Modeling variation in mass-length relations and condition indices of lake trout and Chinook salmon in Lake Huron: a hierarchical Bayesian approach

Commonly used approaches to studying mass-length relations and condition indices often do not adequately address covariance between mass-length parameters, usually ignore heterogeneity in individual variance for body mass at a given length, and assume that length distributions of fish samples are similar across regions and years. We used body mass at selected lengths as condition indices based on statistical modeling and a hierarchical Bayesian approach to inferences, and our approach allowed us to avoid using restrictive assumptions. We estimated spatial and annual variation in mass-length relations, where the process errors in parameters are drawn from a multivariate distribution. We also estimated region-, year-, and size-group-specific variance for individual variation in mass at given lengths. We applied our approach to study mass-length relations of lake trout Salvelinus namaycush (1977-2005) and Chinook salmon Oncorhynchus tshamytscha (1983-2004) in U.S. waters of Lake Huron. We found that small lake trout were able to maintain their condition in response to declines in prey availability, whereas Chinook salmon of the same size could not. Similarly, large Chinook salmon exhibited a greater and more rapid decline in body condition than did lake trout of the same size. We also found that spatial differences in recent temporal trends in condition of large fish altered the ranks of the three lake trout management regions. Ignoring spatial heterogeneity led to a biased overall average mass-length relation for lake trout. The large temporal variation in mass-length parameters suggested that it was better not to assume isometric growth for a specific year, even though the overall average exponent for Chinook salmon was nearly 3.0. In our study, conventional application of Fulton's condition factor to a relatively narrow size range was able to capture qualitative long-term trends but missed some important short-term changes because of the additional variation of length-related bias and the limitation of sample sizes.