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Suggested Citation:"General-Purpose References." National Research Council. 1995. Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology. Washington, DC: The National Academies Press. doi: 10.17226/2121.
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CALIBRATING THE CLOCK: USING STOCHASTIC PROCESSES TO MEASURE THE RATE OF EVOLUTION 149 and Hudson (1991) and Rogers and Harpending (1992). Lundstrom et al. (1992b) note that the effects of variable population size on gene frequency distributions can readily be confounded with the effects of hypervariable regions in the sequences. A careful assessment of the interaction of these two effects seems important, as does a detailed treatment of the effects of spatial structure and population subdivision on the analysis of sequence diversity. The Monte Carlo likelihood methods developed for sequence data in Griffiths and Tavaré (1994a) adapt readily to situations like this. See, for example, Griffiths and Tavaré (1994b.) They offer a practical approach to inference from very complicated stochastic processes. These techniques are based on genealogical arguments that provide the cornerstone of a firm quantitative basis for the analysis of DNA sequence data and our understanding of genomic diversity. REFERENCES General-Purpose References General-Purpose References Arratia, R., and S. Tavaré, 1994, "Independent process approximations for random combinatorial structures," Adv. Math. 104, 90-154. Avise, J.C., 1986, "Mitochondrial DNA and the evolutionary genetics of higher animals," Philos. Trans. R. Soc. London, Ser. B 312, 325-342. Ethier, S.N., and T.G. Kurtz, 1993, "Fleming-Viot processes in population genetics," SIAM J. Control Optim. 31, 345-386. Ewens, W.J., 1979, Mathematical Population Genetics, New York: Springer-Verlag. Ewens, W.J., 1990, "Population genetics theory-the past and the future," pp. 177-227 in Mathematical and Statistical Developments of Evolutionary, Theory, S. Lessard (ed.), Holland: Kluwer Dordrecht. Felsenstein, J., 1982, "Numerical methods for inferring evolutionary trees," Quarterly Review of Biology 57, 379-404. Felsenstein, J., 1988, "Phylogenies from molecular sequences: inference and reliability," Annu. Rev. Genet. 22, 521-565. Hudson, R.R., 1991, "Gene genealogies and the coalescent process," pp. 1-44 in Oxford Surveys in Evolutionary Biology 7, D. Futuyma and J. Antonovics (eds.). Tavaré, S., 1984, "Line-of-descent and genealogical processes, and their applications in population genetics models," Theor. Popul. Biol. 26, 119-164.

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As researchers have pursued biology's secrets to the molecular level, mathematical and computer sciences have played an increasingly important role—in genome mapping, population genetics, and even the controversial search for "Eve," hypothetical mother of the human race.

In this first-ever survey of the partnership between the two fields, leading experts look at how mathematical research and methods have made possible important discoveries in biology.

The volume explores how differential geometry, topology, and differential mechanics have allowed researchers to "wind" and "unwind" DNA's double helix to understand the phenomenon of supercoiling. It explains how mathematical tools are revealing the workings of enzymes and proteins. And it describes how mathematicians are detecting echoes from the origin of life by applying stochastic and statistical theory to the study of DNA sequences.

This informative and motivational book will be of interest to researchers, research administrators, and educators and students in mathematics, computer sciences, and biology.

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