time alone: Z = 1 + sin terms + cos terms 

 multiplicative: Z = I + M + M(sin terms + cos terms) 

 multiplicative (no intercept) : Z = M + M(sln terms + cos terms) 



where: I = intercept 



Z = mean of log-transformed catch, count or density 

 M = multiplier, flow (for impingement data) 



or season (for seasonally occurring taxa) . 



The best model, by definition, had 1) maximum R"^ and 2) all 

 parameter estimates significantly different from 0. The residuals were 

 then analyzed for autocorrelation if the data were equally spaced in 

 time. If autocorrelation was evident, the order of the autoregressive 

 process was determined. If the data were not equally spaced in time, 

 the best harmonic regression model was used to provide values for the 

 missing months or weeks in the following way. The variance ( o ^) of the 

 residuals from the best regression model was estimated and assumed to 

 come from a N(0,a'^) distribution. A pseudoresidual, R*, was generated 

 using a random number, n » from the standard normal distribution, and the 

 estimated variance ( a^): 



R* = (n) * (6 2) 



This was added to the predicted value for a week or month unless season 

 for that time period had previously been determined to be 0. In that 

 event, a replaced the missing value. The parameters associated with 

 the deterministic (harmonic) and autoregressive processes were estimated 

 and forecasts for the 1982-1983 sampling period were generated by PROC 

 ARIMA (SAS 1982). 



The best regression models determined from 1976-1982 data were 

 considered a description of average abundance fluctuations over those 

 years. The models were used to generate a forecast for 1983. The 

 actual 1983 data were compared to the forecast through the use of upper 

 and lower 95% confidence intervals and percent error. Interpretations 

 were then made as to how well the model forecasted the 1983 data. 



