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THE ROLE OF DEVELOPMENTAL BIAS IN

A SIMULATED EVO-DEVO SYSTEM

SEAN THOMAS PSUJEK

Submitted in partial fulfillments of the requirements

For the degree of Doctor of Philosophy

Department of Biology

CASE WESTERN RESERVE UNIVERSITY

May, 2009

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

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*We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents Abstract ...... 2 List of Figures ...... 4 Chapter 1 : Introduction ...... 6 Chapter 2 : Background ...... 12 Modeling in Evo-devo ...... 12 Influence of evolution on gene regulation ...... 14 Chapter 3 : The Developmental Model ...... 15 Introduction ...... 15 The developmental model ...... 16 An example demonstrating development of a neural circuit ...... 22 Chapter 4 : Characterizing Developmental Bias ...... 25 Introduction ...... 25 Visualization of bias in this system ...... 26 An intrinsic bias exists in the developmental system ...... 26 Developmental bias varies with genotype ...... 30 Degenerate genotypes have different patterns of bias ...... 33 Genotypes along a neutral network differ in their pattern of bias ...... 34 Regulatory structure shapes developmental bias ...... 36 Chapter 5 : Characterizing the Interaction between Developmental Bias and Selection ...... 42 Introduction ...... 42 The evolutionary simulation ...... 42 Visualization of fitness and local bias ...... 44 Conceptual Framework ...... 45 Results ...... 50 Lineage analysis ...... 52 Population analysis ...... 64 Initial epoch ...... 67 Final epoch ...... 68 Intermediate epochs ...... 70 Chapter 6 : Discussion ...... 73 Characterizing Developmental Bias ...... 75 Characterizing the Interaction between Developmental Bias and Selection ..... 78 Future Work ...... 81 Conclusions ...... 83 Chapter 7 : References ...... 83

The Role of Developmental Bias in a Simulated Evo-Devo System

Abstract

SEAN THOMAS PSUJEK

The success of the Modern Synthesis has resulted in forces of evolutionary change other than natural selection being marginalized. However, recent work has attempted to show the importance of non-selective influences in shaping organic form. One such force is developmental bias, the differential produced of phenotypes. I use a simulation model of neural development to explore questions of general interest about developmental systems. From an analysis of the bias in the production of phenotypic variants in the developmental model, I find the pattern of developmental bias varies strongly with the genotype even among phenotypically-neutral genotypes. In addition to this genotype- dependent developmental bias (local bias), an intrinsic bias exists in the developmental system (global bias). I also show that developmental bias varies among related genotypes that produce the same phenotype. Finally, I illustrate how a pattern of bias emerges from the manner in which mutations affect the regulatory structure of the wild- type genotype. These results suggest that developmental bias could have a strong influence on the direction of evolutionary modification. In subsequent analyses exploring the interaction of developmental bias and selection during adaptive evolution, I find developmental bias guides phenotypic transitions with the result that multiple

2 phenotypic pathways are taken towards the target phenotype across simulations. I also find higher-fitness phenotypes often become accessible with the accumulation of selectively-neutral mutations. The change in accessibility is due to alterations of the regulatory structure of the genotypes through the neutral mutations. This lability of developmental bias recommends a comparative approach to the experimental investigation of bias in natural systems. The alteration of phenotypic accessibility following the accumulation of neutral mutations can be conceptualized as a population moving along a network of isofitness genotypes linked by mutations (neutral networks).

The phenotypes produced by non-fitness-neutral neighbors of the neutral genotypes are likely to vary as the population moves to different regions of the network. These networks are created by the mutational operator and the degeneracies of the dual mappings of genotype to phenotype and phenotype to fitness. Topological properties of the neutral networks could lead to insights into the impact on evolvability of developmental systems.

List of Figures Figure 1-1: A radially-represented uniform distribution of genotypes leading to a non-uniform distribution of phenotypes through a developmental process...... 7 Figure 3-1: Model gene and sequences corresponding to protein types...... 18 Figure 3-2: The three stages of development in the formation of a three-neuron circuit with three synaptic connections...... 21 Figure 3-3: Genome that produces the three-connection circuit in Figure 3-2, stage 3...... 22 Figure 3-4: The differentiation steps as generated by the genome in Figure 3-3...... 24 Figure 4-1: Developmental bias exists in the model system...... 28 Figure 4-2: Ten most commonly produced neural circuits through random sampling of genotypes and the number of sampled genotypes that result in the given circuit...... 30 Figure 4-3: Local bias patterns for four specific genotypes...... 31 Figure 4-4: Local bias patterns for eight genotypes that produce the same neural circuit from our random sample...... 33 Figure 4-5: Local bias patterns along a neutral network...... 35 Figure 4-6: New phenotypes are produced from mutations that alter the gene regulatory structure of the wild-type...... 37 Figure 4-7: Neutral mutations produce the same phenotype even though they may affect gene regulation. .. 38 Figure 4-8: Regulatory networks for the eight genotypes used in Figure 4-5...... 40 Figure 4-9: Neutral mutations change the developmental context in which subsequent mutations operate. . 41 Figure 5-1: The target circuit used in the evolutionary simulations...... 43 Figure 5-2: Plots of developmental bias, neural architecture fitness, and the combination of bias and fitness...... 45 Figure 5-3: Degeneracies between the levels of genotypes, phenotypes, and fitness can arise through the developmental process and fitness evaluation...... 46 Figure 5-4: Networks of isofitness genotypes can exist due to the degeneracies in mappings from genotype to phenotype to fitness...... 49 Figure 5-5: Best and average fitness of the population over the course of five successful evolutionary simulations...... 52 Figure 5-6: Multiple pathways to a target phenotype exist...... 54 Figure 5-7: Local bias patterns dictate phenotypic changes on a lineage during evolution...... 56 Figure 5-8: Neutral mutations lead to higher fitness phenotypes...... 59 Figure 5-9: Neutral mutations lead to higher fitness architectures throughout the course of an evolutionary simulation...... 60 Figure 5-10: Fitness neutrality affords a transition to a higher-fitness phenotype...... 61 Figure 5-11: A higher-fitness phenotype became available through changes in the regulatory structure via neutral mutations...... 63 Figure 5-12: Developmental bias dictated the phenotypic transitions at the population level...... 65 Figure 5-13: Plots of the average Hamming distance between all pairs of individuals that are on the neutral network of the fittest individual at a given generation...... 67 Figure 5-14: Average number of neutral mutations during the final epoch for the five simulations presented in Figure 5-5...... 70 Figure 5-15: Average neutrality differs between the same epoch across two simulations...... 71 Figure 5-16: Portals to higher fitness neutral networks appear as the population diffuses on the neutral network...... 72

Acknowledgments

First of all, I would like to thank the National Science Foundation for their IGERT fellowship and the faculty who were awarded the grant at Case Western Reserve University. Without this fellowship, I doubt I would have been able to combine my eclectic research interests into a program of study.

I am particularly indebted to my advisor, Randy Beer, for guidance and support beyond the normal expectations for a research advisor. It truly was an honor to be a student of his.

I would also like to thank Wallace Arthur at the National University of Ireland, Galway for a short internship in his lab. He was very generous with his time in working with me on the research presented here.

More thanks go to the members of Randy‟s lab at Case Western Reserve, The Beer Nuts, for all the productive conversations, distractions, and free food notices.

Finally, I am grateful to my parents for always encouraging me in my exploration of how and why things work.

Chapter 1 : Introduction There is a growing recognition that natural selection is not the sole determinant of the direction of evolutionary change. Selection‟s supposed dominance became firmly established following the success of the Modern Synthesis (e.g., Ford 1971), with its integration of genetics and natural selection (Fisher 1930, Haldane 1932, Wright 1932).

However, this paradigm is being strongly challenged. Gould and Lewontin made a forceful call for the recognition of other factors in evolution by presenting alternatives to the pervasive view that selection is omnipotent in shaping organic form (Gould and

Lewontin 1979). Even as Charles Darwin laid out his theory of evolution by natural selection in The Origin of Species, he acknowledged that “Natural Selection has been the main but not exclusive means of modification” (Darwin 1859).

In addition to selection, another key force in setting the direction of evolutionary change is developmental bias (also “developmental constraints”) (Alberch 1982, Alberch and Gale 1985, Maynard Smith et al. 1985, Arthur 2004b, Brakefield 2006). The phenotypes upon which selection acts are produced through a complex process of development that links genotype to phenotype. Alterations in DNA sequences can result in phenotypic changes; however, because of the non-linearity of the developmental process (e.g., due to epistatic interactions between genes, pleiotropy, and the structure of gene regulation), some phenotypic changes may be more likely than others. Given a uniform distribution of genotypes (e.g., all single-base mutants of a wild-type genotype) development is likely to result in a non-uniform distribution of phenotypes (Figure 1-1).

Developmental bias is therefore defined as the differential production of phenotypes given uniform genetic variation. This bias could have a large role in determining the direction of evolutionary change since developmental processes determine which phenotypes are accessible from a given genotype, and selection can only act on those available phenotypes.

Phenotypes

Genotypes

Development

Figure 1-1: A radially-represented uniform distribution of genotypes leading to a non-uniform distribution of phenotypes through a developmental process. Each of these rays represents a unique genotype or phenotype. The length of a genotype ray indicates the magnitude of a mutation from a wild-type genotype. Under phenotypes, the length of each ray indicates the number of genotypes resulting in that phenotype through the developmental process. In the figure, some phenotypes are produced by multiple genotypes; whereas, other phenotypes are not generated at all.

There is some indirect evidence for development‟s impact on evolutionary change.

For example, Alberch and Gale (1985) compared the phylogenetic patterns of digit reduction in two orders of amphibians. These patterns differ: frogs have typically lost phalangeal elements preaxially (digit I); whereas, salamanders have lost these elements postaxially (digits IV and V). Interestingly, the ontogenies of the two orders differ and are correlated with their respective pattern of diversity. Differentiation of the digits occurs in frogs from III and IV to V and II and finally to I. In salamanders, differentiation starts with I and II, proceeds to digits III and IV, and ends with V.

Alberch and Gale also experimentally manipulated the number of cells in the limb buds of developing embryos using a mitotic inhibitor. In frogs, this resulted in either the loss or phalangeal reduction of digit I. Salamanders showed a loss postaxially in digit IV

(Alberch and Gale 1983). The authors concluded that the pattern of digit reduction for frogs and salamanders during evolution has mirrored their developmental pathways.

In addition, Gomez-Mestre and Buchholz (2006) explored whether developmental plasticity has cultivated evolutionary diversification by examining within-species variability and across-species differences in larval development in anurans. In the family

Pelobatoidea, large differences in larval period are seen, reflecting the environments in which they live, that is, long-lasting or ephemeral ponds. Through altering the rearing temperature, they demonstrated plasticity in larval period which was correlated with body shape differences. The authors then tested for and found a correlation between the larval period and body shape across species. These similarities suggest that selection has resulted in a shift of the developmental reaction norms through genetic accommodation.

Their results allowed them to conclude that the morphometric differences among species of spadefoot toads and parsley frogs reflect within-species morphological variation caused by plasticity in the larval developmental rate.

Other evidence suggests that some evolutionary changes are not constrained by developmental bias but are instead shaped primarily by selection, especially in the short- term (Frankino et al. 2005 and Frankino et al. 2007). Frankino et al. (2005) found the scaling relationship between forewing area (FW) and body size (BS) in insects was easily shaped by selective forces, despite a strong genetic correlation between them which might have been expected to constrain independent change in the traits. However, under the selection regimes of either high or low “wing loading” (i.e., small FW relative to BS or large FW relative to BS), the majority of these allometric changes occurred through alterations of forewing area. The scaling relationship could also have been altered through changes in body size; however, this occurred in the correct direction in only one lineage. Similarly, in artificial selection experiments for the allometric relationship between forewing and hindwing size, the lineages showed rapid evolution of the allometric intercept (Frankino et al. 2007). Yet again, an asymmetry existed in the response to selection; in the lineages whose selection pressure was for a small forewing

8 relative to hindwing, changes in the intercept were due entirely to changes in the hindwing (Frankino et al. 2007). Both sets of experiments demonstrated rapid evolution of scaling relationships despite strong genetic correlations between the traits. However, the contribution of each trait to the allometry appeared to be biased.

One phenotypic trait in which developmental bias is likely to play a key role is neural architecture. An organism‟s behavior is critical to its survival; and behavior is largely mediated by the structure of the nervous system. Bias in the development of neural connections could prevent the production of phenotypic variants in which behaviors, through the elimination of connections, are poorly executed or even completely abolished (e.g., in locomotor circuits). Besides this buffering role, developmental bias could also open opportunities for evolutionary change. Bias could lead to phenotypes exhibiting novel behaviors due to new connections formed between specific neuronal regions. In fact, connectivity changes in neural circuitry have led to the creation of novel behaviors (Nishikawa 1997). For example, novel sensory afferents that coordinate the timing of jaw movements have evolved independently at least four times in the phylogeny of frogs, resulting in a novel mechanism of tongue protraction (Nishikawa

1997). However, it is currently unknown whether there is any bias in the development of the nervous system for the formation of these types of sensory feedback connections.

To identify what impact development has had on evolutionary pathways, Arthur

(2004a) suggested two avenues to explore. The first attempts to collect direct evidence of a directional role of developmental bias in evolution by mapping the range of phenotypic variation of a population against the selective forces in an adaptive landscape in which the population is evolving. The second endeavors to gather indirect evidence by relating developmental bias with the frequency of evolutionary changes, as in the study of digit reduction (Alberch and Gale 1985). Because developmental bias may vary based on the phenotypic trait chosen and the differences in developmental mechanisms, it would also

9 be useful to explore what features of development shape bias. This would involve mapping genetic variation with phenotypic variation as developmental mechanisms or regulatory structures are altered. Some researchers have begun linking genetic variation to phenotypic variation in animal model systems (Kopp et al. 2000, Brakefield et al.

2003) but have not yet altered the mechanisms or gene regulatory networks involved in the formation of the trait. However, some work has begun investigating the genotype-to- phenotype consequences of different mechanisms of development using mathematical models (Salazar-Ciudad and Jernvall 2004).

A computational model of neural development could address many of the needs outlined above in exploring the role of developmental bias. Because the model is simplified, some conclusions may not be directly applicable to natural systems, but it could nevertheless provide insight into developmental bias and how bias is shaped by altering developmental processes. By placing the developmental model within an evolutionary simulation, a computational model could also directly show the interplay between developmental bias and selection by mapping bias against the simulation‟s selective pressure. Even though an initial model may be simple, the elements and processes of the model can be made more biologically realistic. Both the model‟s results as well as feedback from biological experimentation can and should dictate which elements and processes are made more realistic. Idealized models, such as those of

Salazar-Ciudad and Jernvall (2002) and the one used here, can help to clarify and explore general questions on the role of developmental bias in evolution. For example:

How do developmental bias and selection interact? How is bias shaped by developmental mechanisms? Are there motifs in developmental mechanisms that predict patterns of bias? What developmental mechanisms affect the robustness of bias?

In this study, I analyze developmental bias in a computational model of neural development and explore the interaction between selection and developmental bias

10 during adaptive evolution. In the analysis of developmental bias, I demonstrate that the developmental system has an intrinsic bias. Second, I show that developmental bias varies with the genotype; this includes variation among different genotypes producing the same phenotype. Third, I show that related genotypes (through a series of single- base mutations) which produce the same phenotype differ in their pattern of bias.

Finally, I demonstrate how regulatory structure shapes developmental bias. Through the characterization of developmental bias exhibited by the model, I find that a strong local dependency of developmental bias has the potential to influence the pattern of phenotypic changes that occur during evolution. That is, the phenotypes accessible through the developmental process strongly depend on a particular genotype.

