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The relationship between the error catastrophe, survival of the flattest, and natural selection.

Tejero H, Marín A, Montero F - BMC Evol. Biol. (2011)

Bottom Line: Previous works are explicitly reinterpreted in the light of the results obtained in this paper.The main conclusion of this paper is that the entry into error catastrophe is a specific case of survival of the flattest acting on phenotypes that differ in the trade-off between replicative ability and mutational robustness.So we propose to consider the transition to error catastrophe as a phenomenon of intra-quasispecies selection, and survival of the flattest as a phenomenon of inter-quasispecies selection.

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Affiliation: Departamento de Bioquímica y Biología Molecular I, Universidad Complutense de Madrid, Avd, Complutense s/n, 28040 Madrid, Spain.

ABSTRACT

Background: The quasispecies model is a general model of evolution that is generally applicable to replication up to high mutation rates. It predicts that at a sufficiently high mutation rate, quasispecies with higher mutational robustness can displace quasispecies with higher replicative capacity, a phenomenon called "survival of the flattest". In some fitness landscapes it also predicts the existence of a maximum mutation rate, called the error threshold, beyond which the quasispecies enters into error catastrophe, losing its genetic information. The aim of this paper is to study the relationship between survival of the flattest and the transition to error catastrophe, as well as the connection between these concepts and natural selection.

Results: By means of a very simplified model, we show that the transition to an error catastrophe corresponds to a value of zero for the selective coefficient of the mutant phenotype with respect to the master phenotype, indicating that transition to the error catastrophe is in this case similar to the selection of a more robust species. This correspondence has been confirmed by considering a single-peak landscape in which sequences are grouped with respect to their Hamming distant from the master sequence. When the robustness of a class is changed by modification of its quality factor, the distribution of the population changes in accordance with the new value of the robustness, although an error catastrophe can be detected at the same values as in the general case. When two quasispecies of different robustness competes with one another, the entry of one of them into error catastrophe causes displacement of the other, because of the greater robustness of the former. Previous works are explicitly reinterpreted in the light of the results obtained in this paper.

Conclusions: The main conclusion of this paper is that the entry into error catastrophe is a specific case of survival of the flattest acting on phenotypes that differ in the trade-off between replicative ability and mutational robustness. In fact, entry into error catastrophe occurs when the mutant phenotype acquires a selective advantage over the master phenotype. As both entry into error catastrophe and survival of the flattest are caused by natural selection when mutation rate is increased, we propose differentiating between them by the level of selection at which natural selection acts. So we propose to consider the transition to error catastrophe as a phenomenon of intra-quasispecies selection, and survival of the flattest as a phenomenon of inter-quasispecies selection.

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Phenotype Fraction vs the selection coefficient (s). The amplification factors of the master and mutant phenotype are Am = 10 and Ak = 2, respectively. In both cases the degradation factor is D = 1, and the sequence length is ν = 20. The selection coefficient is evaluated as in equation 6.
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Figure 1: Phenotype Fraction vs the selection coefficient (s). The amplification factors of the master and mutant phenotype are Am = 10 and Ak = 2, respectively. In both cases the degradation factor is D = 1, and the sequence length is ν = 20. The selection coefficient is evaluated as in equation 6.

Mentions: Taking this into account, and inserting equation (3) into equation (6), it follows that the error threshold is the value of q for which s = 0. That is to say, for q < qc the mutant phenotype has a selective advantage over the master phenotype, so s > 0 (Figure 1). It would therefore be incorrect to say that selection prevails before the error threshold, while mutation prevails beyond it. Instead, the master phenotype is selected before the error threshold, while the mutant phenotype is selected beyond this threshold. Thus, entry into error catastrophe is the selection of the mutant phenotype because of the selective advantage provided by its greater mutational robustness. This phenomenon has previously been called survival of the flattest [39-41].


The relationship between the error catastrophe, survival of the flattest, and natural selection.

Tejero H, Marín A, Montero F - BMC Evol. Biol. (2011)

Phenotype Fraction vs the selection coefficient (s). The amplification factors of the master and mutant phenotype are Am = 10 and Ak = 2, respectively. In both cases the degradation factor is D = 1, and the sequence length is ν = 20. The selection coefficient is evaluated as in equation 6.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3037306&req=5

Figure 1: Phenotype Fraction vs the selection coefficient (s). The amplification factors of the master and mutant phenotype are Am = 10 and Ak = 2, respectively. In both cases the degradation factor is D = 1, and the sequence length is ν = 20. The selection coefficient is evaluated as in equation 6.
Mentions: Taking this into account, and inserting equation (3) into equation (6), it follows that the error threshold is the value of q for which s = 0. That is to say, for q < qc the mutant phenotype has a selective advantage over the master phenotype, so s > 0 (Figure 1). It would therefore be incorrect to say that selection prevails before the error threshold, while mutation prevails beyond it. Instead, the master phenotype is selected before the error threshold, while the mutant phenotype is selected beyond this threshold. Thus, entry into error catastrophe is the selection of the mutant phenotype because of the selective advantage provided by its greater mutational robustness. This phenomenon has previously been called survival of the flattest [39-41].

Bottom Line: Previous works are explicitly reinterpreted in the light of the results obtained in this paper.The main conclusion of this paper is that the entry into error catastrophe is a specific case of survival of the flattest acting on phenotypes that differ in the trade-off between replicative ability and mutational robustness.So we propose to consider the transition to error catastrophe as a phenomenon of intra-quasispecies selection, and survival of the flattest as a phenomenon of inter-quasispecies selection.

View Article: PubMed Central - HTML - PubMed

Affiliation: Departamento de Bioquímica y Biología Molecular I, Universidad Complutense de Madrid, Avd, Complutense s/n, 28040 Madrid, Spain.

ABSTRACT

Background: The quasispecies model is a general model of evolution that is generally applicable to replication up to high mutation rates. It predicts that at a sufficiently high mutation rate, quasispecies with higher mutational robustness can displace quasispecies with higher replicative capacity, a phenomenon called "survival of the flattest". In some fitness landscapes it also predicts the existence of a maximum mutation rate, called the error threshold, beyond which the quasispecies enters into error catastrophe, losing its genetic information. The aim of this paper is to study the relationship between survival of the flattest and the transition to error catastrophe, as well as the connection between these concepts and natural selection.

Results: By means of a very simplified model, we show that the transition to an error catastrophe corresponds to a value of zero for the selective coefficient of the mutant phenotype with respect to the master phenotype, indicating that transition to the error catastrophe is in this case similar to the selection of a more robust species. This correspondence has been confirmed by considering a single-peak landscape in which sequences are grouped with respect to their Hamming distant from the master sequence. When the robustness of a class is changed by modification of its quality factor, the distribution of the population changes in accordance with the new value of the robustness, although an error catastrophe can be detected at the same values as in the general case. When two quasispecies of different robustness competes with one another, the entry of one of them into error catastrophe causes displacement of the other, because of the greater robustness of the former. Previous works are explicitly reinterpreted in the light of the results obtained in this paper.

Conclusions: The main conclusion of this paper is that the entry into error catastrophe is a specific case of survival of the flattest acting on phenotypes that differ in the trade-off between replicative ability and mutational robustness. In fact, entry into error catastrophe occurs when the mutant phenotype acquires a selective advantage over the master phenotype. As both entry into error catastrophe and survival of the flattest are caused by natural selection when mutation rate is increased, we propose differentiating between them by the level of selection at which natural selection acts. So we propose to consider the transition to error catastrophe as a phenomenon of intra-quasispecies selection, and survival of the flattest as a phenomenon of inter-quasispecies selection.

Show MeSH