20 - Fish Farming

Summary

Aims of the project

You are given data on the current distribution in size and age of a particular species of fish on some fishing banks. You are invited to help establish a sensible fishing strategy (size of net mesh and frequency of harvest) so that the stocks of fish can be maintained at a viable level. As part of this, you are required to develop a model for the growth rate of fish.

Mathematical ideas used

Leslie matrices (Chapter 2) are used to describe the evolution of the age distribution and differential equations (Chapter 7) to describe the growth of the fish. Least squares fitting (Chapter 5) is a further optional technique.

MATLAB techniques used

Much of the above analysis can be accomplished with the M-files listed below. You may have to modify some of these in the course of your study. In each case typing help will give information on the purpose and usage. You will also make use of standard MATLAB commands such as eig (eigenvalues), plot and bar (bar graphs).

fishy.m – loads fish data

leslie.m – example of population evolution (see Chapt 2)

lmfish.m – basic Leslie matrix for fish population

fodesol.m – graphical and numerical solution of first order ODE

mparft.m – multi-parameters least squares fit

mparst4.m – example set up for the above

resid4.m – residuals function for the above

fishdat.m – uses fishy.m to load data for above fit

Preliminary look at the problem

Use the command fishy to load some data on the fish. Typing help fishy will show you what is there.