Furthermore, related genotypes, through phenotypically-neutral mutations, also show different patterns of bias. This local dependency of bias is apt to determine phenotypic transitions during evolution. Through the analysis of the interaction between developmental bias and selection during adaptive evolution, I do find that different sequences of phenotypic transitions occur and that the phenotypic changes are dictated by the local bias patterns. Also, local bias patterns during evolution show that higher- fitness phenotypes, although initially unavailable, become accessible after the accumulation of selectively-neutral mutations. These mutations allow the development of higher-fitness phenotypes through changes to the regulatory structure of the genotype. I also find that some populations experience an increase in their mutational robustness during evolution due to an indirect selective pressure against deleterious mutations. Finally, the epochal nature of adaptive evolution shown in these results can be conceptualized as a population diffusing over a network of selectively-neutral genotypes until a relatively rare mutation leads to a higher-fitness network.

Chapter 2 : Background

Modeling in Evo-devo As described above, one use of computational models is to clarify and explore general questions; therefore, it is not surprising to find computational models used in the relatively new field of evolutionary-developmental biology (evo-devo). Below I describe a representative sample of research using computational models to explore the intersection of evolutionary and developmental biology.

Considering the significance of the structure and modification of gene networks in producing morphological differences over evolutionary time (Carroll et al. 2001, Wray

2003), much work has explored the evolution of gene networks. Salazar-ciudad et al.

(2000) used generalized reaction-diffusion models of gene networks to investigate their pattern formation capabilities. Their results demonstrated the inherent pattern formation capacity of gene networks and indicated that the formation of complex patterns could be explained by the combination of basic patterns produced by simpler networks. With the finding of hierarchic and emergent networks, which have different properties, the authors suggest that the emergent networks, being simpler than the hierarchic networks, may have been generated or recruited early in evolution. However, because hierarchic networks can produce similar patterns as emergent networks upon combination, hierarchic networks may have replaced emergent networks during evolution. Salazar-ciudad et al. suggest that biological gene networks may be understood through comparison to the basic networks found in their study and further suggest that model networks can act as a working hypothesis for the structure of a biological network exhibiting a similar pattern generated by the model network (2000).

In similar work to Salazar-ciudad et al. (2000), Solé et al. (2003), using the pattern formation capabilities of gene networks, investigated the minimal complexity requirements in terms of pattern forming genes for the production of a high diversity of

12 phenotypes. Using a simple Boolean model of genes with only two gene types; genes which only interact within a cell, and genes which interact between cells, they found a complexity threshold that, once crossed, produces a very large number of patterns. They relate this finding to the Cambrian explosion during which a rapid diversification of body plans occurred and suggest that this rapid increase in morphological complexity might have resulted, in part, from changes in the pattern of gene regulation.

Despite the informative results of the studies mentioned above, two recent reviews have reminded researchers that there may not have been an adaptive origin of any given genetic network and instead may have been the result of other forces of evolution such as genetic drift, mutation, and recombination (Solé and Valverde 2006, Lynch 2007).

Another example of modeling in the field of evo-devo is Paulien Hogeweg‟s work with morphogenesis (Hogeweg 2000a, Hogeweg 2000b). Using a model of cellular automata to simulate the collective behavior of cells, she has looked at the evolutionary dynamics of morphogenesis as governed by differential cell adhesion, gene regulation, and intercellular signaling. In her evolutionary simulations, morphogenesis arises, not as a result of an explicit selective pressure, but as a side-effect of the maximization of the number of cell types. Hogeweg identified several morphogenetic mechanisms and concluded that complex shapes can develop from a single cell undergoing cellular differentiation with the additional requirement of cell surface minimization. Her simulations showed a “mosaic-like” pattern during evolution, in that, morphological features reoccurred and combined in different ways (Hogeweg 2000b). She describes this as morphogenesis occurring in the “shadow” of neutral paths which preserve cell differentiation. That is, there is a set of useful phenotypes that consistently remain near the neutral path that gets exploited during evolution. She likens this to convergent evolution and makes the comparison to the morphological similarities between separate species of cichlid fishes in the African great lakes that occupy similar ecological niches.

As a final example of modeling work in evo-devo, I describe the work by

Yampolsky and Stoltzfus (2001). Although their model does not include any developmental processes, the authors state why the results are relevant to the field of evo-devo and discuss the extension of their model‟s results to morphogenesis.

Yampolsky and Stoltzfus used a population-genetic model to explore whether mutation can act as an orienting force in evolution. Unlike other such models in which mutation is treated as a weak pressure on allele frequencies, mutation in their model generates new alleles. Their results show that the bias in the introduction of allelic novelty did determine the predominant direction of evolutionary change. As mentioned above, the authors then extend the idea of a mutational bias to developmental bias, in which developmental operators respond differentially to perturbation. These biases offer a new mode of evolutionary causation in addition to the ones recognized by the Modern

Synthesis; selection, drift, and migration. The recognition of these biases sheds new light on a variety of problems in evolutionary biology encountered since the synthesis.

Influence of evolution on gene regulation Considering the conserved nature of many gene families across phyla, it seems fairly clear that evolutionary changes in the developmental pathways producing morphology have been the result of changes in the temporal and spatial patterns of gene expression

(e.g., Gerhart and Kirchner 1997, Carroll et al. 2001).

Often changes in the spatiotemporal pattern of gene expression result from cis- regulatory changes. Cis-regulatory elements are short, non-coding sections of DNA that control the activity of a single, nearby gene (reviewed in Wray 2003b). These elements include the basal promoter, an “upstream” promoter, enhancers, silencers, and insulators. The sequence of the basal promoter includes the TATA box, a 7 base sequence of TATAAAA. The basal promoter is found in all protein-coding genes. In contrast, the upstream promoter‟s structure and associated binding factors vary according to

14 particular gene. The binding of transcription factors to an enhancer increases the rate of transcription. Interestingly, enhancer regions can be located upstream, downstream, and even within the gene. Silencers are control regions that repress their associated gene if bound. Finally, insulators act to prevent regulatory elements of one gene influencing another. These regulatory elements often act together to control the expression of a gene.

As a unit, these elements are modular in that they act independently of other cis- regulatory elements to affect the expression of a gene at different times and places.

As an example of how changes to these elements can lead to morphological differences over evolutionary time, the variation in axial morphology between chicken and mouse coincides with the spatiotemporal distribution of Hoxc8 (Belting et al. 1998).

In their work, Belting et al. (1998) found that changes of just a few nucleotides in the enhancer region were sufficient to delay the activation of Hoxc8 in chicken with the result that Hoxc8 was expressed in more posterior body regions.

Several individual reports in the scientific literature emphasize the greater importance of cis-regulation over alternations in the coding regions of genes in producing evolutionary changes in morphology (e.g., Carroll et al. 2001, Wittkopp 2004,

Wray 2003a, Wray 2007). However, Hoekstra and Coyne (2007) argue strongly that no conclusions can be drawn on the relative importance of regulatory versus structural changes.

Chapter 3 : The Developmental Model

Introduction Creating a simulation model of neural development involves the selection and abstraction of known biological elements and processes. In the following sections, I describe what elements were included in the model, how the interaction between those elements was replicated, and the initial conditions used in the simulations. This model is implemented in Mathematica from Wolfram Research (Wolfram Research, Inc, 2007).

The developmental model Even though neural developmental processes such as cell migration, axon guidance, synaptogenesis, and activity-based mechanisms all contribute to create specific and stereotyped neural connectivity patterns (Gupta et al. 2000, Dantzker and Callaway

2001, Kozloski et al. 2001), cellular projections, or neurites, often need to make a final choice among nearby cells for the creation of synaptic partners (Sanes and Yamagata

1999, Spencer et al. 2000, Benson et al. 2001). I chose this mechanism of target cell identification as the basis of establishing neural connections in our model. R. W. Sperry hypothesized that the patterning of synaptic connections rests upon highly specific cytochemical affinities (Sperry 1963). In effect, neurons and their targets have

“identification tags”. Recent molecular studies have supported this hypothesis. For example, SYG-1, a transmembrane protein, is required in a pre-synaptic neuron for the correct localization of synapses in C. elegans (Shen and Bargmann 2003). Also,

Yamagata and others have identified another group of transmembrane proteins,

Sidekicks (Sdks), neurites use to target specific lamina in vertebrates (Yamagata et al.

2002). In addition, Dscam, a cell surface protein in Drosophila capable of tens of thousands of isoforms (Schmucker et al. 2000) is necessary for target selection in the

Drosophila olfactory system (Hummel et al. 2003) and in the mechanosensory system

(Chen et al. 2006). It even appears as if Dscam is involved in a pre- and post-synaptic matching mechanism (Zhu et al. 2006). I generalize Sperry‟s chemoaffinity hypothesis and these findings in the model by creating a synaptic connection between neurons in which a single matching protein pair has been expressed.

The expression of proteins related to cell types is the result of a cellular differentiation process. Much of cellular differentiation is controlled through cell-cell interactions (Gilbert 2006). Of the various types of cell-cell interactions, such as gap junctions, juxtacrine, and paracrine signaling, I use paracrine interactions in order to

16 have a small set of proteins specify multiple cell types (Gilbert 2006). Paracrine interactions result from a secreted protein diffusing into the extra-cellular matrix resulting in a concentration gradient. Cells differentiate by responding to the different concentrations. These proteins are known as morphogens. One of the first morphogens to be identified was Bicoid (Bcd), whose concentration gradient is involved in segmentation pre-patterning along the antero-posterior axis in the Drosophila embryo

(Driever and Nüsslein-Volhard 1988). Although the interpretation of positional information appears to be a much more dynamic process than was previously thought

(Jaeger and Reinitz 2006, Jaeger et al. 2007), for this model, cell fate is determined through gradients as a static coordinate system. The response thresholds to a morphogen are largely determined in natural systems by the transcription factor‟s affinity to the binding site (Ephrussi and Johnston 2004, Ashe and Briscoe 2006). This concentration- dependent responsiveness of genes through the number and strength of binding sites in the enhancer regions of a gene is replicated in our model by the threshold region of the gene. Gradients in natural systems can direct the formation of three to seven cell types

(Ashe and Briscoe 2006). Morphogens in the model are able to activate genes at seven different thresholds.

The morphogens that drive the differentiation process and the synaptic proteins that determine neural connectivity are the products of genes. Genes in this model have a regulatory section and a coding section and are composed using two bases, represented as „A‟ and „C‟ (Figure 3-1A). Each gene has a fixed length of 57 bases.

A Model gene

Regulatory section Coding section

CCAAA CCCAC AAACA CAACA AAAAAACAACCACACACAACACACA CACCA AAAAAAC

Repression 1 Repression 2 Threshold Type Modifier Activation 1 Activation 2 Protein

B Coding section sequences Protein types Protein shapes

i) CCxxx xx Intra-cellular signal/TF (Int) ...

ii) CAxxx xx Extra-cellular signal/TF (Ext) ...

iii) ACxxx xx Pre-synaptic marker (Pre) ...

iv) AAxxx xx Post-synaptic marker (Post) ...

Figure 3-1: Model gene and sequences corresponding to protein types. A). Genes are divided into a regulatory and a coding section. The regulatory section is further subdivided into regions that determine if a gene is activated or repressed. The coding section is divided into two regions that determine a protein‟s function and its binding region. Two bases, „A‟ and „C‟, are used to generate genes. Genes are a fixed length of 57 bases each. B). The four protein types in the model. The first two bases in the protein type region determine a protein‟s function. The other three bases (represented by „x‟s) do not affect protein type. In the protein modifier region, any base sequence can occupy the five positions represented by the „[]‟s, resulting in 25 uniquely identifiable proteins for each type. The final two positions in this region do not change a protein‟s modifier.

The coding section of the gene produces the four types of protein families used in development (Figure 3-1B). Proteins in the model can act as signaling chemicals/transcription factors within cells (i) or between them (ii), or as a pre-synaptic marker (iii) or a post-synaptic marker (iv). Morphogens in the model (i.e., type ii proteins) act as both a transcription factor and an extra-cellular signal. Although it is uncommon for transcription factors (TFs) to diffuse into the extra-cellular matrix and act as morphogens, I continue to use the term “transcription factor”, instead of “paracrine factor”, for these secreted proteins to avoid confusion with the basal role of this type of

18 protein in the model. Also, I use “diffuse” in a general sense when describing the action of these proteins. The modifier region uniquely identifies proteins that are of the same type, in effect creating a protein family. There is no translation component of converting base sequences into amino acids that define a protein in this model; therefore, the base sequence of the first five positions in the modifier region results in 32 proteins for each type. Mutations occurring in the final three positions of the protein type and the final two positions of the modifier regions do not alter the protein‟s type or identity, respectively. This adds stability to the developmental system for later evolutionary simulation studies and, more importantly, allows us to link the developmental bias seen in this study (through single-base mutations) and the direction of evolutionary changes.

The regulatory section contains two repression sites, two activation sites, and a threshold region. Gene expression is blocked or activated by the binding of a transcription factor to the repression or activation sites. Binding occurs if the sequence of a protein‟s modifier region exactly matches the sequence of the regulatory site. A gene‟s threshold region determines if a transcription factor secreted by another cell is of sufficient strength to activate or repress that gene. The TF activates or represses if it binds to a regulatory region and has a concentration greater than the level encoded in the threshold region. This threshold is simply the number of base „A‟s. The concentration of a protein is determined by a static exponential decay function, chosen so that proteins secreted by cells can only act a short distance away and therefore on just a few cells. A TF produced within a cell need only match a repression or activation site of a gene to result in transcription being blocked or activated. It is assumed that the concentration of the protein is of sufficient strength because it is produced within the cell. The regulatory region allows gene expression to be blocked or activated via TFs that are produced within the same cell or secreted by a distant cell. As in natural systems (Wray 2003), genes can

19 be controlled under different contexts through multiple regulatory sites for both repression and activation.

Although genes, proteins, and their interactions are greatly idealized in this model, the model still captures the dual nature of robustness and sensitivity to perturbations found in biological genetic systems. In natural systems, some robustness to mutation occurs through the degeneracy in the translation of mRNA codons to amino acids. Due to the “wobble position” in the mRNA codon, multiple base sequences correspond to a particular amino acid. Therefore, point mutations in the DNA sequence are unlikely to change the amino acid in the protein being generated. In contrast, a point mutation in the DNA sequence coding for hemoglobin confers protection against malaria. In the model, robustness is added by including base positions in genes that do not affect protein type or identity. Yet a single mutation in other base positions can alter the function of a protein, in that way, conferring sensitivity to mutation.

Other processes of development, such as cell division, cell migration, and maturation, are not incorporated into the model, and therefore act as initial conditions.

To reduce the complexity of this model, the number of cells and their positions used in a simulation are predetermined. Cell number and location remain fixed during the simulation. During development the initial differentiation occurs through an unequal distribution of control signals inside the zygote which, after cell division, results in different fates in the daughter cells (for example, Rose and Kemphues 1998). I approximate this cell polarity that initiates differentiation by introducing a TF into one of the cells at the beginning of our simulation. Because each cell contains exact copies of the genotype, this transcription factor is labeled as the „symmetry-breaking protein‟.

After initiation, the differentiation period stops after a pre-determined number of time steps. In early simulations, I noted that the differentiation process either stops or falls into a cyclic expression of genes within a short period, due to the small number of genes

20 in the genome as well as the small number of cells. Because of this, I felt there was no need to incorporate a function that determined when the system reached an equilibrium state. Instead, I limited the number of time steps that the differentiation process could undergo and identified the phenotype produced at that point in time.

In summary, this model of neural development proceeds through three stages to generate the connectivity of neural circuits (Figure 3-2). In stage 1, cells are placed at fixed locations in a planar environment and the symmetry-breaking protein is inserted into one cell. In stage 2, cells differentiate over a predetermined number of time steps by expressing different pre- and post-synaptic surface proteins. This differentiation is controlled by a genetic regulatory network involving intra- and extra-cellular signaling proteins. Extra-cellular signaling proteins create a concentration gradient and control gene activity via activation and repression thresholds that respond to the concentration of the signaling protein. Finally, in stage 3, neural connections are formed between complementary pairs of synapse-determining surface proteins.

