neutral

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 * TODO List**
 * REF Schuster: studied local mutational steps what this meant for how sequences **percolated****through sequence space by neutral mutations**
 * REF Kimura: neutral evolution
 * CLARIFY: equation molecular clock
 * REF: Huynen (1998, REF) found that the degree of drift on a network is linear with the degree of neutrality
 * REF: Zukerkandle (how to spell?)
 * REF: Gould, punctuated equilibrium
 * REF: Nimwegen (REF) have also shown that: the probability of making long neutral path detours is greater than going through fitness valleys, and moreover, the probability of going though a short deep valley is greater than wide shallow valleys.
 * REF: Recent studies on actual proteins (?) show that many structure have the same function (Ekland et al 1995 REF) (CHECK THIS).

=Evolution on a neutral network=

[|Percolation] on neutral paths
Besides considering what the specific adaptive RNA secondary structure landscape might mean for the information threshold, we can also consider what effect the global properties of the RNA landscape may have for long term evolution. In this sense, Schuster (REF) studied local mutational steps what this meant for how sequences **percolated** **through sequence space by neutral mutations**, i.e. the same structure. He found that, allowing two step compensatory mutations, that many sequences can change completely without changing structure. In other words they can percolate throughout genotype space. Secondary structure can be achieved by all types sequences, //and// there are mutational links, or connections, between all these sequences. This illustrates the **neutral path** concept, which describes a series of nearest neighbour sequences that fold into indentical structures. This is true for **typical structures** and is a direct result of the **degeneracy** in the landscape.

Such insights suggest that the properties of evolutionary landscapes could have profound consequences for how evolution can proceed, namely by the way that a population is distributed on the landscape and how it can percolate through it. Interestingly, genetic algorithms normally assume "infinite" populations in the sense of starting everywhere in the landscape. In constrast, biological systems will always have finite populations that are **localized within the landscape.** This may have consequences for how evolution proceeds because the population is much smaller than the possible phenotypes, and because the genotype-phenotype mapping is so non-linear. What then becomes important is how rugged the landscape is, which determines:
 * local optima
 * small [|correlation length], i.e. how far from initial position such that fitness is correlated (see correlation landscapes)
 * redundancy, i.e. how many identical structures
 * overrepresentation of identical structures, i.e. they are close by
 * more than expected number of neutral neighbours farther away

These characteristics of the landscape allow for the precolation of identical structures through sequence space, i.e. there are neutral paths. This is more that neutrality per se, because it is a **distributed and connected neutrality**, i.e. not clumped. (Interestingly, the concept of neutral paths can only be visualized in 3D and not in 2D, which illustrates the weakness of the landscape metaphor.) The next question we can ask is: //so what do these properties mean for evolutionary dynamics?//

Adaptive vs neutral dynamics
After the formulation of the concept of neutral mutations there was excessive debate about what drives evolutionary change and diversification. On the one hand there were proponents of adaptive mutations as the main driving force in evolution. On the other hand there was the [|neutral drift / diffusion theory] of **Kimura** (1969 REF).

Neutral drift was based on the finding that molecular variation was much larger than expected given that natural selection should remove it! Moreover, if frogs for instance, there is more sequence level divergence than between mice and humans despite two frogs being phenotypically more similar. This means that variation need not be fitness related. Instead Kimura proposed that genotypes just drifted in time which gave rise to the **[|molecular clock]** concept with diffusion in genotype space as: D = sApL/(3+4pN) on a neutral path D'=lambdaD (NOT CLEAR).

In a study of evolutionary dynamics in a landscape with neutrality, Huynen (1998, REF) found that the degree of drift on a network is linear with the degree of neutrality. So what does this mean for evolutionary dynamics, what does it matter? What do populations see during drift or walks on neutral paths? Results show that the number of **new structures** observed increases over time and doesn't level off. This means that there is always a possibility of finding something better! However, there is a **shadow of similar structures** which follows a population through space.

This work was mentioned by Zuckerhandl (?) at Kimura's memorial lecture, a proponent of adaptive dynamics, to suggest that neutral and adaptive evolution could now be reconciled.

tRNA target structure evolution and [|punctuated evolution]
So lets study simulations of tRNA evolution towards given target structure. We start with homogenous populations and add mutations and replication relative to fitness defined by distance to the target structure.

Typical results show that initially populations approach a given structure very fast, which could be explained as going towards the **typical structure**, i.e. the average. Then structural change slows down and show phenotypic punctuated evolutionary dynamics (i.e. leaving the typical structure). How can we understand such **punctuated evolution**?

Punctuated evolution is somewhat of a controversial term since neo-Darwinism postulates that:
 * evolutionary change should be gradual
 * successful monster can't find mates!
 * small steps are assumed to be better for finding good things

However [|Gould] (REF) suggested that:
 * the fossil record is very **punctuated** and the evolution is [|epochal]
 * there neo-Darwinism can't be true!

Here we see, in simulations of RNA evolution that:
 * stasis is drift on neutral paths
 * sudden phenotypic change happens when "better" structures are found in a new area of the neutral network

This illustrates how continual gradual evolutionary change (mutations) can lead to sudden jumps in phenotype space, suggesting how the two points of view can be reconciled. This doesn't mean that this is the mechanism that explains epochal evolution in the fossil record. For instance, the previously discussed example of virus evolution in bird-like and human-like hosts, also showed epochal evolution. In that case however it was the dynamics of spatial pattern formation that lead to punctuated evolution. In both cases however, epochocal evolution arises due to higher order dynamics above the level of the replicator. Interestingly, Lenski's group (Elena et al. 1996) found similar results in //E. coli// evolution experiments, i.e. epochal evolution with fitness related to cell size.

Population structure
To understand how the population is distributed on the fitness landscape it is necessary to visualize it. This can be done using [|principal component analysis] (PCA) and plotting individuals according to the first two axes of variation. What is observed is clusters of individuals, i.e. several quasi-species. As the population becomes bigger there are more clusters. These quasi-species represent several "fittest" structures and their "mutant clouds".

Evolutionary optimization
In the study by Huynen et al (1996) it becomes clear that RNA optimization in time is:
 * epoochal
 * there is loss of diversity / divergence during pheonotypic transitions, i.e. [|bottlenecks]
 * this is followed by a build up of variation

Studies by van Nimwegen (REF) have also shown that:
 * the probability of making long neutral path detours is greater than going through fitness valleys
 * moreover, the probability of going though a short deep valley is greater than wide shallow valleys.

Moreover, it is clear that a give structure can be formed by many different sequences, and so one can travel far on the neutral network. Moreover, close by sequences give many different structures and therefore one doensn't have to go far! Recent studies on actual proteins (?) show that many structure have the same function (Ekland et al 1995 REF) (CHECK THIS). So one could then ask: //why do more complex things evolve?// Well:
 * complexity can give rise to new functions
 * redundancy in sequence-structure mapping could be greater for more complex structures!
 * more neutrality in more complex structures?

So we have seen that evolution on a neutral can lead populations to discover new better structure leading to epochocal evolution. But where exactly populations go on the neutral network? Can we say more about this?

Next: Phenotypic error threshold