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Inference Methods for Multiple Merger Coalescents

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Evolutionary Biology

Abstract

Some populations, including a diverse group of marine populations such as Pacific oysters and Atlantic cod, are highly fecund. Models of high fecundity—coupled with a skewed offspring distribution—have coalescent processes, which admit (simultaneous) multiple mergers of ancestral lineages associated with them. In contrast, the celebrated and extensively employed Kingman’s coalescent only admits pairwise mergers of ancestral lineages. We review multiple merger coalescent models derived from population models, which admit high fecundity and skewed offspring distribution. Inference methods that have been developed based on these multiple merger coalescent models will also be reviewed. In fact, multiple merger coalescent models are able to predict the excess singletons (relative to Kingman’s coalescent predictions) observed in the commercially important Atlantic cod. These models may be applicable to a wide range of natural populations—including a diverse group of marine organisms, viruses, and plants which distribute seeds—with significant implications.

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References

  • Árnason E (2004) Mitochondrial cytochrome b variation in the high-fecundity Atlantic cod: trans-Atlantic clines and shallow gene genealogy. Genetics 166:1871–1885

    Article  PubMed  PubMed Central  Google Scholar 

  • Árnason E, Halldórsdóttir K (2015) Nucleotide variation and balancing selection at the Ckma gene in Atlantic cod: analysis with multiple merger coalescent models. PeerJ 3:e786. doi: 10.7717/peerj.786, URL http://dx.doi.org/10.7717/peerj.786

    Google Scholar 

  • Barton NH, Etheridge AM, Véber A (2010) A new model for evolution in a spatial continuum. Electron J Probab 7:162–216

    Article  Google Scholar 

  • Barton NH, Etheridge AM, Véber A (2013) Modelling evolution in a spatial continuum. J Stat Mech 2013:1002

    Article  Google Scholar 

  • Berestycki N (2009) Recent progress in coalescent theory. Ensaios Mathématicos 16:1–193

    Google Scholar 

  • Berestycki J, Berestycki N, Schweinsberg J (2007) Beta-coalescents and continuous stable random trees. Ann Probab 35:1835–1887

    Article  Google Scholar 

  • Berestycki J, Berestycki N, Schweinsberg J (2008) Small-time behavior of beta coalescents. Ann Inst H Poincaré Probab Statist 44:214–238

    Article  Google Scholar 

  • Bhaskar A, Clark A, Song Y (2014) Distortion of genealogical properties when the sample size is very large. PNAS 111:2385–2390

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Birkner M, Blath J (2008) Computing likelihoods for coalescents with multiple collisions in the infinitely many sites model. J Math Biol 57:435–465

    Article  PubMed  Google Scholar 

  • Birkner M, Blath J (2009) Measure-valued diffusions, general coalescents and population genetic inference. In: Blath J, Mörters P, Scheutzow M (eds) Trends in stochastic analysis. Cambridge University Press, Cambridge, pp 329–363

    Google Scholar 

  • Birkner M, Blath J, Capaldo M, Etheridge AM, Möhle M, Schweinsberg J, Wakolbinger A (2005) Alpha-stable branching and beta-coalescents. Electron J Probab 10:303–325

    Article  Google Scholar 

  • Birkner M, Blath J, Möhle M, Steinrücken M, Tams J (2009) A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks. ALEA Lat Am J Probab Math Stat 6:25–61

    Google Scholar 

  • Birkner M, Blath J, Steinrücken M (2011) Importance sampling for Lambda-coalescents in the infinitely many sites model. Theor Popul Biol 79:155–173

    Article  PubMed  PubMed Central  Google Scholar 

  • Birkner M, Blath J, Eldon B (2013a) An ancestral recombination graph for diploid populations with skewed offspring distribution. Genetics 193:255–290

    Article  PubMed  PubMed Central  Google Scholar 

  • Birkner M, Blath J, Eldon B (2013b) Statistical properties of the site-frequency spectrum associated with Λ-coalescents. Genetics 195:1037–1053

    Article  PubMed  PubMed Central  Google Scholar 

  • Birkner M, Blath J, Steinrücken M (2013c) Analysis of DNA sequence variation within marine species using Beta-coalescents. Theor Popul Biol 87:15–24

    Article  PubMed  Google Scholar 

  • Blath J, Cronjäger M, Eldon B, Hammer M (2016) The site-frequency spectrum associated with Ξ-coalescents. http://biorxiv.org/content/early/2015/08/28/025684

  • Bolthausen E, Sznitman A (1998) On Ruelle’s probability cascades and an abstract cavity method. Comm Math Phys 197:247–276

    Article  Google Scholar 

  • Broquet T, Viard F, Yearsley JM (2013) Genetic drift and collective dispersal can result in chaotic genetic patchiness. Evolution 67(6):1660–1675. doi:10.1111/j.1558-5646.2012.01826.x, url <Go to ISI>://WOS:000319874800012

    Google Scholar 

  • Cannings C (1974) The latent roots of certain Markov chains arising in genetics: a new approach, I. Haploid models. Adv Appl Probab 6:260–290

