Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
CALIBRATING THE CLOCK: USING STOCHASTIC PROCESSES TO MEASURE THE RATE OF EVOLUTION 150 Detailed References Detailed References Anderson, S., A. Bankier, B. Barrell, M. deBruijn, A. Coulson, J. Drouin, I. Eperon, D. Nierlich, B. Roe, F. Sanger, P. Schreier, A. Smith, R. Staden, and I. Young, 1981, "Sequence and organization of the human mitochondrial genome," Nature 290, 457-465. Arratia, R., and S. Tavaré, 1992, "Limit theorems for combinatorial structures via discrete process approximations," Random Struct. Algebra 3, 321-345. Arratia, R., A.D. Barbour, and S. Tavaré, 1992, "Poisson process approximations for the Ewens sampling formula," Ann. Appl. Probab. 2, 519-535. Arratia, R., A.D. Barbour, and S. Tavaré, 1993, "On random polynomials over finite fields," Math. Proc. Cambridge Philos. Soc. 114, 347-368. Arratia, R., A.D. Barbour, and S. Tavaré, 1994a, "Logarithmic combinatorial structures," Ann. Probab., in preparation. Arratia, R., D. Stark, and S. Tavaré, 1994b, "Total variation asymptotics for Poisson process approximations of logarithmic combinatorial assemblies," Ann. Probab., in press. Cann, R., M. Stoneking, and A.C. Wilson, 1987, "Mitochondrial DNA and human evolution," Nature 325, 31-36. Di Rienzo, A., and A.C. Wilson, 1991, "Branching pattern in the evolutionary tree for human mitochondrial DNA," Proceedings of the National Academy of Sciences USA 88, 1597-1601. Estabrook, G.F., C.S. Johnson, Jr., and F.R. McMorris, 1976, "An algebraic analysis of cladistic characters," Discrete Math. 16, 141-147. Ethier, S.N., and R.C. Griffiths, 1987, "The infinitely-many-sites model as a measure valued diffusion," Ann. Probab. 15, 515-545. Ewens, W.J., 1972, "The sampling theory of selectively neutral alleles," Theor. Popul. Biol. 3, 87-112. Felsenstein, J., 1992, "Estimating effective population size from samples of sequences: A bootstrap Monte Carlo integration approach," Genet. Res. Camb. 60, 209-220. Flajolet, P., and A.M. Odlyzko, 1990, "Random mapping statistics," pp. 329-354 in Proc. Eurocrypt '89, J.-J. Quisquater (ed.), Lecture Notes in Computer Science 434, Springer-Verlag. Fleming, W.H., and M. Viot, 1979, "Some measure-valued Markov processes in population genetics theory," Indiana Univ. Math. J. 28, 817-843. Goncharov, V.L., 1944, "Some facts from combinatorics," Izv. Akad. Nauk. SSSR, Ser. Mat. 8, 3-48 [in Russian]; "On the field of combinatory analysis," Trans. Am. Math. Soc. 19, 1-46. Griffiths, R.C., 1987, "An algorithm for constructing genealogical trees," Statistics Research Report 163, Department of Mathematics, Monash University. Griffiths, R.C., 1989, "Genealogical-tree probabilities in the infinitely-many-sites model," J. Math. Biol. 27, 667-680. Griffiths, R.C., and S. Tavaré, 1994a, "Simulating probability distributions in the coalescent process," Theor. Popul. Biol. 46, 131-159. Griffiths, R.C., and S. Tavaré, 1994b, "Sampling theory for neutral alleles in a varying environment," Philos. Trans. R. Soc. London, Ser. B 344, 403-410.
