Minimal+eco-evolutionary+model+of+emerging+higher+levels+of+selection

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TO DO: - Improve explanation on why we move up on the trade-off (in stead of down)

=A minimal eco-evolutionary model of emerging higher levels of selection=

The hypercycles were a proposed solution for the information threshold problem. Once we had implemented the hypercycles in a CA model, we observed that we could use this model to study the emergence of mesoscale patterns (spiral waves), their stability against parasites, and higher levels of selection. However, we can also go back one step and ask: what kind of dynamics do we get if we make a minimal model of a replicator (i.e. an "RNA") and a potential parasite? Such a model was made by Takeuchi and Hogeweg (2009).

Consider a system with a replicator R and a parasite L. The parasite can be in a folded (functional) and unfolded state, and only the unfolded state can be replicated. The parameter //l// of a parasite describes which proportion of the time it is folded (and hence cannot be replicated). Both replicators and unfolded parasites can be replicated by a replicator R. The parameter //kL// describes how strongly parasites bind to the replicators. The system can be summarized by these reactions: This system was implemented in space (CA). What happens if we let the system run, and let the parameters //l// and //kL// evolve? The system forms waves in space. There is a difference between young waves (that have just arisen) and older waves. In young waves, the average //l// value of parasites is high, while in older waves the average value of //l// is lower (see figure; blue = high //l//, yellow = low //l//). Hence, we see that over the lifetime of the wave the parasites in the wave become stronger, because they spend less time in their folded state and more time being replicated.

However, if we look at a longer timescale we see that the average value of //l// in the system goes up: the system seems to evolve weaker parasites! How can this be? Remember that the parasites can evolve two parameters: If we look at the evolution of these two parameters, we observe an **emergent trade-off** between //kL// and //l//. This trade-off is not inherent to the individuals, but rather emerges because of selection on the higher level entities (the waves). Evolutionary trajectories first converge towards this trade-off and then move upward along the trade-off line, increasing both //kL// and //l//, leading to parasites that bind more strongly to the replicator (high //kL//) but do so less often (high //l//).
 * //l// : how often they are in their folded (inactive) stat//e//
 * //kL// : how strongly it binds to the replicator

Why do we find this trade-off? As said, it emerges from selection on the wave level. Intuitively, you might expect that parasites would become stronger and stronger, increasing both their //kL// and decreasing their //l//. This is also what we see over the lifetime of a wave. However, waves with very strong parasites have a very high probability of dying out ("being eaten up by the parasites") quickly, and will hence not be able to produce many new waves. In this way, selection at the wave level poses a maximum on the strength of the parasites. Why then do we move up on the trade-off (in stead of down, towards lower //l// and //kL//)? Again, we need the level of waves to understand this: If //l// is high the probability of "births" of new waves is larger, because these starting waves experience little trouble from the parasite. (NEED MORE/BETTER EXPLANATION)

The waves we see in this model: Hence, these waves should be seen as **//Darwinian entities//**, upon which selection can act. This model shows an example of long-term evolution on the level of these mesoscale patterns.
 * "are born", "live for some time" and "die"
 * "mature": the strength of the parasite changes over the lifetime of a wave
 * "mutate" (see "mature") and can be selected
 * compete with each other

A final note: this system has now evolved parasites that are in a folded state most of the time. In this folded state, these parasites might have some different (ribozymatic?) function. Hence, this system shows a potential for ecosystem based information accumulation //through// its parasites.

Next: Hypercycles and timescales


 * References**


 * Takeuchi N and Hogeweg P**, Multilevel selection in models of prebiotic evolution II: a direct comparison of compartmentalization and spatial self-organization. PLoS Comp Biol. (2009)

(CHANGELOG 2014-2015)

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