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Developmental Structuring of Phenotypic Variation: a Case Study with a Cellular Automata Model of Ontogeny

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Developmental Structuring of Phenotypic Variation: a Case Study with a Cellular Automata Model of Ontogeny Developmental Structuring of Phenotypic Variation: A Case Study with a Cellular Automata Model of Ontogeny Wim Hordijk∗ Konrad Lorenz Institute for Evolution and Cognition Research Klosterneuburg, Austria [email protected] Lee Altenberg University of Hawai`i at M¯anoa Honolulu, Hawai`i, USA 96822 [email protected] ∗ Corresponding author Abstract Developmental mechanisms not only produce an organismal phenotype, but they also structure the way genetic variation maps to phenotypic variation. Here we re- visit a computational model for the evolution of ontogeny based on cellular automata, in which evolution regularly discovered two alternative mechanisms for achieving a selected phenotype, one showing high modularity, the other showing morphological in- tegration. We measure a primary variational property of the systems, their distribution of fitness effects of mutation. We find that the modular ontogeny shows the evolution of mutational robustness and ontogenic simplification, while the integrated ontogeny does not. We discuss the wider use of this methodology on other computational models of development, as well as real organisms. 1 Introduction The idea that phenotypic variation could ever be \unbiased" is a historical artifact coming from two main sources: First were the early characterizations of quantitative genetic variation for single traits or small numbers of traits. Such measurements are actually projections of the extremely high dimensionality of organismal properties into very few dimensions. When the additive genetic variance was measured for these low-dimensional projections, positive additive genetic variance was discovered to be ubiquitous, and this finding was confirmed by selective breeding experiments that showed populations were widely responsive to artificial selection, so these trait values could be changed. The second step was the extrapolation of these low-dimensional observations to the entire organism, resulting in the adoption of the classical infinitesimal model of quantitative genetics (Fisher, 1918; Barton et al., 2017) as a plausible model for the entire, high-dimensional organismal phenotype, in which genetic variation is essentially a gas that can fill any selective phenotypic bottle (enunciated by Hill and Kirkpatrick (2010) who summarize, \almost anything can be changed if it shows phenotypic variation" and \combinations of traits, even those unfavorably correlated, can be changed"). Once the premises of this \pan-variationism" are accepted, pan-selectionism is the natural conclusion | in other words, if variation is diffusing in every phenotypic direction, the only source of information that shapes an organism's phenotype is natural selection. Breaking away from the pan-variationist paradigm has been a prolonged process. Rupert Riedl's analysis was pioneering in this regard (Riedl, 1975, 1977, 1978), pointing out that the very ability to infer phylogenies based on phenotypes requires that natural selection be limited in its ability to erase the phenotypes of the past. Riedl proposed, furthermore, that complex phenotypes which require multiple simultaneous trait changes would often be impossible to evolve without the advent of genes that happen to make the right pleiotropic combination of multiple trait changes, and that such genes produce a genotype-phenotype map \in which gene interactions have imitated the patterns of functional interactions in the phenome." (Riedl, 1977). In the 1980s came the identification of \developmental constraints" as sources of infor- mation other than natural selection that shape evolution (Bonner, 1982). Subsequently, it was recognized that development also focuses phenotypic variation along certain dimensions, 1 thus enhancing the likelihood of evolution taking these paths (Roth and Wake, 1985). To- gether these have been combined into the concept of \developmental bias" (Yampolsky and Stoltzfus, 2001). This term `bias', however, still makes reference to the pan-variationist frame (Fillmore, 1976; Lakoff, 2014) that poses \unbiased" phenotypic variation as somehow a viable concept, and even perhaps a most-parsimonious null hypothesis. When viewed from the vantage point of developmental mechanisms, it is clear that the processes that produce the physical structures of organisms will also structure the phenotypic variation that results from genetic and environmental variation. The idea of \unbiased" phenotypic variation is, from this vantage point, as sensible as the idea of \unstructured development" | which of course, makes no sense at all. The question we need to be asking, then, is not how development biases phenotypic