# Competition (ecology)

When living things use the same limited resource and thereby mutually impair one another, they are in competition with one another . On a supra-individual level, populations or species compete, and according to a few authors also biocenoses and ecosystems as a whole.

In relation to species (species), a distinction is made between

In population biology competition is widely regarded as an important factor in the density-dependent regulation of population densities , and in evolutionary biology and the theory of ecological societies as a selection factor .

The ecological principle of exclusion of competition postulates that species with identical or very similar ecological niches cannot permanently coexist.

## Mathematical modeling of the competition

The most widely used competing mathematical model is the Lotka-Volterra model (established by Vito Volterra in 1926 and Alfred J. Lotka in 1932). It is a further development of the logistic function . The model takes into account both intra- and interspecific competition.

The combination of both situations is usually formulated with type 1 = x and type 2 = y as:

${\ displaystyle {\ frac {dx} {dt}} = a_ {1} x (1 - {\ frac {x + cy} {K_ {1}}})}$
${\ displaystyle {\ frac {dy} {dt}} = a_ {2} y (1 - {\ frac {y + dx} {K_ {2}}})}$

The constants indicate in order: intrinsic growth rates, interaction constants and capacities. ${\ displaystyle a_ {i}, c, d, K_ {i}}$

For the motivation and interpretation of the system of equations, it is helpful to recall the case of an isolated population whose growth takes place according to the logistic differential equation: For x = 0 or y = 0, the present model again yields the well-known case of intraspecific competition, as described by the logistic equation. The case of two species thus results from a direct generalization of the one-dimensional case.

The model is not very elegant. Transition to dimensionless quantities leads with

${\ displaystyle u_ {1}: = {\ frac {x} {K_ {1}}}, u_ {2}: = {\ frac {y} {K_ {2}}}, p_ {1}: = c {\ frac {K_ {2}} {K_ {1}}}, p_ {2}: = d {\ frac {K_ {1}} {K_ {2}}}, p_ {3}: = {\ frac {a_ {2}} {a_ {1}}}, r: = a_ {1} t}$

on:

${\ displaystyle {\ frac {du_ {1}} {dr}} = u_ {1} (1-u_ {1} -p_ {1} u_ {2})}$
${\ displaystyle {\ frac {du_ {2}} {dr}} = p_ {3} u_ {2} (1-p_ {2} u_ {1} -u_ {2})}$

In this form, the properties of the model are clearly visible. In addition to the three trivial fixed points, one obtains a fixed point at:

${\ displaystyle u_ {1} ^ {*} = {\ frac {1-p_ {1}} {1-p_ {1} p_ {2}}}}$
${\ displaystyle u_ {2} ^ {*} = {\ frac {1-p_ {2}} {1-p_ {1} p_ {2}}}}$

This fixed point represents a stable equilibrium between type x and type y. In the other cases either type x or type y (or both) dies out (according to the model). In contrast to the one-dimensional case, the fixed point of the system is not asymptotically stable in all parameter ranges. Stability conditions can be proven that result in the intra-species competition acting more strongly than interspecific competition. Only in this case can two types coexist (assuming the validity of the model). This is the abstract basis of the well-known non-competition principle. More details can be found in the introductory text by John Maynard Smith linked below.

## Exclusion of competition and coexistence of species

Following the Lotka-Volterra model, two species can only coexist with each other if the competitive effect on individuals of their own species (intraspecific) is stronger than that on individuals of another species (interspecific). If the competition is asymmetrical, so that individuals of one species have a stronger effect on individuals of the other than on their fellow species, the weaker competitor would inevitably be displaced. For example, one plant species can displace another from one location because it grows taller and shades the other, i.e. that is, it is superior in the competition for light. Translated into the language of niche theory : the fundamental niche of the second kind is completely overlapped by that of the first kind. The weak competitor (the second type) no longer has a realized niche in the presence of the strong competitor (the first type) and therefore dies out. This means exclusion of competition.

In ecological field research, the lack of a realized niche and thus complete exclusion of competition can ultimately never be proven. It can always be the case that when a previously neglected or a still unknown factor is included, there is either a competition-free area (i.e. a location of the inferior plant species that the superior competitor cannot colonize for physiological reasons), or that the weaker species then (completely or partially) gains in competitive power, so that the assumptions of the existing Lotka-Volterra model no longer apply under these boundary conditions (example: the weaker-growing species can grow better in the event of a lack of water or nutrients and thus be superior to the competition).

In general, there seem to be very many cases in ecology in which two species coexist with each other, although one of them is (supposedly or actually) competitive. These cases are each a challenge for ecological theory because an explanatory factor has to be found. For example, the following factors are possible:

• The two species are actually not or only hardly in competition with one another, because they both cannot exhaust their (habitat) capacity K, i. i.e., staying too seldom.
• The inferior species is faster in colonizing new habitats that become free (strategy of a "pioneer species").
• The environmental conditions fluctuate in such a way that both species are alternately superior in competition (whereby the time to exclude competition must not be sufficient!).
• Both types “avoid each other”. Mathematically, this means that you have aggregated (or clumped) distribution patterns over different microhabitats (often . English as "patches") is. This significantly reduces the effective competitive strength.

Almost all of these strategies and cases have in common that the equilibrium case of the model is not reached. Most of the time, the time that the superior species would need to oust its competitor is not sufficient.

In addition to the cases described above, however, it can happen that two species are in competition with one another, although they have no contact whatsoever and may occupy completely different niches. This is the case, for example, when both species are hunted by the same predator. In principle, the predator has a free choice between his prey objects. However, he may prefer a species, or one of the species has a strategy or adaptation to avoid the predator. Figuratively speaking, the types of prey now compete for "enemy-free space". This case is known as "apparent competition".

### Example of coexistence

In the intertidal zone of rocky shores animals occur with strongly overlapping niche: mussels ( Mytilus californianus ), chitons , limpets , barnacles and barnacles . These grazing and filtering species serve as food for the starfish ( Pisaster ochraceus ). If all specimens of the starfish in an area are removed in the experiment, the number of original species is reduced to one or two. The explanation for this is that a predator keeps the density of the superior competitors low and thereby reduces the competition for the inferior species and thereby ensures their continued existence.

## Competitive situations

• Food competition → competition over the earth for z. B. Light ; underground about water and ions .
• Mating partner (mostly the males compete for the females; only intraspecific)

## literature

• M. Begon, M. Mortimer, DJ Thompson: Population Ecology. Spectrum, Heidelberg 1997, ISBN 3-86025-258-5 .
• J. Murray: Mathematical Biology. 2nd Edition. Springer, Berlin 2002, ISBN 3-540-57204-X .
• J. Maynard Smith: Models in Ecology. Cambridge University Press, Cambridge 1974, ISBN 0-521-20262-0 .

## Individual evidence

1. However, there are different definitions of "competition", see e.g. BEF Keller: Competition: current usages. In: EF Keller, EA Lloyd (Ed.): Keywords in evolutionary biology. Harvard University Press, Cambridge 1992, pp. 68-73.
2. ^ PA Keddy: Competition. Kluwer, Dordrecht 2001, ISBN 0-7923-6064-8 .
3. Andrew Cockburn: Evolutionary Ecology. Gustav Fischer, Stuttgart / Jena / New York 1995, p. 12.