Structural equation models and small sample bias reduction with application to fishery data

An overview of structural equation models is presented along with an application to fishery data involving estimation and significance testing of the density dependent component of recruitment in 6 cod populations. Estimates and standard errors are based on normal theory and large sample properties of maximum likelihood estimates. The data sets analyzed involve small sample sizes so a sensitivity analysis of the effect (in terms of bias) of small sample sizes and other deviations in model assumptions is conducted. The analysis indicates that sample size is the most influential factor considered on the bias of parameter estimates. The reliability of indicator variables is also important. – Two methods of reducing the bias in estimates are considered, they are the jackknife and a method based on a Taylor’s series expansion of the log likelihood function. The bias reduced estimators are investigated by simulating several confirmatory factor models. Neither the Jackknife nor the Taylor’s series biased reduced estimator works sufficiently well to warrant their application in practice. Both estimators consistently reduce bias in the maximum likelihood estimates only when little bias exists. A difficulty realized in the investigation is that the expectations of some estimators are unbounded and this makes bias reduction difficult

Statistical inference about the relative efficiency of a new survey protocol, based on paired-tow survey calibration data

Paired-tow calibration studies provide information on changes in survey catchability that may occur because of some necessary change in protocols (e.g., change in vessel or vessel gear) in a fish stock survey. This information is important to ensure the continuity of annual time-series of survey indices of stock size that provide the basis for fish stock assessments. There are several statistical models used to analyze the paired-catch data from calibration studies. Our main contributions are results from simulation experiments designed to measure the accuracy of statistical inferences derived from some of these models. Our results show that a model commonly used to analyze calibration data can provide unreliable statistical results when there is between-tow spatial variation in the stock densities at each paired-tow site. However, a generalized linear mixed-effects model gave very reliable results over a wide range of spatial variations in densities and we recommend it for the analysis of paired-tow survey calibration data. This conclusion also applies if there is between-tow variation in catchability

A spatiotemporal model for snow crab (Chionoecetes opilio) stock size in the southern Gulf of St. Lawrence

We develop a high resolution spatio-temporal model of stock size and harvest rates for snow crab (Chionoecetes opilio) in the Southern Gulf of St. Lawrence, which supports an economically important fishery off the east coast of Canada. It is a spatial and weekly model during 1997-2014 that utilizes within-season depletion based on catch per unit of effort (CPUE; kg per pot), and also biomass values from a survey designed specifically for this stock. The model is formulated in a state-space framework. The main contribution of the model is to provide a better understanding of fishery-dependent factors that affect CPUE. There is strong evidence of density-dependence in the relationship with CPUE and stock biomass, in addition to a general increase in CPUE catchability over time that may be related to changes in gear soak time, and spatial variation in catchability. We also find that a natural mortality rate of 0.4 provides a better fit to survey results. Model results suggest that there is no evidence of effort saturation in the fishery.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

A state-space stock assessment model for northern cod, including under-reported catches and variable natural mortality rates

A state-space assessment model for the northern cod (Gadus morhua) stock off southern Labrador and eastern Newfoundland is developed here. The model utilizes information from offshore trawl surveys, inshore acoustic surveys, fishery catch age-compositions, partial fishery landings, and tagging. This is done using an approach that avoids the use of subjective data-weighting. Estimates of fishing mortality rates (F) are usually conditional on assumptions about natural mortality rates (M) in stock assessment models. However, by integrating much of the information on northern cod it is possible to estimate F and M separately. It is also possible to estimate a change in the offshore survey catchability by including inshore acoustic biomass estimates. The proposed model also accounts for biased total catch statistics which is common problem in stock assessments. The main goal of the model is to provide realistic projections of the impacts of various levels of future fishery catches on the recovery of this stock. The projections incorporate uncertainty about M and catch. This is vital information for successful future fisheries. The model has been developed for the specific data sources available for northern cod but it could be adapted to other stocks with similar data sources.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

Spatiotemporal variations in juvenile mortality and cohort strength of Atlantic cod (Gadus morhua) off Newfoundland and Labrador

Juvenile mortality is an important factor affecting the spatiotemporal dynamics of fish recruitment, but estimation of the spatiotemporal variations in juvenile mortality rates remains challenging. We developed a state-space metapopulation dynamics model to simultaneously estimate spatiotemporal variations in juvenile mortality rates and cohort strength and applied this general modelling framework to data from multiple surveys for juvenile (ages 2–5) Atlantic cod (Gadus morhua) stocks off Newfoundland and Labrador (NL). We found large-scale synchronized dynamics of decreasing juvenile mortality rates and increasing cohort strength from offshore surveys off eastern and southeastern NL, suggesting improving reproduction and survival rates for juvenile cod. No synchronized patterns of juvenile mortality rates and cohort strength were detected for cod stocks off southern and western NL, indicating more complex cod population spatial structures in those areas. Our study demonstrates the potential of juvenile mortality to cause temporally variable and spatially synchronized dynamics of fish recruitment, and the spatial patterns of juvenile mortality and cohort strength indicate some potential mismatch between cod population structure and current management units off NL.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

Estimation of growth parameters based on length-stratified age samples

Response-selective stratified sampling (RSSS) has been well studied in the statistical literature; however, the application of the resulting statistical theories and methods to a specific case of RSSS in fisheries studies, namely length-stratified age sampling (LSAS), is inadequate. We review nine estimation approaches for RSSS found in the statistical and fisheries science literature in terms of three sampling components: the first phase length composition sample, the second phase age composition sample, and the sampling scheme. We compare the performance in terms of RRMSE (relative root mean squared error) for von Bertalanffy (vonB) growth model parameter estimation using an extensive simulation study. We further demonstrate methods by applying the two best-performing and the most popular methods to estimate the vonB model parameters for American plaice (Hippoglossoides platessoides) in NAFO Divisions 3LNO. Our simulations demonstrated that mis-specifying one or more of the three sampling components increases the RRMSEs, and this effect is magnified when the age distribution is incorrectly specified. The optimal approach for data based on LSAS is the empirical proportion approach, and we recommend this method for growth parameter estimation based on LSAS data.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

A state-space spatial survey-based stock assessment (SSURBA) model to inform spatial variation in relative stock trends

An age-structured, spatial survey-based assessment model (SSURBA) is developed and applied to the Grand Banks stock (NAFO Divisions 3LNO) of American plaice (Hippoglossoides platessoides) in Newfoundland and Labrador. The state-space model is fit to annual spatial (i.e., three divisions) stock size-at-age research vessel (RV) survey indices that are assumed to be proportional to abundance. We model index catchability (q) as a logistic function of fish length, which varies with age, cohort, and the time of the survey; therefore, the model facilitates the estimation of q values that change spatially and temporally following changes in fish growth and survey gears. The SSURBA model produces division-level estimates of fishing mortality rates (F), stock productivity, and stock size relative to the logistic catchability assumption with q = 1 for fully selected ages. The spatial model allows us to include additional survey information compared with the space-aggregated assessment model (all of 3LNO) that is currently used to assess stock status. The model can provide estimates of relative catch, which we compare with reported catch trends to partially validate the model.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author