Mutation & selection
A lineage that copies itself with errors. Below a certain error rate it stays centred on one genotype while its members vary. Above that rate the population carries on and the identity is gone.
This card sits in the community and evolutionary band, where the question is whether a lineage can persist while it varies. The standard model of that question is Eigen's quasispecies, published in 1971: a population of replicators that copy themselves imperfectly, so that every generation spreads away from its parent sequence and selection pulls it back. One number, the error rate, decides whether the pull wins, and the model is exact about what is lost when it fails. This page reads that model through a later two-genotype simplification by Bull, Meyers and Lachmann, and through two experiments, one in digital organisms and one in plant pathogens, that tested what selection actually holds on to.
On this site a basin is the set of conditions a system comes back from. Push a marble around the inside of a bowl and it rolls back to the bottom; the bowl is its basin, and the rim is its edge, the push beyond which it does not come back. Finding basins, and their edges, is the point of the Laboratory. This lineage has one basin. This is a reading page, so the basin below is the one the published model states; nothing here was run or measured.
| basin | what it returns to | what pushes it | its edge |
|---|---|---|---|
| 1. Centred on one genotype | balance around the leading genotype while its members vary | the copying error rate | the error threshold: above it the identity is lost and the population carries on |
1. Centred on one genotype. A genotype is the sequence a replicator carries. Every generation copies itself with errors, so the population spreads into a cloud of variants around its leading genotype, and selection pulls it back because the faithful copies outbreed the ones that drifted. The push is the copying error rate. As it rises, the leading genotype's share of the population falls gradually. The edge: the error threshold, the rate at which the leading genotype keeps no more of its offspring than its mutants keep of theirs ("The threshold"). Above it the replicators go on replicating with nothing to centre on: the identity is lost and the population is kept ("Identity lost, population kept"). Extinction is a separate edge further out, where the best genotype cannot reproduce itself fast enough to maintain a minimum population. Drugs that raise a virus's mutation rate aim at that second edge, and Bull, Meyers and Lachmann (2005) class them as an extinction catastrophe. Two experiments, Wilke and colleagues (2001) in digital organisms run at a 4-fold higher mutation rate and Codoñer and colleagues (2006) in viroids, tested which lineage holds its centre under heavy mutation, and in both it was the one whose neighbouring sequences were nearly as fit. Neither experiment crossed the threshold, so no crossing on record. The threshold itself is Eigen's (1971).
Every rule and figure below is quoted from the papers listed at the bottom, with the date read. No simulation on this page and nothing measured here.
What the model is
Bull, Meyers and Lachmann open with the definition: "Quasispecies are clouds of genotypes that appear in a population at mutation–selection balance." Copying makes the cloud. Selection keeps it gathered.
Their simplified version has two genotypes. "Genotype A₁ has fitness w₁, and of those w₁ offspring a fraction 1 − μ₁ retain the A₁ genotype." The remainder are mutants, and "Its mutants are converted into the other genotype, A₂." So A₁ breeds faster and loses a share of what it breeds to A₂.
the leading genotype copies itself → a fraction of the copies carry errors → the errors form a cloud around it → selection favours the copies that stayed close → the leading genotype copies itself
That loop holds a position in the space of possible sequences. Nothing encloses the population. What keeps it gathered is that the faithful copies outbreed the ones that drifted.
The threshold
The paper names the edge as the error threshold, "a mutation rate below which populations equilibrate in a traditional mutation–selection balance and above which the population experiences an error catastrophe."
In the two-genotype model its position is simple to state. "The error threshold is the point at which both genotypes have identical replacement rates." A₁'s advantage in speed is spent on the copies it loses to error. At the threshold what it keeps is no more than A₂ keeps, and the population stops being organised around it.
The approach is gradual. An error catastrophe "is the culmination of a gradual decrease in the equilibrium frequency of A₁ rather than a dramatic one." The leading genotype thins as the error rate rises, and the threshold is where that decline finishes.
Identity lost, population kept
This is the result the card is about. Crossing the threshold leaves the population in place, and the paper says so directly: "An error catastrophe is not equivalent to a population extinction." The replicators go on replicating. What ends is the population's organisation around one genotype.
Extinction is a separate event with its own condition, which the paper places where "the best genotype cannot reproduce itself to maintain a minimum population size." It then applies the distinction to the practical use of the idea, drugs that raise a virus's mutation rate. Lethal mutagenesis by such drugs is, in the paper's words, "an extinction catastrophe," and it places that outside error catastrophe proper.
