Your code looks appropriate, so the problem lies in convergence (or lack thereof). I would start simple and build up.   Try a simple regression (i.e., one predictor) and drop the RANDOM statement.  Try Laplace rather than quad. Try the tips in this paper by Kiernan, Tao and Gibbs http://tinyurl.com/puka8l7 ; note in particular the recommendation for NRRIDG or NEWRAP methods for the Poisson distribution.   Hopefully some combination of tweaked options will give convergence. Then you can add on: random streams, additional predictors, etc.   Other comments: "cf" is a count, not a rate. If the sampling effort is the same in all streams in all years, then analysis of the count is fine. But if effort (or some other metric that turns your count into a rate) differs, then you should ponder including an offset. Does each predictor variable have a linear relationship with log(cf)? There could be an optimal range, and something like a quadratic model might work well enough. Your current code would allow intercepts to vary among streams (aka, random intercepts). It would be nice to consider allowing slopes to vary among streams (aka, random slopes) but with only 13 years (i.e., 13 observations for each stream), there's only enough information for a single parameter estimate (so, only one predictor, entered linearly). Nice perhaps, but not too feasible. Check for overdispersion. Check for multicollinearity if you can build up to a multiple regression. At some point in time, consider autocorrelation.   Good luck!   ... View more