Simplified Explanation
When evolutionary biologists describe competition between species, they generally assume that each species is a single genotype whose descendants are mostly accurate copies. (Such genotypes are said to have a high reproductive fidelity.) Evolutionarily, we are interested in the behavior and fitness of that one species or genotype over time.
Some organisms or genotypes, however, may exist in circumstances of low fidelity, where most descendants contain one or more mutations. A group of such genotypes is constantly changing, so discussions of which single genotype is the most fit become meaningless. Importantly, if many closely related genotypes are only one mutation away from each other, then genotypes in the group can mutate back and forth into each other. For example, with one mutation per generation, a child of the sequence AGGT could be AGTT, and a grandchild could be AGGT again. Thus we can envision a cloud of related genotypes that is rapidly mutating, with sequences going back and forth among different points in the cloud. Though the proper definition is mathematical, that cloud, roughly speaking, is a quasispecies.
Quasispecies behavior exists for large numbers of individuals existing at a certain (high) range of mutation rates. Essentially all species on earth, apart from groups of inbreeding mammals and self-cloning plant populations, are quasispecies.
Read more about this topic: Quasispecies Model
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