Evolvability is defined as the capacity of a system for adaptive evolution. Evolvability is the ability of a population of organisms to not merely generate genetic diversity, but to generate adaptive genetic diversity, and thereby evolve through natural selection. In order for a biological organism to evolve by natural selection, there must be a certain minimum probability that new, heritable variants are beneficial. Random mutations, unless they occur in DNA sequences with no function, are expected to be mostly detrimental. Beneficial mutations are always rare, but if they are too rare, then adaptation cannot occur. Early failed efforts to evolve computer programs by random mutation and selection showed that evolvability is not a given, but depends on the representation of the program as a data structure, because this determines how changes in the program map to changes in its behavior. Analogously, the evolvability of organisms depends on their genotype–phenotype map. This means that genomes are structured in ways that make beneficial changes more likely. This has been taken as evidence that evolution has created not just fitter organisms, but populations of organisms that are better able to evolve. Alternative definitions Andreas Wagner describes two definitions of evolvability. According to the first definition, a biological system is evolvable: if its properties show heritable genetic variation, and if natural selection can thus change these properties. According to the second definition, a biological system is evolvable: if it can acquire novel functions through genetic change, functions that help the organism survive and reproduce. For example, consider an enzyme with multiple alleles in the population. Each allele catalyzes the same reaction, but with a different level of activity. However, even after millions of years of evolution, exploring many sequences with similar function, no mutation might exist that gives this enzyme the ability to catalyze a different reaction. Thus, although the enzyme's activity is evolvable in the first sense, that does not mean that the enzyme's function is evolvable in the second sense. However, every system evolvable in the second sense must also be evolvable in the first. Pigliucci recognizes three classes of definition, depending on timescale. The first corresponds to Wagner's first, and represents the very short timescales that are described by quantitative genetics. He divides Wagner's second definition into two categories, one representing the intermediate timescales that can be studied using population genetics, and one representing exceedingly rare long-term innovations of form. Pigliucci's