In ecology, the competition–colonization trade-off is a stabilizing mechanism that has been proposed to explain species diversity in some biological systems, especially those that are not in equilibrium. In which case some species are particularly good at colonizing and others have well-established survival abilities. 
The concept of the competition-colonization trade-off was originally proposed by Levins and Culver, the model indicated that two species could coexist if one had impeccable competition skill and the other was excellent at colonizing. The model indicates that there is typically a trade-off, in which a species is typically better at either competing or colonizing. A later model, labelled The Lottery Model was also proposed, in which interspecific competition is accounted for within the population.
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Mathematical models.
Levins and Culver model.
Where:
formula_3 fraction of patches that are occupied by species formula_4;
formula_5 colonization rate of species formula_4;
formula_7 mortality rate of species formula_4 (independent of patch density).
Species 1 = competitor, can colonize in area that is uninhabited "or" inhabited by species 2 formula_9.
Species 2 = colonizer, can only colonize in uninhabited areas formula_10.
Species 2 is subject to displacement by its competitor formula_11.
If species 2 has a higher colonization rate it can coexist with species 1: formula_12.
This model is described as the displacement competition model, it has been observed in marine mollusks and fungi. This model makes two large assumptions: 
1. "a propagule of a superior competitor takes over a patch from an adult of the inferior competitor".
2. The adult must be displaced fast enough to ensure that it does not reproduce while it is being displaced.
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Lottery model.
Colonization rate is now described by interspecific competition.
formula_15 and formula_16. Both f and g ; 0.
An increase in p1 is related to a decrease in the colonization rate of species 2.
g ; f implies a competitive advantage of species 1 and c2 ; c1 implies a colonization advantage for species 2.
In plants.
The competition-colonization trade-off theory has primarily been used to examine and describe the dispersal-linked traits of a plant's seeds. Seed size is a primary feature that relates to a species ability to colonize or compete within a given population, the effect of seed size was displayed in dicotyledonous annual plants. Turnbull and colleagues indicated that the competition/colonization trade-off has a stabilizing effect on the population of plants.
In algae.
For example, in a classic study on an intertidal zone in Southern California, it was shown that when a boulder was overturned, it would quickly be colonized by green algae and barnacles (which were better colonizers). However, if left undisturbed, the boulders would eventually be overtaken by red algae (which was the stronger competitor in the long term).
In bacteria.
It has been shown experimentally that in a two-species artificial metacommunity of motile strains "on-chip," bacteria "Escherichia coli" is a fugitive species, whereas "Pseudomonas aeruginosa" is a slower colonizer but superior competitor. The pattern of ecological succession driving dynamics of the metacommunity in a patchy habitat landscape is as follows: Starting with a pristine one-dimensional (array) archipelago of island habitats (patches) which is inoculated with "E. coli" and "P. aeruginosa" from opposite ends; locally "E. coli" colonizes first and later "P. aeruginosa" takes over while at the landscape scale "E. coli" persists as a fugitive species scrambling for patches.
References.
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