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

Abstract

We examined annual changes in relative abundance of Lake Michigan fishes using linear models with correlated errors in space and time. Abundance of bloater (Coregonus hoyi), deepwater sculpin (Myoxocephalus thompsoni), slimy sculpin (Cottus cognatus), alewife (Alosa pseudoharengus), and rainbow smelt (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 describing abundance included fixed effects of year, port, depth, and interaction 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 and slimy sculpin abundances depended on port. Cubic trends in the abundance of bloater and quadratic trends in deepwater sculpin and rainbow smelt abundances were similar among ports, permitting lakewide inferences for these species. Mean bloater abundance was low throughout the 1970s, increased during the 1980s, and reached high levels by 1990. Mean abundances of deepwater sculpin and rainbow smelt increased from 1973 to the mid-1980s and declined thereafter. The linear model with correlated errors can be readily applied to repeated-measures data from other fixed-station fishery surveys and is appropriate for data exhibiting spatial and temporal autocorrelations.