CALIBRATING THE CLOCK: USING STOCHASTIC PROCESSES TO MEASURE THE RATE OF EVOLUTION 151 Griffiths, R.C., and S. Tavaré, 1994c, "Unrooted genealogical tree probabilities in the infinitely-many-sites model," Math. Biosci., in press. Hansen, J.C., 1994, "Order statistics for decomposable combinatorial structures," Random Struct. Alg. 5, 517-533. Horai, S., and K. Hayasaka, 1990, "Intraspecific nucleotide sequence differences in the major noncoding region of human mitochondrial DNA," Am. J. Hum. Genet. 46, 828-842. Kimura, M., 1969, "The number of heterozygous nucleotide sites maintained in a finite population due to steady influx of mutations," Genetics 61, 893-903. Kimura, M., and J.F. Crow, 1964, "The number of alleles that can be maintained in a finite population," Genetics 49, 725-738. Kingman, J.F.C., 1974, "Random discrete distributions, " J. R. Stat. Soc. 37, 1-22. Kingman, J.F.C., 1977, "The population structure associated with the Ewens sampling formula," Theor. Popul. Biol. 11, 274-283. Kingman, J.F.C., 1982a, "On the genealogy of large populations," J. Appl. Probab. 19A, 27-43. Kingman, J.F.C., 1982b, "The coalescent," Stoch. Processes Appl. 13, 235-248. Kolchin, V.F., 1976, "A problem of the allocation of particles in cells and random mappings," Theory Probab. Its Applic. (Engl. Transl.) 21, 48-63. Kolchin, V.F., 1986, Random Mappings, New York: Optimization Software, Inc. Lundstrom, R., 1990, Stochastic Models and Statistical Methods for DNA Sequence Data, PhD thesis, Department of Mathematics, University of Utah. Lundstrom, R., S. Tavaré, and R.H. Ward, 1992a, "Estimating mutation rates from molecular data using the coalescent," Proceedings of the National Academy of Sciences USA 89, 5961-5965. Lundstrom, R., S. Tavaré, and R.H. Ward, 1992b, "Modeling the evolution of the human mitochondrial genome," Math. Biosci. 122, 319-336. Maddison, D.R., 1991, "African origin of human mitochondrial DNA reexamined," Systematic Zoology 40, 355-363. McMorris, F.R., 1977, "On the compatibility of binary qualitative taxonomic characters," Bull. Math. Biol. 39, 133-138. Mutafciev, L., 1984, "On some stochastic problems of discrete mathematics," pp. 57-80 in Mathematics and Education in Mathematics (Sunny Beach), Sophia, Bulgaria: Bulgarian Academy of Sciences. Nei, M., 1992, "Age of the common ancestor of human mitochondrial DNA," Mol. Biol. Evol. 9, 1176-1178. Rogers, A., and H. Harpending, 1992, "Population growth makes waves in the distribution of pairwise genetic differences," Mol. Biol. Evol. 9, 552-569. Schurr, T., S. Ballinger, Y. Gan, J. Hodge, D.A. Merriwether, D. Lawrence, W. Knowler, K. Weiss, and D. Wallace, 1990, "Amerindian mitochondrial DNAs have rare Asian mutations at high frequencies, suggesting they derived from four primary maternal lineages," Am. J. Hum. Genet. 47, 613-623. Slatkin, M., and R.R. Hudson, 1991, "Pairwise comparisons of mitochondrial DNA sequences in stable and exponentially growing populations," Genetics 129, 555-562.
CALIBRATING THE CLOCK: USING STOCHASTIC PROCESSES TO MEASURE THE RATE OF EVOLUTION 152 Templeton, A.R., 1992, "Human origins and analysis of mitochondrial DNA sequences," Science 255, 737-754. Vigilant, L., R. Pennington, H. Harpending, T. Kocher, and A.C. Wilson, 1989, "Mitochondrial DNA sequences in single hairs from a South African population," Proceedings of the National Academy of Sciences USA 86, 9350-9354. Vigilant, L., M. Stoneking, H. Harpending, K. Hawkes, and A.C. Wilson, 1991, "African populations and the evolution of human mitochondrial DNA," Science 253, 1503-1507. Ward, R.H., B.L. Frazier, K. Dew, and S. Piabo, 1991, "Extensive mitochondrial diversity within a single Amerindian tribe," Proceedings of the National Academy of Sciences USA 88, 8720-8724. Watterson, G.A., 1975, "On the number of segregating sites in genetical models without recombination," Theoret. Popul. Biol. 7, 256-276. Wright, S., 1968, Evolution and the Genetics of Populations, Vol. 2, Chicago: University of Chicago Press.