The quasispecies model is a description of the process of the Darwinian evolution of certain self-replicating entities within the framework of physical chemistry. Put simply, a quasispecies is a large group or cloud of related genotypes that exist in an environment of high mutation rate, where a large fraction of offspring are expected to contain one or more mutations relative to the parent. This is in contrast to a species, which from an evolutionary perspective is a more-or-less stable single genotype, most of the offspring of which will be genetically accurate copies.
It is useful mainly in providing a qualitative understanding of the evolutionary processes of self-replicating macromolecules such as RNA or DNA or simple asexual organisms such as bacteria or viruses (see also viral quasispecies), and is helpful in explaining something of the early stages of the origin of life. Quantitative predictions based on this model are difficult because the parameters that serve as its input are impossible to obtain from actual biological systems. The quasispecies model was put forward by Manfred Eigen and Peter Schuster based on initial work done by Eigen.
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.