The quasispecies model is a description of the process of the Darwinian evolution of certain self-replicating entities within the framework of physical chemistry.
A quasispecies is a large group or "cloud" of related genotypes that exist in an environment of high mutation rate (at stationary state[1]), 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.
[2] 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.
In evolutionary terms, we are interested in the behavior and fitness of that one species or genotype over time.
[5] Some organisms or genotypes, however, may exist in circumstances of low fidelity, where most descendants contain one or more mutations.
Though the proper definition is mathematical, that cloud, roughly speaking, is a quasispecies.
[7] In a species, though reproduction may be mostly accurate, periodic mutations will give rise to one or more competing genotypes.
[8] In a quasispecies, however, mutations are ubiquitous and so the fitness of an individual genotype becomes meaningless: if one particular mutation generates a boost in reproductive success, it can't amount to much because that genotype's offspring are unlikely to be accurate copies with the same properties.
For example, the sequence AGGT has 12 (3+3+3+3) possible single point mutants AGGA, AGGG, and so on.
If 10 of those mutants are viable genotypes that may reproduce (and some of whose offspring or grandchildren may mutate back into AGGT again), we would consider that sequence a well-connected node in the cloud.
If instead only two of those mutants are viable, the rest being lethal mutations, then that sequence is poorly connected and most of its descendants will not reproduce.
The analog of fitness for a quasispecies is the tendency of nearby relatives within the cloud to be well-connected, meaning that more of the mutant descendants will be viable and give rise to further descendants within the cloud.
[9] When the fitness of a single genotype becomes meaningless because of the high rate of mutations, the cloud as a whole or quasispecies becomes the natural unit of selection.
Quasispecies represents the evolution of high-mutation-rate viruses such as HIV and sometimes single genes or molecules within the genomes of other organisms.
[13] Quasispecies was also shown in compositional replicators (based on the Gard model for abiogenesis)[14] and was also suggested to be applicable to describe cell's replication, which amongst other things requires the maintenance and evolution of the internal composition of the parent and bud.
However, the quasispecies model does not predict the ultimate extinction of all but the fastest replicating sequence.
At equilibrium, removal of slowly replicating sequences due to decay or outflow is balanced by replenishing, so that even relatively slowly replicating sequences can remain present in finite abundance.
As a consequence, the sequence that replicates fastest may even disappear completely in selection-mutation equilibrium, in favor of more slowly replicating sequences that are part of a quasispecies with a higher average growth rate.
[18][19] The mutation rate and the general fitness of the molecular sequences and their neighbors is crucial to the formation of a quasispecies.
If the mutation rate is too high, exceeding what is known as the error threshold, the quasispecies will break down and be dispersed over the entire range of available sequences.
Then the total number of i-type organisms after the first round of reproduction, given as
Its diagonal entries will be eigenvalues corresponding to certain linear combinations of certain subsets of sequences which will be eigenvectors of the W matrix.
Assuming that the matrix W is a primitive matrix (irreducible and aperiodic), then after very many generations only the eigenvector with the largest eigenvalue will prevail, and it is this quasispecies that will eventually dominate.
The components of this eigenvector give the relative abundance of each sequence at equilibrium.
W is not primitive if it is periodic, where the population can perpetually cycle through different disjoint sets of compositions, or if it is reducible, where the dominant species (or quasispecies) that develops can depend on the initial population, as is the case in the simple example given below.
[citation needed] The quasispecies formulae may be expressed as a set of linear differential equations.
we can write: The quasispecies equations are usually expressed in terms of concentrations
This eigenvalue corresponds to the eigenvector [0,1,1,1], which represents the quasispecies consisting of sequences 2, 3, and 4, which will be present in equal numbers after a very long time.