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= = =Individual vs population-based diversity=

As mentioned before there are several biological examples of population-based and individual-based diversity: In fact these alleles are conserved orthologs in these different species ([|Ben-Shahar et al. 2002]).
 * [|cGMP]-dependent [|protein kinases] coming in 2 alleles
 * in [|Drosophila] this is expressed as population based diversity in the rover / sitter polymorphism (cf [|C. elegans])
 * in [|bees] this is expressed as individual-based diversity when bees become foragers due to over-expression of cGMP-dependent proteins

To study under what conditions individual- and population-based diversity evolve Pagie and Hogeweg ([|2000]) used a model based on the [|restriction-modfication (RM) system] in bacteria: The results of this model shows that the system, more or less arbitrarily, goes to one of two attractors:
 * multiple genes in each bacteria possible
 * but also population-based diversity possible
 * also [|plasmids] carrying the genes:
 * [|restriction enzymes] that cut DNA at specific motifs
 * modification enzymes that prevent cutting by [|methylation] of DNA
 * this system allos protection of own DNA while cutting foreign DNA such as those of viruses. However it has one weakness in that methylation cannot distinguish foreign and native DNA
 * the environment was modelled as a spatial CA with bacteria and the number of plasmids, possibly many types, and viruses which can infect the bacteria
 * literature at the time did not reveal whether diversity of plasmids was population- or individual-based
 * bacteria grow, but with a penalty depending on the number of plasmids (not essential for results) and can die
 * moreover plasmids mutate and there is a small chance of new plasmids, with vertical as well as horizontal inheritance of plasmids
 * viruses infect bacteria and if not methylated they die, if methylated they can survive and reproduce
 * 1) **Individual-based diversity**
 * empty space
 * virus regions
 * many plasmids per bacteria (clever!)
 * wave patterns in space
 * 1) **Population-based diversity**
 * little empty space
 * few viruses
 * different plasmids as different spatial regions
 * one plasmid per bacteria (stupid, but happy)
 * static patterns in space

To better understand there results a more controlled approach was made:
 * //every 1000 time steps an extra plasmid was introduce in a single bacteria//

Results show that:
 * the initially introduced plasmid spreads over the whole field and takes over (since viruses are also methylated)
 * this happens continually with new plasmids
 * then there is a change in the system after a certain number of added plasmids and the system becomes population based!
 * at this stage there is a very wavy pattern and adding a single plasmid allows it to take over the whole field:
 * this is because two neighbouring bacteria each loose opposite plasmids and this chance is large when you have more plasmids
 * they then become mutually exclusive and isolated from reciprocal viruses, i.e. they only need simply another methylation than other
 * then all bacteria loose all plasmids except a unique one
 * new plasmids then no longer spread in the system (cf bird influenza)

These results show that for a low diversity of plasmids there is only one attractor, i.e. individual-based diversity. However for high plasmid diversity the system can switch to a population-based solution (also due to small costs imposed on having plasmids) and viruses die out.

Next: Sparse fitness evaluation