Caracterización de los complejos RBCb/SA-UK-T.

Computational approaches to modelling evolution may be categorised into two classes on the basis of their motivation. First, there are evolutionary models whose purpose is to explore and explain some aspect of biological evolution. Second, there is a large class of ‘biologically inspired’ approaches to adaptive search and optimisation. In reality, these two classes overlap at a technical level, and, so long as the fact is kept in mind that evolution frequently doesnot act as an optimisation process, both purposes have much to gain from each other.

One form that computational models of evolution may take is simply an im- plementation of a mathematical quantitative genetic model, where the role of the computer is simply to perform large numbers of iterated calculations. In the last few decades however, evolutionary computing is more likely to consist of a bottom-up computational implementation of an adaptive process, rather than a top-down analytical approach. Evolutionary algorithms are a class of adaptive search algorithms based on natural evolution. Numerous varieties have been pro- posed, including genetic algorithms (Holland, 1975, Goldberg, 1989), evolutionary programming (Koza, 1992) and evolutionary strategies (described in B¨ack et al., 1997).

In essence, an evolutionary algorithm consists of a population of individuals (which may be as small as one member) representing either a set of candidate solutions to a particular problem or agents located in a particular environment. Each solution is assigned a fitness value, representing its proximity to the target solution or level of adaptedness to its environment. The fittest individuals are selected to reproduce, either asexually or via recombination, and the newly cre- ated offspring, possibly modified by some form of mutation, constitute the next

3.2 Existing computational models 47

generation of solutions. Theoretically, and in practice, the average fitness of the population will increase over successive iterations of this selection/mutation cycle.

Genotypic representation

During evolution, new individuals are created via the modification of existing indi- viduals in a population. The range of individuals that are mutationally accessible from a given individual will depend on what types of genotypic change are pos- sible. In turn, the range of possible changes will depend on how a genotype is represented. The original genetic algorithm proposed by Holland (1975) used a bit-string representation, in which each locus represented a single binary allele. Mutations to such a representation involved randomly ‘flipping’ the bits at some loci to create a new individual. Possible alternatives to bit-string representations include: continuous value representations, consisting of a sequence of real valued numbers that were mutated by adding small amounts of random noise (Goldberg, 1989); tree representations, in which a solution (usually an algorithm) is encoded as a binary tree of operators and values. Considerable effort has been invested in determining which representation and associated mutation operators are most effective for the solution of particular search problems.

One way of interpreting the evolutionary implications of a particular genotypic representation is in terms of its effect on the adaptive landscape (as described in §2.3). The choice of representation (and the nature of the problem) will affect how the correlation between the fitness of a given individual and that of its adaptive neighbours. If neighbouring fitness values are closely correlated, the resulting landscape will be smooth, and potentially easy to search. As correlation decreases, the landscape becomes increasingly rugged, and the number of local optima in which search can become trapped will increase. One landscape characteristic of considerable interest in the last decade is neutrality: the presence of plateaus or ridges of mutationally adjacent individuals of equal (or very nearly equal) fitness. Many natural and artificial systems display the hallmarks of neutrality (Kimura, 1983, Shipman et al., 2000). The dynamics of populations evolving on neutral landscapes are of particular interest because they provide potential explanations for periods of evolutionary stasis (Bornholdt and Sneppen, 1998), escape from local optima (van Nimwegen and Crutchfield, 2000), robustness (Wilke et al., 2001) and open-ended evolution (Wilke, 2001).

48 A Computational Model of Developmental Cell Lineages

Another implication of different genotypic representations is that the mutation operators associated with a particular representation may bias the distribution of variation they produce (Bullock, 1999, 2001). As in studies of natural evolution (§2.3.2), the potential effects of variational structure on artificial evolution are relatively unexplored. The issue of mutation bias is addressed further in Chapter 6.

Evolving development

In the discrete and real valued representations described above, an individual solu- tion is generally encoded directly into the genotype. This situation clearly differs from biology where the object of selection, the phenotype, is derived from the genotype via a complex dynamic process. The developmental models described in §3.2.2 above embody a similar level of indirection. The application of developmen- tal mappings to real world design problems is currently a topic of much interest. By exploiting properties of developmental mappings such as modularity, redundancy and canalisation, it is anticipated that the scalability and robustness of evolution- ary systems can be increased (Roggen and Federici, 2004). The choice of genotype representation remains important when evolving a developmental system. While most cell chemistry models share a common interaction network structure, a wide variety of different schemes for encoding this network have been proposed. The simplest approaches involve using weight matrices to specify the strength of inter- action between nodes (Wagner, 1996, Siegal and Bergman, 2002). Other models have used elaborate ‘artificial chemistries’ to determine affinities between genes and regulatory factors. In these models, the strength of binding may be derived from sequence matching (Eggenberger, 1997, Reil, 1999), fractal patterns (Bentley, 2003) or production rules (Suen and Jacob, 2003).

Azevedo et al. (2005) took an unusual approach to modelling the evolution of development. They were interested in studying how the complexity of an ontogeny (represented as a cell lineage) could be reduced during evolution with stabilising selection on the phenotype (represented by the terminal cell fates of the lineage). This model did not use an explicit representation of the genotype that produced an ontogeny, and mutation operators were therefore defined directly in terms of modifications to the cell lineage. The methodology and results of Azevedo et al. (2005) are of particular relevance to the studies of this thesis and are described further in Chapters 5 and 6.