Many definitions exist for the term `evolvability'. The most general of these is "the capacity to evolve" [e.g. Smith, 2003], i.e. the capacity for some entity or group of entities to undergo change, or as Suzuki  puts it, "the possibility (potential ability) of evolving a variety of genotypes or phenotypes". Most, however, agree on a more limited definition of evolvability: summarised by Nehaniv  as "the ability to reach `good' solutions via evolution", and implicitly appealing to a requirement for direction within evolution. Likewise, Altenberg  offers "the ability of a population to produce variants fitter than any yet existing"; Wagner and Altenberg : "the genome's ability to produce adaptive variants when acted on by the genetic system"; and Kirschner and Gerhart : "the capacity to generate heritable selectable phenotypic variation". A key issue addressed by these definitions is access to adaptation: the degree to which the evolving system is able to gain adaptive traits (termed `accessibility' in Volkert ) and the amount of evolution required to transform the existing system into a system which possesses these traits. Also important for evolvability, though implied rather than stated explicitly in these definitions, is the maintenance of existing traits: without which the gaining of new traits is largely academic. To use Kirschner and Gerhart's own words, evolvability (in a biological context) requires a capacity "(i) to reduce the potential lethality of mutations and (ii) to reduce the number of mutations needed to produce phenotypically novel traits" [Kirschner and Gerhart, 1998].
In part due to its unfortunate association with ideas of group selection, the study of evolvability is still in its relative infancy. Nevertheless, as understanding of biology, complex systems and, more recently, evolutionary computation has increased; it has become apparent that considerable insight can be made into evolvability phenomena. Research into evolvability follows three broad themes: (i) the characteristics of evolvable systems and the requirements for a system to exhibit evolvability; (ii) actual sources of evolvability within biological and non-biological systems; and (iii) the evolution of evolvability.
Some of the most significant insights into evolvability have been made by Michael Conrad . In particular, he speculates that evolvable systems are a very unique kind of system that reflects a balance between the need for phenotypic stability on the one hand and the pressure towards genetic exploration on the other. Following from studies of complex systems, it is known that the functioning of randomly-connected systems becomes more unstable as complexity increases yet more sensitive to (e.g. genetic) change as complexity decreases. According to Conrad , these competing pressures can only be satisfied in systems that display compartmentalisation, component redundancy, and multiple weak interactions.
Of these requirements, compartmentalisation is perhaps easiest to understand. A compartment is a group of components whose interactions are mostly internal to the group. Consequently, a change (e.g. due to genetic variation) within one of the group's components is most likely to have its effect limited to other members of the group rather than percolating to the entire system. Likewise, multiple changes to the system are likely to affect separate sub-systems rather than have a compound (and probably lethal) effect upon a single sub-system. In Kirschner and Gerhart , the authors describe compartmentalisation as a significant source of de-constraint within biological organisation. Constraints upon evolutionary change occur where one part of a system in unable to change because of the un-welcome effects a change would have upon other parts of the system to which it has strong linkage. An example of constraint is where a gene codes for an enzyme which carries out different roles within more than one different pathway or the same pathway carrying out a different role within a different type of cell; and where a change to the gene would improve its function within one context but lead to a lethal change within the other. If, however, the enzymes within both contexts were coded by separate genes, then both enzymes could vary - and be selected for - independently. Following this logic, it would make evolutionary sense to have genetic independence between both pathways.
However, in Hansen [2003b] the author argues that modularisation is not always the best solution for evolvability. In actual biological systems, there exists a substantial level of pleiotropy between characters: with one gene having an influence (via use of the same protein) upon the function of more than one tissue, organ or trait. Hansen suggests that this is due to increased variational potential out-weighing the interference caused by pleiotropy. In particular, it would seem that pleiotropy should be encouraged in the early stages of adaptation, with an evolving sub-system making use of functional building blocks used elsewhere within the organism. Depending upon the selective pressure placed upon the two sub-systems, their sensitivity to change, and the role of the shared function, it might then make continued sense for the shared function to co-adapt within both systems via this pleiotropic link. Indeed, Hansen suggests that in some cases the evolution of modularity may not be a necessary condition for the evolution of evolvability.
