Micro+and+macrolevel+dynamics

Prev: Vesicles and the information threshold

TO DO:
 * Add explanation of strength of parasites
 * Extend/improve explanation of why direction of movement on the trade-off is reverted
 * Extend explanation of self-tuning death rate

=Micro and Macrolevel dynamics: intricate implicit mutual interactions=

In the previous sections, we have first seen examples of emerging higher level patterns on which selection could act (e.g. spiral waves in the hypercycles, and waves in the minimal eco-evolutionary model) and later examples of predefined higher levels (e.g. Wilson's trait groups, cells in the stochastic corrector and vesicles). However, we have not yet been able to directly compare the dynamics of emerging and predefined higher levels.

This was done by Takeuchi and Hogeweg (2009). They also implemented the model we discussed as the minimal eco-evolutionary model for emerging higher levels of selection in a different way, with a predefined micro and macrolevel: __Microlevel:__ __Macrolevel:__
 * Two types of molecules: replicators (R) and parasites (P), ie an RP-system.
 * Parasites are either in a folded or unfolded state. They can only be replicated if they are unfolded, but when they are folded they can perform a certain task, which in this model is assumed to be lipid production. Hence, parasites in the folded state enhance the growth of the vesicle they are in. The parameter //l// describes the fraction of the time the parasite is folded, the parameter //kL// how well it binds to the replicators (as before).
 * Ongoing mutations (in contrast to the stochastic corrector, which had no mutations).
 * Explicitly defined vesicles, modeled in a CPM
 * Growth rate of vesicle depends on the number of folded parasites inside.[[image:binf/vesicles1.png width="560" height="259" align="right"]]
 * Vesicles can divide once they contain a certain minimum number of molecules.

Results of this model first of all show a nice example of (stochastic) correction: an ancestor trace on the values of //kL// shows that although //kL// values might be quite high at any given time, the long ancestor has a relatively low value of //kL// (and hence is a relatively weak parasite). The explanation for this is that on the short term, within vesicles stronger parasites are selected. However, on the long long-term between-vesicle selection selects for vesicles that contain relatively weak parasites because these vesicles contain more replicators and hence grow faster. (Stochastic) variation between vesicles allows for this higher level selection.

In the long run, we again find that there is a trade-off between //kL// and //l// (as we saw in the non-vesicle model) and that over time, both the value of //kL// and //l// increases. This makes sense, because folded parasites increase the growth rate of vesicles (and high //l// -> many folded parasites). However, if this dependancy of vesicle growth rate on folded parasites is removed, the direction of movement on the trade-off changes and instead vesicles with both low //l// and low //kL// are selected. This means that in this case the selection for fast replication of the parasite dominates. HOWEVER, this result is only found for high mutation rates. [EXPAND ON THIS EXPLANATION: Why are low kL/l parasites replicated faster than high kL/l parasites?]

Why does this happen? And why can this system still sustain itself (ie why aren't the vesicles killed by fast-growing parasites)?

To investigate this, we measure the death rates of vesicles. We consider these as a function of delta-//l//, the distance from the bifurcation value of //l//, the value at which the parasites become too strong and the system becomes unsustainable. Compare low //kL// parasites (lower left corner of graph, fast replication) and high //kL// parasites (upper right corner, strong binders but folded most of the time). For high //kL// values, the death rate of the vesicle is lower than for low //kL// as long as you are before the bifurcation point (//delta-l// > 0), BUT beyond the bifurcation point (//delta-l// < 0) the death rate is lower for low //kL//. Within vesicles, there is selection for stronger parasites and hence for lower values of //l//, i.e. vesicles will move to the left on the x-axis. If mutation rate is high, evolution is fast and hence the system will be close to the bifurcation point. Selection for lower death rate of the vesicles will then lead to selection of lower //kL//.

Furthermore, if //kL// is lower the overall within-vesicle dynamics will be slower (EXPLANATION WHY?). Then, the effect of stochasticity increases. This stochasticity can "save the vesicles": Within-host selection for stronger values will often push vesicles past the bifurcation point (//delta-l// < 0), but since for low //kL// de internal dynamics towards vesicle death are slower more vesicles might be saved by a stochastic fluctuation that pushes them back to the other side of the bifurcation (//delta-l// > 0). For //delta-l// > 0, on the other hand, the system evolves towards faster dynamics and a smaller effect of stochasticity. In this way, the death rate tunes itself! (MORE EXPLANATION NEEDED)

__What does this model tell us about explicitly defined vs emerging higher levels?__

Comparing this model to the non-vesicle case:
 * Explicit higher level entities (vesicles) are less stable than emerging higher level entities (waves), especially at high mutation rates.
 * Stochasticity is maximized and used, both for correction and tuning.
 * Implicit interactions (in explicit multilevel models) can automatically mutually tune the "parameters" (compare to the previous vesicle model, where parameters had to be tuned by hand).

__Bottom line__ In multilevel biological systems you should expect the levels not to be independent, but very much dependent on each other. And we should expect that the levels affect each other, both from micro to macrolevel and from macro to microlevel. Then, asking the question "what level is causing the observed dynamics?" (e.g. selfish gene, or part of the group selection vs kin selection debate) is actually non-informative, because what happens at a certain level will always influence __and__ be influenced by the other levels in the system.


 * 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) - Added page