1) Cell placement 2) Differentiation 3) Target identification

1 1 1

2 3 2 3 2 3

1 unit

Figure 3-2: The three stages of development in the formation of a three-neuron circuit with three synaptic connections. In stage 1 cells are placed at fixed distances in a planar environment. In stage 2, cells differentiate through signaling proteins which result in the expression of synapse-determining surface proteins. Signaling proteins control gene activity through a concentration gradient. In stage 3, neural connections are formed between cells having complementary surface proteins.

An example demonstrating development of a neural circuit A genome capable of producing the three-connection, three-neuron circuit shown in

Figure 3-2 (stage 3) consists of eight genes (Figure 3-3A). Figure 3-3A shows the full genome whereas 3-3B shows the reduced and simplified genome which will be used to illustrate the process of development. The genome has been reduced by including only the Activation 1 region of the four possible transcription binding sites. In addition, I simplified the representation of the genome by giving a decimal representation of the threshold value encoded for each gene, showing what type of protein is encoded by the gene, and listing only the relevant bases of the protein modifier region.

Protein A Repr 1 Act 1 Repr 2 Act 2 Threshold Type Modifier 1 ACCCC CCCCC ACCCC ACCCC CCCCCCCCCCCCCCCCCCCCCCCCC ACCCC CCCCCCC

2 ACCCC CCCCC ACCCC ACCCC CCCCCCCCCCCCCCCCCCCCCCCCC AACCC CCCACCC

3 ACCCC CCCCC ACCCC ACCCC CCCCCCCCCCCCCCCCCCCCCCCCC CACCC CCCCACC

4 ACCCC CCCCA ACCCC ACCCC AAAAAAAAAAAAACCCCCCCCCCCC ACCCC CCCCACC

5 ACCCC CCCCA ACCCC ACCCC AAAAAAAAAAAAAACCCCCCCCCCC AACCC CCCCCCC

6 ACCCC CCCCA ACCCC ACCCC AAAAAAAAAAAAACCCCCCCCCCCC CACCC CCCACCC

7 ACCCC CCCAC ACCCC ACCCC AAAAAAAAAAAAAAAAAAAACCCCC ACCCC CCCACCC

8 ACCCC CCCAC ACCCC ACCCC AAAAAAAAAAAAAAAAAAAACCCCC AACCC CCCCACC

B 1 CCCCC 1 Pre CCCCC

2 CCCCC 1 Post CCCAC

3 CCCCC 1 Ext CCCCA

4 CCCCA 13 Pre CCCCA

5 CCCCA 14 Post CCCCC

6 CCCCA 13 Ext CCCAC

7 CCCAC 20 Pre CCCAC

8 CCCAC 20 Post CCCCA

Figure 3-3: Genome that produces the three-connection circuit in Figure 3-2, stage 3. A). The actual sequence of bases comprising the genome. B). The same genome reduced and simplified for demonstration purposes. These reductions and simplifications included taking only the Activation 1 region of the four possible binding sites, giving a decimal representation of the threshold value encoded for each gene, listing the type of protein, and including the relevant bases of the protein modifier region. The threshold region in A encodes the concentration level to which a gene will respond to a transcription factor by the number of base

„A‟s in this region. If no base „A‟s appear in the threshold region (as in genes 1, 2, and 3), the threshold defaults to 1 (i.e., near zero concentrations of a signal will not repress or activate a gene). Each cell in Figure 3-3 contains this set of genes.

In time step 1 of development, the differentiation process is initiated by the introduction of a TF (the symmetry-breaking protein) into cell 1 (Figure 3-4A). This protein binds to the activation regions of genes 1, 2, and 3, thus expressing those genes to produce a pre- and a post-synaptic marker and an extra-cellular signaling protein.

In time step 2, the extra-cellular protein produced by cell 1 diffuses across the space separating the cells and results in gene expression in cell 2 but not in cell 3, because cell

2 is closer than cell 3 to cell 1 (Figure 3-4B). Three genes are expressed in cell 2, because the protein signal matches the activation regions of those genes and is of a concentration greater than the threshold of those genes. This signal results in a pre- and post-synaptic marker and a new extra-cellular signal in cell 2.

In time step 3, extra-cellular signal CCCAC, secreted by cell 2, diffuses in the environment and results in differential gene expression (Figure 3-4C). Because of the concentration levels of the protein at the nearby cells, only the genes in cell 3 are expressed. Genes 7 and 8 express a pre- and a post-synaptic marker. Since no more signaling proteins are produced, activity within the genome has reached a steady state; gene expression stops during the remainder of the differentiation period.

A Cell 1 1

CCCCC 1 CCCCC 1 Pre CCCCC

CCCCC 2 CCCCC 1 Post CCCAC

CCCCA CCCCC 3 CCCCC 1 Ext CCCCA 2 3

B Cell 2 Cell 3 1

CCCCA 15 CCCCA 12 4 CCCCA 13 Pre CCCCA 4 CCCCA 13 Pre CCCCA

CCCCA 15 CCCCA 12 5 CCCCA 14 Post CCCCC 5 CCCCA 14 Post CCCCC

CCCAC 15 12 CCCCA 15 CCCCA 12 6 CCCCA 13 Ext CCCAC 6 CCCCA 13 Ext CCCAC 2 3

C Cell 1 Cell 3 1

CCCAC 15 CCCAC 31 7 CCCAC 20 Pre CCCAC 7 CCCAC 20 Pre CCCAC

CCCAC 15 CCCAC 31 8 CCCAC 20 Post CCCCA 8 CCCAC 20 Post CCCCA 31

2 3

Figure 3-4: The differentiation steps as generated by the genome in Figure 3-3. Only the relevant genes are shown at each time step. A) The symmetry-breaking protein is introduced into cell 1. B) Differential gene expression through an extra- cellular signal. Because cell 2 is closer to cell 1 than cell 3, only the genes in cell 2 are activated. C) Continued differential gene expression through extra-cellular signals. Note that expressed surface proteins are bound in the cell‟s membrane and do not degrade over the growth period. However, signaling proteins act for only one time step before being degraded. This compresses the time for the developmental sequence to play out. Instead of incorporating the time to set up a chemical gradient, I chose an exponential decay function that calculates concentration based on distance. This generates a gradient with a sharp decay that allows gene thresholds to match the distances in our two-dimensional growth surface. Concentration in this model is therefore a function of distance and not of both distance and time.

Once the differentiation period ends, the list of surface proteins expressed by each cell is converted by a function into the connectivity matrix for the network. In this example, the expression pattern of surface proteins (Figure 3-4C; and stage 2 in Figure

3-2) generates the three-connection circuit shown in stage 3 of Figure 3-2. The function that determines neural connectivity ignores complementary surface proteins expressed in the same cell (i.e., no self-connections are formed). Although self-connections (or autapses (Van der Loos and Glaser 1972)) are found throughout the mammalian brain

(Karabelas and Purpura 1980, Park et al. 1980, Pouzat and Marty 1998) and also in invertebrates (in Aplysia (Gardner 1977)), I did not include self-connections as part of the phenotype since autapses appear to maintain the precision of action potential timing

(Bacci and Huguenard 2006), a functional role for neural connectivity not under investigation here.

For the results presented on developmental bias below, I used a three-neuron system. Having few neurons, and therefore few neural connections, a small number of phenotypes are generated in this system. There are n2-n connections in an n-neuron circuit if every neuron connects to every other neuron. Then, if each connection can either be present or absent, a three-neuron system will generate 26, or 64, possible phenotypes.

Chapter 4 : Characterizing Developmental Bias The results in this chapter have been published in Evolution & Development by Psujek and Beer. I am responsible for the majority of the work presented in the published paper. R.D. Beer provided guidance and critical comments.

Introduction With the abstracted developmental model, the first step is to determine if it exhibits bias in the production of phenotypic variants and, if so, how much of that bias is due to the model‟s abstractions. In the following sections, I describe the representation

25 of developmental bias in this system, demonstrate the bias produced by the developmental system as well as by specific genotypes, and analyze how regulatory structure shapes developmental bias.

Visualization of bias in this system As defined above, developmental bias is the differential production of phenotypes through uniform genetic variation. Developmental bias is represented as the set of phenotypes expressed after a wild-type genotype has had all possible mutations of the same magnitude performed to it (as depicted in Figure 1-1). Because of this uniform genetic variation, any bias shown is a result of genetic hierarchies, not of the lack of genetic variation. The phenotype generated by the developmental model is the connectivity of a neural circuit. Because this trait is not continuous and a measure of closeness for these phenotypes is lacking, I plot developmental bias by arbitrarily arranging the phenotypes in a circular array (as in Figure 4-1). Each of the 64 possible neural architectures is represented in these plots (gray radial lines). Bold radial lines overlaying the gray lines represent particular phenotypes produced by the developmental system, with the length of the line indicating the fraction of genotypic variation (e.g., fraction of all possible single-base mutations or fraction of randomly generated genotypes) resulting in that circuit.

An intrinsic bias exists in the developmental system Given this model of the development of neural connectivity, does it exhibit bias in the production of the various phenotypes? Yes (Figure 4-1). I randomly generated 20 million genotypes composed of nine genes of fifty-seven bases, generated the phenotypes encoded by those genotypes, and plotted the fraction of genotypes that result in a particular phenotype. Nine genes were used for this sample instead of eight genes in the hand-coded genotype shown in Figure 3-3. The “extra” gene might result in further cell signaling proteins. It is apparent in Figure 4-1 that not only are some phenotypes

26 produced far more often than others, but some phenotypes are not generated at all from our sample of genotypes. Of the 64 possible circuits of three-neurons, only 27 different circuits are produced (bold radial lines) from the random genotypes. Even though the sample of 20 million genotypes is extremely small compared to the size of genotype space, the general pattern of bias exhibited in Figure 4-1 was fairly stable as we increased the sample size. That is, the commonly produced circuits (Figure 4-2) were also the commonly produced circuits at smaller genotype sample sizes. I therefore concluded that the sample accurately represented the distribution of phenotypes produced by the developmental system over genotype space.

Figure 4-1: Developmental bias exists in the model system. Of the 64 possible neural circuits (gray radial lines), 27 (bold radial lines) were produced from a random sample of 20 million genotypes of 9 genes. The length of the solid lines represents the fraction of sampled genotypes that produce a particular phenotype and is determined by log10 fraction + c, with c arbitrarily chosen to obtain positive and non-zero values from the logarithmic function. This value also seemed to visually bring out both the rarity of genotypes for a specific architecture as well as their abundance. The scale range in this plot is 0% (center) to 100% (outer perimeter) (shown by the concentric circles). The circles with dark lines represent powers of 10, starting at the outside with 100 and decreasing. Examples of the generated circuits are shown in the figure. The number of genes for our sample genotypes was based on the number of genes used to create three- neuron circuits when hand-designing genomes. The scale range and arbitrary circular arrangement of possible phenotypes is the same for all developmental bias figures.

For this idealized model, one expectation is that bias is correlated with simple properties of the neural circuits. For example, the bias seen could simply be that the model is less likely to produce a circuit of a greater number of connections. Yet, plotting the probability of producing a circuit of x-connections from our random sample of genotypes shows no simple pattern (not shown). Rather, the biased distribution of phenotypes shown in Figure 4-2 reflects aspects of the developmental model and the initial conditions of neuronal spacing and the introduction of the symmetry-breaking protein. In general, the more heterogeneous the pattern of connections is in a circuit, the less likely it will be produced by random sampling of genotypes (Figure 4-2). The ten most commonly produced circuits shown in Figure 4-2 are simple in terms of connectivity. They either have all possible connections, no connections, two ordered connections (i.e., reciprocal connections or a pair of connections originating from/terminating on the same neuron), or simply one connection. No circuit has four or five connections. In addition, the pattern of bias seen in Figure 4-2 is a result of asymmetry in the development process. The transcription factor that starts the developmental process is always introduced into cell 1. Therefore, connections to/from cell 1 are more commonly generated by random genotypes than circuits only containing connections between cells 2 and 3 (e.g., compare the number of genotypes that result in

4-2B to the number that produce 4-2G). Finally, it is easier to establish connections to nearby cells than to more distant cells with this particular spacing, due to the randomized expression threshold. By randomly generating the base sequences in the threshold region, on average, the threshold for any given gene will be 12 or 13. For an extra-cellular signal secreted by cell 1, its concentration at cell 3 will be 11.93. Because the concentration of a signal has to be greater than the threshold to activate a gene, circuits 4-2B and C are more commonly produced than 4-2D and E. Because the specific initial conditions of cell spacing and insertion of the symmetry-breaking protein used above have an impact on the pattern of bias shown, other initial conditions were selected to determine the degree of effect those parameters had on bias. These other cases also resulted in developmental bias and the patterns differed in varying degrees from the bias pattern seen in Figure 4-1 (results not shown). Although a study of the effects of model parameters on bias is important, the focus of this investigation is to characterize developmental bias for one specific case. Further results presented in this chapter follow from the initial conditions depicted in Figure 3-4A.

Figure 4-2: Ten most commonly produced neural circuits through random sampling of genotypes and the number of sampled genotypes that result in the given circuit.

Because Figure 4-1 represents the phenotypes produced by a random sampling of genotype space, we refer to this pattern as the global bias of the developmental system.

By sampling over the entire genotype space, global bias averages over variation of bias produced by individual points in genotype space. Therefore, this characterizes the bias intrinsic to the developmental system.

Developmental bias varies with genotype The global bias of the system depicted in Figure 4-1 represents what neural circuits would be commonly produced through a uniform sampling of genotype space; however, an evolutionary trajectory does not sample genotypes in this way. Instead, the phenotypes represented in the next generation depend upon selection and subsequent

30 mutation of genotypes in the current generation. Therefore, the differential production of phenotypes through uniform variation (that is, through all possible single-base mutations) of an individual genotype is defined as local bias. Local bias is determined by performing all individual base substitutions on a given genotype, developing each mutant phenotype, and finally calculating the fraction of mutations that result in a particular phenotype. Averaging the local bias patterns for a large number of randomly chosen genotypes would result in the global bias pattern.

A * B

* C D

Figure 4-3: Local bias patterns for four specific genotypes. Each genotype produces a different wild-type phenotype (indicated by asterisks in the figure). The phenotypes accessible through single-base mutations are also shown around each plot. The length of the solid lines represents the fraction of single-base mutations that result in a particular neural circuit. As in the global

bias plot, the circles with dark lines represent powers of 10, starting at the outside with 100 and decreasing.

Local bias patterns for unique genotypes are different from each other and from the global bias pattern (Figure 4-3). Four genotypes that generate different phenotypes were arbitrarily chosen and their local bias pattern derived. In contrast to Figure 4-1, the fractions of mutations, instead of genotypes, that result in a given phenotype determine the length of the bold lines. Although each local bias pattern shares the common feature of a large number of mutations resulting in a neural circuit with no connections, each pattern shows a strong dependence on the original phenotype (asterisked circuits). That is, the majority of mutations are neutral with respect to the phenotype in that they do not change the neural circuit produced. However, there are a few mutations that do alter the neural circuit generated through development. For example, in Figure 4-3B, there are mutations that result in a fully-interconnected circuit or a reversal of the original neural connection.

Because of these dissimilarities between local biases, and their dissimilarity to the global bias of the system, local patterns of bias appear to depend more on the interactions of development as directed by a particular genotype than on the overall mechanisms of the developmental system. In contrast, if local biases of many, different genotypes strongly matched the global bias pattern, this would indicate that the developmental mechanisms of the model dictate what phenotypes are produced. But because phenotypic accessibility is so locally dependent, that is, the genotypes in the current population would strongly dictate which phenotypes are generated in the next generation through genetic variation, it is likely developmental bias would have a strong impact on the evolutionary pathway taken.

