Multi-level+evolution

Prev: Hypercycles in space Next: Minimal eco-evolutionary model of emerging higher levels of selection


 * TODO List**
 * REF to Kauffman: evolution to edge of chaos will always occur, and REF that it need not?
 * REF Boerlijst & Hogeweg about info threshold not solved
 * more detail on why system destroyed when going from 6 to 5 cycles
 * REF hypercycle in space with mutations
 * REF Crutchfield
 * REF why spirals need to be initialized in PDE
 * REF Boerlijst Hogeweg 1995? on spirals and parasites in PDE?

Multi-level evolution: emergent levels of selection
The previous section has shown that all properties of the ODE system can be reversed in a spatial system due to the emergence of mesoscale patterns (spiral waves). In the ODE after 5 or more species the hypercycle becomes a limit cycle and becomes unstable. In contrast in the CA it becomes a pattern of spiral waves, which is globally stable and can be resistant to strong parasites. Next to these differences, we also observe a reversion in the direction of selection on death rate:

In the ODE model, increasing the death rate is clearly a disadvantage. However, if we allow for mutations in the death rate of individuals in the CA, we see that a higher death rate can evolve! The reason for this is that mutants with a higher death rate that take over the core of a spiral will cause it to rotate faster, and faster spirals take over from slower ones. This happens because competition occurs in empty space and with greater death rate there is more empty space and thus a faster rotating spiral. (Note that this does not include a trade-off where higher death rates lead to a change in some other parameter like birth rate, instead it is purely a higher-level entity (spirals) reversing the fitness effects of the hypercycle molecules).

This illustrates how local interactions in space lead to non-local selection criteria in the form of spirals. Therefore, in contrast to the ODE, we do not get the phenomena of **once only selection** because locally stronger molecules can win and globally faster spirals win. Spiral waves can therefore be said to enslave the molecules they are made up of because the fate of these molecules is completely determined by how good the spiral is that they live in. Hence we get positive selection for higher death rates and for giving catalysis which is a reversal of selection relative to the ODE.

This argument only holds for the case that there are stable spirals. However, they do only occur for a certain parameter range of death rate, birth rate and catalysis rates. If e.g. the death rate of the mutants is too high, the spirals will disappear. And once there are no more spirals, the selection for early death will disappear as well and the direction of selection will again be reversed: Spirals -> selection for higher death rate -> faster spirals -> selection for even higher death rate -> spirals disappear (start of chaotic behaviour) -> selection of lower death rate

These reversals of the direction of selection will cause the sytem to evolve to those regions on the border between spirals and spiral break-up, and hence lead to **evolution to the** [|edge of chaos], or **border of order**, as implied by our //invasion criterion// assessment. (Note the comparison with the border line between Class II and Class III CA's, i.e. Class IV)

__//So what does this all mean for the information threshold?//__

Well it certainly is **not** solved! A further look at the invasion of cycle shorting mutants shows that cycles of 5 manage to outcompete cycles of 4 because complex spirals cannot compete with stable spirals, which would suggest that cycles of 5 are the minimum cycle length. From the other direction we see that cycles of 6 out compete cycles of 7, because they rotate faster. However when going from 6 to 5 we see that parasites can invade and kill the system. (NEED MORE INFO HERE). Hence the system collapses, and we cannot sustain hypercycles and increase information (Boerlijst & Hogeweg 1991? REF). Next to this selection for shorter, less-resistant cycles, another important drawback is that we have only studied the system's resistance to parasites by invasion experiments. This technique assumes that mutants enter the system at a low rate, and hence that mutation rate is low. However, if we study the information threshold we should actually consider systems with a high mutation rate! In a CA model in which mutations constantly happen at a certain rate, the system actually only shows limited stability against parasites (REF Boerlijst & Hogeweg?), because then the number of spirals in the field constantly decreases until the system eventually dies out.

We have however gained a very important insight from this study, namely the concept of **multi-level evolution**. We have seen that individual interactions lead to spatial patterns (mesoscale) which through mutation and selection (Darwinian evolution) affect individual interactions and therewith spatial patterns. This has implications for how we view the evolution of complex systems and how we model them:
 * Traditional view: we have a model with a variable and we determine what happens to that variable in evolution
 * CA view (Crutchfield (1989? 1995?)): we have micro rules (constant rock bottom) which leads to macro entities with their own behaviour
 * Here: evolutionary systems break open the rock bottom by changing the parameters of the system!

//Hence we must let go of this idea of a static simple rock bottom because:// //**the lowest level does not make sense except in light of higher level processes.**//

One more point to consider with respect to spirals is that they are **very generic** and occur in many different systems. This means that conclusions that are drawn from them are very fundamental! For instance, in PDEs spirals do not arise spontaneously as in CAs due to minimum scale, but they need to be initialized (REF). However once initialized we see that they cannot be resistant to parasites since parasites will be in all cores and the system dies out. However this is due to the **everything being everywhere problem** (cf attofox). When a threshold is used for a probability of a molecules being present (i.e. to conserve mass) the PDE shows the same properties as the CA (Boerlijst & Hogeweg 1995?). Spirals are therefore generic, as are the conclusions drawn from them.

Next: Minimal eco-evolutionary model of emerging higher levels of selection

Crutchfield 1989? 1995? Kauffman 1969 Boerlijst & Hogeweg 1991? Boerlijst & Hogeweg (1995) Spatial gradients enhance persistence of hypercycles. //Physica D// 88: 29-39. [|Download PDF]
 * References**

(CHANGELOG 2014-2015)

- Elaborated on explanation of evolution towards the border of order - Added picture