Ecological Archives M085005A3
John R. Morrongiello and Ronald E. Thresher. 2015. A statistical framework to explore ontogenetic growth variation among individuals and populations: a marine fish example. Ecological Monographs 85:93–115. http://dx.doi.org/10.1890/132355.1
Appendix C. Supplementary methods and results: Calculation of relative abundance indices using fisheryderived CPUE estimates.
Commercial trawl fishery catch and effort data were used as an index of relative Abundance for all zones except NC where these data were not available and published statewide mean CPUE estimates were used instead (Rowling et al. 2010). Log book data spanned the period 1986–2010 and were filtered to remove invalid records following the rules of Knuckey et al. (2010) and Haddon (2011); in particular: only positive trawl catches were analysed; Danish seine data were excluded due to different selection biases; a minimum of five different vessels fishing per zone per year was required (to ensure commercial confidentiality); the recorded average trawl depth was sensible (between 10–410 m); and the recorded effort was sensible (between 0.5–10 hours).
We modeled standardized annual catch rates (CPUE kg.h^{1}) for each of the six zones, conditioned on positive catches, using a normal GLM on natural log transformed CPUE (Haddon 2011):
where Ln(CPUEi) is the catch rate for the ith trawl, X_{ij}are the values of explanatory variables j for the ith trawl, β_{j} are coefficients for N factors to be estimated and α is the intercept. Explanatory factors included Year, Vessel, Depth (20m bin categories) and Month. A series of increasingly complex models (Table C1) were fit to each zone's catch data using the biglm package (due to large data sets) in R and optimal models were selected using Akakie's Information Criterion (AIC). Abundance estimates are zonespecific rather than global as the latter could not easily be calculated across zones due to large differences in fishery history, fishing intensity and apparent regional selectivity.
Overall year effects were backtransformed from GLM Year coefficients with a biascorrection for lognormality using:
where γ_{t }is the Year coefficient for year t and σ_{t} is its standard error. Year effects for each zone (CPUE_{t}) were divided by their averages to form zonedependent time series of yearly relative Abundance.
There were significant declines in the CPUEderived Abundance index for CBS and WBS (0.082 and 0.055 kg.h.yr^{1} respectively; linear regressions, n = 25 years; 0.509 ≤ R² ≤ 0.816; both P ≤ 0.001), an increase for ETAS (0.025 kg.h.yr^{1}; linear regression, n = 25 years, R² = 0.297, P = 0.004), and no significant trend for NSW, EBS, WTAS (range: 0.011–0.010 kg.h.yr^{1}; linear regression, n = 11–25 years; 0.018 ≤ R²≤ 0.139; P ≥ 0.067) or NC (0.4262 kg.day.yr^{ 1}; linear regression, n = 27 years, R² = 0.003, P = 0.797).
Table C1. Statistical model structures used to estimate tiger flathead annual indices of abundance and the corresponding zones to which they were applied.
model 
factors 
zone 
1 
Year 

2 
Year + Vessel 

3 
Year + Vessel + Depth 

4 
Year + Vessel + Month 

5 
Year + Vessel + Depth + Month 
CBS, WTAS 
6 
Year + Vessel + Depth:Month 
NSW, EBS, ETAS, WBS 
Literature cited
Haddon, M. 2011. Catch rate standardization 2010 (Data from 1986 to 2009). Pages 44–179 in G. N. Tuck, editor. Stock Assessment for the Southern and Eastern Scalefish and Shark Fishery 2010 Part 2. Australian Fisheries Management Authority and CSIRO Marine and Atmospheric Sciences, Hobart.
Knuckey, I., J. Day, M. Zhu, M. Koopman, N. Klaer, K. Ridgway, and G. Tuck. 2010. The influence of environmental factors on recruitment and availability of fish stocks in southeast Australia. Final Report to Fisheries Research and Development Corporation  Project 2005/006. Fishwell Consulting and CSIRO.
Rowling, K., A. Hegarty, and M. Ives, editors. 2010. Status of Fisheries Resources in NSW 2008/09. Industry and Investment NSW, Cronulla.