Degenerate genotypes have different patterns of bias The global bias pattern (Figure 4-1) demonstrates a huge degeneracy in the developmental system; that is, there are many genotypes that produce the same phenotype. Yet, these degenerate genotypes do not exhibit the same pattern of local bias

(Figure 4-4).

A B C D

E F G H

Figure 4-4: Local bias patterns for eight genotypes that produce the same neural circuit from our random sample. The phenotype produced by each genotype is shown in Figure 3-6B and is represented by the longest ray in each plot here. In this figure and in Figure 4-5, the concentric circles representing the scale have been removed for clarity but the scale remains the same as in Figure 4-3.

The eight randomly sampled genotypes used in Figure 4-4 each create the same phenotype (shown in Figure 4-2B) and are therefore considered neutral genotypes. Yet these genotypes display different patterns of bias. Although some of the structure of the bias pattern is the same (namely, a large number of mutations that do not change the phenotype or that create a fully-unconnected circuit), each shows some differences in the phenotypes produced through genomic variation. For example, base substitutions in the genotype used in Figure 4-4A produce two phenotypes, either the wild-type or the fully- unconnected circuit. In contrast, performing single-base mutations on the genotype used

33 in Figure 4-4B results in four additional phenotypes being produced. As another example, again barring the wild-type and the fully-unconnected phenotype, mutations to the genotype used in Figure 4-4E result in phenotypes not produced through mutations of the genotype used in Figure 4-4F. The opposite is also true; mutations to the genotype for Figure 4-4F result in phenotypes not produced by the genotype for Figure 4-4E. The genotypes used in the figure were chosen to display some of the diversity in local biases among degenerate genotypes.

These results suggest that a particular evolutionary pathway taken by a population would strongly depend on the local biases of individuals within the population (again, note the differences in the patterns of bias for genotypes used in Figure 4-4E and F).

Even though these genotypes are phenotypically-neutral (and selectively-neutral if fitness is based solely on phenotype), some genotypes might be more likely to lead to phenotypes having a higher fitness than other genotypes due to their pattern of bias.

Although these degenerate genotypes create a neutral set (in relation to phenotype), it is unclear whether some or all of the genotypes are linked by a pathway of single-base mutations which do not alter the phenotype, thereby creating a neutral network

(Schuster et al. 1994). If so, this neutrality would allow mutations to accumulate that do not change the phenotype yet do change the developmental context in which further mutations act. This change in context could lead to new phenotypes becoming accessible as shown by the local bias pattern.

Genotypes along a neutral network differ in their pattern of bias As shown in the previous section, even though randomly generated genotypes may produce the same phenotype, their local biases are often different. But does the pattern of bias change as neutral mutations accumulate in a genotype? In fact, the patterns of bias do change (Figure 4-5).

A B C D

0 6 28 32

E F G H

65 130 250 301

Figure 4-5: Local bias patterns along a neutral network. Number below each figure is the number of neutral single-base mutations in the wild-type genotype. The phenotype produced by the wild-type genotype (and by all of the mutant genotypes) is shown in Figure 4-2B and is represented by the longest ray in each plot here.

Starting with a single randomly generated genotype from the sample above, I identified all neutral mutations, that is, base-substitutions that do not change the phenotype, and randomly selected one mutation to create a new mutant genotype. I then repeated this process to create a list of genotypes in which nearest neighbors differed in genotype sequence by only one base. In this way, a network of neutral genotypes linked by single-base substitutions was created. Movement along this network corresponded to the accumulation of single-base mutations. Base substitutions that reversed previous mutations were not allowed. Figure 4-5 shows the local bias patterns for eight genotypes along this neutral network. Below each plot is the number of bases that differ from the original genotype. Figure 4-5A shows the local bias for the original genotype (therefore the difference is 0).

In Figure 4-5, the pattern of bias changes along the neutral network, sometimes repeating previous patterns (Figure 4-5B and D) or showing a similar pattern but with

35 more mutations resulting in the same phenotypes (compare Figure 4-5C and E). At one point along the neutral network, the genotype demonstrated a more biased production of phenotypes (i.e., fewer phenotypes generated through mutation as in Figure 4-5G) but then the genotype became less biased as more neutral mutations accumulated (Figure 4-

5H). However, more dramatic is the difference in the phenotypes produced by the genotypes used in Figure 4-5A and H. Only phenotypically-neutral mutations have accumulated between the original genotype used in Figure 4-5A and the one used in

Figure 4-5H; yet, these neutral mutations have altered the possible non-trivial phenotypes (i.e., neither the wild-type nor the fully-unconnected circuit) produced by mutations of the genotype. The three non-trivial phenotypes shown in Figure 4-5A are not the same three non-trivial phenotypes shown in Figure 4.5H.

Since selection acts on the phenotypes produced through mutation of the previous generation‟s genotypes, it appears in this model system that developmental bias would have a strong effect on the pathway taken by evolution. Even though these eight genotypes produce the same phenotype, neutral mutations have altered the phenotypes available through further genetic mutation in a genome. That is, the particular phenotypic transitions made during evolution depend on the where the population resides on the neutral network.

Regulatory structure shapes developmental bias How does a particular pattern of bias emerge from a genotype? Patterns of bias are determined by the way in which mutations impact the regulatory structure of the wild- type (Figs. 4-6 and 4-7). For the pattern of bias in Figure 4-5A, there are three single- base mutations which result in a phenotype different from the wild-type circuit (and the trivial fully-unconnected circuit). The effects of these mutations are shown in Figure 4-6.

Mutations 292 and 301 directly alter the regulatory structure of the wild-type genotype.

This changes the expression pattern of surface proteins, resulting in new phenotypes

36 being produced. The third base substitution, mutation 446, affects the phenotype by changing the gene product. The mutation acts to change a signaling protein from one that acts within the cell to one that acts between cells. This results in gene expression in cells not normally affected by the signaling protein, and therefore a new phenotype is formed.

SymProt

Post 5 Extra 3 Pre 5 Post 26

Intra 16

2 3

Mutation 292

1 SymProt 1 SymProt Post 5 Extra 3 Post 26 Mutation 301 Post 5 Extra 3 Pre 5 Post 26 Intra 16 Intra 16 Pre 5 2 3 2 3

Mutation 446

SymProt 1

Post 5 Extra 3 Post 26

Extra 16

Pre 5 2 3

Figure 4-6: New phenotypes are produced from mutations that alter the gene regulatory structure of the wild-type. The symmetry-breaking protein (shaded ellipse labeled SymProt) initiates development and is shown at the beginning of each regulatory network with connections to the genes it binds. Genes are represented as rectangles labeled in italics by their product. Arrows in the gene regulatory networks represent transcriptional activation connections. The circuit diagrams show the expressed surface proteins as well as the neural connections formed from those surface proteins. Because of mutation 292 (number refers to base position in the genotype), the surface protein Pre 5 (key-type solid rectangle, Post 5 is depicted as a lock-type solid rectangle) is expressed in cell 1 resulting in reciprocal neural connections from cells 1 and 2. Mutation 301 also allows Pre 5 to be activated by the symmetry-breaking protein similar to mutation 292 but eliminates the regulatory activation connection from Intra 16. This prevents the production of Pre 5 in cell 2 which results in a neural connection only from cell 1 to cell 2.

Mutation 446 changes the protein type from Intra 16 to Extra 16 resulting in Pre 5 being expressed in cells 1 and 3.

Regulatory changes can also leave the phenotype unchanged (Figure 4-7). Mutation

66 eliminates a regulatory connection between genes, thereby altering the expression pattern of surface proteins; however, this change does not affect the neural connection formed. New genes can be included in the original regulatory structure without effect, as shown by mutation 495. Finally, point mutation 439 changes the response threshold of

Intra 16 but this does not alter the phenotype.

1 SymProt

Post 5 Extra 3 Post 26

Intra 16

Pre 5 2 3

Mutation 66

1 1 SymProt SymProt

Post 5 Extra 3 Post 26 Mutation 495 Post 5 Extra 3 Post 26

Intra 16 Intra 16 Intra 29

Pre 5 Pre 5 Intra 19 2 3 2 3

Mutation 439

SymProt 1

Post 5 Extra 3 Post 26

Intra 16

Pre 5 2 3

Figure 4-7: Neutral mutations produce the same phenotype even though they may affect gene regulation. Lines with a bar endpoint represent transcriptional repressive connections. Mutation 66 eliminates a regulatory connection from the Extra 3 to Post 5 preventing the expression of Pre 5 in cell 2 yet the same neural connection is formed. Mutation 495 results in additional genes becoming incorporated, through a change in threshold, into the regulatory network; however, these genes do not have an effect on the phenotype because they do not produce surface

proteins. Finally, mutation 439 changes the regulatory threshold for Intra 16 yet this does not alter the phenotype.

Even though these mutations do not change the phenotype being formed (Figure 4-

7), they can accumulate and change the developmental context in which further mutations act. The accumulation of these phenotypically-neutral mutations can therefore result in different patterns of bias, as shown in Figure 4-5. This developmental context is in large part a product of the gene regulatory network contained within the genotype (Figure 4-8). The context dependency of mutations on fitness has been shown in bacteria (Remold and Lenski 2004).

A SymProt B SymProt

Post 5 Extra 3 Post 26 Post 5 Extra 3 Post 26

Intra 16 Intra 16

Pre 5 Pre 5

C SymProt D SymProt

Post 5 Extra 3 Post 26 Pre 23 Post 5 Extra 3 Post 26 Pre 23

Intra 16 Intra 29 Intra 16 Intra 13

Pre 5 Intra 18 Pre 5

E SymProt F SymProt

Post 5 Extra 3 Post 10 Post 23 Post 5 Extra 3 Pre 5 Post 23

Intra 16 Intra 16

Pre 5

G SymProt H SymProt

Post 5 Extra 11 Pre 16 Post 5 Extra 11

Pre 5 Pre 5 Intra 2

Figure 4-8: Regulatory networks for the eight genotypes used in Figure 4-5. Although these networks are different through the creation or elimination of new regulatory connections, they each create the same neural connection.

Small, subtle changes to the regulatory networks caused by the neutral mutations are enough to change the pattern of bias. For example, the elimination of the regulatory connection from the gene Extra 3 to Post 5 in Figure 4-8B as mutations accumulate in the genotype whose regulatory structure is shown in Figure 4-8A dramatically changes

40 the local bias pattern (shown in Figure 4-5A and B). The alteration of the regulatory network changes the expression pattern of surface proteins, which results in different phenotypic consequences after a point mutation has been applied at the same location in each genome (Figure 4-9).

A Original regulatory structure

1 1 SymProt SymProt Mutation 292 Post 5 Extra 3 Post 26 Post 5 Extra 3 Pre 5 Post 26

Intra 16 Intra 16

Pre 5 2 3 2 3

B New regulatory structure (Hamming distance = 6)

SymProt 1 SymProt 1 Mutation 292 Post 5 Extra 3 Post 26 Post 5 Extra 3 Pre 5 Post 26

Intra 16 Intra 16

Pre 5 2 3 2 3

Figure 4-9: Neutral mutations change the developmental context in which subsequent mutations operate. The two genotypes used in A and B lie along a neutral network and therefore create the same phenotype. However, neutral mutations have altered the regulatory structure of the new genotype resulting in different phenotypic consequences through a point mutation applied at the same location in each genotype. For the original genotype, mutation 292 causes an additional connection to be formed, resulting in reciprocal connections between neurons 1 and 2 (A). The same point mutation in the new genotype leaves the phenotype unchanged (B) due to the loss of the activation regulatory connection from Extra 3 to Post 5 by neutral mutations.

The two genotypes used in Figure 4-9A and 4-9B lie along a neutral network and therefore create the same phenotype. For the original genotype, the point mutation results in a new connection being formed between neurons 1 and 2 (Figure 4-9A). The point mutation applied to the same location in the new genotype leaves the phenotype unchanged (Figure 4-9B).

Chapter 5 : Characterizing the Interaction between Developmental Bias and Selection

Introduction From the preceding analysis on the developmental model‟s bias in the production of phenotypic variants, it seems likely that an evolutionary pathway taken by a population, that is, the sequence of phenotypic changes undergone by the population, would depend on developmental bias. The differences in the patterns of bias shown by phenotypically- neutral genotypes shown in Figure 4-4 indicate that the phenotypic changes would depend on the local biases of individuals within the population. In effect, two populations composed of individuals of different genetic backgrounds under the same selective pressure would experience different phenotypic changes during evolution.

Alternatively, the lability of patterns of bias as phenotypically-neutral mutations accumulate in the genotype, as seen in Figure 4-5, suggests that developmental bias may have a reduced effect on differences in evolutionary pathways taken by genetically distinct populations. For Figure 4-5A and B, the two genomes used differed by only six bases yet exhibited large differences in their production of non-trivial phenotypes.

Therefore, even a small population of genetically similar individuals is likely to show a wide range of accessible phenotypes. Due to this lability of developmental bias, it is possible that two populations consisting of fairly different genetic backgrounds would exhibit overlapping ranges of accessible phenotypes and are therefore likely to follow similar phenotypic changes due to selection. In this chapter, I explore the interaction between developmental bias and selection in evolutionary simulations under a selective pressure for a specific circuit.

The evolutionary simulation The evolutionary simulation, or genetic algorithm, that I employ is based on principles of natural selection and genetics (Holland 1975, Goldberg 1989). As the

42 selective pressure, I chose to evolve neural connectivity towards a target phenotype. This phenotype was chosen because it had multiple connections and was considered difficult to build based on a random sampling of genotype space. Of 20 million randomly generated genotypes, only three resulted in the formation of this neural connectivity pattern (data not shown). Because of these factors, a selective pressure for this neural circuit would not pose a trivial task for adaptive evolution. The fitness function assigned a value from 0 and 1 to each individual genotype based on the Hamming distance between the circuit produced by the genotype and the target architecture. Hamming distance is the number of differences between the connectivity matrix of the individual and of the target circuit. The target phenotype is shown in Figure 5-1.

Figure 5-1: The target circuit used in the evolutionary simulations. The selective pressure is based on the Hamming distance between the connectivity matrix of this circuit and the circuit produced by the genotype.

The selection of individuals to produce offspring in the next generation was based upon fitness, with higher fitness individuals being more likely to reproduce.

Reproduction was asexual in this model. Offspring were mutants of the parent genotypes such that one and only one mutation was created from parent to offspring. This high mutation rate was chosen for a rapid exploration of genotype space by a population.

Each evolutionary simulation was initialized with a population of 100 individuals consisting of three cells (arranged as in Figure 3-2, step 1) with identical genotypes of nine genes in each cell. Each gene was fifty-seven bases long and composed of only two bases, resulting in 2513 possible genotypes. Each individual genotype was randomly generated. Population size remained constant during the simulation. The simulation 43 proceeded for 300 generations. The developmental model and evolutionary simulations were implemented in Mathematica from Wolfram Research (Wolfram Research, Inc,

2007).

Visualization of fitness and local bias In order to study the interaction of developmental bias and selection, it was necessary to relate phenotypic variation and selective pressure towards the target phenotype. As shown previously, the pattern of developmental bias can be represented as a radial array of lines representing the different possible phenotypes and whose length is a function of the fraction of all single-base substitutions of a wild-type (WT) genotype.

Figure 5-2A shows such a plot for an arbitrarily chosen genotype. Lines representing each of the sixty-four possible circuits were arranged according to fitness (see below) in a radial array (gray radial lines). From single-base substitutions in the WT genotype (the ray representing the WT phenotype is indicated by the open circle), six phenotypes (bold radial lines) are accessible (that is, produced through mutations). This notion of phenotypic accessibility is similar to the concept of “phenotypic neighborhood” proposed by Dichtel-Danjoy and Felix (2004). Figure 5-2B shows a gray-scaled representation of fitness values for each of the possible circuits (maximum fitness (1) = white, minimum fitness (0) = dark gray). The direction of the target phenotype is indicated by the asterisk. Segments representing isofitness phenotypes were arranged together resulting in wedge-shaped regions in the figure. Finally, in Figure 5-2C, the local bias pattern is superimposed on the fitness plot. For this genotype, the target phenotype cannot be produced through single-base mutations; yet, this genotype can produce a phenotype having a higher fitness than the wild-type (ray in the light gray region to the left of narrow wedge representing maximum fitness).