One process in which compartmentalisation appears to play a crucial role is during the embryonic development of multi-cellular organisms [Kirschner and Gerhart, 1998]. Development is characterised by the differentiation of the organism into increasingly more specialised compartments. The initial segmentation of the embryo is dependent upon concentration biases in the fertilised egg. However, as development proceeds, separate compartments rapidly become independent of the activities - and therefore of the errors - occurring in other compartments. Hence, a failure caused by genetic change (or otherwise) in one compartment will not impede upon the development of the entire system. Likewise, evolution can carry out morphological exploration within one compartment without affecting other compartments: another example of de-constraint.
Compartmentalisation also appears within the spatial arrangement of genes within a genome. This phenomenon, called epistatic clustering, occurs in both prokaryotes and eukaryotes. In prokaryotes, it is particularly apparent in the form of operons: where a group of genes with tightly-linked products are located proximal in the genome and are transcribed within a single transcription event. Functionally, this is advantageous for prokaryotes because they save time and energy when expressing new pathways in response to changes in the environment. However, it also aids evolvability by improving the efficacy of horizontal gene transfer since, due to their proximal locations in the genome, it is likely that the genes in an operon would be transferred to other prokaryotes as a single unit. The other prokaryote would in effect receive an entire metabolic pathway, which is far more likely to improve its fitness than a group of un-related genes [Poole et al., 2003]. Eukaryotes, by comparison, transfer genes during sexual recombination. After crossover, a pathway is more likely to be preserved if the genes which code for it are located close together within a chromosome. Evolvability might therefore be improved in a genome which expresses modularity in the form of epistatic clustering [Pepper, 2003].
Redundancy appears in many forms in biological systems. This section introduces functional redundancy, structural redundancy, and weak linkage.
Examples of functional redundancy in biology include: at the genomic level, gene families, pseudo-genes and polyploidy; and at the phenotypic level, allozymes (functionally equivalent enzymes) and homogenous tissues. In a sense, functional redundancy is another form of compartmentalisation where functionally similar, or equivalent, components conceptually form groups that limit the affect of perturbations from other kinds of component [Conrad, 1990]. This buffering occurs in response to both genetic change: where redundant copies help maintain the previous role of the component that has been changed; and phenotypic perturbation: by allowing multiple steady states in the space of phenotypic behaviour. Consequently, functional redundancy provides a means of overcoming the opposing requirements for phenotypic stability and the increased complexity (more components) needed to support genetic change.
Functional redundancy underlies Ohno's theory of `evolution by gene duplication' [Ohno, 1970]. This theory proposes that the majority of molecular evolution has occurred through a process of gene duplication and divergence: whereby genes recursively duplicate (possibly through misaligned crossover) and evolve separately into genes that encode proteins with increasingly more specialised functions. (This process may also be involved in the evolution of modularity - see Wagner and Altenberg .)
Structural redundancy occurs where biological components such as proteins, chromosomes, and pathways have higher complexity than is required to fulfill their phenotypic task. Structural redundancy improves evolvability by acting as a genetic buffering mechanism which limits or gradualises the effect of genetic change. An example is non-coding DNA, which effectively segregates genes, making it more likely that crossover junctions will form between, rather than within, genes: and therefore limiting the disruptiveness of recombination. Another example (see section 5.3) is the mutation buffering provided by redundant amino acids during the evolution of protein structures. Structural redundancy can also enable the formation of new evolutionary mechanisms. A good example is transposons, which make use of structural redundancy within the genome and may play a role in producing mutational hot-spots (where genetic change occurs faster than in other regions of the genome) in addition to their roles (described earlier) in gene duplication and gene formation.
Weak interactions are another form of redundancy, but one that occurs at the interconnection level. A weak interaction has a small informational effect: such as the bond made by an individual amino acid at an enzyme's binding site; whereas a strong interaction has a large informational effect: such as the binding of a substrate at a binding site. In the case of weak interactions, the net effect is one of integration - the summing of the effect of multiple weak interactions from many different sources. Removing or adding a single interaction will have little effect upon this sum, and hence the effect it produces. For strong interactions, by comparison, each interaction is capable of having a decisive effect: for example, the inputs to a logical AND function are strong signals since each can individually determine the output of the function. According to Conrad , redundancy through multiple weak interactions is the best way of compromising genetic instability and phenotypic stability within a system, since it allows a system to have many components and interactions (and therefore a high degree of genetic control) whilst limiting the impact of any particular component or interaction (and therefore the effect of a phenotypic change).
