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Publication Date



UM campus only

Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PHD)


Marine Biology and Fisheries (Marine)

Date of Defense


First Committee Member

Jerald S. Ault

Second Committee Member

Elizabeth A. Babcock

Third Committee Member

Donald L. DeAngelis

Fourth Committee Member

Steven G. Smith

Fifth Committee Member

James A. Bohnsack


Federal mandate requires that all US fish stocks be exploited at or below sustainable rates. To meet this requirement in data-limited fisheries, length-based models have been developed to estimate total mortality rate using only length frequency samples and a lifetime growth model. The goal of this dissertation was to develop methodologies to better understand and apply length-based assessment models and improve the accuracy of their estimates. This goal was achieved through objectives to: (1) quantify the analytical biases in existing length-based models due to non-equilibrium stock structure and a truncated upper selection bound; (2) derive a new model to ameliorate these biases; (3) quantify the new model’s sensitivity to uncertainty in input parameters, gear selectivity, and variability in length-at-age; and, (4) Validate the results of length-based models through simulation and application to real data. Understanding analytical model biases identified specific parameter ratios that determined expected model results. Positive bias was observed when estimation models did not incorporate an upper selection bound, no compelling reason was found to not apply truncated models in the future. The choice between assuming equilibrium average length or incorporating non-equilibrium transition remains situation specific. For short lived species <15 years the simplicity of an equilibrium model will largely outweigh any potential lag in mortality estimates while for long lived species>25 years a non-equilibrium model will likely be the optimal choice if any change in mortality rate has occurred. Application of the non-equilibrium model requires further research as the current stanza based approach performed poorly in the most recent sample years and has no means of estimating a gradual change in mortality rate. Furthermore, the use of AIC to choose the number of sample bounds without accounting for process error frequently overestimated the predicted number of changes in mortality rate and produced unrealistic estimates in the final years of observed average length. Despite the differences found between models the collection of accurate data remains the primary concern in the application of any length-based model. Defining an accurate lifetime growth model and correctly identifying sample selection bounds remain the most important factors in producing robust and reliable mortality estimates. High exploitation of many stocks has overshadowed both the differences between estimation models and the importance of accurate natural mortality rate estimates in past assessments. Future management action to achieve sustainable exploitation will make unbiased estimation models and accurate natural mortality estimates increasingly critical to identifying sustainable exploitation rates. The observed mortality estimate sensitivity to selection bound accuracy both validated the need for the new truncated model developed in this dissertation and the need for careful consideration when estimating the bounds applied in the model. If used correctly with accurate and precise input data, the new length-based mortality estimator presented can provide an accurate, robust, and flexible method for fisheries stock assessment that is a significant improvement over the previous models.


Length-Based; Mortality Rate; Data-Limited