Organisation at Population Level 35
in the phase space (two-dimensional space N 1 and N 2 where time is absent),
and conducting the related mathematical exploration we find that:
• If K 1 < r 2 /α 12 and, at the same time, K 2 < r 1 /α 21 , the system is in a stable
equilibrium, thus both populations permanently coexist. This occurs
because the size increase of one population inhibits its own growth
more than it inhibits the growth of its competitor. In this case competition can last infinitely, because it has low enough intensity, i.e.
Gause’s law does not apply.
• In every case where the previous condition does not apply, the system
is not in stable equilibrium, therefore the competition cannot continue for a long time. Depending on the parameters’ values, one of the
two populations will predominate while the other will be eliminated.
Even though the above analysis is based on a very simple competition
model, its qualitative conclusions cover all possible outcomes of a two species competition. The power of the competitive exclusion principle becomes
obvious, though it does not have a universal application. Research has shown
that there are examples in nature of two species’ coexistence when the intensity of competition is reduced for various reasons, such as the variability of
the species’ characteristics (e.g. through natural selection) or environmental
variability (e.g. through selective predation, periodical fluctuation of natural
factors etc.).
Simple competition models represent approximations of a strategic
nature. Their essential qualitative conclusion is that competition cannot
cause permanent oscillations to populations’ sizes, but it may lead to the
elimination of one of the competitors or, under specific preconditions, to
coexistence of the two populations. Therefore, competition has the ability
to lead to the alteration of an ecosystem’s composition.
3.4.3 Predator-Prey interaction
The most significant and widespread interaction between two populations is
the predator-prey interaction. It corresponds to the general trophic relationship where one organism consumes the other, i.e. the interactions between
carnivore and herbivore, herbivore and plant, parasite and host etc.
The term predator mostly refers to carnivores, although it can be generalised to include herbivores and parasites. Parasites are organisms that
feed on their host, which is either not killed or is killed at a slow rate.
Various funguses, bacteria and insects represent parasite examples. General
predator-prey interaction can be divided into four categories:
• Predators that kill numerous preys (mostly carnivores and some
herbivores)
in the phase space (two-dimensional space N 1 and N 2 where time is absent),
and conducting the related mathematical exploration we find that:
• If K 1 < r 2 /α 12 and, at the same time, K 2 < r 1 /α 21 , the system is in a stable
equilibrium, thus both populations permanently coexist. This occurs
because the size increase of one population inhibits its own growth
more than it inhibits the growth of its competitor. In this case competition can last infinitely, because it has low enough intensity, i.e.
Gause’s law does not apply.
• In every case where the previous condition does not apply, the system
is not in stable equilibrium, therefore the competition cannot continue for a long time. Depending on the parameters’ values, one of the
two populations will predominate while the other will be eliminated.
Even though the above analysis is based on a very simple competition
model, its qualitative conclusions cover all possible outcomes of a two species competition. The power of the competitive exclusion principle becomes
obvious, though it does not have a universal application. Research has shown
that there are examples in nature of two species’ coexistence when the intensity of competition is reduced for various reasons, such as the variability of
the species’ characteristics (e.g. through natural selection) or environmental
variability (e.g. through selective predation, periodical fluctuation of natural
factors etc.).
Simple competition models represent approximations of a strategic
nature. Their essential qualitative conclusion is that competition cannot
cause permanent oscillations to populations’ sizes, but it may lead to the
elimination of one of the competitors or, under specific preconditions, to
coexistence of the two populations. Therefore, competition has the ability
to lead to the alteration of an ecosystem’s composition.
3.4.3 Predator-Prey interaction
The most significant and widespread interaction between two populations is
the predator-prey interaction. It corresponds to the general trophic relationship where one organism consumes the other, i.e. the interactions between
carnivore and herbivore, herbivore and plant, parasite and host etc.
The term predator mostly refers to carnivores, although it can be generalised to include herbivores and parasites. Parasites are organisms that
feed on their host, which is either not killed or is killed at a slow rate.
Various funguses, bacteria and insects represent parasite examples. General
predator-prey interaction can be divided into four categories:
• Predators that kill numerous preys (mostly carnivores and some
herbivores)