variation, but rather, how development structures it. This is the framework that we adopt here. It is hypothesized in Altenberg (2005) (and more recently Runcie and Mukherjee (2013)) that organismal variation actually lies on very low-dimensional manifolds embedded within the high-dimensional trait space. Within this framework, a principal open problem in evolutionary theory is to understand in what ways the developmental structuring of phe- notypic variation may itself be systematically shaped by the evolutionary process. That is the question pursued here. 1.1 Ontogeny as a Dynamical System Ontogeny in many animals exhibits several properties of an autonomous dynamical system, in which the trajectory of the system is set by the initial conditions. In common animal development, the mother creates the initial conditions for the zygote (often some form of egg), and development occurs in isolation from environmental interaction, until the organism \hatches". Development may be less autonomous in placental mammals because of continu- ing material inputs from the mother, but most of the dynamical interactions of development occur internally within the embryo and fetus itself. It is a generic property of dynamical systems that the trajectories converge toward at- tractors. Attractors may be fixed points, cycles, or strange attractors. Whole subsets of different initial conditions will converge toward the same attractor, comprising its domain of attraction. Different domains of attraction will converge toward different attractors. The dynamics of epigenesis and ontogeny result from the complex interactions of the genome, oocyte cytoplasmic structure, and multicellular interactions once embryogenesis has begun. This entire process we can refer to as the generative properties of the genotype- phenotype map. The problem of concern here | how changes in the genome map to changes in the phenotype | can be referred to as the variational properties of the genotype-phenotype map. This distinction, introduced in Altenberg (1995), has been found to be useful in a number of studies (c.f. Jernvall and Jung (2000); Salazar-Ciudad (2006); Reiss et al. (2008); de la Rosa (2014); Porto et al. (2016); Laubichler et al. (2018)). The way the phenotype is generated from the genotype during development is clearly what structures phenotypic variation, so the variational properties are derived from the generative. There is yet no general theory as to how evolution may shape the variational structure of phenotypic variation. Many computational models have been explored to try to tease out 2 the regularities which may be eventually guide us to a general theory (Tsuchiya et al., 2016; Dong and Liu, 2017; Scholes et al., 2017). Here we revisit one such computational model which has produced intriguing results: the cellular automaton model of development, EvCA. The cellular automaton is, as the name suggests, an autonomous dynamical system. Its dynamics are specified by initial conditions of its multi-variable state, and rules which determine the changes of the state from one time to the next. Cellular automata (CAs) exhibit complex attractors and domains of attraction, and moreover, allow one to watch their development progress. Here, we will define a task that the CA must achieve to stay \alive", and model a population of evolving CAs whose determining rules are mutated and recombined and subject to selection. The distribution of fitness effects of mutation (DFE). Traditionally, the quantity of interest in evolutionary simulations has been the fitness of the digital organisms. Here our focus is on the variational properties of these organisms, and we investigate a principal quantification of how genetic variation maps to phenotypic variation, the distribution of fitness effects of mutation (DFE), which is the probability distribution over the changes in fitness caused by mutation of a given genotype. The distribution of fitness effects of mutation provides a quantitative way to characterize the widely used concepts of mutational robustness, deleterious mutation, and evolvability. It is the probability distribution of mutant offspring’s fitnesses relative to the parent's fitness. The distribution can be divided into three regions: (1) the lower tail, comprising deleterious mutations, (2) the measure near 1 (the parent's relative fitness), comprising the neutral mu- tations, which quantifies mutational robustness, and (3) the upper tail of the distribution, where the advantageous mutations occur, which characterizes evolvability. This quantifi- cation of evolvability was introduced in Altenberg (1994, 1995). Its use as a statistic to guide variation operators in evolutionary algorithms goes back to Rechenberg (1973), who introduced the integrated upper tail as the \success probability". It should be noted that there has been controversy and confusion in the literature about whether evolvability
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