A Length-Based Population Model for Hard-to-Age Invertebrate Populations

A Length-Based Population Model for Hard-to-Age Invertebrate Populations

T.J. Quinn II, C.T. Turnbull, and C. Fu

A Length-Based Population Model for Hard-to-Age Invertebrate PopulationsThis is part of Fishery Stock Assessment Models
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Invertebrates such as shrimp and prawns are notoriously difficult to age, but much information about their length, growth, and harvest is routinely collected. We construct a length-based population model that utilizes and explains such harvest and survey information. The model contains population parameters for recruitment, growth, and mortality, and the data are used in conjunction with the model to estimate parameters. Our model is an extension of the model of Deriso and Parma (1988), which determines probability distributions of abundance and catch as a function of length. Our extension of their model is to "discretize" the length distribution, to allow more general selectivity and natural mortality representations, and to generalize the model for two sexes. These enhancements provide a more flexible approach to length-based modeling, although the solutions are recursion equations that are more difficult to compute. We illustrate application of the model to the Torres Strait prawn (Metapenaeus sp.) fishery in Australia. For this invertebrate population, dynamics occur rapidly over the course of a year, so the time step for the data and the model is monthly. Relative trends in estimated recruitment and abundance are similar among model configurations, which depend on the model parameters to be estimated, but absolute estimates differ substantially. While the model is able to fit the harvest and length frequency data, there is not enough information to jointly estimate all model parameters, especially catchability and natural mortality. However, estimates of growth and selectivity parameters are robust and differ from those obtained from tagging data collected from a different time period. Further resolution of model parameters should be possible with additional research survey information.

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