Thank you for your response! Given your advice I've been building and running models for the data separately for each study period as well as combined together to compare AIC. In each of my model sets I have also included covariates such as Region.Label (my transect names, 17 total), vegetation type (factor), shrub cover, herb cover, and moon illumination (all continuous), as well as study.period (factor) for my combined data. I selected models using a stepwise process where I chose the univariate model with the lowest AIC and continued to add covariates until the AIC no longer decreased (I also checked these models against the models with no covariates).
For my Pre study period data the top model for the detection function was the hazard rate key function with Region.Label, moon, herb cover, and shrub cover included (AIC= 9949.484).
In my Post study period the top model for detection function was the half-normal key function with only Region.Label included as a covariate (AIC = 3467.127).
In the combined data the top model was the hazard rate key function with all covariates included (AIC = 13429.586)
Since the sum of AIC for the models where study periods are separate (9949.484 + 3467.127 = 13416.61) is less than the AIC of the combined data, then I should keep the datasets separate, correct? Looking at options for comparing density estimates of the two study periods with different detection functions, would a t-test be my best option? I reviewed the two-stage models in the Distance Sampling Methods and Applications book, but these models require only 1 detection function if I am understanding them correctly.
Thank you again for your assistance!