Predators and Prey: the Lotka–Volterra model
The first model describing the interaction between two populations in the ecosystem is the Lotka–Volterra model. It applies to a predator-prey system (population of predators feeds on the individuals of the prey species). The model was proposed in 1920s in parallel by Vito Volterra as a model of a population, and by Alfred Lotka as a model of a chain of chemical reactions. Volterra proposed this model to explain the phenomenon that was observed after the First World War. It was noted that the population of predatory fish in the Adriatic Sea had increased. This was considered a paradox, because it would seem that all species should be negatively affected by the war. Volterra based on his model showed that the increase in the number of predators was natural because fishing was stopped during the war, and thus the population of predators could return to its natural state.
The model takes the following assumptions:
- In the environment there are only two species: the prey and the predators.
- If there are no predators in the environment, prey have favorable conditions (i.e., the are no additional limitations in the environment) and their population increases exponentially (according to the Malthus model).
- If there are no prey in the environment, the predators do not have food, which means lack of energy necessary for survival and reproduction, resulting in extinction of the species (population size decreases exponentially).
- Assuming that both species exist in the environment, some part of prey are killed by predators. Food provides the energy necessary for predators for reproduction, and thus the size of their population grows.
- Hunting is only possible in case of direct contact. Individuals move randomly, so the number of contacts is proportional to the number of individuals of both species.
- A specific spatial distribution of individuals in the environment is not taken into account. We consider only the average density of individuals.
http://en.alife.pl/predators-and-prey-the-Lotka-Volterra-model
