Living organisms function according to complex mechanisms that operate in different ways depending on conditions. Evolutionary theory suggests that such mechanisms evolved as result of a random search guided by selection. However, there has existed no theory that would explain quantitatively which mechanisms can so evolve in realistic population sizes within realistic time periods, and which are too complex. In this paper we suggest such a theory. Evolution is treated as a form of computational learning from examples in which the course of learning is influenced only by the fitness of the hypotheses on the examples, and not otherwise by the specific examples. We formulate a notion of evolvability that quantifies the evolvability of different classes of functions. It is shown that in any one phase of evolution where selection is for one beneficial behavior, monotone Boolean conjunctions and disjunctions are demonstrably evolvable over the uniform distribution, while Boolean parity functions are demonstrably not. The framework also allows a wider range of issues in evolution to be quantified. We suggest that the overall mechanism that underlies biological evolution is evolvable target pursuit, which consists of a series of evolutionary stages, each one pursuing an evolvable target in our technical sense, each target being rendered evolvable by the serendipitous combination of the environment and the outcome of previous evolutionary stages.
KeywordsIdeal Function Turing Machine Parity Function Neutral Mutation Statistical Query
Unable to display preview. Download preview PDF.
- 5.Darwin, C.: On the origin of species by means of natural selection. John Murray, London (1859)Google Scholar
- 7.Drake, J.W., et al.: Rates of spontaneous mutation. Genetics 148, 1667–1686 (1998)Google Scholar
- 16.Kearns, M., Vazirani, U.: An Introduction to Computational Learning Theory. MIT Press, Cambridge (1994)Google Scholar
- 21.Roff, D.A.: Evolutionary Quantitative Genetics. Chapman & Hall, New York (1997)Google Scholar
- 22.Ros, J.P.: Learning Boolean functions with genetic algorithms: A PAC analysis. In: Whitley, L.D. (ed.) Foundations of Genetic Algorithms, pp. 257–275. Morgan Kaufmann, San Mateo, CA (1993)Google Scholar
- 25.Valiant, L.G.: Knowledge infusion. In: Proc. 21st National Conference on Artificial Intelligence, AAAI 2006, pp. 1546–1551 (2006)Google Scholar
- 28.Wright, S.: Evolution and the Genetics of Populations, A Treatise. University of Chicago Press, Chicago (1968-78)Google Scholar