Project number: 2003-041
Project Status:
Budget expenditure: $318,426.18
Principal Investigator: Norman G. Hall
Organisation: Murdoch University
Project start/end date: 28 Sep 2003 - 1 Sep 2008


Sound estimates of natural and fishing mortality form the basis of fishery stock assessment and modelling. Without these data, the extent to which the spawning biomass has been reduced or the effectiveness of management measures in sustaining wild fish stocks cannot be determined. These estimates of mortality are crucial if the commonly-used reference points for fishing mortality and biomass are to be used in managing fisheries. Considerable advances have been made in obtaining estimates of mortality when data on the age composition of the annual catch are available. However, when there are only data on the length composition of the catches, analyses become more complex and the algorithms are not as well defined. Although information is usually available within the biological and fishery data that allows estimation of total mortality, the information on natural mortality must usually be obtained from empirical models that relate natural mortality to characteristics of the life history for other fish species or by estimating the relationship between total mortality and fishing effort, thereby obtaining an estimate of natural mortality by subtraction. Furthermore, there is a need to understand how natural mortality varies with size. Although the study of mortality deserves to be a primary focus of fishery research, it is difficult and thus often set aside. For many of Australia’s finfish stocks, there is a need to develop length-based methods to estimate mortality, which can be used to monitor the stock status of the recreational fisheries, and to obtain improved estimates of natural mortality that can be used in assessing sustainability. The project falls within FRDC’s Natural Resources Sustainability Program and is intended to increase and apply knowledge of stock assessment methods by developing methods of estimating mortality using length composition data which, compared with age composition data, are relatively inexpensive to collect.


1. To develop methods for estimating natural, fishing and total mortality from length composition data and, in particular, to enable the following objectives to be achieved.
2. To estimate total mortality by applying Length Frequency Analysis (LFA) methods to length composition data.
3. To estimate total mortality by applying a length-based method of relative abundance analysis to length composition data from consecutive years.
4. To estimate natural mortality from the changes in length composition data that accompany a change in minimum legal length.
5. To estimate natural mortality using a length-based fishery model
6. To determine whether these length-based methods can be used to estimate a size-dependent (rather than constant) natural mortality.

Final report

ISBN: 978-0-86905-988-3
Author: Norm Hall
Final Report • 2017-09-29


The objectives of this project were to develop length-based approaches for estimation of natural, fishing and total mortality, and to explore the application of these methods to the data from selected fisheries. The methods that were developed were essentially length-based versions of age-based approaches that are typically applied for stock assessment when appropriate and when representative age samples are available from either research or catch sampling. 
The study explored several methods to estimate mortality from length samples.  The simpler of these approaches assume that, as fishing mortality increases, fewer fish will survive to reach larger sizes.  Accordingly, the size composition becomes increasingly truncated at the right when fishing mortality increases.  Length FrequencyAnalysis and length-based catch curve analysis assess the extent to which the shape of the right-hand tail of the size distribution is reduced, and taking growth into account, use this information to estimate total mortality. The problem becomes more complicated, however, when annual recruitment varies. Relative Abundance Analysis attempts to track peaks and troughs in the length compositions in successive years, thereby identifying strong and weak year classes. By taking year class strength into account, the decline in the right-hand tail of the length distribution can be assessed more reliably, thereby improving the accuracy of the estimate of total mortality. An increase in minimum legal size allows smaller fish that would previously have been caught to survive and grow to the new minimum size.  If there are adequate data and the change in minimum size is sufficiently great, the change in the length compositions before and after the change in minimum size can be used to estimate the natural mortality. Finally, by analyzing the combined set of time series of fishery data, length and age samples, and attempting to track year classes through the catch-per-unit-of-effort, age-composition and length-composition data in successive years, it is possible to obtain estimates of both natural and fishing mortality. The precision of the estimates is dependent of the information content of the data, however.  This last analysis was extended to assess whether, for Tailor, there was evidence of length-dependent natural mortality.
The methods and software developed in this project were applied to length data for the Western Yellowfin Bream in Shark Bay, Tarwhine, Breaksea Cod, Dhufish, Snapper from NSW, Mud Crabs, King George Whiting, and Tailor.  The data for King George Whiting and Mud Crabs were found to be inappropriate for analysis using the approaches developed in this study. Although catch curve and relative abundance analysis produced highly inconsistent estimates of mortality for Breaksea Cod, reasonable and realistic estimates of mortality were produced for the other species. For Tailor, it was found that the assumption of constant natural mortality  resulted in a better fit of the fishery model than that which was obtained by using the length-dependent natural mortality assumption.
The analyses that were undertaken in this study demonstrated that the length-based approaches, while less precise and reliable than age-based methods, had potential for use in stock assessment. This is particularly the case for recreational fisheries, for which length samples are likely to be more readily available than age samples.

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