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  • REF: Sewell Wright
  • REF: Kauffmann NK landscapes
  • REF: royal road John Holland
  • REF: melani mitchell royal road
  • REF: van Nimwegen 2000
  • CLARIFY: goes as far as can with Darwinian selection, but Darwinian selection does work as far as possible (NOT CLEAR)
  • REF: Adami et al AVIDA
  • PAGES: split into separate pages?

Constructed landscapes and landscapes as a metaphor

The (adaptive) landscape metaphor is of course useful to give an intuitive idea of what kind of things could be going on, and was originally proposed by Sewall Wright (REF?). However, the concept is also flawed:
  • it is misleading: in 2D there cannot be neutrality
  • it is misleading with only point mutations: in mutli-D there are many more mutational operators which make "nearness" hard to define
    • what is closeness with respect to cross-over?
  • fixed dimensions: duplications lead to changes in dimensions which cannot be accomodated in a landscape of fixed dimensions
  • constant fitness: in landscape metaphor the evolutionary pressured are assumed to be constant, however normally they would change, but sea-scape doesn't really help as metaphor

In the following we study constructed landscape that explore particular aspects of adaptive landscapes. Moreover, we aim to make a connection between coding structure and spatial pattern formation, both of which can leave evolutionary signatures in their own right. Here our main question is: what kind of traces do evolutionary processes leave on evolved entities?.
And these are:
  • not there because they are functional
  • not there for biochemical reasons
  • only there because it has evolved in a certain process / way

Landscape studies

We have already mention the NK landscape studied by Kauffman (1993) with respect to Boolean networks. He studied the effect of ruggedness and how it affects evolution. His main conclusions were that the landscape shouldn't be too rugged otherwise one gets stuck on local optima. However this was prior to the discovery of neutrality. As with other constructed landscapes however, the NK landscape was made with a prior idea of what to study, i.e. how ruggedness affects evolution. In contrast the RNA landscape follows from the properties of its sequences and their folding and we have to study what the effects of that are.

The Royal Road

This landscape was developed by John Holland's group to study the building block hypothesis. In this line of thinking, building blocks were considered ideal for evoltution. They would allow for a smooth landscape were evolution does not get stuck on local optima (deception). The building blocks would allow for big jumps in fitness by means of cross-over. The thinking in genetic algorithms was that cross-over could be used with building blocks to get fast evolution and spread of innovations, with cross-over as the main mechanism (They were apparently unaware of the concept neutrality and/or its potential role in evolution).

In the model the genotype is represented by a bit-string with blocks that only give fitness when they have a certain configuration. Melani Mitchell (REF) then used this landscape to prove the effectiveness of cross-over and blocks for evolution. Her results however showed that cross-over hardly made any difference! Cross-over doesn't help! The main reason for this was that the population was always so conserved in genotype space that cross-over doesn't really make that much difference except at the initial stages of evolution. The main reason for mentioning this example, besides introducing Royal Road landscapes, is that this is a nice example of a constructed landscape which was made to prove a certain point, i.e. it was the easiest case for the cross-over building block hypothesis. Therefore this represents an all the more powerful proof that cross-over does in fact not help within this evolutionary scenario.

Neutrality on the royal road: what is neutral

van Nimwegen (2000?) used the royal road landscape to study neutrality and in particular: what is neutral? He varied population size and mutation rates in the Royal Road and found:
  • epochal evolution
  • increased mutation leads to an increase in maximum fitness, but over the information threshold, i.e. cannot keep fittest, but keeps the part of string that is allowed given the information threshold
  • goes as far as can with Darwinian selection, but Darwinian selection does work as far as possible (NOT CLEAR)
  • with lower population size: more stochasticity and earlier information threshold

So how does this help to understand what is neutral? or what difference in fitness is neutral? Well, from these results it becomes clear that neutral is when one is above the information threshold. So instead of phrasing neutrality in terms of "flat is neutral", here we say "neutral is what natural selection sees as flat!". The information threshold determines what can be selected, and selection defines its own neutrality with respect to the mutation rate.

Evolving to robustness: evolutionary signature?

In the RNA evolution we have seen that as lamdba increases (i.e. evolving to flatter parts of that landscapes), robustness comes for free. Robustness is therefore an evolutionary signature, but how can we identify it in natural populations? Well we would expect high variability per position for any robust solution, i.e. more neutral cases. Is this true?

To address this issue we take a look the AVIDA artifial world (Adami et al REF) which incorporates self-replicating programs in an attempt to define an artificial world for open-ended evolution. This is interesting in several ways, because it helps us to reallise that:
  • so far we have take the process of replication for granted
  • in AVIDA the process of replication actually has to evolve in terms of copying computer code which can copy and evolve
  • one drawback is that it is as hard to study as living systems, i.e. a lot can change and one needs to devise good observational techniques to see what is happening.

Adami et al (REF) observed the system by viewing variation in lines of code in the population over time (FIG), and what is observed is:
  • fitness increases over time
  • population variation decreases during fitness increases: selection and bottlenecks
  • variation only increases on neutral path after selection
  • as fitness contributing location increase more code gets meaning and there is less space for neutrality
  • there is increasing robustness while being neutral

What we see is therefore: both reduction in variation due to selection, and increase in variation due to neutrality, both taking place over time! It would appear difficult to make any predictions about detecting an evolutionary signature for evolution to neutrality.

Next: Accuracy and relevance of RNA landscape