pheno

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 * TODO List**
 * REF Eigen Schuster 1979
 * CLARIFY: the equation part
 * CLARIFY: Their results were striking in that the error threshold didn't seem to apply for phenotypes! With only one mutation per replication means a large lambda independent on mutational distance? This means there is no error threshold (NOT CLEAR). However, the assume only single mutation, but for calculating the information threshold requires more that one (precolation of TIMESCALES?).

=Phenotypic error threshold=

In the previous section we have gained some insight into the structure of the genotype-phenotype mapping of RNA secondary struture, and therefore gain some handle on how evolution could proceed in such a landscape. The question we ask here is: //what does such a landscape mean for the **information threshold?**//

Previously we found that the conditions for the error threshold was: Q > 1/sigma. This condition translates to a conditions for information of: L < ln(sigma)/(1-q). However, if mutants have the same fitness (phenotype) then L must be zero! i.e. the genotype will be constantly drifting, and the system will always be below the information threshold. This means that we need re-phrase our original question to: //can we maintain a phenotype? i.e. are we above the **phenotypic**// **error threshold?**

Takeuchi et al ([|2005]) addressed this issue using a model based on the original quasi-species model (Eigen and Schuster 1979) and included a master phenotype and mutant phenotypes. All phenotypes replicate and can mutate to the same and other phenotypes, with no back mutations. This leads to similar quasi species equations except that lambda is now the fraction of mutations that is the same as master neutrality.

(NOT SURE ABOUT THIS SECTION) This model leads to the following survival condition for the master equation: sigma Q + sigma (1-Q) lambda > 1 where Qe = Q + (1-Q) lambda > 1 / sigma, i.e. at each position.

The question the becomes, how can one calculate lambda? For simplicity, we assume the additive assumption, i.e. base substitutions are independent (no epistasis, smooth landscape). From this one can obtain:

q = sigma^(-1-N) - lambda / (1 - lambda)

Interestingly, the additive assumption assumes a smooth landscape and therefore shouldn't work, since we know that the RNA landscape is rugged. However it does work.

In constrast Reidys ([|2001]) analysed the phenotypic error threshold but only included single mutations. Their results were striking in that the error threshold didn't seem to apply for phenotypes! With only one mutation per replication means a large lambda independent on mutational distance? This means there is no error threshold (NOT CLEAR). However, the assume only single mutation, but for calculating the information threshold requires more that one (precolation of TIMESCALES?).

Takeuchi et al (2005) considered all possible mutation distances and showed that although neutrality helps the error threshold, it doesn't cease to exist. Interestingly all mutations were considered to be independent although in real RNA they are not. However the additive assumption appeared to be a good match apparently because the positive and negative epistatic effects compensate each other: D of neutral mutations < average D, i.e. local enough (epistasis or ruggedness non-local). This means that a **wrong assumption** can work relative to a certain problem, however emphasis is on testing assumptions using simulations:
 * simulations take more knowledge into account
 * can test the assumptions of analytical solutions
 * both combined give more insight

Finally, these results show that the information threshold can be alleviated somewhat with neutrality, however as sequences get longer neutrality tends to decrease! This means that neutrality doesn't allow us a means to solve the information threshold.

Next: Coding structures