Abstract
The coalescent with recombination is widely accepted as the key model to understand genetic diversity within a species. Many theoretical properties of the model are well understood, but formulating and implementing efficient inference methods remains a challenge. A major breakthrough has been to approximate the coalescent with recombination by a Markov chain along the sequences. Here we describe a new tool, RECJumper, for inference in the Markov approximated coalescent model. Previous methods are often based on a discretisation of the tree space and hidden Markov models. We avoid the discretisation by using particle filtering, and compare several proposal distributions. We also investigate runs of homozygosity, and introduce a new summary statistics from spatial statistics: Ripley’s K-function. We find that (i) choosing an appropriate proposal distribution is crucial to obtain satisfactory behaviour in particle filtering, (ii) tree space discretisation in HMM-methodology is non-trivial and the choice can influence the results, and (iii) Ripley’s K-function is a much more informative statistics than runs of homozygosity for recombination rate estimation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beaumont, M.A., Zhang, W., Balding, D.J.: Approximate Bayesian computation in population genetics. Genetics 162(4), 2025–2035 (2002)
Cappé, O., Moulines, E., Rydén, T.: Hidden Markov Models. Springer, New York (2004)
Cawley, S.L., Pachter, L.: HMM sampling and applications to gene finding and alternative splicing. Bioinformatics 19(suppl. 2), 36–41 (2003)
Doucet, A., Johansen, A.M.: A tutorial on particle filtering and smoothing: fifteen years later. Handb. Nonlinear Filtering 12(3), 656–704 (2009)
Durbin, R., Eddy, S.R., Krogh, A., Mitchison, G.: Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press, Cambridge (1998)
Durrett, R.: Probability Models for DNA Sequence Evolution. Springer Science & Business Media, Berlin (2008)
Gordon, N.J., Salmond, D.J., Smith, A.F.M.: Novel approach to nonlinear/non-gaussian bayesian state estimation. IEE Proc. F - Radar Sign. Process. 140(2), 107–113 (1993)
Griffiths, R.C., Marjoram, P.: Ancestral inference from samples of DNA sequences with recombination. J. Comput. Biol. 3(4), 479–502 (1996)
Harris, K., Nielsen, R.: Inferring demographic history from a spectrum of shared haplotype lengths. PLoS Genet. 9(6), 1–20 (2013)
Hobolth, A., Jensen, J.L.: Markovian approximation to the finite loci coalescent with recombination along multiple sequences. Theoret. Popul. Biol. 98, 48–58 (2014)
Li, H., Durbin, R.: Inference of human population history from individual whole-genome sequences. Nature 475(7357), 493–496 (2011)
Mailund, T., Halager, A.E., Westergaard, M., Dutheil, J.Y., Munch, K., Andersen, L.N., Lunter, G., Prüfer, K., Scally, A., Hobolth, A., Schierup, M.H.: A new isolation with migration model along complete genomes infers very different divergence processes among closely related great ape species. PLoS Genet. 8(12), 1–19 (2012)
McVean, G.A., Cardin, N.J.: Approximating the coalescent with recombination. Philos. Trans. Roy. Soc. B: Biol. Sci. 360(1459), 1387–1393 (2005)
Myllymki, M., Mrkvika, T., Grabarnik, P., Seijo, H., Hahn, U.: Global envelope tests for spatial processes. J. Roy. Stat. Soc.: Ser. B (Statistical Methodology) (2016)
Palacios, J.A., Wakeley, J., Ramachandran, S.: Bayesian nonparametric inference of population size changes from sequential genealogies. Genetics 201(1), 281–304 (2015)
Rasmussen, M.D., Hubisz, M.J., Gronau, I., Siepel, A.: Genome-wide inference of ancestral recombination graphs. PLoS Genet. 10(5), 1–27 (2014)
Schiffels, S., Durbin, R.: Inferring human population size and separation history from multiple genome sequences. Nat. Genet. 46(8), 919–925 (2014)
Simonsen, K.L., Churchill, G.A.: A Markov chain model of coalescence with recombination. Theor. Popul. Biol. 52(1), 43–59 (1997)
Wakeley, J.: Coalescent Theory: An Introduction. W. H. Freeman, San Francisco (2009)
Wiegand, T., He, F., Hubbell, S.P.: A systematic comparison of summary characteristics for quantifying point patterns in ecology. Ecography 36(1), 92–103 (2013)
Wilton, P.R., Carmi, S., Hobolth, A.: The SMC’ is a highly accurate approximation to the ancestral recombination graph. Genetics 200(1), 343–355 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Nielsen, S.V., Simonsen, S., Hobolth, A. (2016). Inferring Population Genetic Parameters: Particle Filtering, HMM, Ripley’s K-Function or Runs of Homozygosity?. In: Frith, M., Storm Pedersen, C. (eds) Algorithms in Bioinformatics. WABI 2016. Lecture Notes in Computer Science(), vol 9838. Springer, Cham. https://doi.org/10.1007/978-3-319-43681-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-43681-4_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43680-7
Online ISBN: 978-3-319-43681-4
eBook Packages: Computer ScienceComputer Science (R0)