# Detection Functions in Distance package - R

Hi guys, this is more of a knowledge question than r code fix. I hope this is ok to post on here.
If any of you are familiar with detection functions and Buckland et al., Distance sampling methods, I would love your help on two main things:

(1) Choosing the right model
(2) Is an unequal binned detection function ok to use...?

(1) I have two simple detection functions on a population of marine mammals. One from just a null hazard rate, and the other from a half normal with cosine adjustment. The hazard rate model produces a lower AIC (which indicates the better model) however the detection probability starts at roughly 0.6 at zero distance and reduces rapidly whereas, the half normal detection probability is near to 1 at zero distance. Should you aim to have a model with a detection probability closer to 1 at zero? Once I add a covariate to the hazard rate detection model, for example seastate, the detection probability is then reduced even further, say 0.4 at 0 distance, but again, with a lower (better) AIC. What my question is, is a half normal model which has a higher AIC but a closer detection prob of 1 at zero distance, better than a model which has considerably lower AIC (better score) but then a probability detection of around 0.4 at zero distance? Abundance estimates vary greatly between the two (half normal is about 200 animals, whereas hazard rate with covariate is about 1,000).

(2) Secondly, I believe there is rounding to zero in the data, and so in R i have fit a detection function to unequal binned data (for example: distance bins of: 0, 50, 100, 300, 600, 900, 1200...etc). Doing this significantly reduces the AIC (by 100's). However, is this a good idea to use a detection function which has been "molded" to the data? When I call the ddf.gof function however, no Q-Q graph and resulting cramer von mises is plotted, but only chi-square. Even though the AIC is much lower, and the plot looks "nicer", the CV score is higher. I am unsure whether it is good practice to bring a model like this through to the DSM stage.