Stochastic+corrector+model

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=Stochastic corrector model= The potential role of group selection in the origin of life was studied by [|Szathmary] and Demeter ([|1987]). They asked the question whether group selection could help overcome the information threshold? They developed a model based on ideas similar to the model of D.S. Wilson, but then in a prebiotic setting. This model is called the //stochastic corrector model//. The model considers two explicit levels: molecules and vesicles (which contain the molecules). They consider two types of molecules, X and Y, which together form a replicase that can replicate both X and Y, causing growth of the vesicles. Hence, vesicles need both X and Y to grow and grow fastest if [X] = [Y]. However, parameters are chosen such that X replicates faster than Y, making the system unstable. Vesicles grow and split without any interchange of molecules (i.e. an extreme grouping case). In this process, however, vesicle composition could change due to stochastic processes during vesicle division and because of stochastic replicator dynamics. Moreover, multi-level selection is explicitly implemented in that vesicles need both X and Y molecules to replicate (i.e. cooperation), but within a single vesicle X outcompetes Y. The question here is then: //can group selection stabilize the system?//

Although the two dynamics are separated, i.e. intra- and inter-vesicle dynamics, they are statistically related in that the replication dynamics are used as a parameter in the vesicle dynamics. However, the population of vesicles is considered to be constant (no extinction). The model results show that both molecules can be maintained in the system due to group selection, and that even the master cell (which contains equal amounts of X and Y) can persist. However, this happens only if there are few replicators per vesicle. In other words, this system works when the number of molecules is small because this makes it easier to get similar ratios by stochastic correction and because it makes selection within vesicles weak. However, when considering the information threshold we should note that stochasticity lowers the information threshold, because the effective population becomes smaller (hence more stochasticity and a higher probability of losing the master sequence by chance). Similarly, limited diffusibility (either because of local behaviour and low diffusion rates (or because of unpermeable vesicle boundaries?)) lowers the information threshold because in the case of local competition and low diffusion, the master sequence will not compete with an "average population", but mostly with copies of itself. These latter points were not realized in the model since there was no mutation!

Therefore, although the model shows that group selection can help to maintain information given certain molecules, group selections only works under those conditions that worsen the case for information relative to the information threshold if mutation is included.

Next: Vesicles and the information threshold

**Szathmary E & Demeter L** (1987) Group selection of early replicators and the origin of life. J. theor. biol. 128:463-486 [| link]  (compare **D.S. Wilson** (1975) The theory of group selection. Proc. Nat. Acad. Sci USA 72:143-146 [|link])
 * References**

(CHANGELOG 2014-2015) - Extended explanation of the model - Added picture