### 4.1.2 Objective

As sources of examples for our modelling investigations we shall take a variety of species including fish, whales and edible animals , namely red deer. The harvesting of fish, whaling and the killing of deer (for venison) have been the subject of much heated debate in the United Kingdom between animal rights groups and those who earn their living from the killing and sale of the animal foodstuffs. It can be argued that populations should be harvested in such a way as to:

1. prevent the species from becoming extinct because of over-kill;
2. allow the livelihoods of those involved to continue, often in the time honoured traditions that they follow.

For our initial example we shall look at a population of fish, say cod, living in the North Sea. The general principals involved would apply equally well to any species of fish living in any sea. In modelling terms, the problem may be stated as follows:

Certain species of fish in the North Sea are known to be severely depleted, cod being a good example. The evidence for this was the fact that fishermen were having to travel further and further from their normal fishing grounds and were catching less and less fish. Over fishing can lead to the extinction of a species and as a result men will loose their livelihoods and there may be unknown and possible catastrophic effects on other species of marine life. Clearly, agreements concerning the amount of fish permitted to be caught are necessary, particularly in international waters. How do governments, or those in authority, decide on a global figure of fish which can be caught on a long term basis in order that the fish population is preserved rather than destroyed?

Modelling species can be difficult and we shall start by looking at a simplified model which will allow us to build up our assumptions and ideas gradually.