So the model contains two different losses. A lineage can lose its identity and keep existing, or it can stop existing. The card asks about the first. On these sources the first is shown in the model, and the drug case is the second.
What selection holds on to
If the lineage's identity is carried by a cloud, selection should act on clouds. Quasispecies theory says it does, in the words of the 2001 study that tested it: "selection favours the cloud of genotypes, interconnected by mutation, whose average replication rate is highest." Bull and colleagues put it the same way for high mutation rates, where "the quasispecies distribution as a whole rather than a single genotype is the target of selection."
In digital organismsWilke, Wang, Ofria, Lenski and Adami tested it in self-replicating computer programs. "Forty pairs of populations were derived from 40 different ancestors in identical selective environments, except that one of each pair experienced a 4-fold higher mutation rate." In twelve pairs, the genotype that evolved at the lower rate "achieved a replication rate >1.5-fold faster than its counterpart." Each of those pairs then competed across a range of mutation rates: "In each case, as mutation rate was increased, the outcome of competition switched to favour the genotype with the lower replication rate." The winners "occupied lower fitness peaks" and "were located in flatter regions of the fitness surface and were therefore more robust with respect to mutations."
In a plantCodoñer, Darós, Solé and Elena found the same reversal in living pathogens, two viroid species competing inside one host plant. Under optimal conditions the fast, genetically uniform species won. Then "the slow-growth species was able to outcompete the fast species when the mutation rate was increased."
Read against the card, this says which lineages keep their identity under heavy variation. A genotype whose mutational neighbours are nearly as good as it is loses little when it miscopies. What survives heavy mutation is a neighbourhood of sequences that tolerates being varied.
The part that may generalise
The framework states its loss event in terms of identity. The quasispecies model gives it a clean worked case in which identity is lost while the material carries on, with extinction arriving later at a separate condition of its own.
Whether the framework's conditions already separate those two losses, or whether its loss event would need a second threshold to express what this model shows, is left open here.
What would show this reading wrong
A replicator model in the same terms in which the leading genotype held its equilibrium frequency above its stated error threshold would break the reading of the threshold given here.
Evidence that error catastrophe and extinction coincide in every real replicating population would reduce the two-losses reading to a property of the model.
If the reversals in the two competition experiments turned out to depend on something other than robustness to mutation, the reading of what selection holds on to would fail.
Honest limits
This is a reading of published work. Nothing on this page was measured, simulated or replicated here, and this card carries no live panel. Spatial structure plays no part in the reading given here.
Eigen's 1971 paper is cited from its bibliographic record. The publisher's copy is paywalled and was not read. Everything quoted about the model's rules comes from Bull, Meyers and Lachmann's simplified version, and the general form of the threshold for long sequences is not stated on this page because it was not read from a primary source.
The digital-organism and viroid studies are quoted from their published abstracts. Their methods and data were not read, so no claim is made here about how the fitness surfaces were measured or how large the effects were beyond the figures quoted.
Sources
Eigen, M. (1971). Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58(10), 465–523. The original quasispecies model. Cited from its record; full text paywalled and not read. doi.org/10.1007/BF00623322
Bull, J. J., Meyers, L. A., & Lachmann, M. (2005). Quasispecies made simple. PLOS Computational Biology, 1(6), e61. Source of the definition, the two-genotype model, the error threshold, the gradual approach, the distinction between error catastrophe and extinction, lethal mutagenesis, and selection on the distribution. doi.org/10.1371/journal.pcbi.0010061
Wilke, C. O., Wang, J. L., Ofria, C., Lenski, R. E., & Adami, C. (2001). Evolution of digital organisms at high mutation rates leads to survival of the flattest. Nature, 412(6844), 331–333. Source of the quasispecies prediction as quoted, the forty paired populations, and the competition reversal. Quoted from the abstract. doi.org/10.1038/35085569
Codoñer, F. M., Darós, J. A., Solé, R. V., & Elena, S. F. (2006). The fittest versus the flattest: Experimental confirmation of the quasispecies effect with subviral pathogens. PLOS Pathogens, 2(12), e136. Source of the viroid competition result. Quoted from the abstract. doi.org/10.1371/journal.ppat.0020136
Related on this site: Living Structures, the column this belongs to; the self-maintaining membrane, the same question of holding a distinction against spreading, asked of a physical boundary; and the taxonomy for the axis this card sits on.