### 4.2.2 Assumptions

We assume that there is enough space and food for fishes; no descases, no predators. The main parameters defining the size of the population are the birth-rate and death-rate.

The Birth-rate

We shall make a series of assumptions, not all of which are realistic, but which will suffice to start the modelling process.

1. females lay eggs at a constant rate throughout their natural lives;
2. the breeding rate is constant for all fish;
3. the mortality rate is zero for all young fish;
4. the biith-rate depends on the population as a whole, not just on the females;
5. the gestation cycle can always be neglected.

These assumptions essentially give a birth-rate which is

1. independent of the age of the fish;
2. independent of the sex of the fish;
3. constant over a prolonged time.

The Death-rate

Again, we shall make a series of assumptions, ot all of which are realistic, but which will suffice to start the modelling process.

1. the natural life cycle is constant for all fish;
2. the death-rate due to predators is zero, we are assuming that there are no predators;
3. the death-rate due to disease is zero, we are assuming that the fish are always disease free;
4. the relative death-rates of males and females in the population is the same (see 1);

These assumptions essentially give a death-rate which is

1. independent of the age of the fish;
2. independent of the sex of the fish;
3. constant over a prolonged time.

We are now in a position to be able to build our simple model.