previous ::
next
A Duality Identity between a Model of Bacterial Recombination and the Wright–Fisher Diffusion
Xavier Didelot, Jesse E. Taylor, Joseph C. Watkins
Abstract
In this article, we establish, using a duality argument, an identity stating that the Laplace transform of the length of a contiguous bacterial recombination region equals the probability of choosing a given allele in a stationary population evolving according to the one-dimensional Wright–Fisher diffusion model. Beyond giving us an improved inferential strategy for parameter estimation in bacterial recombination, the matching of the selection and recombination parameters in the identity also suggests the existence of an intriguing formal relationship between gene conversion and the ancestral selection graph.
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.imsc/1233152950
Digital Object Identifier: doi:10.1214/074921708000000453
References
[1] Didelot, Xavier and Falush, Daniel (2007). Inference of bacterial microevolution using multilocus sequence data. Genetics 175 1251–1266.
[2] Donnelly, P. and Kurtz, T. G. (1999). Genealogical processes for Fleming–Viot models with selection and recombination. Ann. Appl. Prob. 9 1091–1148.
Mathematical Reviews (MathSciNet):
MR1728556
Zentralblatt MATH:
0964.60075
Digital Object Identifier: doi:10.1214/aoap/1029962866
Project Euclid: euclid.aoap/1029962866
[3] Ethier, S. N. and Kurtz, T. G. (1986). Markov Processes: Characterization and Convergence. John Wiley & Sons, New York.
Mathematical Reviews (MathSciNet):
MR838085
[4] Falush, D., Kraft, C., Taylor, N. S., Correa, P., Fox, J. G., Achtman, M. and Suerbaum, S. (2001). Recombination and mutation during long-term gastric colonization by Helicobacter pylori: Estimates of clock rates, recombination size, and minimal age. Proc. Natl. Acad. Sci. USA 98 15056–15061.
[5] Falush, D., Stephens, M. and Pritchard, J. K. (2003). Inference of population structure using multilocus genotype data: Linked loci and correlated allele frequencies. Genetics 164 1567–1587.
[6] Fearnhead, P., Smith, N. G., Barrigas, M., Fox, A. and French, N. (2005). Analysis of recombination in Campylobacter jejuni from MLST population data. J. Mol. Evol. 61 333–340.
[7] Feil, E. J., Holmes, E. C., Enright, M. C., Bessen, D. E., Day, N. P. J., Chan, M.-S., Hood, D. W., Zhou, J. and Spratt, B. G. (2001). Recombination within natural populations of pathogenic bacteria: short-term empirical estimates and long-term phylogenetic consequences. Proc. Natl. Acad. Sci. USA 98 182–187.
[8] Frisse, L., Hudson, R. R., Bartoszewicz, A., Wall, J. D., Donfack, J. and Di Rienzo, A. (2001). Gene conversion and different population histories may explain the contrast between polymorphism and linkage disequilibrium levels. Am. J. Hum. Genet. 69 831–843.
[9] Griffiths, R. C. and Marjoram. P. (1996). Ancestral inference from samples of DNA sequences with recombination. J. Computational Biology 3 479–502.
[10] Guillemin, F. and Simonian, A. (1995). Transient characteristics of an M/M/∞ system. Advances in Applied Probability 27 862–888.
Mathematical Reviews (MathSciNet):
MR1341889
Zentralblatt MATH:
0829.60058
Digital Object Identifier: doi:10.2307/1428137
JSTOR: links.jstor.org
[11] Guttman, D. S. and Dykhuizen, D. E. (1994). Clonal divergence in Escherichia coli as a result of recombination, not mutation. Science 266 1380–1383.
[12] Hudson, R. R. (1983). Properties of a neutral allele model with intragenic recombination. Theoretical Population Biology 23 183–201.
[13] Jolley, K. A., Wilson, D. J., Kriz, P., McVean, G. and Maiden, M. C. J. (2005). The influence of mutation, recombination, population history, and selection on patterns of genetic diversity in Neisseria meningitidis. Mol. Biol. Evol. 22 562–569.
[14] Kingman, J. F. C. (1982). The coalescent. Stochastic Processes and their Applications 13 235–248.
Mathematical Reviews (MathSciNet):
MR671034
Zentralblatt MATH:
0491.60076
Digital Object Identifier: doi:10.1016/0304-4149(82)90011-4
[15] Krone, S. M. and Neuhauser, C. (1997). Ancestral process with selection. Theor. Pop. Biol. 51 210–237.
[16] Maynard Smith, J., Smith, N. H., O’Rourke, M. and Spratt, B. (1993). How clonal are bacteria? PNAS 90 (10) 4384–4388.
[17] McVean, G., Awadalla, P. and Fearnhead, P. (2002). A coalescent-based method for detecting and estimating recombination from gene sequences. Genetics 2002 1231–1241.
[18] Milkman, R. and Bridges, M. M. (1990). Molecular Evolution of the Escherichia coli Chromosome. III. Clonal Frames. Genetics 126 505–517.
[19] Nakabachi, Atsushi, Yamashita, Atsushi, Toh, Hidehiro, Ishikawa, Hajime, Dunbar, Helen E., Moran, Nancy A. and Hattori, Masahira (2006). The 160-kilobase genome of the bacterial endosymbiont Carsonella. Science 314 267.
[20] Neuhauser, C. and Krone, S. M. (1997). The genealogy of samples in models with selection. Genetics 145 519–534.
[21] Pradella, S., Hans, A., Spröer, C., Reichenbach, H., Gerth, K. and Beyer, S. (2002). Characterisation, genome size and genetic manipulation of the myxobacterium Sorangium cellulosum So ce56. Arch. Microbiol. 178 484–492.
[22] Preater, J. (1997). M/M/∞ transience revisited. Journal of Applied Probability 34 1061–1067.
Mathematical Reviews (MathSciNet):
MR1484036
Zentralblatt MATH:
0895.60094
Digital Object Identifier: doi:10.2307/3215018
JSTOR: links.jstor.org
[23] Roijers, F., Mandjes, M. and van den Berg, H. (2007). Analysis of congestion periods of an M/M/∞-queue. Performance Evaluation 64 737–754.
[24] Suchard, M. A., Weiss, R. E., Dorman, K. S. and Sinsheimer, J. S. (2003). Inferring spatial phylogenetic variation along nucleotide sequences: A multiple change-point model. Journal of the American Statistical Association 98 427–437.
Mathematical Reviews (MathSciNet):
MR1995719
Zentralblatt MATH:
1041.62095
Digital Object Identifier: doi:10.1198/016214503000215
[25] Wiuf, C. and Hein, J. (2000). The coalescent with gene conversion. Genetics 155 451–462.
previous ::
next
Institute of Mathematical Statistics Collections
