Spatio-temporal+pattern+formation+as+prerequisite+for+evolving+complex+(regulatory)+individuals

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=Conjecture: spatio-temporal pattern formation as prerequisite for evolving complex (regulatory) individuals=

Take the density classification CAs as an example:
 * what can be constructed or evolved with or without spatial pattern formation (remembering that so far we have seen that with pattern formation everything can change)?
 * what can we do with this observation?

Crutchfield (Mitchell et al. 1994) set up the paradigm system of density classification, i.e.:
 * deciding whether a CA has majority 1's or 0's, but can't count and must transform states
 * majority 1's should become 1 and vice versa (cf Class I CAs)
 * however the CA should be sensitive to initial conditions (cf Class iV CAs)
 * this was done with 1D CA's with 149 positions, 3 neighbours, 2^149 arbitrary initial conditions and 2^2^7 possible rules

From this Mitchell et al (1994) obtained a best solution of 84% initial conditions correctly classified given a certain length of simulation run.

==Evolved computation and (versus) mutational priming==

Pagie and Hogeweg (2000) took this paradigm system (i.e. nice non-linear mapping!) and used it to study how it evolves in space and co-evolution using the following model: The model was then compared in CAs with spatial pattern formation and mixed CAs.
 * density classification CA as a model for recognition of environmental cues
 * co-evolution fo CA rules and intiial conditions in space where fitness depends on % correctly classified
 * mutation of solves in rule tables of 1's and 0's.

If random initial conditions are used the problem is too hard and there is no evolutions. Therefore the fitness criteria was adjusted so that fitness function is lowest for 50% classification and maximum at 0 and 100% classified. In this way easy initial conditions out compete hard ones until they become solved and then harder problems can invade. Results show: But do solvers solve?
 * choatic waves of two types of initial conditions, i.e. majority 1s or 0s): this can only happen if there is variation in initial conditions where two-lineages self-organize into population-based diversity
 * when hard cases are tested on solver performance, i.e. nearly 50% 0's and 1's: solvers sovle on average 75% of cases, which is not too far from 85%, which shows phenotypic generlizability or individual-based diversity
 * moreover, when tested on actually encountered initial conditions, solvers are at 90% correct classification!

It is also interesting to note that the system **keeps evolving** since the problem has **no solution**! This is different to a function with solution and is of course a nice feature for continuous evolution!

Now shuffle the field! Results:
 * there is variation in the population but no speciation as above (in non-mixed we see that several lineages survive)
 * fitness to encountered intial conditions is either very high or low when the population converges on one value, i.e. 1's or 0's, and they have evolved to be Class 1 and just classifies in a certain way
 * however this value can switch very easily: 1 mutation switches classification, i.e. the system is **primed** mutationally
 * (Note that there is still local selection, i.e. sparse fitness evaluation)

Clearly we now have evolved two ways of adapting: Evolution has therefore optimized its potential given external constraints:
 * 1) **Regulatory switching** with "sensor", i.e. solving the initial condition
 * 2) **Mutational switching** with no sensor, i.e. pick up environment by evolutionary change, an //evolutionary based solution//
 * structuring its genome so that it allows for more than random chance of good mutations
 * we did not introduce any new mechanism in the evolutionary process
 * here evolutionary information integration is required

Actually Mitchell et al (1994) also evolved in space, but only found 1 in 1000 good solutions. However he evolved on a random set of initial conditions and classifiers on evolved in two ways: block solutions and signal solutions (particle based). Block solutions do not evolve in space as they are fooled by co-evolution of initial conditions. Signal solutions do do well.

Next: Mutational priming

**Pagie LWP & Hogeweg P** (2000) Information integration and red queen dynamics in coevolutionary optimization. Proceedings CEC 2000, pp. 797-806. [|DownLoad PDF].
 * References**
 * Mitchell MC, Crutchfield JP & Hraber PT** (1994) Evolving cellular automata to perform computations: Mechanisms and impediments. //Physica D// 75:361-391.