A little history on where WR came from. Back in the mid 1970s, two biologists by the names of R. O. Andersen and G. J. Wege published an article covering their work on LMB growth and a new statistical method that they had developed to track health of a fishery. That publication can be found here:
"Wege, G. J., and R. O. Anderson. 1978. Relative Weight (Wr): A New Index of Condition for Largemouth Bass. Pages 79-91 in G. D. Novinger and J. G. Dillard, editors. New Approaches to the Management of Small Impoundments. American Fisheries Society, North Central Division, Special Publication 5, Bethesda, Maryland."
Because this work so was well accepted for LMB, it was extended by other researchers and now Standard Weight (WS) expressions have been developed for several other species of fish.
Now, how did Anderson and Wege come up with their Standard Weight expression and how has the scientific community continued to develop these equations?
Anderson and Wege started with a simple assumed equation for fish weight: Weight = Fish Density x Length3. Since Density has units of weight divided by length3, Density times Length cubed give units of weight.
Now, Anderson and Wege sampled 18 ponds in the midwest over a period of time gathering length and weight data from hundreds, maybe thousands of LMB. They measured each fish's weight and length and sorted the data so they had data only from the upper 75th percentile of their sample lot. They then did a regression analysis on this data allowing their ficticious density value and length exponent to vary giving them a best-fit equation (line) through that data set. That best-fit becomes their Standard Weight expression (equation) for that fish with respect to its length. Their equation ended up being:
Log10(WS) = -5.316 + 3.191Log10(Total Length, mm)
In 1991 Henson took another look at the largemouth bass data and in his masters thesis provided the equation now recognized as the more accurate expression which is:
Log10 (WS) = -5.528 + 3.273Log10 (Total Length, mm)
Anderson and Wege then took their WS and defined Relative Weight (WR) equal to Actual Weight (Wact) divided by WS x 100%. When WR is equal to 100%, Wact is equal to WS and, therefore, that fish is deemed healthy.
But the overall fisheries biology crowd has looked at this a little differently. Because the calculation of WS uses only the 75th percentile of fish from a sample, pond managers generally say a fish is healthy when its WR is greater than 90%.
You can't discuss WR without talking about WS. It's really the Standard Weight chart or equation you're asking about. I'd highly suggest getting the article cited above to read the entire way they collected their samples and how they manipulated that data to get to the Standard Weight equation.
So, that's the history of WR. I hope this answered your initial question.
Terry
