What is the best way to select a model for estimating asymptotic richness using rrssoptim?

I want to estimate the asymptotic richness derived from the relationship
between the number of sampling survey and the resulting number of fish
species. I used the function rrssoptim to fit my data to the asymtoptic
models (weibull, monod, logistic, lomolino, negexpo). I am interested in
the asymptotic richness. According to AiCc, the best model is the weibull
(-38.48772), but the c (asymptote) was not significant and its CI95% band
was very wide! On the other hand, the asymptote of models negexpo and monod
were significant and the CI band was substantially narrower. My question
is: should I choose the model with lower CI for the c or should I choose
that with lowest AIC?

Riguel Feltrin Contente