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Evolution and Development of a Multicellular Organism: Scalability Evolution and Development Diego Federici Keith Downing of a Multicellular Organism: Department of Computer and Scalability, Resilience, and Information Science Norwegian University of Science Neutral Complexification and Technology N-7491 Trondheim, Norway [email protected] [email protected] Abstract To increase the evolvability of larger search spaces, several indirect encoding strategies have been proposed. Among Keywords these, multicellular developmental systems are believed to Genetic algorithms, development, offer great potential for the evolution of general, scalable, and scalability, fault tolerance, neutral self-repairing organisms. We reinforce this view, presenting the complexification results achieved by such a model and comparing it against direct encoding. Extra effort has been made to make this comparison both general and meaningful. Embryonal stages, a generic method showing increased evolvability and applicable to any developmental model, are introduced. Development with embryonal stages implements what we refer to as direct neutral complexification: direct genotype complexification by neutral duplication of expressed genes. The results show that, even for high-complexity evolutionary targets, the developmental model proves more scalable. The model also shows emergent self-repair, which is used to produce highly resilient organisms. 1 Introduction When considering similarly structured fitness landscapes, it is well understood that the bigger the search space, the longer the search will take. This makes the evolution of large phenotypes one of the most serious problems in the field of evolutionary computation (EC). On the other hand, biological systems seem to have come to terms with this scalability problem, since living organisms can easily contain trillions of cells (each cell being itself a structure of baffling complexity). These systems rely upon an artifice, the emergent process during which a single replicating cell develops into the mature organism. Inside each cell, an identical set of genes interacts to provide the instructions for development. Morphology emerges as initially identical cells interact with their local environment to assume specific roles. Ontogeny is the result of the distributed process during which a relatively small genotype de- compresses into a large phenotype. For example, it is estimated that there are only 30–40 thousand genes in the human genotype (45 million out of the 109 DNA bases), while 1014 cells constitute a mature phenotype [14, 20]. However, even if evolving direct representations of structures of similar complexity is incon- ceivable, is not yet well understood under which circumstances a developmental process can be beneficial to EC. n 2006 Massachusetts Institute of Technology Artificial Life 12: 381–409 (2006) Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/artl.2006.12.3.381 by guest on 25 September 2021 D. Federici and K. Downing Evolution and Development of a Multicellular Organism Specific open questions regard: The evolvability of complex phenotypes The scalability of methods based on development The properties of such systems This article addresses these issues with an empirical study of a model of multicellular development, which is compared with direct encoding. In addition we include a discussion and propose a test suited for this analysis. Results show that: Development with embryonal stages (DES), a method inspired by the biological mechanisms of gene duplication and diversification, has significant benefits for evolvability. DES implements neutral complexification and operates by preventing pleiotropy1 among different stages of development. Development results are more scalable than direct encoding for both regular and high- complexity targets. The remainder of the article is organized as follow: Section 2 contains an introduction to artificial and biological development and describes neutral complexification. Section 3 discusses the evo- lutionary task. Section 4 describes the adopted multicellular development model, and Section 5 gives details of the evolutionary methods for direct encoding (DE) and artificial embryogeny (AE [37]). Section 6 presents results from the simulations concerning the use of embryonal stages, scalability comparison between DE and AE, performance under various AE settings, and emergent and evolved regenerative features of the AE model. Section 7 contains the conclusions. 2 Development Since the search space grows exponentially with the genotype size, the evolution of large phenotypes should benefit from parsimonious encodings. Among these indirect encodings, development uses a genetically encoded growth program in several recursive steps. Matrix rewriting [25] and cellular encoding [18] are seminal approaches, developing phenotypes following the rewrite rules specified in the genotype. Parsimony arises from the fact that rewriting rules can be applied an arbitrary number of times, so that the genotype size should be highly independent of the phenotype size. Still, if with DE it is possible to alter phenotypic traits by mutating the expression of the corresponding genes, then rewrite rules introduce an additional level of indirection. Mediated by the development process, genes can be linked to many (or no) phenotypic traits. For example, consider the following grammars: Genotype Phenotype S ! aSa producing aaaaa ...S...aaaaa, (1a) S ! aSb producing aaaaa ...S...bbbbb. (1b) A single change (respectively, mutation) in the rule (genotype) induces a phenotypic change proportional to the number of substitutions (developmental steps). 1 Pleiotropy: one gene controlling more than one phenotypic trait. 382 Artificial Life Volume 12, Number 3 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/artl.2006.12.3.381 by guest on 25 September 2021 D. Federici and K. Downing Evolution and Development of a Multicellular Organism This difference has notable implications from the evolutionary perspective. First, as shown in the previous example, it highlights how small genotype differences can have huge phenotypic consequences because of pleiotropic effects. Secondly, it challenges the general intuition that small phenotypic changes are obtained from comparably small genotype alterations. For example, imagine a scenario in which the fitness is proportional to the similarity between the candidate and the target string ‘‘aaaaa . S. aabaa’’. The phenotype produced by the grammar (1a) is just one step away from scoring maximum fitness; nevertheless the optimal grammar can be quite different (i.e., distant in genotype space): 9 S ! aS1a > > > > S1 ! aS2a = > producing aaaaa ...S...aabaa: ð2Þ > S2 ! aS3b > > ;> S3 ! aS3a When, as in the previous case, we have a low correlation between the genotype and phenotype spaces, the incremental refinement of the phenotype requires long walks in genotype space and therefore more time. If we concede that EC is based on the principle that optimal solutions can be found by small incremental refinements to selected candidates, then target solutions residing in regions of high cor- relation should be easier to evolve. In general, an AE system will not present a constant correlation across all the phenotype space (see for example [26]), but will be characterized by regions of highs and lows. The question is: What general methods can AE systems adopt to increase the average correlation in the areas occupied by their targets? Here we argue that a viable possibility is to incrementally reduce the impact of the pleiotropy introduced by the rewriting process itself. 2.1 Rewriting, Gene Reuse, and Pleiotropy At each rewrite step, any gene can influence the whole development process. The reuse of genes in different contexts and at different times is what makes indirect encoding parsimonious and hypothetically more apt to exploit sources of regularity. Still, in general, a high level of reuse is opposed to a high degree of specialization. For example, if the same rewrite rules were used in the development of all digits—toes and fingers—they would necessarily be identical. Similarly if gene AB is used in different phases of de- velopment to produce, for instance, trait At1 at time t1 and trait Bt2 at time t2, an alteration of AB’s expression will often affect both traits. Therefore, the genetic linkage of otherwise unrelated pheno- typic traits may impose a tradeoff, limiting evolutionary search to regions of suboptimal solutions. Also, in AE, the earlier a gene is activated, the greater effect it has on development: the phenotypic characteristics appearing first are built upon to produce the mature organism. Therefore, we expect that modifications affecting early phases of development will have bigger phenotypic consequences via a domino effect: they will propagate at each rewriting step (see also Section 6.1.2). It is then possible to see how mutations affecting early phases of development will less frequently produce small phenotypic changes. This seems valid also in natural evolution. From the observation of embryogenesis, it is seen that early phases of development are similar among related species. Additionally, adult vertebrates present many structural homologies: for example, in the forelimbs of species belonging to mammals, birds, and reptiles [17]. In fact, the conservation of development is so consistent that, by comparing the homologies in different species, it is often possible to deduce their genetic relatedness (see for example [33, 17], but also [35]). Artificial
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