fig2B and Fig2C, they "erase" the internal states, and ask computer algorithms to reconstruct them. What are the researchers trying to test here?

If you're curious:

In Phylogenies101, we consider all transitions equally likely (eg, black-to-white is as likely as white-to-black).

Mk2 is an algorithm that allows differential transitions (eg, black-to-white is more likely than white-to-black).

BiSSE is an algorithm that allows differential transitions, and also allows character state to influence the rate of speciation and extinction (so it's a really complicated model!).