A small genetic change to a weak interaction will typically lead to a small phenotypic change. This means that a system with weak interactions is highly controllable at the genetic level, and suggests why weak interactions are a key component of many evolvable structures seen in biology. The benefit of weak interactions can also be seen in results by Volkert and Conrad  and Volkert  in the context of enhancing evolvability in a non-biological system. In this work, the authors studied the behaviour of random and evolved dynamic network models (non-uniform cellular automata) with and without weak interactions; and found that weak interactions could improve the exploratory scope (access to behaviours), the performance of evolved networks, and the stability of evolved networks when exposed to random genetic mutation.
Weak interactions occur extensively in regulatory pathways. Regulatory pathways, in turn, are thought to have been of considerable importance to the evolution of complex multi-cellular organisms [Kirschner and Gerhart, 1998]. Examples of multiple weak interactions are the calcium ions whose concentration controls the secretion of neurotransmitters in the brain; and the interactions between the binding site, enzymes, enhancers, and control signals that lead to the formation of a transcription complex in eukaryotes. In each of these cases it is the net effect of all of the interactions that controls the activation level. Because of this, the strength of activation can be varied gradually through the addition and removal of components and interactions, and can respond flexibly to new sources of regulation.
The effect of redundancy is to increase the tunability of evolution such that most mutations lead to small or neutral changes to an organism's fitness. Proteins, for example, exhibit all three forms of redundancy discussed above. Functional redundancy results from the presence of gene families and polyploidy and reduces the impact of deleterious variants by offering functional alternatives. Structural redundancy results from the presence of extra amino acids and allows a protein's shape (and therefore its activity) to be varied more gradually than a protein with no structural redundancy. Weak linkage occurs during protein folding where weak interactions such as hydrogen bonding, hydrophilic interaction and Van der Walls interactions produce the protein's functional shape: and allows small changes in the protein's shape and chemistry by adding and removing bonds. The shape of the protein, in effect, can evolve along either of these redundancy axes through a process of gradual change which Conrad  calls mutation buffering to reflect the fact that a protein, or other structure, can experience a number of mutations with little or no change to its functionality. Evolution through redundancy, in this respect, is a clear example of how neutral evolution can lead to adaptation.
Conrad ,Conrad  has attempted to explain the role of redundancy in evolution by appealing to the notion of an organism's adaptive landscape: a solution space which associates every possible phenotypic conformation of the organism with a fitness value and arranges phenotypes such that those which are proximal are separated by a single mutation. Adaptation, generally speaking, is only possible along upward running paths within this landscape i.e. those where a series of neutral or positive mutations link a lower-fitness phenotype with a higher-fitness phenotype. Adaptation is highly unlikely if more than one mutation is required in parallel or if the organism must move to a lower fitness level before a positive mutation is possible. Roughly speaking, the effect of redundancy is to introduce new dimensions to the adaptive landscape, presenting adaptive paths which were not present prior to the introduction of redundancy. Conrad  calls this phenomenon extra-dimensional bypass.
Neutrality is a form of redundancy which has attracted substantial interest in recent years. The theory of neutral evolution was originally postulated by Kimura  in order to explain the high levels of polymorphism (multiple alleles for a gene) found within natural populations. According to the selectionist theory of evolution prevalent at the time, evolution occurs through gene substitution: where the selective advantage gained by infrequent positive mutations causes them to replace less-fit alleles within the population. From this, it follows that mutant alleles will either be removed immediately (due to a negative impact) or move quickly to fixation (due to a positive impact). Consequently polymorphism would only be expected to occur where there is balancing selection brought on by a heterozygotic advantage14. However, experimental measurement of genetic diversity has shown that polymorphism readily occurs when there is no heterozygotic advantage. Kimura's neutral theory of evolution, in response to this, proposed that the majority of evolutionary change occurs through the random fixation (through genetic drift) of neutral mutations: mutations which occur often and have no affect upon fitness. The implication of this is that, most of the time, evolution proceeds through a random walk of the fitness-equivalent solutions within genetic space; and only infrequently does a positive mutation lead this walk into higher fitness regions of the genetic space. The potential routes that such a random walk can follow form what is known as a neutral network: a graph of solutions, each of which has the same fitness, and each of which can be reached by a series of neutral mutations (a neutral walk) from any other member of the neutral network.