Figure 5-2: Plots of developmental bias, neural architecture fitness, and the combination of bias and fitness. A) A local bias pattern from an arbitrarily chosen genotype. Six phenotypes (bold radial lines) of the sixty-four possible neural circuits (gray radial lines) are accessible from single-base substitutions of the wild-type phenotype (indicated by the open circle). B) Plot of a range of gray-scaled fitness values (maximum fitness – white, minimum fitness – dark gray) for each possible phenotype given a target circuit (indicated by the asterisk). Circuits having equal fitness values were arranged together resulting in wedges-shaped regions of fitness values. The fitness of a neural circuit is based on the Hamming distance between it and the target circuit. C) Fitness overlaid with the local bias pattern (radial lines of bias were arranged as in the fitness plot). With these two plots combined, it is apparent that the maximum fitness phenotype cannot be built with this genotype. However, a phenotype having a higher fitness value than the wild-type is accessible.

Conceptual Framework To more easily understand the interaction between the forces of selection, developmental bias, and mutation during adaptive evolution, I present a conceptual framework here that makes explicit the links between the genotype, phenotype, and fitness levels and describes features of those mappings relevant to the dynamics of a population moving over these levels during evolution. This framework will be used throughout the remainder of this chapter to interpret the results.

In order to determine the interaction between developmental bias and selection, a clear link needs to be made between genetic and phenotypic variation and between phenotypic variation and selective pressures (Arthur 2004a, Brakefield 2006). Figure 5-

3 shows a simple representation of those three levels. At the genotype level are sequences of three-bases in which each base position can be either an „A‟ or a „C‟. There are

45 therefore 23 or 8 possible genotypes, all of which are shown. Single-base substitutions link the genotypes, creating a cubic structure to genotype space. At the phenotype level are neural architectures of two cells. Excluding self-connections, there are four possible circuits of two neurons. The process of development connects the genotypic and phenotypic levels. Finally, a fitness function connects the phenotypic and fitness levels by creating a fitness value for each of the neural circuits. In this example, a circuit with no connections receives the lowest fitness value of 0, whereas the circuit having reciprocal connections has the maximum fitness of 1.

Figure 5-3: Degeneracies between the levels of genotypes, phenotypes, and fitness can arise through the developmental process and fitness evaluation. At the genotype level, all possible three-position sequences of two bases are shown with connections between them representing point mutations. Each genotype is mapped to a two-neuron circuit through the process of development (open, block arrows). Finally, each circuit is assigned a fitness value through a fitness evaluation (gray, block arrows). The many-to-one mappings between the levels create neutrality. That is, some changes in genotype sequence do not result in fitness differences. The degeneracy between genotypes and phenotypes creates phenotypic neutrality. The degeneracy between phenotype and fitness results in fitness neutrality. For example, the shaded region around the four genotypes represents all possible point mutations of genotype CCA. Even though two of the mutations result in a different phenotype, ultimately, all mutations do not change the fitness value of the wild-type phenotype for CCA.

With this simple example, it is clear that there exists a many-to-one mapping between the genotype and phenotype levels as well as between the phenotype and fitness levels. These degeneracies between the levels indicate that some molecular differences at the genotype level are selectively neutral at the fitness level (Kimura 1983, Fontana et al.

1993). The mapping of genotype to phenotype results in phenotypic neutrality; that is, multiple genotypes create the same phenotype. In this example, genotypes CCC and CAA each form the circuit with a single connection from cell 2 to cell 1. In addition, the fitness function results in fitness neutrality in which different phenotypes have the same fitness value. For example, the two circuits with a single connection between neurons have a fitness value of 0.5.

The forces of selection, mutation, genetic drift, and developmental bias act at and across these levels. Driving movement in genotype space is the mutational operator. In our example, this is limited to single-base substitutions and therefore a change in sequence from any given genotype can be in only one of three directions. Different mutational operators would create more links between genotypes in this space. (The exploration of the advantages of different mutational operators is an active research area in artificial evolutionary systems (e.g., Sastry and Goldberg 2004)). Developmental bias then drives the production of phenotypes in the next generation. In Figure 5-3, uniform genetic variation is represented as the gray region surrounding the WT genotype CCA.

This mutational neighborhood, when translated through the developmental process, results in the production of either the circuit with a connection from cell 2 to cell 1 or the circuit with the reverse connection. Of the three possible mutations, two change the WT phenotype of CCA (connection from cell 1 to cell 2) to a new phenotype (connection from cell 2 to cell 1); therefore, the developmental bias of this genotype is towards the new phenotype. However, all three mutations are selectively neutral; they either do not 47 change the phenotype (hence the fitness stays the same) or they change the phenotype yet its fitness value remains the same. Finally, selection links fitness and the next generation‟s set of genotypes through fitness-proportionate selection of parents.

In Figure 5-4, I show a more complicated and condensed example of these levels of evolution in order to emphasize the existence of neutral networks, the transitions between those networks, and the phenotypic pathways adaptive evolution might take as a population moves over the networks. These aspects of the conceptual framework have been explored in biological (Langlade et al. 2005, Koelle et al. 2006) and artificial systems (Huynen et al., 1996, van Nimwegen et al. 1997, Fontana and Schuster 1998). In

Figure 5-4, each genotype consists of a sequence of four bases, all sixteen of which are shown in the figure. Each node also shows the phenotype produced by that genotype as well as its fitness level. As in Figure 5-3, all edges between nodes represent single-base substitutions, our mutational operator. These connections between base-sequences create a four-dimensional hypercube. With this model of development, genotype space is a 513-dimensional hypercube. From each node, mutations can lead to genotypes having a higher-, neutral-, or lower-fitness. The fitness neutrality of a node is simply the number of edges leading to isofitness genotypes. For example, the node AACC (left-hand side of

Figure 5-4) has a neutrality of 2 since two of the four nodes connected to it (ACCC and

AAAC) have the same fitness. In the genotype space, there are selectively-neutral genotypes that are linked by single-base substitutions. These neutral networks are composed of genotypes producing the same phenotype and/or genotypes having the same fitness. In Figure 5-4, a gray scale has been used for the borders of each node and the edges between nodes to highlight the neutral networks. For a population of individuals on a neutral network, population neutrality is the average number of neutral mutations. There are two neutral networks for a fitness level 0.67, one to the left in the figure, the other to the right. The neutral networks demonstrate how mutations can

48 change the genotype without changing the phenotype and also eventually lead to nodes having higher-fitness phenotypes. We describe these mutations as portals (using the terminology in Crutchfield 1988) to identify movement to a neutral network of a different fitness value (portals are shown as dashed lines in Figure 5-4). Figure 5-4 also illustrates how an individual starting from the same node (for example, the topmost node) can have different phenotypic transitions on its way to the fittest phenotype.

Figure 5-4: Networks of isofitness genotypes can exist due to the degeneracies in mappings from genotype to phenotype to fitness.

In contrast to Figure 4-3, each node in genotype space shows not only the base sequence but also the produced phenotype and its assigned fitness value. Again, connections between nodes represent the mutational operator, single-base substitutions. The borders of each node have been grey-scaled to match the fitness values, the darker the color the higher the fitness. Connections between isofitness genotypes are shaded the same color, identifying the neutral networks in genotype space. Dashed lines represent transitions between isofitness nodes or networks, i.e. portals. In this example, there are two neutral networks having a fitness value of 0.67. One consists of four nodes to the left of the figure; the other is composed of three nodes to the right of the figure. Populations residing on those two networks would show different phenotypic transitions due, not only to the neutral networks themselves, but also to the availability of higher fitness phenotypes. For example, the even though the neutral networks have the same fitness value, each is composed of different phenotypes. In addition, the phenotypic neighborhood of genotype AAAC contains the target phenotype; whereas, the phenotypic neighborhood CCAA includes a higher-fitness phenotype, but not the target phenotype.

Results Of 100 evolutionary simulations we performed, 5 were successful. That is, the best fitness of the population reached the maximum fitness during the 300 generation limit for the simulation. This low success rate illustrated the difficulty of finding the target phenotype; yet, compared to the random generation of genotypes that resulted in the

3 target phenotype , the evolutionary process‟ performance is much better. 20 *10 6

Eleven other simulations were partially successful in that the population exhibited increases in best fitness during the simulation and may have produced the target phenotype at some generation but did not consistently produce the target circuit by the end of the simulation. The successful evolutionary simulations demonstrated an epochal pattern of fitness increases towards the maximum fitness of 1.0 (Figure 5-5). That is, best and average fitness tended to remain constant for many generations and then increase quickly to a new fitness plateau. Figure 5-5 shows best and average fitness of the population at a given generation over the course of five simulations. Occasionally, the population lost these high-fitness individuals through deleterious mutations resulting in a decrease in the best-fitness value of the population (Figure 5-5B-E), thereby breaking up the best fitness plateaus. In nearly all of the simulations, the best fitness at the start of

50 the simulation was 0.33 corresponding to a circuit with no connections. However, one simulation had at least one individual at a fitness of 0.5 in the initial population (Figure

5-5E). In addition, the time period spent at a given best-fitness plateau varied across the simulations. For example, the number of generations spent at a fitness value of 0.33 for simulation C was roughly 2.5 times the number of generations for simulation A. Besides differences in the time a population spent at a fitness plateau, the jumps in fitness values differed between the simulations. Figure 5-5A shows only one intermediate best-fitness value between the initial value of 0.33 and the final value of 1.0; whereas, the simulation in Figure 5-5D passed through three intermediate fitness values.

These epochal patterns of evolution were indicative of periods of phenotypic stasis followed by abrupt changes; but, it is unclear what genotypic changes, if any, occurred during evolution. To investigate the forces driving the phenotypic changes over the course of the evolutionary simulation, I first analyzed the lineage of ancestors of the fittest individual at the final generation for each successful simulation. I then analyzed the population as a whole as it moved over the neutral networks established by the mappings from genotype to phenotype to fitness.

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Figure 5-5: Best and average fitness of the population over the course of five successful evolutionary simulations. Gray horizontal line at fitness value of 1.0 indicates the maximum fitness. During the simulation, fitness increases in an epochal pattern. Black points represent the best fitness at a generation. Gray points indicate the average fitness of the population. Occasionally, the fittest individual at a given generation is lost resulting in a decrease in fitness (Simulations B – E). Also, the number of generations at a fitness plateau differs between the runs. In addition, the fitness values attained over the course of evolution differ between these three simulations. In a majority of the simulations (A – D), the best-fitness at the first generation is 0.33; however, simulation E shows that at least one individual in the initial population had a fitness of 0.5.

Lineage analysis Determining the lineage of ancestors of the fittest individual at the final generation allowed me to follow phenotypic changes, if any, over the course of the simulation and map those changes onto genetic variation. To determine the lineage, the process is worked backwards in time by finding the parent (again, reproduction was asexual in this model) of the fittest individual at the last generation and then its parent, and so on until the first generation. With the lineage, I was also able to test whether the phenotypic

52 changes were primarily due to selection or developmental bias by relating developmental bias to the selective pressure (as in Figure 5-2C) for each genotype along the lineage. If selection was the main determinant of evolutionary change, I would expect to see many, if not all, phenotypic variants accessible from a given genotype along the lineage. On the other hand, if developmental bias had a strong role in determining evolutionary change, the expectation is that there would be few phenotypic variants accessible from a particular genotype.

Because the phenotypes accessible from a given genome through single-base substitutions (i.e., local bias) varies strongly with the genotype (Psujek and Beer 2008), even for those producing the same phenotype, it is likely that the phenotypic changes seen across evolutionary simulations will be different. Indeed, the sequences of phenotypic transitions for the lineage of the fittest individual did vary across the five simulations (Figure 5-6).

A * *

B *

C *

D * *

E *

Figure 5-6: Multiple pathways to a target phenotype exist. A) – E) depict the phenotypic transitions of a lineage from five successful evolutionary simulations. The target phenotype is denoted by an asterisk above. These transitions occur in the lineage of the fittest individual at the end of the simulation. The target phenotype is shown at the end of each sequence of phenotypes. Because each initial population‟s genotypes are randomly generated, it is likely that the initial circuits do not have any connections, as in four of the examples shown here. Even though each simulation is able to produce the target phenotype, the sequence of phenotypic changes during evolution is different.

Although the majority of the simulations started with the same phenotype (that is, a circuit having no neural connections), the sequence of changes in circuit architecture for a lineage varied across the simulations. Occasionally, the target phenotype was reached and then lost during the lineage (Figure 5-6A and D). However, this is not surprising

54 since the mutation rate was very high; each offspring always had one base mutated. With such a high mutation rate, it was likely that high fitness individuals would produce offspring with deleterious mutations.

Some of the phenotypic transitions seen on a lineage during evolution were due to different local biases. Figure 5-7 shows the local bias patterns for consecutive genotypes in the lineages from evolutionary simulations B and C represented in Figure 5-6. In the generation preceding a change to a new phenotype, the local bias pattern was seen to dictate the resultant phenotypic change that occurred though a random mutation. That is, even though the genotypes in the proceeding generation produced the same circuit, the phenotypes accessible from the respective genotypes were different. In the fitness/bias plot in Figure 5-7A the target circuit was accessible; yet, it was not accessible in the fitness/bias plot for Figure 5-7B. In addition, two phenotypes were shown in the fitness/bias plot in Figure 5-7B that were not seen in the fitness/bias plot of Figure 5-7A.

This result supports the expectation that developmental bias is likely to have a strong impact on the particular evolutionary pathway taken (Psujek and Beer 2008).

Figure 5-7: Local bias patterns dictate phenotypic changes on a lineage during evolution. For two simulations shown in Figure 5-5 (B and C), the wild-type genotype produced the same phenotype; yet, because the local bias patterns differ between the two genotypes, the phenotypic transitions were different. In A), the target phenotype was available and a mutation resulted in the production of that phenotype. In B), only another phenotype of equal fitness was available and random mutation resulted in a transition to that phenotype. The dashed, vertical line represents a phenotypic transition. Again, the open circle represents the direction of the wild-type phenotype and the asterisk represents the direction of the target phenotype (as per Figure 5.2).

Mutations that did not alter the phenotype accumulated during evolution, allowing new phenotypes to become accessible (Figure 5-8). From the results of the lineages for three simulations shown in Figure 5-8, the local bias plots indicated a higher-fitness

56 architecture was unable to be produced through mutation in an earlier generation (first column of plots). At a later generation, the higher fitness phenotype became available

(second column) and, eventually, mutation led to the production of the higher fitness phenotype as the offspring of the previous generation‟s individual (third column).

Because mutation was random, the number of generations varied between when the higher-fitness phenotype became accessible and when it was produced.

Figure 5-8: Neutral mutations lead to higher fitness phenotypes. A), B), and C) show a sequence of fitness/local bias plots for the lineage of the fittest individual from three evolutionary simulations. The generation number is presented in the upper left of each plot. For each of the three sequences, the first plot shows that a higher fitness phenotype is not accessible from this genotype. However, after many generations in which neutral mutations (the wild-type phenotype represented by the open circle remains the same) accumulate in the genotype, a higher fitness phenotype becomes accessible, as shown in the second plot of each sequence by the bold ray. In the third plot, mutation and selection eventually lead to the higher fitness phenotype being produced during evolution and becoming the new wild-type phenotype. Because mutation is random, several generations pass between the generation in which the higher-fitness phenotype becomes accessible and the generation in which that phenotype is actually produced. Details as per Figure 5.2.

