Predator-Prey Model 4 – Lotka-Volterra Equation (2)

Part 4. Lotka-Volterra Equation (2) – The Meaning of the Equation (1)

 

Before researching the equation, we have to suppose virtual situation because the Lotka-Volterra Equation only works at the limited environment to achieve best research results. At first, the food supply of the predators only rely on the prey’s population. Secondly, the prey can find enough amount of food for surviving in the area. Thirdly, the changing rate of the population is depend on the size. Fourthly, the local environment of the prey and predator does not change or affect by other external sources and their genetic adaptation is very low or not happened. Lastly, the only food of predators is the prey; it means that the predator does not have various palates.

The equation of prey is like this:

In this equation, the x means the number of the prey and y means the number of the predator. The value t symbolizes time, and dx/dt represents the growth rates of the populations over time. Other variables (such as , ,  and ) are the parameters that explains the relationship between the predator and the prey.

As you see above, the food supply is unlimited in the prey’s area, so the prey reproduce continuously; this growth directs αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. Also, if x or y is zero, the predation is not accepted. With these two terms the equation above can be interpreted as: the change in the prey’s numbers is given by its own growth minus the rate at which it is preyed upon.

Predator-Prey Model 1 – What are the Predator and Prey

Part 1. What are the Predator and Prey – The Basic Definition

 

Many modern people do not familiar the relationship between predators and preys; we are living in a capitalistic society, so the capital already substituted this relationship. However, predator-prey model – it also called prey-predator model, predator-prey interaction, and prey-predator interaction – is applied to not only the nature, but also human society (human relation).

Before researching this model, we have to define “predator” and “prey” thoroughly. A predator means the animal that kills and eats other animals such as a lion, an eagle and a tiger. A prey means the creature that is hunted and eaten by predators such as a gazelle, an insect and a fly. Also, the relationship between a predator and a prey is not applicable to animals; it can apply to animals and plants (bears and berries, pandas and eucalyptus trees, and so on).

Most of the predator-prey model requires special assumptions. These suppositions may look awkward and strange, but they are necessary because they are needed to keep the model simple. The first assumption is that the predator species is only dependent on a single prey species to supply food. The second is that the prey species has an unlimited food supply. The third is that the predator species is the only threat to the prey species.