There are good reasons, and an increasing amount of evidence, to believe that neutral evolution benefits evolvability. Some of this evidence emanates from research into evolutionary computation and is discussed in section 7.4.2. However, the benefits of neutrality can also be seen directly within the evolution of RNA structures [Huynen et al., 1996,Huynen, 1996,Schuster, 2000]. The mapping between RNA sequence and RNA secondary structure has a number of interesting features. First, sequence space is very rugged. Mutating a small number of bases can result in a very different structure which, ordinarily, would suggest a fitness landscape that is difficult to traverse. However, there are a small number of possible RNA structures and these are represented by a relatively large number of RNA sequences: suggesting a high degree of neutrality. Test-tube experiments have shown that the neutral networks which correspond to different structures are well-connected: meaning a neutral walk within a particular neutral network can eventually lead to other neutral networks that correspond to a considerable number of alternative RNA structures. This, in turn, supports a mode of evolution where a population diffuses within a particular neutral network until a chance mutation leads one member of the population to a higher-fitness neutral network; at which point selection pulls the rest of the population towards the fitter neutral network and the process begins again [Huynen, 1996]. In essence, neutrality overcomes the ruggedness of the RNA sequence landscape which, in the absence of neutrality, would make evolution very difficult. Huynen  calls this phenomenon `smoothness within ruggedness'.
Neutrality is enabled by redundancy in the form of both structural redundancy and multiple weak interactions. However, Toussaint and Igel  offer a view that whilst sources of neutrality are redundant in a static sense, i.e. their current state does not contribute to an organism's current fitness; they are not redundant from an evolutionary perspective. Genotypes corresponding to different locations in a neutral network, in their own words: "can encode different exploration strategies and thus different information; a genotype encodes not only the information on the phenotype but also information on further explorations." According to this view, genetic information that is redundant within a generation serves to encode `strategy parameters' that affect self-adaptation of the genotype between generations. An example of this occurs within HIV sequences, which appear to make use of the neutral properties of the genetic code in order to encourage or discourage mutation at particular gene loci. Each amino acid can be coded by more than one nucleic acid codon. Accordingly, the codons for a particular amino acid form a neutral network. Within this network, there are access points (via point mutations) to other neutral networks corresponding to other amino acids. However, some codons have more access points than others and are therefore more likely to undergo non-synonymous mutation. In HIV, codons with relatively many neutral neighbours are more likely to occur in functionally important areas of the genome whereas codons with relatively many non-neutral neighbours are more likely to occur in areas that tend to be recognised by a host's immune system [Stephens and Waelbroeck, 1999].
In a sense [Lones and Tyrrell, 2001b], the redundant components of the genome form an evolutionary scratch-pad that serves both to record previous avenues of search and to suggest future avenues of search, augmenting the static role played by non-redundant genetic components.
Whilst simple concepts like compartmentalisation and redundancy explain the underlying evolvability of biological systems, there are numerous other complex and adaptive mechanisms which also contribute to evolvability. Transfer of DNA, for example, allows genes to move from one environment to another. In eukaryotes, this occurs during recombination and leads to offspring with novel combinations of parental alleles: in effect, increasing the explorative power of evolution in its search for adaptation. In prokaryotes, `horizontal' DNA transfer can occur between members of both the same and different species, and is an important factor behind the ability of bacteria to adapt rapidly to changing environmental conditions [Poole et al., 2003].
In Kirschner and Gerhart , the authors discuss the flexible roles of `exploratory mechanisms' such as epigenetic and developmental processes in supporting evolvability. These mechanisms make use of compartmentalisation and redundancy to de-constrain their roles within organism construction and maintenance from mutational change in the components and structures that they construct and maintain. The immune system, for instance, makes no prior assumptions about what constitutes `self' and, therefore, evolution is free to change the constitution of `self'. Likewise, during the development of the limb structures of complex multi-cellular organisms, growth of the nervous and vascular systems occurs relative to the growth of cartilage. Consequently, changes in limb size and shape can be achieved through mutation of the cartilage growth process without requiring (highly unlikely) corresponding mutations in the growth processes of the nervous and vascular systems. (Further insight into the implications of phenotypic plasticity upon evolvability can be found in Poole et al.  and Dawkins .)
