User:Ruud Koot/Nupedia/The Quasispecies model (brief version)

The quasispecies [kwaa'-zei-spee"-seez ] model is a description of the process of the Darwinian evolution of self-replicating entities within the framework of physical chemistry.  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.  Quantitative predictions based on this model are difficult because the parameters that serve as its input are hard to obtain from actual biological systems.  The quasispecies model was put forward by Manfred Eigen [maan'-fRed ei'-gen]  and Peter  Schuster [pay'-teR shuu'-steR]  1 based on initial work done by Eigen.2

The model rests on four assumptions:
 * 1) The self-replicating entities can be represented as sequences composed of a small  number of building blocks--for example, sequences of RNA consisting of the four bases  adenine, guanine, cytosine, and uracil.
 * 2) New sequences enter the system solely as the result of a copy process, either correct or erroneous, of other sequences that are already present.
 * 3)  The substrates, or raw materials, necessary for ongoing replication are always present in sufficient quantity.  Excess sequences are washed away in an outgoing flux.
 * 4) Sequences may decay into their building blocks.  The probability of decay does not depend on the sequences' age; old sequences are just as likely to decay as young sequences.

In the quasispecies model, mutations occur through errors made in the process of copying already existing sequences. Further, selection arises because different types of sequences tend to replicate at different rates, which leads to the suppression of sequences that replicate more slowly in favor of sequences that replicate faster. However, the quasispecies model does not predict the ultimate extinction of all but the fastest replicating sequence. Although the sequences that replicate more slowly cannot sustain their abundance level by themselves, they are constantly replenished as sequences that replicate faster mutate into them. 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.

Due to the ongoing production of mutant sequences, selection does not act on single sequences, but on mutational "clouds" of closely related sequences, referred to as quasispecies. In other words, the evolutionary success of a particular sequence depends not only on its own replication rate, but also on the replication rates of the mutant sequences it produces, and on the replication rates of the sequences of which it is a mutant. 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.3 Mutational clouds as predicted by the quasispecies model have been observed in RNA  viruses and in in vitro RNA replication.4

In mathematical terms, the main result from quasispecies theory can be put as follows: Suppose that sequences of type j replicate with rate aj, decay with rate dj, and mutate into  sequences of type i with probability qij. Then, the different competing quasispecies are given by the eigenvectors of the matrix W, whose components are wij = ajqij-djδij, where δij is 1 if i=j and 0 otherwise. The relative growths of the quasispecies are given by the corresponding eigenvalues. In selection-mutation equilibrium, only a single quasispecies prevails, the one corresponding to the largest eigenvalue of W.

1 M. Eigen and P. Schuster, The Hypercycle: A Principle of Natural Self-Organization (Berlin: Springer, 1979). 2 M. Eigen, "Selforganization of Matter and the Evolution of Biological Macromolecules," Naturwissenschaften 58 (1971): 465-523. 3 P. Schuster and J. Swetina, “Stationary Mutant Distributions and Evolutionary Optimization," Bulletin of Mathematical Biology 50 (1988): 636-660. 4 E. Domingo and J. J. Holland, "RNA Virus Mutations and Fitness for Survival," Annual Review of  Microbiology 51 (1997): 151-178; C. L. Burch and L. Chao, "Evolvability of an RNA Virus is Determined by its Mutational Neighbourhood," Nature 406 (2000): 625-628.

For Further Reading
Eigen, M., J. McCaskill and P. Schuster. "The Molecular Quasi-species." Advances in Chemical Physics 75 (1989): 149-263. Novak, M. A. "What is a Quasi-species?" Trends in Ecology and Evolution 7 (1992): 118-121.