Hypercycles+and+timescales

Prev: Minimal eco-evolutionary model of emerging higher levels of selection Next: Nicholson-Baily host-parasitoid model


 * TODO List**
 * REF Hogeweg about non-cycle topologies! 1994?????

=Hypercycles and time scales=

Coming back to hypercycles, let's consider why we considered hypercycles (and not other structures) in the first place: because this was the only stable configuration in ODEs. However we have not considered non-cycle topologies in a CA! Lets try (Hogeweg 1994?):

We will look at a model of minimal size. We have seen in the CA model that 6 and 5 cycles can resist parasites, while 4 and 3 cycles die out. However, for cycles of 2 there is ecological persistence in the presence of parasites, although the parasite is in the majority. Hence we consider the cycle of two with a parasite:

//But what happens if we add evolution of the parameters?// We find (Hogeweg 1994?) that the catalysis of B by A  doesn't change, but that A and P compete for B, i.e. both A and P increase the amount of catalysis they receive, and B hence gives more catalysis. However, because A evolves faster than P it wins the competition and P dies out. What we see is therefore that where previously in an **ecological timescale** the parasite could remain in the system, on an **evolutionary timescale** it is rejected from the system.

//Why does this happen?// What we see is that the introduction of P leads to wavy patterns and **empty** space which can be invaded by the [|mutualists]. The mutualists obviously do not "want" to be invaded by the parasite and therefore the B population evolves to become smaller (less catalysis from A). The mutualists form blobs in space consisting of mainly A and a little B. Because these blobs are harder to invade for the parasite, they stay in the system for longer and hence A gets more catalysis from B. B is therefore, by lowering its own received catalysis and therefore its own abundance, altruistically helping A. For the parasite to stay in the system, it should outcompete A in the competition for catalysis by B. Therefore, the parasite will also increase its received catalysis. It cannot do so too fast, however, because if it becomes too strong it will also kill all B's in its neighbourhood and therewith itself.

So at an **individual level** there is only positive selection to get more catalysis where A and P compete locally for catalysis. However on a **wave level** there is also selection for high catalysis for A, but for P it is limited by wave survival. Hence A is always at an advantage relative to P, can evolve to higher values of received catalysis faster, and wins.

This illustrates an important concept of a system (A, B and P) where it can be ecologically stable, but on an evolutionary time scale parasites are excluded, illustrating the danger of separating such time scales. We discuss this issue more explicitly in the next section: eco-evo timescales.

Next: Nicholson-Baily host-parasitoid model

 Hogeweg P (1994) Multilevel evolution: replicators and the evolution of diversity. Physica D 75, 275-291. [|PDF-file]
 * References**

(CHANGELOG 2014-2015)

- Rewritten the explanation "Why does this happen" - Added figure - Removed text:

Another point is that the whole hypercycle concept is clearly ODE derived.

Next we look at another attempt at crossing the information threshold, namely vesicles and group selection.