This action of phenotypically-neutral mutations resulting in the accessibility of higher-fitness phenotypes occurred often throughout the course of a single evolutionary simulation (Figure 5-9). For the periods of generation 1 to 87, 99 to 177, and 177 to 237, a higher fitness phenotype was not accessible until the accumulation of neutral mutations resulted in one. In reference to the conceptual framework presented earlier, this individual was randomly moving along a neutral network defined by a fitness level until it reached a portal to a higher-fitness neutral network. For the successful runs, a mutation eventually occurred resulting in the individual moving to the higher-fitness neutral network. The process repeated until the target phenotype was produced. The degeneracy in the mapping of genotype-to-phenotype created the neutral network on which the individual was moving.

Figure 5-9: Neutral mutations lead to higher fitness architectures throughout the course of an evolutionary simulation. A) – J) show the fitness/local bias plots of individuals in the lineage of the fittest individual at generation 300. Again, the dashed, vertical lines represent a phenotypic transition and the bold rays represent the previously inaccessible higher-fitness phenotype. Over the course of the simulation, higher fitness phenotypes are unavailable until neutral mutations alter the pattern of bias. For example, in generation 177, the fitness/bias plot shows that the maximum fitness phenotype is not able to be generated. By generation 208, neutral mutations (the wild-type phenotype has remained unchanged) have accumulated in the genome resulting in a new ray in the maximum fitness region (the vertical, white wedge). By generation 237, mutations have resulted in the maximum fitness phenotype becoming the new wild-type individual. This phenomenon of neutral mutations resulting in higher-fitness phenotypes is also evident in the fitness/bias plots for generations 1, 85, and 87 and for 99, 148, and 177. The phenotypes generated by these individuals in the lineage, until the target phenotype is reached, are shown in Figure 5-6D.

Besides phenotypic neutrality, fitness neutrality also had a role in the evolution towards the target phenotype (Figure 5-10). For the simulation represented in Figure 5-

10, a higher-fitness phenotype only became available after making a phenotypic transition from one equal-fitness phenotype to another. At no point during the lineage

60 from generation 151 to generation 205 did a higher fitness phenotype become accessible

(data not shown). However, when the transition was made to the equal-fitness phenotype at generation 205, a phenotype having a higher fitness became accessible. At generation 208, a mutation resulted in the new phenotype being produced.

Figure 5-10: Fitness neutrality affords a transition to a higher-fitness phenotype. At generation 151, no higher-fitness phenotypes are available. Yet, after making a transition to an equal-fitness phenotype, a higher-fitness phenotype becomes available (bold ray) which becomes the new wild-type after a few generations. The phenotypes produced by these individuals in the lineage are shown as the last four networks in Figure 5-6C.

Underlying the phenotypic changes seen during evolution were modifications to the genotype that altered the regulatory network and/or the genetic context in which subsequent mutations took place. Shown in Figure 5-11 are the regulatory changes through neutral mutations that led to a higher-fitness phenotype becoming accessible and the mutation that eventually produced that circuit. To produce the higher-fitness phenotype, the expression of pre-synaptic protein, Pre 19, in cell 2 needed to be halted.

Since there were redundant genes for Pre 19, both of which resulted in the expression of

Pre 19 in cell 2, two changes to the regulatory structure were needed. Eliminating the expression of Pre 19a in cell 2 was done through mutations to the gene that 1) altered the gene product in the protein modifier region so that the protein was not recognized during the formation of neural connections and 2) changed the Activation 1 region so that it was not activated by the transcription factor Extra 29. To eliminate the expression of Pre 19b in cell 2, a mutation in the Activation 1 region of Extra 20

61 eliminated activation of the gene by the symmetry-breaking protein. These changes to the regulatory structure allowed the higher-fitness phenotype to become accessible through a mutation, which eventually occurred at generation 177, that lowered the threshold for activation of gene Post 19. This change in threshold resulted in Post 19 being produced in cell 3 creating the neural connection from cell 1 to cell 3. Prior to these regulatory changes, this mutation would have altered the phenotype yet the fitness would have remained the same as the wild-type. With the change in developmental context, the mutation was now beneficial; the phenotypic change resulted in a higher- fitness circuit than the wild-type.

Figure 5-11: A higher-fitness phenotype became available through changes in the regulatory structure via neutral mutations. A) The fitness/bias plots for the genotypes along the lineage for this simulation (run 4 in Figure 5-5D). B) The neural connections between the three cells as well as the expression pattern of proteins during development. C) Simplified versions of the regulatory structures encoded by the genotypes showing only the pertinent connections. The activation threshold for Post 19 is shown as in the gray-filled square to the right of the gene. The higher-fitness phenotype only became accessible at generation 148 when the pre-synaptic protein, Pre 19, was not expressed in cell 2. Two changes to the regulatory structure were required for this to occur since there are redundant genes coding for Pre 19, both of which resulted in the expression of Pre 19 in cell 2. One, the expression of gene Pre 19a needed to be halted. This occurred in two ways: 1) a mutation at generation 104 changed the protein modifier region so that the gene product wasn‟t recognized during the formation of neural connections and 2) another mutation at generation 105 altered the Activation 1 region of Pre19a so that the gene was not activated by

Extra 29. Two, at generation 148, a mutation in the Activation 1 region of Extra 20 eliminated expression of the gene by the symmetry-breaking protein. These changes to the regulatory structure allowed the higher-fitness phenotype to become accessible through a mutation that lowers the threshold for activation of gene, Post 19, from 12 to 11. The change in threshold would result in protein Post 19 being produced in cell 3 through activation of its gene by Extra 29. This threshold mutation occurs at generation 177 with the result that a neural connection is formed from cell 1 to cell 3. Had this mutation occurred prior to these regulatory changes, it would be have been selectively-neutral. Because the developmental context has changed, the mutation is now beneficial, creating a phenotype of higher fitness than the wild-type.

Population analysis Even at the population level, developmental bias dictated the phenotypic changes seen during evolution (Figure 5-12). In Figure 5-5A, the best fitness of the population increased from 0.67 to 1.0; whereas, the population‟s best fitness in Figure 5-5C increased from 0.67 to 0.83 before increasing to 1.0. These transitions could simply be the result of a chance mutation resulting in the production of the target phenotype in one simulation but not in the other. However, the average of the local bias patterns for all individuals in the two populations (population bias) showed the target phenotype was completely inaccessible through mutagenesis of the population for the simulation in

Figure 5-5C (Figure 5-12). For run 3 in Figure 5-12, the population bias indicated a higher-fitness phenotype was available, but not the target phenotype (no ray exists in the white wedge-shaped area). Mutations of the population only resulted in the production of the higher-fitness phenotype. For run 1, the target phenotype was available and, in the next generation, mutations in the population resulted in the production of this phenotype. Other fitness-increasing phenotypic transitions showed a similar result; the particular phenotype produced was dictated by the phenotypic variants accessible from the population.

Figure 5-12: Developmental bias dictated the phenotypic transitions at the population level. Averaging the local bias patterns for all individuals in the population results in a population bias pattern. The filled circle represents the phenotype of the individual in the population having the best fitness. In two of our simulations, A) and B), with the same best fitness phenotype at a generation preceding a phenotypic transition, the difference in the population bias patterns determined the change in phenotype. The population bias for run 3 (corresponds to Figure 5- 5C) at generation 207 indicated that the target phenotype was not accessible through mutagenesis of the population; yet, it was available for the population in run 1 (Figure 5-5A). For run 1, mutations resulted in the production of the target circuit in the next generation. Mutations in the population for run 3 can and did only result in the production of a higher-fitness phenotype, but not the target. Note that the target phenotype became available after the best-fitness transition for run 3.

From the data presented on the analysis of a particular lineage of individuals, it was apparent that the accumulation of neutral mutations was important in the evolution towards the target architecture. This process can be conceptualized as an individual randomly moving along a neutral network until it encounters a portal to a neutral

65 network at a higher-fitness level. However, evolution occurs at the level of a population of individuals. What then is the movement of the population over these neutral networks and what are the forces driving this movement?

The movement of a population on a neutral network in genotype space was visualized by using Hamming distance as a metric of relatedness between individuals (Figure 5-13).

In Figure 5-13, each plot shows the average Hamming distance over all pairs of individuals having the same fitness value as that of the fittest individual at a given generation. The vertical, gray lines in each plot indicate best fitness transitions, either increases or decreases, as shown in Figure 5-5 (Figure 5-13A-E correspond to Figure 5-

5A-E). Using these transitions as well as the range of fitness values, I defined three periods that occur during an evolutionary simulation: 1) the initial epoch in which no individual has a fitness value greater than 0.33, 2) intermediate epochs in which members of the population are at a fitness level between 0.33 and 1, and 3) the final epoch in which members of the population have reached a fitness value of 1.

In the following subsections, I investigate the internal and external forces of evolution acting on the population during evolution for these epochs. The initial and final epochs are described first since the population during these epochs is roughly residing at either end of the fitness range and, therefore, the explanations are clearer.

Since the fully unconnected circuit is the most common phenotype from our global bias sample (see Fig 4-1), the initial population in most simulations (e.g. Figure 5-5A-D) comprises genotypes having this level of fitness. Although there are seven neural circuits having a lower fitness than the fully-unconnected circuit, they are never produced in the initial epoch for these five simulations. Therefore, for the initial epoch, individuals are effectively only likely to increase in fitness. For the final epoch, the maximum fitness has been reached and therefore individuals can only decrease in fitness.

Figure 5-13: Plots of the average Hamming distance between all pairs of individuals that are on the neutral network of the fittest individual at a given generation. Gray, vertical lines indicate a fitness transition as shown in Figure 5-5. For A) – D), the entire population lies on the neutral network at the initial generation and, because, the genotypes are randomly generated, the average Hamming distance is roughly 256, half the distance across the 513 dimensional genotype space. In E), one individual has a higher fitness than the remainder of the population and is therefore the sole individual on the neutral network. The Hamming distance is therefore zero.

Initial epoch For the initial epoch in several simulations (Figure 5-13A-D), the population was initially spread throughout genotype space due to the random generation of genotypes but then became clustered due to sampling error. That is, simply due to chance, some isofitness individuals were selected more often to be parents than others. This is also known as genetic drift. Due to the random creation of genotypes, the Hamming distance between any two individuals, on average, was 256 bits, approximately half the distance of

67 this space. Yet, the average pair-wise distance for each simulation quickly decreased.

Even though all individuals had an equal likelihood of having offspring (since they all had the same fitness value), some individuals had more offspring than others through sampling error in the population (data not shown). This resulted in a clustering of the population and therefore a reduction in the average Hamming distance for the population. Eventually, one individual made the transition to a higher-fitness phenotype reducing the average Hamming distance to 0 since it was the only individual at that time on the higher-fitness neutral network.

Once an individual made the transition to a higher-fitness neutral network, the average Hamming distance increased steadily from 0 as its progeny, with the resultant accumulation of neutral mutations, numbered more and more in the population. The increase in average Hamming distance indicates the population is diffusing along the neutral network. Given enough time, it is expected that a rough equilibrium would be established through the diffusive force of mutation and the cropping forces of selection and sampling error. In fact, for the final epoch in Figure 5-13B, the average Hamming distance did appear to plateau (with some minor fluctuations).

Final epoch For the final epoch, there is some theoretical and simulation evidence that suggests the population would not diffuse over the entire neutral network but instead tend to move to highly connected areas of the neutral network (van Nimwegen et al. 1999). In other words, the population would evolve mutational robustness as an indirect selective pressure (through stabilizing selection on the target phenotype). As the conditions in our simulations were similar to van Nimwegen et al.‟s (1999), I looked for this phenomenon in the results. Figure 5-14 shows the average number of neutral mutations for the final epoch for the five successful simulations. Some simulations show an increase in average number of neutral mutations (i.e., increase in mutational robustness) during the final

68 epoch (Figure 5-14B, D, and E) whereas others do not or it is unclear (Figure 5-14A and

C).

Although the analytical and simulation models of van Nimwegen et al. (1999) both indicated an increase in mutational robustness should occur during evolution, there are confounding issues here that may have detracted from this phenomenon. First of all, the changes seen in the population neutrality (average number of neutral mutations) might have been transient as the length of time the population has had to evolve at this epoch was relatively short compared to the size of the network. There simply had not been enough time for the population to diffuse over the network and reach a highly connected region of genotype space. Also, population size was shown to strongly affect population neutrality (van Nimwegen et al. 1999). For these simulations, the population size on the neutral network is very small during the first few generations following a fitness transition since one individual makes the transition. Even after the population on the neutral network has grown to nearly the population size of the simulations (100 individuals), the size was small enough to prevent the population neutrality from reaching the maximum for the network. Unlike the simulation in van Nimwegen et al.‟s work, we were not able to enumerate the network due to its size and therefore were not able to determine the minimum and maximum neutrality, the average neutrality over the entire network, nor the spectral radius of the network‟s adjacency matrix. Although the authors state that one could infer the structure of the neutral network from accurate measurements of the transient population dynamics, there is an additional issue that may prevent comparing the results from separate evolutionary simulations.

A major confounding issue for comparing mutational robustness results across simulations is that the neutral networks may not form a single-component network in genotype space. There might be many, disjoint neutral networks for the target phenotype and their properties may differ (for example, the two networks of fitness 0.67 in Figure

5-4). Therefore, it may not be surprising that the indirect selective pressure towards mutational robustness during the final epoch was evident in some simulations and not in others.

Figure 5-14: Average number of neutral mutations during the final epoch for the five simulations presented in Figure 5-5. B), D), and E) show an increase in the mutational robustness during evolution at this stage as expected from results van Nimwegen et al. (1999). A) shows a decrease in neutral mutations but the final epoch for this simulation is considerably short due to our cutoff on the number of generations. The number of generations is comparable to the final epoch for D) yet it shows a clear increase in the number of neutral mutations. The scale for the number of neutral mutations is the same for all plots.

Intermediate epochs During the intermediate epochs under a directional selective pressure for the target phenotype, mutational robustness also increased. Of the simulations, only two had a lengthy and mostly unbroken intermediate epoch (Figure 5-5A and E). Figure 5-15 shows

70 the average neutrality for genotypes on the neutral network during this intermediate epoch for the two simulations. The population neutrality in Figure 5-15A appeared to remain roughly constant during the epoch; whereas, there was a general trend of increasing neutrality for the simulation in Figure 5-15B, despite the shorter period of time spent at this fitness level. It is possible that these two neutral networks were not connected or, considering the higher neutrality for the simulation in Figure 5-15A, the population was already in a highly connected region of the network. Upon closer inspection, I found the most-fit phenotypes produced by these two simulations at the end of the epoch were different yet they had the same fitness. This is likely why there was a large difference in the population neutrality; some phenotypes were more robustly built. In fact, the neutrality of the most-fit genotype for the population in Figure 5-15A was 22 mutations greater than the neutrality for Figure 5-15B.

Figure 5-15: Average neutrality differs between the same epoch across two simulations. Average number of neutral mutations for the intermediate epoch for simulations shown in Figure 5-5A and E.

In the lineage analysis, the fitness/bias plots demonstrated that it was often true that higher-fitness phenotypes were unavailable initially but became accessible after several generations of accumulating neutral mutations in the genotype. At a population level, instead of seeing these changes in availability in the pattern of bias as in Figs. 5-8 and 5-

9, the average number of beneficial mutations was computed for the subset of the population on the best-fitness neutral network (that is, the best fitness at a given

71 generation). Figure 5-16 shows this plot of beneficial mutations over the course of a simulation. For the initial epoch, there were no beneficial mutations possible for the first few generations. Eventually, the average number of beneficial mutations increased until, by chance, a mutation actually resulted in the fitness increase. During the intermediate epoch, there was a much longer period initially during which there were no portals to a higher-fitness neutral network. Eventually the population encountered and moved past several portals (i.e., an increase followed by a decrease in the average number of beneficial mutations as the population diffused along the neutral network) before making the transition to the target architecture and maximum fitness. The data in Figure

5-16 can be described in a Carollesque manner as a group of individuals moving down a darkened hallway with open doorways of different sizes leading off to other hallways.

