- title = "Open Problems in the Spectral Analysis of Evolutionary Dynamics",
- author = "Lee Altenberg",
- booktitle = "Frontiers of Evolutionary Computation",
- editor = "Anil Menon",
- series = "Genetic Algorithms And Evolutionary Computation Series",
- volume = "11",
- chapter = "4",
- publisher = "Kluwer Academic Publishers",
- address = "Boston, MA, USA",
- year = "2004",
- pages = "73--102",
- keywords = "genetic algorithms, genetic programming",
- ISBN = "1-4020-7524-3",
-
URL = "
http://dynamics.org/Altenberg/FILES/LeeOPSAED.pdf",
-
DOI = "
doi:10.1007/1-4020-7782-3_4",
-
abstract = "For broad classes of selection and genetic operators,
the dynamics of evolution can be completely
characterised by the spectra of the operators that
define the dynamics, in both infinite and finite
populations. These classes include generalised
mutation, frequency-independent selection, uniparental
inheritance. Several open questions exist regarding
these spectra: 1. For a given fitness function, what
genetic operators and operator intensities are optimal
for finding the fittest genotype? The concept of rapid
first hitting time, an analog of Sinclair's rapidly
mixing Markov chains, is examined.
2. What is the relationship between the spectra of deterministic infinite population models, and the spectra of the Markov processes derived from them in the case of finite populations?
3. Karlin proved a fundamental relationship between selection, rates of transformation under genetic operators, and the consequent asymptotic mean fitness of the population. Developed to analyse the stability of polymorphisms in subdivided populations, the theorem has been applied to unify the reduction principle for self-adaptation, and has other applications as well. Many other problems could be solved if it were generalised to account for the interaction of different genetic operators. Can Karlin's theorem on operator intensity be extended to account for mixed genetic operators?",
- notes = "Revised 2010",
- size = "26 pages",
