Bringing Mathematics to Life in Fisheries Modelling

Ian Montgomery* and Gail Hood

Institute of Marine Ecology
University of Sydney

Contact: monty@bio.usyd.edu.au

Background

Quantitative Training in Fisheries is a set of interactive, electronic modules created and used by the Quantitative Training Unit for Fisheries (QTUF) at the University of Sydney. The Unit was established in early 1995 by the Australian Fisheries Research and Development Corporation (FRDC) and the University's Institute of Marine Ecology.

The modules provide education in the quantitative methods used in the monitoring and management of exploited stocks of marine organisms. The modules are used in a variety of circumstances including self-instruction, presentation by class convenors, as a vehicle for exercises performed in classes and as electronic course notes provided for class participants.

The modules, developed in Macromedia Authorware 4, are provided in a single package on a hybrid CD-ROM which can be used on either Macintosh or Windows platforms. There are seven core modules, covering the following topics:

1 Simple Population Models
2 Parameter Estimation
3 Stock-recruitment Relationships
4 Growth of Individuals
5 Biomass-dynamic Models
6 Stratified Random Surveys
7 Standardised Indices of Abundance

The core modules are presented as a menu selection in a navigational module and there is also a tutorial module to explain the conventions used in the design of the graphical user interface.

The primary target of the modules is fisheries scientist and fisheries managers. They are also aimed at honours students and post-graduates who are interested in careers or research in this area.

Bringing Models to Life

Fisheries models help scientists monitor changes in fish stocks so that they can provide the necessary information to the managers who are responsible for policies for the sustainable use of these stocks. Many models exist to describe different aspects of fisheries. These vary in complexity, and some are conceptually difficult. This provides challenges for both education and communication.

Multimedia tools, such as Authorware, provide the opportunity to present these concepts not only visually but as real-time, interactive manifestations of these mathematical models. It has been our experience that Authorware can handle demanding algorithms on conventional computers with speed and precision.

The package contains many models but we will demonstrate a particularly interesting one which illustrates the power of the authoring program. The example is parameter estimation by a numerical search. Some statistical packages, such as Excel, use a numeric solver to do this but the process is invisible to the user. Here the problem is represented as a topographical surface in parameter space and the numerical search can be seen as the movement of a search object to find peaks or valleys in the surface. These locations represent the optimal values of the parameters being fitted.

We will show a segment used to teach the theory behind the method and then the application of the method to solving a stock assessment problem in fisheries. Both components are interactive and permit the user to control the simulation.