The likelihood that an individual will accidentally stumble through a doorway as the group mills about increases with the size of the doorway and with the number of individuals near the doorway.

Figure 5-16: Portals to higher fitness neutral networks appear as the population diffuses on the neutral network. Figure shows the average number of beneficial mutations for all epochs for the simulation in Figure 5-5A. As the population diffuses, portals appear and

occasionally disappear until a mutation eventually leads to the higher-fitness phenotype.

For unsuccessful and partially successful simulations, no evidence was found indicating developmental bias was responsible for preventing the eventual production of the target phenotype. In an unsuccessful simulation, the population also passed by a portal occasionally but the average number of beneficial mutations was so low that there was a very slim chance of a mutation resulting in movement to a higher-fitness neutral network. For a partially successful simulation, it appeared that sampling fluctuations were responsible for the loss of higher-fitness genotypes before they became established in the population (not shown).

Chapter 6 : Discussion Although proposed as an alternative evolutionary force by various authors (notably,

Gould and Lewontin 1979), the impact developmental bias (or constraint) has on the direction of evolutionary change in species remains unclear (Arthur 2001, Brakefield et al. 2003). To answer this question directly, the structure of phenotypic variation of organismal characters needs to be mapped against the structure of the selective pressures on those characters. Some researchers have begun the process of linking genetic variation to phenotypic variation and relating these changes to fitness in natural systems (Kopp et al. 2000, Brakefield et al. 2003). A computational model system, such as the one presented in here, affords a complementary methodology with which to explore the role of developmental bias in evolution: less realistic, but able to explore vastly greater combinations of conditions. In chapter 4, I show that a computational model allowed me to differentiate the concepts of global and local bias, to illustrate the local dependency of patterns of bias, to demonstrate that the pattern of developmental bias is altered by the accumulation of phenotypically-neutral mutations, and to perform a detailed analysis of how a particular pattern of bias emerges from the genotype. These

73 results suggest that development could have a large role in determining the pathways of evolutionary change. By incorporating the developmental model within an evolutionary simulation and “replaying” evolution again and again in order to make comparisons between simulations, this is indeed the case. In chapter 5, from analyses of a lineage of one individual for each simulation, I show that local bias dictated the phenotypic transitions during evolution and, although higher-fitness phenotypes were not often accessible immediately following a phenotype transition, they became available after neutral mutations had accumulated in the genotype. Analyses at the population level demonstrated how the forces of genetic drift (sampling error), mutation, selection, and developmental bias interact during evolution. In some cases, phenotypic accessibility, as shown through population bias plots, was responsible for the best-fitness transitions during evolution. During the initial epoch, genetic drift was strongly evident in the way it clustered the population into subpopulations. At later epochs, the population diffused along the neutral network through mutations of a founding individual until equilibrium was established by selection and genetic drift. In some instances, the diffusion appeared to be directed towards highly connected regions of the neutral network as a result of an indirect selective pressure towards mutational robustness.

Despite what has been possible with this model, the implications of the results are limited since the model has many simplifications - from the level of genes and their interactions to how gene products are used to form the phenotypic trait. Also, the way in which developmental bias is determined is simplistic in the model; in nature, gene mutations involve more than simply point mutations. However, these limitations can be overcome by tailoring the model to a particular system or by making the model more biologically realistic. For example, since gene regulation appears to be an important component in the evolution of organisms (Carroll et al. 2001, Wray 2003), determining developmental bias by including other small-scale mutational operators that can affect

74 the regulatory sites of genes, such as insertion, deletion, and duplication, would give a more biologically accurate view of the phenotypes accessible from a specific genotype.

Another way in which the model could be made more realistic, especially if the number of cells is increased, is to incorporate neurite outgrowth in the neural developmental process. Instead of assuming that neurites extend in all directions, including a growth cone process by which neurite growth is guided by chemoattractants and chemorepellants would make the model‟s formation of neural connections more directed, as is found in natural systems (Purves and Lichtman 1985). Fortunately, the current understanding of this process is already able to facilitate modeling how growth cones are guided in the developing embryo (reviewed by Chilton 2006).

Characterizing Developmental Bias Although the model used in this study is quite abstract, compared with natural developmental systems, it affords an exploration of questions of general interest. From an analysis of the developmental model, patterns of bias were shown to have a strong local dependency on particular genotypes. Genotypes that produced different phenotypes as well as different genotypes that produced the same phenotype commonly had different patterns of bias. Therefore, the phenotypes that are available in the next generation through mutations of the current generation would strongly depend upon the genotypes represented in the current generation. Different populations are likely to have different evolutionary pathways because of this local dependency (as depicted in Figures

1 and 2 in Arthur 2004a). As Schuster and Fontana (1999) stated “phenotypic innovation is mediated, and hence, biased by the genotype-phenotype map.” These results show that the phenotypes produced in subsequent generations would be strongly dictated by the genotypes comprising earlier generations.

Even when local genotype-dependent variation is averaged out, these results indicate that bias exists within the developmental system. In other words, the developmental

75 system itself has a differential capability for constructing certain phenotypes over others.

By randomly selecting genotypes from the space of all possible genotypes and determining what phenotypes were produced by the developmental system, I averaged over the variation in genotype-dependent bias to determine the bias intrinsic to the model developmental system. In Figure 4-1, it can be seen that some neural architectures are apparently difficult to create and, of those that are produced, some phenotypes are more commonly built than others. Which phenotypes were easily built reflected inherent features of the system. Perhaps as the complexity of the developmental system increases, the “difficult” phenotypes would eventually be produced. Yet, the commonly produced neural architectures would nearly remain the same since additional developmental mechanisms would probably not affect the production of these common phenotypes.

That is, even if the developmental system is capable of constructing all possible phenotypes, this does not imply that it would do so with equal probability.

As in this model developmental system, natural developmental systems may have an intrinsic bias in the production of phenotypes. For example, the observation that adult centipedes in over 3000 extant species (Lewis 1981) only have an odd number of leg- bearing segments, although there is large variation in the number of segments in the order Geophilomorpha (Minelli et al. 2000), could be an example of global bias in which the developmental system for the formation of trunk segments of this class has an inherent bias towards the production of an odd number of segments (Arthur and Farrow

1999). A possible molecular explanation of why the variation in number of leg-bearing segments is always odd has been provided by Chipman et al. (2004) and Chipman and

Akam (2008). Chipman et al.‟s work (2004) with Strigamia maritima in the order

Geophilomorpha suggests the variation in segment number in increments of two is due to variation in the number of cycles of a primary segmentation oscillator in which each cycle produces two segments. This double segment periodicity is then converted into

76 single segments through the intercalated expression of caudal (Chipman et al., 2004).

Although it is unclear whether basal orders of centipedes also show a double segment periodicity and pattern intercalation, the pattern of segmentation shown by

Geophilomorpha, that is, a large number of trunk segments and the formation of all segments during embryogenesis, is a derived pattern (Chipman and Akam, 2008).

Perhaps the global bias of the segmentation system is becoming more labile over time.

For example, one specimen of Stigmatogaster subterranea, also of the order

Geophilomorpha, has recently been found consisting of an even number of leg-bearing segments (Leśniewska et al. 2008). This specimen, unlike one reported by Kettle et al.

(1999) in which the even number of leg-bearing segments in a specimen of Strigamia maritima was due to a homeotic transformation of a normally legless terminal segment into one bearing the special rearward-pointing legs, has a “perfectly patterned trunk” and “looks like a normal centipede” (M. Leśniewska, personal communication). In fact, the developmental system controlling segmentation in Stigmatogaster subterranea appears rather labile as a high incidence of segmental anomalies have been found in multiple populations within and outside its natural range (Leśniewska et al. 2008). It would be interesting to see what differences exist between the gene networks controlling segmentation in this species and others of the Geophilomorpha, a derived order of the class Chilopoda, as well as in species of the basal orders, such as Lithobiomorphs.

The global bias of our model developmental system derives, in part, from the specific set of initial conditions and mechanisms used. However, altering the placement of cells and inserting the symmetry-breaking protein into other cells resulted in patterns of bias having the same general features as the one shown in Figure 4-1. In other words, the bias pattern in Figure 4-1 is not simply a result of our specific initial conditions; yet, there is some dependency of global bias on the initial conditions. I also investigated the global bias pattern seen after altering the mechanisms of the developmental model. Adding a

77 separate threshold region for repression in the model gene resulted in a slightly varied bias pattern (results not shown). Further work should entail investigating how model parameters affect developmental bias, especially as the model is made more biologically realistic.

Characterizing the Interaction between Developmental Bias and Selection To gain a qualitative understanding of the role of developmental bias in evolution, I performed evolutionary simulations using the biologically-motivated developmental model presented above. The dependency of developmental bias on the dynamics of the developmental process was a major component of the evolvability of our system. That is, the developmental system had a capacity to vary in phenotypic availability over time through alterations in the regulatory structure encoded in the genotype. (See Pigliucci

2008 for a current review of the various definitions of evolvability and how this concept might contribute to a new evolutionary synthesis.) Not only did phenotypic accessibility change after phenotypic transitions, but higher-fitness phenotypes often only became available after the accumulation of selectively-neutral mutations. Across simulations, the differences in local bias patterns for individuals in the populations resulted in different phenotypic pathways taken during adaptive evolution. This local dependency of developmental bias can also be found in natural systems. Dichtel-Danjoy and Felix

(2004) collected data from phenotypic accessibility experiments on vulva development in three species of nematodes and showed differing ranges of phenotypic variants across the species. Burch and Chao (2000) found for two related populations of the RNA bacteriophage Φ6 with similar initial fitness values that one population experienced mostly beneficial mutations whereas the other population acquired deleterious mutations. Both populations had been derived from a single ancestor and had recovered in fitness after acquisition of a common deleterious mutation. By controlling for the possibility that a chance advantageous mutation was the result of the fitness differences,

78 the authors demonstrated that the difference in response to subsequent mutations of the two populations was likely due to the changes in genetic context caused by the accumulation of mutations during fitness recovery.

This capacity to vary in phenotypic availability is due to the genotype-to-phenotype and phenotype-to-fitness mappings. The degeneracies of these two mappings create selectively-neutral sets of genotypes. The mutational operator then links the genotypes in these sets creating neutral networks over which the population moves. Both mappings suggest, and the results here show, that there are multiple paths to a target phenotype.

Although Kimura (1983) originally focused neutrality theory on molecular evolution, neutrality can be extended to the level of development, in which different developmental trajectories lead to similar phenotypes (e.g., Raff 1996). Because of this many-to-one mapping from genotype to phenotype, neutral mutations can accumulate in the genotype, altering the developmental processes resulting in what has been termed

“developmental system drift” (True and Haag 2001) or “phenogenetic drift” (Weiss and

Fullerton 2000). Both mappings also suggest that an indirect selective pressure against deleterious mutations can result in a flow of the population from regions of the neutral network where many mutations lead to lower-fitness phenotypes towards highly interconnected regions in which mutations are neutral.

The genotype-to-phenotype degeneracy creates a flow in genotype space towards the production of the same phenotype but fine-tunes the regulatory structure so that it is less easily perturbed by mutations. The phenotype-to-fitness degeneracy results in movement towards the production of phenotypes that are more robustly constructed from among the set of iso-fitness phenotypes. However, it is unclear why some populations show movement (e.g., the two populations in Figure 5-15) toward highly interconnected regions of the network and others do not. Perhaps the two populations reside on regions of the neutral network that are vastly removed from each other and

79 given enough time the population in Figure 5-15B would reach the same population neutrality as the population in Figure 5-15A. Alternatively, the set of isofitness genotypes across genotype space might consist of multiple components; that is, there are neutral networks at a given fitness level that are not linked by any combination of single-base substitutions. If there are multiple components to the set of neutral genotypes, the flow depends on the properties of the component on which the population resides. If the two populations used in Figure 15 were residing on separate components, it would explain the different trends in the average number of neutral mutations for the two populations and it is likely that no length of time would result in the neutrality of the second population reaching the level of the first population‟s neutrality.

The flow of a population, driven by stabilizing selection, towards highly connected regions of a neutral network could lead to portals to higher-fitness neutral networks.

During an intermediate epoch, there are only three types of mutations possible: 1) beneficial, 2) neutral, and 3) deleterious. An increase in mutational robustness for the population is produced by the elimination of those individuals that are more likely to have deleterious mutations and is represented by a reduction in the average number of possible deleterious mutations in the population. This reduction in deleterious mutations can be accomplished in multiple ways during the intermediate epochs. There can be in increase in the number of neutral mutations, an increase in the number of beneficial mutations, or an increase in the number of both neutral and beneficial mutations in the pattern of bias. Since beneficial mutations, i.e., portals, are rare it is most likely that the increase in mutational robustness is due to the increase in neutral mutations. However, the possibility remains that the flow of the population as it gains mutational robustness could also be directed towards portals to higher-fitness phenotypes.

The exploration of selectively-neutral phenotypic variants due to these neutral networks has important consequences for the evolution of organisms. Human influenza

A (H3N2) evades immunity through transitions between antigenic clusters that correspond to neutral networks (Koelle et al., 2006). Not only do the degeneracies from genotype to phenotype to fitness affect molecular evolution as in the formation of the glycoprotein Hemagglutinin, which is targeted by human immune systems, in Koelle et al.‟s work (2006) but they also affect the evolution of regulatory networks. Isalan et al.

(2008) rewired E. coli regulatory networks and overlaid them on the wild-type background. They found that many of the rewired strains had similar growth yields.

Furthermore, under several selective pressures, some strains demonstrated fitness advantages over the wild-type. Due to the degeneracies in the mappings from genotype to phenotype to fitness, populations can explore a neutral network until a mutation eventually confers a fitness advantage.

Future Work Presented below are three possible directions to pursue following this study. One avenue to follow, continuing with the model developed here, would be to explore how model parameters affect the developmental bias exhibited by the system. By varying over a wide range of initial conditions, we could more accurately determine the effect these have on the pattern of developmental bias. In addition, incrementally making the model more biologically realistic and comparing the patterns of bias seen across the various models would illustrate what features and mechanisms have a strong influence on developmental bias.

Another avenue would be to perform further computational modeling work on topological motifs of the neutral networks that afford evolvability. One such motif could be the degree of percolation of the neutral networks. That is, the degree to which the

81 neutral networks extend throughout genotype space. A network traversing much of the volume of genotype space is likely to vary widely in its phenotypic accessibility. However, the degree of percolation might not need to be very high for higher-fitness phenotypic variants to be found. In successful simulations, transitions to higher-fitness neutral networks during the intermediate epochs occurred, on average, after the average pairwise Hamming distance between individuals in the population reached 60 bases,

12% of the distance across genotype space.

A third avenue, in a combination of biological experimentation and computational modeling, would be to compare the segmentation mechanism of the centipede Stigmatogaster subterranea with that of similarly derived species, such as

Strigamia maritima, as well as more basal species. A specimen of S. subterranea has recently been found that breaks the class-wide developmental dictate of generating only an odd-number of leg-bearing segments (Leśniewska et al. 2008). In addition, this species appears to exhibit a high frequency of segmental anomalies (Leśniewska et al.

2008) suggesting a character of the species could be a high level of developmental instability. Considering that the segmentation mechanism uncovered in S. maritima, also of the order Geophilomorpha, incorporates the Notch/Delta pathway (Chipman and

Akam, 2008), which is involved in other arthropod segmentation (e.g., in spiders

Stollewerk et al. 2003), begs the question of what modifications to the segmentation mechanism have been made over evolutionary time. A computational model of what is currently known of the genetic pathways underlying segmentation in centipedes could identify the possible range of behavior of the gene networks and help drive biological experimentation on possible changes to the networks that appear to have broken a global bias of the segmentation system.

Conclusions Although abstract, this model offers a conceptual understanding of the interaction of developmental bias and selection that is useful in shaping experimental programs.

