Lotka-Volterra rules explained in the example

02-19  Source: Network gathering  Views:3 


Lotka-Volterra rules explained in the example

A fox on the hunt - the Lotka-Volterra rules explain the dynamics of predator-prey relationship.

The inventors of the Lotka-Volterra Rules

Independently, in the mid-20s employed two scientists from various disciplines with the dynamics of predator-prey relationship in the animal kingdom. The Austro-American chemist and actuary Alfred J. Lotka and the Italian mathematician and physicist Vito Volterra came across the same laws which they formulated in mathematical equations. According to them, the three Lotka-Volterra rules are named.

The predator-prey relationship using the example of an oversight

At first glance, the Lotka-Volterra rules seem complicated. With a sample from the animal world it can, however, illustrate well.

  • The first Lotka-Volterra rule states that the population size (ie the total of all individuals of a species in a particular place) vary from predators and prey at constant conditions periodically. Here follows the maximum of robbers with a time delay to the maximum prey.
  • Take for example a forest area with foxes (the robbers) and rabbits (the prey). Rabbits multiply known very quickly - so their population is increasing at the beginning of the observation rapidly. Thus, the foxes have a lot to eat and multiply because of this increased food supply also good. With an increasing number of foxes, however, the stock of rabbits reduced again. Thereby, it is again the foxes bad: You will find less to eat, die and reproduce poorly. Thus, the population of rabbits recovered - and the cycle begins anew.
  • In addition, the time factor comes from the second part of this rule: Young foxes take longer to grow up as bunnies and go take some time to himself to hunting. The predator population therefore later reaches its maximum when the rabbit population.
  • On these findings is based on the second Lotka-Volterra-rule. It reads: Assuming unchanged conditions vary, the average size of the predator and prey population over a longer period considered by a constant mean. If several years so foxes and rabbits are counted, the populations are approximately equal on average each year.
  • However, what happens when external influences such as an environmental toxin can be a great part of foxes and rabbits die? According to the third rule, the prey population recovers always faster than the predator population. The rabbits have on the one hand the advantage that they multiply faster than the foxes. Secondly, they do not suffer from the decimated food supply as the foxes.

Everything just pure theory? - The limits of the rules

These rules apply only under certain conditions, in practice, their significance is limited.

  • Generally it should be noted that the Lotka-Volterra rules establish a theoretical model that only in consideration isolated predator-prey populations has its validity.
  • In nature, however, the relationship between predator and prey are far more complex. Mostly chasing a robber is not only one kind of prey animals and has, in turn prey several predators. So hunt foxes and birds, mice and other animals and rabbits fall next foxes and birds of prey and other predators prey.
  • In addition, the population sizes are sometimes influenced by other factors. For example, could all foxes succumb a population of a deadly disease, but does not hit the rabbit - or vice versa. The Lotka-Volterra rules then no longer correct.

Nevertheless, the rules in practical ecology of value, because they at least provide useful assessments in the development of population sizes.

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