Using linear models with correlated errors to analyze changes in abundanceof Lake Michigan fishes: 1973-1992

We examined annual changes in relative abundance of Lake Michigan fishes us ing linear models with correlated errors in space and time. Abundance of bl oater (Coregonus hoyi), deepwater sculpin (Myoxocephalus thompsoni), slimy sculpin (Cottus cognatus), alewife (Alosa pseudoharengus), and rainbow smel t (Osmerus mordax) was monitored with bottom trawls at 10 discrete depths ( between 18 and 110 m) off eight fixed ports from 1973 to 1992. The model de scribing abundance included fixed effects of year, port, depth, and interac tion terms as well as quadratic and cubic effects of year and depth because changes in abundance were not strictly linear. Observed temporal trends in abundance varied with species and depth. Additionally, trends in alewife a nd slimy sculpin abundances depended on port. Cubic trends in the abundance of bloater and quadratic trends in deepwater sculpin and rainbow smelt abu ndances were similar among ports, permitting lakewide inferences for these species. Mean bloater abundance was low throughout the 1970s, increased dur ing the 1980s, and reached high levels by 1990. Mean abundances of deepwate r sculpin and rainbow smelt increased from 1973 to the mid-1980s and declin ed thereafter. The linear model with correlated errors can be readily appli ed to repeated-measures data from other fixed-station fishery surveys and i s appropriate for data exhibiting spatial and temporal autocorrelations.