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A growing body of evidence points to the existence of genotype networks in both protein and RNA phenotypes, and to their importance for evolutionary innovation. This evidence comes from comparative analysis of protein and RNA genotypes and phenotypes, from laboratory evolution experiments, and from computational analysis of RNA and model protein structures. This evidence shows that many genotypes can form the same phenotype, even for molecules of modest size. They form vast connected networks of genotypes that often nearly span genotype space. This means that two molecules with the same phenotype may share little or no sequence similarity. A series of mutational changes on a genotype network can preserve a phenotype while exploring an ever-changing spectrum of new phenotypes. Laboratory evolution experiments show that these properties facilitate the evolution of new functions by allowing exploration of new phenotypes, while leaving an existing phenotype unchanged.

Many systems are best viewed as having a continuous range of phenotypes. These include the continuous spectrum of conformations that molecules form through thermal noise, and the many macroscopic forms of organisms that can be continuously transformed into one another. Continuously-valued phenotypes are also abundant on an intermediate level, that of regulatory circuitry and its molecular activity phenotypes. This chapter uses such systems to explain the challenges that continuity poses to understanding innovation. Specifically, it discusses why the principles we find in discrete systems are not straightforwardly transferable to continuous systems. It then considers the progress that has been made towards addressing these challenges for cellular circuits that function in cell biology and development. What little we know hints that two features crucial for evolutionary innovation in discrete systems also exist in continuous systems.

An evolutionary constraint is a bias or limitation in genotypic or phenotypic variation that a biological system produces. Striking phenotypic examples include the absence of photosynthesis in higher animals, and the general lack of teeth in the lower jaw of frogs. Constraints can influence the spectrum of evolutionary adaptations and innovations that are accessible to living things. Based on the cause of constrained phenotypic variation, one can distinguish physicochemical, selective, genetic, and developmental constraints. The latter class of constraints emerges from the processes that produce phenotypes from genotypes. This chapter examines these four causes for molecules, regulatory circuits, and metabolic networks in the genotype space framework. This framework shows that processes of phenotype formation cause the three other classes of constraints. It can help us appreciate why causes of constrained variation are often entangled and not clearly separable. The chapter also shows that the kind of evolutionary stasis that occurs during punctuated and episodic evolution is a consequence of genetic constraints, whose origins the genotype space framework can readily explain.

Recombination causes long jumps through a vast genotype space. Because different regions of this space contain different novel phenotypes, recombination can thus greatly facilitate the exploration of novel phenotypes. At the same time, however, these long jumps may often destroy a parental, well-adapted phenotype. This is a major problem in understanding recombination's role in evolutionary innovation. Based on evidence from proteins and regulatory circuits, this chapter shows that this problem is much less severe than one might think. First, recombination causes much weaker effects than mutation, because it exchanges system parts that are compatible with a given phenotype. Second, past exposure of a system to recombination can dramatically increase the system's robustness to recombination. It may cause the vast majority of recombinants to preserve their parental phenotype, and thus eliminate the problem that recombination destroys well-adapted phenotypes.