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Evaluation of the Relative Weight ( W r ) Index, with New Applications to Walleye
Author(s) -
Murphy Brian R.,
Brown Michael L.,
Springer Timothy A.
Publication year - 1990
Publication title -
north american journal of fisheries management
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.587
H-Index - 72
eISSN - 1548-8675
pISSN - 0275-5947
DOI - 10.1577/1548-8675(1990)010<0085:eotrww>2.3.co;2
Subject(s) - percentile , weighting , mathematics , statistics , stizostedion , standard deviation , population , fish <actinopterygii> , linear regression , regression analysis , body weight , fishery , biology , physics , demography , sociology , acoustics , endocrinology
Relative weight ( W r ) is 100 × W / W s , W being the weight of an individual fish and W the “standard” weight of a fish of the same length. The widespread application of relative weight in fisheries management has been hindered by the slow development of standard weights at length for many important fish species. We found the conventional approach to W s development to be limited by data availability and improperly influenced by sample weighting. We designed and tested a method of W s development that addresses these shortcomings. Our method treats log 10 weight‐log 10 length regression equations for a series of a species' populations as the statistical population to be modeled. First, we predict mean fish weight in 1‐cm total length intervals for each population. Then we find the 75th percentile of the mean weights in each interval, and regress these on length to determine the parameters for the W s equation. Standard‐weight equations determined by our regression‐line‐percentile (RLP) technique were functionally equivalent to published equations for several species tested. We then used the RLP technique to develop W s equations for walleye Stizostedion vitreum based on 114 site‐specific weight‐length regressions for 42,487 fish from across North America. The metric equation is log 10 W s (g) = −5.453 + 3.180 log 10 total length (mm). The English‐unit equation is log 10 W s (lb) = −3.642 + 3.180 log 10 total length (in). There was no important influence of fish length on W r values calculated with these equations. Neither proportional nor relative stock densities of walleyes were correlated meaningfully with W r . Confidence interval width for mean W r in walleye populations is directly predictable from sample size because sample variance is independent of sample size. “Desirable” mean W r target values (100 ± 5) were achieved by approximately one quarter of the lakes in our sample. The RLP technique appears to be a viable approach to the development of W s relationships that should speed and improve the application of W r theory to important fish species.