I've been doing some mixed modelling and obtaining model predictions for the size of a population through time. Each of these predictions comes with a confidence interval calculated from the various components of the model. I would now like to present an average abundance and an associated confidence interval for the entire time span of the study. I can easily average the point estimates of daily abundance to achieve a mean population size through time, but it's not immediately obvious how to calculate the confidence interval.
Is it as easy as averaging the confidence intervals from my daily abundance estimates to achieve an "average" confidence interval, or is this bad form statistically?
Update: I'm using GAMs in the mgcv package by way of the dsm package in R. dsm is two part modelling that incorporates a detection function to model survey count data in a GAM. negative binomial response distribution, REML fitting, mix of smooths and parametric terms, double penalty approach to fitting the smooths. i'm not sure how much more information is relevant, but i can certainly provide more.
I'm thinking one way to do this that may be more statistically valid is to predict while omitting Julian day from the model, thereby getting an abundance estimate (and confidence intervals) that is essentially averaged over my entire survey period. This solves that problem, but what if I want an estimate that covers a narrower selection of dates (say, average abundance for a month or something). I'm unsure how I might do that with the predict function or otherwise.