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= the beneficial effect of the density of species j on species i. Mutualism is in essence the logistic growth equation modified for mutualistic interaction. The mutualistic interaction term represents the increase in population growth of one species as a result of the presence of greater numbers of another species.
Close and long-term interactions are described as symbiosis; [a] symbioses that are mutually beneficial are called mutualistic. [ 2 ] [ 3 ] [ 4 ] The term symbiosis was subject to a century-long debate about whether it should specifically denote mutualism, as in lichens or in parasites that benefit themselves. [ 5 ]
[51] [52] In contrast, Müllerian mimicry is mutually beneficial as all participants are both models and mimics. [53] [54] For example, different species of bumblebee mimic each other, with similar warning coloration in combinations of black, white, red, and yellow, and all of them benefit from the relationship. [55]
In game theory, a win–win game or win–win [1] scenario is a situation that produces a mutually beneficial outcome for two or more parties. [2] It is also called a positive-sum game as it is the opposite of a zero-sum game.
These relations can also be categorized as beneficial, mutualistic, neutral, and pathogenic. [ 80 ] [ 81 ] Microorganisms living as endosymbionts in plants can enhance their host's primary productivity either by producing or capturing important resources. [ 82 ]
This is also called mutually beneficial cooperation as both actor and recipient depend on direct fitness benefits, which are broken down into two different types: by-product benefit and enforcement. By-product benefit arises as a consequence of social partners having a shared interest in cooperation.
The essence of collaborative partnership is for all parties to mutually benefit from working together. There are instances where collaborative partnerships develop between those in different fields to supplement one another's expertise. The relationships between collaborative partners can lead to long-term partnerships that rely on one another. [1]
Cleaning symbiosis is a relationship between a pair of animals of different species, involving the removal and subsequent ingestion of ectoparasites, diseased and injured tissue, and unwanted food items from the surface of the host organism (the client) by the cleaning organism (the cleaner). [5]