Everything about The Quasispecies Model totally explained
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 hard to obtain from actual biological systems. The quasispecies model was put forward by
Manfred Eigen and
Peter Schuster (see note 1) based on initial work done by Eigen(see note 2).
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're 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 are 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 are 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 only exists for large numbers of individuals existing at a certain (high) range of mutation rates.
Quasispecies, fitness, and evolutionary selection
In a species, though reproduction may be mostly accurate, periodic mutations will give rise to one or more competing genotypes. If a mutation results in greater replication and survival, the mutant genotype may out-compete the parent genotype and come to dominate the species. Thus, the individual genotypes (or species) may be seen as the units on which selection acts and biologists will often speak of a single genotype's
fitness.
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. Instead, what matters is the
connectedness of the cloud. For example, the sequence AGGT has 81 (3
4) possible single point mutants, AGGA, AGGG and so on). If 75 of those mutants are viable genotypes that may reproduce (and some of whose offspring or grandchilden may mutate back into AGGT again), we'd 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 won't reproduce. The analogue 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.
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.
Application to biological research
While the applicability of the quasispecies model to real organisms is still a matter of debate in the scientific community, some researchers believe that it accurately represents the evolution of high-mutation-rate viruses such as
HIV and sometimes single genes or molecules within the genomes of other organisms.
Formal background
The model rests on four assumptions:
- 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.
- New sequences enter the system solely as the result of a copy process, either correct or erroneous, of other sequences that are already present.
- The substrates, or raw materials, necessary for ongoing replication are always present in sufficient quantity. Excess sequences are washed away in an outgoing flux.
- Sequences may decay into their building blocks. The probability of decay doesn't 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 doesn't predict the ultimate extinction of all but the fastest replicating sequence. Although the sequences that replicate more slowly can't sustain their abundance level by themselves, they're 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 doesn't 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's 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 (see note 3). Mutational clouds as predicted by the quasispecies model have been observed in RNA viruses and in
in vitro RNA replication (see note 4).
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 zero, there's no exchange by mutation, and each sequence is its own species. 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.
Mathematical description
A simple mathematical model for a quasispecies is as follows: let there be
possible sequences and let there be
organisms with sequence
i. Let's say that each of these organisms asexually gives rise to
offspring. Some are duplicates of their parent, having sequence
i, but some are mutant, and have some other sequence. Let the mutation rate