In addition to the genetic and phenotypic levels, evolvability is also affected by processes which occur at epigenetic and ecological levels. Cytosine methylation is an example of a fairly low-level epigenetic mechanism where information is passed from parent to offspring via DNA patterning. Cytosine is a DNA base which when methylated becomes unstable and easily converted into thymine: producing mutational hot-spots within the genome. Mutational biases, in theory, can lead to differential rates of evolution across the genome, which may be of benefit to evolvability (for more information see, for example, Bedau and Packard ). DNA patterning may also affect evolvability through evolution of the `epigenotype' [Poole et al., 2003]. Higher level forms of epigenetic inheritance such as transmission of learned information from parent to offspring and cultural interaction have an effect upon evolutionary direction through their affect upon mate choice and lifestyle. Therefore it seems likely that, by pushing populations in the direction of increased adaptation, these mechanisms might also have a significant bearing upon evolvability. Finally, differences between the adaptations required for species to occupy particular niches and pressure from competing species also tends to push the evolution of populations in certain directions and, again, these factors can form important sources of evolvability [Poole et al., 2003].
The previous sections all give credence to the notion that biological representations possess evolvability. However, assuming that evolution is individually responsible for generating these biological representations, an outstanding question is: How did evolvability evolve? There is no universally accepted answer to this question. Nevertheless, there are two common answers: that (i) evolvability has hitch-hiked along with the selection of other traits; and that (ii) evolvability is actively selected for.
The first of these reflects the view that most mechanisms which improve evolvability originally evolved for some other purpose and that, therefore, it is not necessary to introduce any new evolutionary mechanisms to explain the evolution of evolvability. Poole et al.  argue that hypermutation, horizontal transfer, sex and recombination, cell-cell interactions and cell adaptations all evolved as stress adaptations. Horizontal transfer, for example, occurs at an accelerated rate when prokaryotes experience stress as a result of low nutrient levels in their environment: their aim being to build new metabolic pathways that will allow them to process alternative nutrients. The role of horizontal transfer (and eventually recombination) in conferring evolvability may have hitch-hiked along with selection for this stress response. Furthermore, in Dawkins , the author argues that sources of evolvability such as segmentation may even have inhibited the fitness of the organisms they originated in, but eventually proliferated due to their ability to support increased morphological exploration and lead their descendants to colonise new niches.
The alternative view is that, in most cases, evolvability has been implicitly selected for its role in improving the adaptability of entire lineages. This can be argued by asserting that any mutation which improves an organism's evolvability will improve the chance of its descendants undergoing adaptation, being selected for, having more offspring: and in the process, passing on their evolvability-enhancing mutation to a greater percentage of the population. In Dawkins' words: Ëvolution has no foresight. But with hindsight, those evolutionary changes in embryology that look as though they were planned with foresight are the ones that dominate successful forms of life."
Nevertheless, it remains difficult to explain how the use of very basic mechanisms of evolvability, such as redundancy, might have evolved. This difficulty has prompted a third, partial, explanation for the evolution of evolvability: that evolvability is a `frozen accident'; an innate property of the planet's biochemistry which might not have evolved within other possible systems of representation. According to this view, biological representations are evolvable because they always have been evolvable.
Evolvability is the relative capacity for organismal lineages to become better adapted to their environment as a consequence of natural selection acting upon essentially random genetic variation. Biological systems are believed to be organised in a way that promotes evolvability. Important sources of evolvability include redundancy, compartmentalisation, exploratory mechanisms, and epigenetic and ecological processes. Redundancy in particular is though to support neutral evolution: a conceptually powerful mode of evolutionary exploration. Whilst it is not known how these sources of evolvability evolved, it has been speculated that this is due both to re-use of mechanisms evolved for other purposes and to lineage selection.
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14Heterozygotic advantage, or overdominance, occurs when a heterozygote (an organism which has a different allele at a particular gene locus within its maternal and paternal chromosomes) has higher fitness than either of the homozygotes (two copies of the same allele). This leads to balancing (or stabilising) selection, resulting in a balanced polymorphism (more than one allele supported by the population) between the two alleles.