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 tshawytscha (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 longterm trends but missed some important short-term changes because of the additional variation of lengthrelated bias and the limitation of sample sizes. Mass–length relations and condition indices constitute a basis for studying physiological condition of fish populations (LeCren 1951; Murphy et al. 1990; Anderson and Neumann 1996; Blackwell et al. 2000) and are also major components in fishery stock assessment (Dutil et al. 1999; Quinn and Deriso 1999; Kimmerer et al. 2005). Many studies have continued to develop condition indices or improve their use in animal ecology, particularly in fishes (Green 2001; Brenden et al. 2003; Lai and Helser 2004; Gerow et al. 2005; Froese 2006). The visibility of condition indices in fisheries literature is very high, and declines in fish condition are commonly of concern (Lambert and Dutil 1997; Cardinale and Arrhenius 2000; Madenjian et al. 2003; Marshall et al. 2004). Such concerns often have direct connections with the * Corresponding author: hej@michigan.gov Received January 12, 2007; accepted September 28, 2007 Published online April 28, 2008 801 Transactions of the American Fisheries Society 137:801–817, 2008 Copyright by the American Fisheries Society 2008 DOI: 10.1577/T07-012.1 [Article]