# Custom «Lotka-Volterra Competition System» Essay Paper Sample

It is natural for organisms that live together in a given ecosystem to compete over resources. The competition is brought about by a number of factors but key among these is the limitation that exists in the very resources that are integral for their survival. A common food between two different species would most definitely have to be competed. This largely depends on the number of the species that feed on the very food stuff. A here for example is a source of protein that is fed on by several carnivores occupying a given habitat and these could be hyenas and leopards or lions among others (Druskat, F., and K. Pescosolido.1998).

The Lotka-Volterra competition system is a mathematical theorem that aims at finding out the intensity of competition that would exist in a virtual habitat. The theorem majors most of its argumentation on the size of the habitat, it assets that the size of the habitat is the number one factor in determining how intense the competition exists between the species occupying the very ecological system. As per the theorem the level of competition is inversely proportional to the level of competition. Basically put, the bigger the habitat the lesser the competition, this is normally so as the prey is normally scattered and the prey is normally likely to be in high numbers. Nature is in such a way that the organism at the bottom of the food chain is normally more than that above it and this explains the logic behind the theorem.

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The SIR Epidemic model on the other hand is a mathematical theorem that seeks to establish the rate at which communicable diseases infect organisms in a given habitation and how they respond to the disease in relation to time. The argument behind this theorem is that nature has its on way of balancing itself, just like humans other organisms in the ecosystem get infected by diseases most of which are communicable but funnily enough it would be hard to find an entire specie swept out by a particular disease and it is this mystery of infection and recovery that the theorem offers a mathematical explanation to.

This theorem just as the one above appreciates the role that the size of the ecosystem plays in determining the rate of infection. A bigger ecosystem would most likely have more organisms in it and therefore instances of infection are high. Communicable diseases are prone to be spread from one organism to the other mainly through agents of communication that would lead to instances of interaction between the organisms. A herd of buffaloes that feed on a common pasture is more likely to suffer a foot and mouth infection all at ago. And the bigger the pasture the more likely that more buffaloes would suffer infections. Therefore the size of the habitat is directly proportional to levels of infections (Kevin, M. 1998). Recovery of a previously infected member of a given specie depends on a number of factors with the size of the habitat still being integral. In a bigger habitat the chances of all or more animals interacting especially on those animals that do not move as a pack are minimal and it becomes hard for a disease to spread unlike a smaller habitat.

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The use of these two theories in a scientific research yielded more or less a common result. The Lotka-Volterra competition system found out that the size of the habitat not withstanding, there is always a tendency of the rate of competition to increase steadily then finally balances and stays constant. This was the very case with the rate of spread of the communicable diseases. The two theories both assert that it reaches a point that all animals are infected in case of the rate of infection and this rate cannot increase any more thus stays constant over a period of time. This is regardless of the size of the habitat and that the size only plays a role in determining the time a bigger habitat takes longer.

The use of these two theories in the study proves to be the best and that implies that the researches could not have done a better job using any other models. These two offer a more practical scenario and the researcher spends time given the size of the habitat under study. The argumentations are realistic and more practical, the only shortcoming of these two theories is the fact that they generally assume that the size of a given habitat is directly proportional to the number of organisms occupying the same. This is never the case as organisms occupy a given habitation on the basis of availability of food, it is therefore not logical that a wider region would by default have more food for the organisms. The theories therefore assume that the distribution of food is constant, it is only in such a case that this would be a reality.

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