Discrete-time Marcov Chain and GOF for behavioral transitions

Good morning everyone,

I am currently assisting a colleague on analyzing data regarding transition
probabilities of dolphin behavior under two different scenarios. References
suggest we should be approaching this using a Markov chain. Other analyses
conducted were GOF tests (which I assume reference comparing experimental
observations to control observations as observed and expected respectively)
and a two tailed Z-test for proportions.

Unfortunately I am at a bit of a loss for how to go about this and trudging
through papers and R documents is yielding few results.

Does anyone have experience with analyzing DTMC that would be willing to
provide some guidance?

Thanks in advance,
Regards

Adam