A graphical approach to assessing relative weight using multiple standards

Different fish populations of a given species naturally enough differ in their length-weight relationships. I will illustrate that this phenomenon (the very existence of which is at the heart of standard weight as a condition index) implies (1) the need for multiple standards (I propose all using all three quartiles) in order to make consistent interpretations of relative weight across length classes, and (2) the need to consider using curved (e.g. quadratic) Ws equations. I will demonstrate these two points graphically, and illustrate a proposed graphical approach to use of a triplet of Ws equations. The approach will use the median Ws equation as a visual baseline, and employ lines representing all three quartiles plotted against length. Then, for a population of management concern, the mean relative weight of fish at a given length can be plotted to see where if falls in the distribution of mean weights at that length, rather than only being able to say whether it is above or below some standard.