Despite the lability of developmental bias, it still acted as an orienting factor in evolutionary change. The local dependency of developmental bias in this model system underscores the need for a comparative approach to the experimental analysis of the role of developmental bias in evolution. As in our simulations, local biases vary in natural systems across similar species for the same trait (Dichtel-Danjoy and Felix, 2004) and even within the same species (Burch and Chao, 2000).

The results presented here demonstrate the usefulness of an idealized model in providing insight into the interaction between developmental bias and selection. With this model, I was able to demonstrate the large role of neutrality in altering patterns of developmental bias with the result that bias did not appear to prevent the eventual production of the target phenotype. However, through rerunning the evolutionary process and comparing the simulations, developmental bias did determine the particular phenotypic changes seen during evolution.

Chapter 7 : References

Alberch, P. 1982. Developmental constraints in evolutionary processes. Bonner J.T. (ed.) Evolution and development: report of the Dahlem Workshop on Evolution and Development. Springer-Verlag. Berlin.

Alberch, P. and Gale, E. A. 1983. Size dependence during the development of the amphibian foot. Colchicine-indiuced digital loss and reduction. J. Embryol. Exp. Morph. 76: 177-197.

Alberch, P. and Gale, E. A. 1985. A developmental analysis of an evolutionary trend: Digital reduction in amphibans. Evolution 39: 8-23.

Arthur, W. 2001. Developmental drive: an important determinant of the direction of phenotypic evolution. Evolution & Development 3: 271-278.

Arthur, W. 2004a. The effect of development on the direction of evolution: toward a twenty-first century consensus. Evolution & Development 6: 282-288.

Arthur, W. 2004b. Biased Embryos and Evolution. Cambridge University Press. Cambridge, UK.

Arthur, W. and Farrow, M. 1999. The pattern of variation in centipede segment number an example of developmental constraint in evolution. J. theor. Biol. 200: 183-191.

Ashe, H. L., and Briscoe, J. 2006. The interpretation of morphogen gradients. Development 133: 385-394.

Bacci, A, and Huguenard, J. 2006. Enhancement of spike-timing precision by autapic transmission in neocortical inhibitory interneurons. Neuron. 49: 119-130.

Belting, H., Shashikant, C. S., and Ruddle, F. H. 1998. Modification and expression and cis-regulation of Hoxc8 in the evolution of diverged axial morphology. Proc. Natl. Acad. Sci. USA 95: 2355-2360.

Benson, D. L., Colman, D. R., and Huntley, G. W. 2001. Molecules, maps, and synapse specificity. Nat. Rev. Neurosci. 2: 899-909.

Brakefield, P. M. 2006. Evo-devo and constraints upon selection. Trends in Ecology and Evolution. 21: 362-368.

Brakefield, P. M., French, V., and Zwaan B. J. 2003. Development and the genetics of evolutionary change within insect species. Annu. Rev. Ecol. Syst. 34: 633-660.

Carroll, S. B., Grenier, J. K., and Weatherbee, S. D. 2001. From DNA to Diversity: Molecular Genetics and the Evolution of Animal Design. Blackwell Science, Inc. Massachusetts.

Chen, B. E., Kondo, M., Garnier, A., Watson, F. L., Püettman-Holgado, R. Lamar, D. L., and Schmucker, D. 2006. The molecular diversity of Dscam is functionally required for neuronal wiring specificity in Drosophila. Cell 125: 607-620.

Chilton, J. K. 2006. Molecular mechanisms of axon guidance. Developmental Biology 292: 13-24.

Chipman, A. D., Arthur, W., and Akam, M. 2004. A double segment periodicity underlies segment generation in centipede development. Current Biology 14: 1250-1255.

Chipman, A. D., Akam, M. 2008. The segmentation cascade in the centipede Strigamia maritime: Involvement of the Notch pathway and pair-rule gene homologues. Developmental Biology 319: 160-169.

Crutchfield, J. P. 1988. Subbasins, Portals, and Mazes: Transients in High Dimensions. Nucl. Phys. B 5: 287-292.

Dantzker, J. L., and Callaway, E. M. 2000. Laminar sources of synaptic input to cortical inhibitory inerneuonrs and pyramidal neurons. Nat. Neurosci. 7: 701-707.

Darwin, C. 1859. On the Origin of Species by Means of Natural Selection. John Murray, London.

Driever, W. and Nüsslein-Volhard, C. 1988. The bicoid protein determines position in the Drosophila embryo in a concentration-dependent manner. Cell 54: 95-104.

Ephrussi, A. and St. Johnston, D. 2004. Seeing is believing: the Biocoid morphogen gradient matures. Cell 116: 143-152.

Fisher, R. A. 1930. The Genetical Theory of Natural Selection. Clarendon, Oxford.

Fontana, W., Stadler, P. F., et al. 1993. RNA folding and combinatory landscapes. Phys. Rev. E 47: 2083-2099.

Ford, E. B. 1971. Ecological genetics. 3rd Ed. Chapman and Hall, London.

Frankino, W. A., Zwaan, B. J., Stern, D. L., Brakefield, P. M. 2005. Natural selection and developmental constraints in the evolution of allometries. Science 307: 718-720.

Gardner, D. 1977. Voltage-clamp analysis of a self-inhibitory synaptic potential in the buccal ganglia of Aplysia. J. Physiol. 264: 894-520.

Gerhart, J. and Kirschner, M. 1997. Cells, Embryos, and Evolution. Blackwell Science, Inc., Malden, MA.

Gilbert, S. F. 2006. Developmental biology. 8th Ed. Sinauer Associates, Massachusetts.

Goldberg, D. E. 1989. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA.

Gomez-Mestre, I. and Buchholz, D. R. 2006. Developmental plasticity mirrors differences among taxa in spadefoot toads linking plasticity and diversity. Proc. Natl. Acad. Sci. USA 103: 19021-19026.

Gould, S. J. and Lewontin, R. C. 1979. The spandrels of San Marco and the Panglossian paradigm. Proc. R. Soc. Lond. B 205: 581-598.

Gupta, A., Wang Y., and Makram, H. 2000. Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex. Science 287: 273-278.

Haldane J. B. S. 1932. The Causes Of Evolution. Longmans, Green and Co., New York.

Hoekstra, H. E. and Coyne, J. A. 2007. The locus of evolution: Evo devo and the genetics of adaption. Evolution 61: 995-1016.

Hogeweg P. 2000a. Evolving mechanisms of morphogenesis: On the interplay between differential adhesion and cell differentiation. J. Theoret. Biol. 203: 317-333.

Hogeweg P. 2000b. Shapes in the shadow: Evolutionary dynamics of morphogenesis. Artificial Life. 6: 85-101.

Holland, J. H. 1975. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI.

Hummel, T., Vasconcelos, M. L., Clemens, J.C., Fishilevich, Y., Vosshall, L. B., and Zipursky, S. L. 2003. Axonal targeting of olfactory receptor neurons in Drosophila is controlled by Dscam. Neuron 37: 221-231.

Huynen, M., Stadler, P. F., and Fontana, W. 1996. Smoothness within ruggedness: The role of neutrality in evolution. Proc. Nat. Acad. Sci. USA 93: 397-401.

Jaeger, J. and Reinitz, J. 2006. On the dynamic nature of positional information. BioEssays 28: 1102-1111.

Jaeger, J., Sharp, D. H., and Reinitz, J. 2007. Known maternal gradients are not sufficient for the establishment of gap domains in Drosophila melanogaster. Mechanisms of Development 124: 108-128.

Karabelas, A. B. and Purpura, D. P. 1980. Evidence for autapses in the substantia nigra. Brain Research. 200: 467-473.

Kettle, C., Arthur, W., Jowett, T., and Minelli, A. 1999. Homeotic transformation in a centipede. Trends in Genetics 15: 393.

Kimura, M. 1983. The Neutral Theory of Molecular Evolution. Cambridge University Press. Cambridge.

Koelle, K., Cobey, S., Grenfell, B., Pascual, M. 2006. Epochal evolution shapes the phylodynamics of interpandemic influenza A (H3N2) in humans. Science 314: 1898- 1903.

Kopp, A., Duncan, I., and Carroll, S. B. 2000. Genetic control and evolution of sexually dimorphic characters in Drosphila. Nature 408: 553-559.

Kozloski, J., Hamzei-Sichani, F., and Yuste, R. 2001. Stereotyped position of local synaptic targets in neocortex. Science 293: 868-872.

Langlade, N. B., Feng, X., Dransfield, D., Copsey, L., Hanna, A. I., Thébaud, C., Bangham, A., Hudson, A., Coen, E. 2005. Evolution through genetically controlled allometry space. Proc. Nat. Acad. Sci. USA 102: 10221-10226.

Leśniewska, M., Bonato, L., and Fusco, G. Segmental abnormalities in a Polish population of Stigmatogaster subterranea (Chilopoda, Geophilomorpha): A multi-year survey. 14th International Congress of Myriapodology. Görlitz, Germany 2008.

Lewis, J. G. E. 1981. The Biology of Centipedes. Cambridge University Press. Cambridge.

Lynch, M. 2007. The evolution of genetic networks by non-adaptive processes. Nature Rev. Genet. 8: 803-813.

Maynard Smith, J., Burian, R., Kauffman, S., Alberch, P., Campbell, J., Goodwin, B., Lande, R., Raup, D., Wolpert, L. 1985. Developmental constraints and evolution: A

86 perspective from the Mountain Lake Conference on evolution and development. Quarterly Review of Biology. 60: 265-287.

Minelli, A., Foddai, D., Pereira, L. A., Lewis, J. G. A. 2000. The evolution of segmentation of centipede trunk and appendages. J. Zool. Sys. Evol. Research. 38: 104- 77.

Nishikawa, K. C. 1997. Emergence of novel functions during brain evolution. Bioscience 47: 341-354.

Park, M. R., Lighthall, J. W., and Kitai, S. T. 1980. Recurrent inhibition in the rat neostiatum. Brain Research. 194: 359-369.

Pouzat, C. and Marty, A. 1998. Autaptic inhibitory currents recorded from interneurones from rat cerebellar slices. J. Physiol. 509: 777-783.

Psujek, S. and Beer, R. D. 2008. Developmental bias in evolution: Evolutionary accessibility of phenotypes in a model evo-devo system. Evolution & Development (10: 375:390.

Purves, D. and Lichtman, J. 1985. Principles of Neural Development. Sinauer Associates, Sunderland.

Raff, R. A. 1996. The Shape of Life: Genes, Development, and the Evolution of Animal Form. University of Chicago Press, Chicago.

Remold, S. and Lenski, R. E. 2004. Pervasive joint influence of epistasis and plasticity on mutational effects in Escherichia coli. Nature Genetics 36: 423-426.

Rose, L. S. and Kemphues, K. J. 1998. Early patterning of the C. elegans embryo. Annu. Rev. Genet. 32: 521-545.

Salazar-Ciudad, I., Garcia-Fernádez, J., and Solé, R. V. 2000. Gene networks capable of pattern formation: From induction to reaction-diffusion. J. Theoret. Biol. 205: 587-603.

Salazar-Ciudad, I. and Jernvall, J. 2002. A gene network model accounting for development and evolution of mammalian teeth. Proc. Natl. Acad. Sci. USA 99: 8116- 8120.

Salazar-Ciudad, I. and Jernvall, J. 2004. How different types of pattern formation mechanisms affect the evolution of form and development. Evolution & Development 6: 6-16.

Salazar-Ciudad, I. 2006. Developmental constraints vs. variational properties : How pattern formation can help to understand evolution and development. J. Exp. Zool. 306B: 107-125.

Sanes, J. R. and Yamagata, M. 1999. Formation of lamina-specific synaptic connections. Curr. Opin. NeuroBiol. 9: 79-87.

Sastry, K. and Goldberg, D. E., 2004, Designing competent mutation operators via probabilistic model building of neighborhoods, in: Proc. 2004 Genetic and Evolutionary Computation Conference II, Lecture Notes in Computer Science, Vol. 3103, Springer, Berlin, pp. 114--125.

Schmucker, D., Clemens, J. C., Shu, H., Worby, C. A., Xiao, J., Muda, M., Dixon, J. E., Zipursky, S. L. 2000. Drosophila Dscam is an axon guidance receptor exhibiting extraordinary molecular diversity. Cell 101: 671-684.

Schuster, P. and Fontana, W. 1999. Chance and necessity in evolution: lessons from RNA. Physica D 133: 427-452.

Shen, K. and Bargmann, C. I. 2003. The immunoglobulin superfamily protein SYG-1 determines the location of specific synapses in C. elegans. Cell 112: 619-30.

Solé, R. V., Fernández, P., and Kauffman, S. A. 2003. Adaptive walks in a gen network model of morphogenesis: Insights into the Cambrian explosion. Int. J. Dev. Biol. 47: 685-693.

Solé, R. V. and Valverde, S. 2006. Are network motifs the spandrels of cellular complexity? Trends in Ecology and Evolution 21: 419-422.

Spencer, G. E., Lukowiak, K., and Syed, N. I. 2000. Transmitter-receptor interactions between growth cones of identified Lymnaea neurons determine target cell selection in vitro. J. Neurosci. 20: 8077-8086.

Sperry, R. W. 1963. Chemoaffinity in the orderly growth of nerve fiber patterns and connections. Proc. Natl. Acad. Sci. USA 50: 703-710.

Stern, D. L. 2000. Perspective: Evolutionary developmental biology and the problem of variation. Evolution 54: 1079-1091.

Stollewerk, A., Schoppmeier, M., and Damen, W. G. M. 2003. Involvement of Notch and Delta genes in spider segmentation. Nature 423: 863-865.

True, J. R. and Haag, E. S. 2001. Developmental system drift and flexibility in evolutionary trajectories. Evolution & Development 3: 109-119.

Van der Loos, H. and Glaser, E. M. 1972. Autapses in neocortex cerebri: synapses between a pyramidal cell‟s axon and its own dendrites. Brain Research 48: 355-360. van Nimwegen, E., Crutchfield, J. P., and Huynen, M. 1999. Neutral evolution of mutational robustness. Proc. Natl. Acad. Sci. USA 96: 9716-9720.

Weiss, K. M. and Fullerton, S. M. 2000. Phenogenetic drift and the evolution of genotype-phenotype relationships. Theoretical Population Biology 57: 187-195.

Wilkins, A. S. 2002. The Evolution of Developmental Pathways. Sinauer Associates, Inc. Sunderland, MA.

Wittkopp, P. J., Hacrum, B. K., and Clark, A. G. 2004 Evolutionary changes in cis and trans gene regulation. Nature. 430: 85-88.

Wolfram Research, Inc., Mathematica, Version 6.0, Champaign, IL. 2007.

Wray, G. A. 2003a. Transcriptional regulation and the evolution of development. Int. J. Dev. Biol. 47:675-684.

Wray, G. A., Hahn, M. W., Abouheif, E, Balhoff, J. P., Pizer, M., Rockman, M. V., Romano, L. A. 2003b. The evolution of transcriptional regulation in eukaryotes. Mol. Biol. Evol. 20: 1377-1419.

Wray, G. A. 2007. The evolutionary significance of cis-regulatory mutations. Nature Rev. Genet. 8: 206-216.

Wright, S. 1932. The roles of mutation, inbreeding, crossbreeding, and selection in evolution. Proceedings of the 6th International Congress of Genetics 1: 356-366.

Yamagata, M., Weiner, J. A., and Sanes, J. R. 2002. Sidekicks: synaptic adhesion molecules that promote lamina-specific connectivity in the retina. Cell 110: 649-60.

Yampolsky, L. Y. and Stoltzfus, A. 2001. Bias in the introduction of variation as an orienting factor in evolution. Evolution & Development 3: 73-83.

Zhu, H., Hummel, T., Clemens, J. C., Berdnik, D., Zipursjky, S. L., and Luo, L. 2006. Dendritic patterning by Dscam and synaptic partner matching in the Drosophila antennal lobe. Nature Neuroscience 9: 349-355.