Evolution in simple systems and the emergence of complexity

Evolution, understood as the powerful interplay of reproduction, variation, and selection, represents an excellent tool for optimization in populations of simple and complex entities even under conditions where only limited information is available. The principle underlying this optimization heuristic was discovered and formulated already by Charles Darwin. In biology variation and selection operate on different molecular entities. Variation involves changes of the nucleotide sequence of a deoxyribonucleic acid (DNA) or ribonucleic acid (RNA) molecule called the genotype. Genotypes are strings of nucleotides and can be understood as elements of a discrete space, called sequence space, with the Hamming distance inducing a metric. The phenotype is derived through unfolding of the genotype.