Question

In the absence of harvesting the populations of two fish species, tuna (predator) and mackerel (prey), are described by the Lotka-Volterra model.
A group of fishermen fish regularly and catch both types of fish at a rate proportional to the size of each fish population. The fishermen put in the same effort regardless of the amount they catch.
Derive and analyze a model that describes the two fish populations with fishing. Further information:
• Fishing has a negative impact on both fish populations.
• The rate of fishing is different for each fish population.
• Let T(t) denote the population of tuna.
• Let M(t) denote the population of Mackerel.

Answer 1

In the given graph M(t) denotes the population of mackarel and T(t) denotes the population of tuna fish. Here the prey and predator concept has been elucidated with respect to the Lotka- Volterra Model which shows the equation between the prey and the predator with respect to the population and time. Since fishing has a negative impact on the population of both the fishes i.e. Tuna and Mackerel.

Since the consumption of Tuna ia higher than Mackerel therefore the rate of fishing of Tuna would be considerably higher than mackerel.