Novel Tools for Analyzing Proportional Size Distribution Index Data

Abstract

Proportional size distribution (PSD) indices are convenient measures for numerically summarizing size structure of fish populations. Several novel methods for analyzing PSD index data were examined as a means for potentially improving inferences of size structure: generalized linear mixed modeling, calculation of location quotients, and simultaneous construction of 100(1 − α)% confidence intervals for PSD indices through multinomial modeling. The methods are demonstrated using simulated and previously published PSD index data. Generalized linear mixed modeling was used to (1) conduct a model selection analysis of PSD index data relative to a change in harvest regulation for walleyes Sander vitreus, (2) partition the variance of PSD index data among spatial, temporal, and environmental attributes, and (3) nonlinearly relate PSD data to adult density for largemouth bass Micropterus salmoides. The location quotient, which is an index for describing relative concentration of proportional data, was used to describe spatial and temporal localization of largemouth bass and walleye PSD index data. Finally, a modified method of constructing simultaneous 100(1 − α)% confidence intervals for multinomial proportions was used to produce 95% confidence intervals for traditional and incremental PSD indices based on length frequency data from muskellunge Esox masquinongy. The approaches described herein can assist fishery biologists in size structure assessments of fish populations and ultimately aid in cost‐effective fisheries management.