    Article  Google Scholar 

  • Dahmer I, Kersting G, Wakolbinger A (2014) The total external length of Beta-coalescents. Comb Prob Comp 23:1010–1027

    Article  Google Scholar 

  • DePristo MA, Banks E, Poplin R, Garimella KV, Maguire JR, Hartl C, Philippakis AA, del Angel G, Rivas MA, Hanna M, McKenna A, Fennell TJ, Kernytsky AM, Sivachenko AY, Cibulskis K, Gabriel SB, Altshuler D, Daly MJ (2011) A framework for variation discovery and genotyping using next-generation DNA sequencing data. Nat Genet 43(5):491–498, doi:10.1038/ng.806, URL http://dx.doi.org/10.1038/ng.806

    Google Scholar 

  • Der R, Epstein CL, Plotkin JB (2011) Generalized population models and the nature of genetic drift. Theoret Popul Biol 80(2):80–99. doi:10.1016/j.tpb.2011.06.004, URL http://dx.doi.org/10.1016/j.tpb.2011.06.004

    Google Scholar 

  • Donnelly P, Kurtz TG (1999) Particle representations for measure-valued population models. Ann Probab 27:166–205

    Article  Google Scholar 

  • Durrett R, Schweinsberg J (2004) Approximating selective sweeps. Theor Popul Biol 66:129–138

    Article  PubMed  Google Scholar 

  • Durrett R, Schweinsberg J (2005) A coalescent model for the effect of advantageous mutations on the genealogy of a population. Stoch Proc Appl 115:1628–1657

    Article  Google Scholar 

  • Eldon B (2009) Structured coalescent processes from a modified Moran model with large offspring numbers. Theor Popul Biol 76:92–104

    Article  PubMed  Google Scholar 

  • Eldon B, Wakeley J (2006) Coalescent processes when the distribution of offspring number among individuals is highly skewed. Genetics 172:2621–2633

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Eldon B, Wakeley J (2008) Linkage disequilibrium under skewed offspring distribution among individuals in a population. Genetics 178:1517–1532

    Article  PubMed  PubMed Central  Google Scholar 

  • Eldon B, Wakeley J (2009) Coalescence times and F st under a skewed offspring distribution among individuals in a population. Genetics 181:615–629

    Article  PubMed  PubMed Central  Google Scholar 

  • Eldon B, Birkner M, Blath J, Freund F (2015) Can the site-frequency spectrum distinguish exponential population growth from multiple-merger coalescents. Genetics 199:841–856

    Article  PubMed  PubMed Central  Google Scholar 

  • Etheridge A (2011) Some mathematical models from population genetics. Springer, Berlin. doi:10.1007/978-3-642-16632-7, URL http://dx.doi.org/10.1007/978-3-642-16632-7

    Google Scholar 

  • Etheridge A, Griffiths R (2009) A coalescent dual process in a Moran model with genic selection. Theor Popul Biol 75:320–330

    Article  CAS  PubMed  Google Scholar 

  • Etheridge AM, Griffiths RC, Taylor JE (2010) A coalescent dual process in a Moran model with genic selection, and the Lambda coalescent limit. Theor Popul Biol 78:77–92

    Article  PubMed  Google Scholar 

  • Ethier S, Griffiths R (1987) The infinitely-many sites model as a measure-valued diffusion. Ann Probab 15:515–545

    Article  Google Scholar 

  • Ewens WJ (1972) The sampling theory of selectively neutral alleles. Theor Popul Biol 3(1):87–112

    Article  CAS  PubMed  Google Scholar 

  • Felsenstein J (2006) Accuracy of coalescent likelihood estimates: do we need more sites, more sequences, or more loci. Mol Biol Evol 23:691–700

    Article  CAS  PubMed  Google Scholar 

  • Flannick J, Thorleifsson G, Beer NL, Jacobs SBR, Grarup N, Burtt NP, Mahajan A, Fuchsberger C, Atzmon G, Benediktsson R, Blangero J, Bowden DW, Brandslund I, Brosnan J, Burslem F, Chambers J, Cho YS, Christensen C, Douglas DA, Duggirala R, Dymek Z, Farjoun Y, Fennell T, Fontanillas P, Forsén T, Gabriel S, Glaser B, Gudbjartsson DF, Hanis C, Hansen T, Hreidarsson AB, Hveem K, Ingelsson E, Isomaa B, Johansson S, Jørgensen T, Jørgensen ME, Kathiresan S, Kong A, Kooner J, Kravic J, Laakso M, Lee JY, Lind L, Lindgren CM, Linneberg A, Masson G, Meitinger T, Mohlke KL, Molven A, Morris AP, Potluri S, Rauramaa R, Ribel-Madsen R, Richard AM, Rolph T, Salomaa V, Segrè AV, Skärstrand H, Steinthorsdottir V, Stringham HM, Sulem P, Tai ES, Teo YY, Teslovich T, Thorsteinsdottir U, Trimmer JK, Tuomi T, Tuomilehto J, Vaziri-Sani F, Voight BF, Wilson JG, Boehnke M, McCarthy MI, Njølstad PR, Pedersen O, Groop L, Cox DR, Stefansson K, Altshuler D (2014) Loss-of-function mutations in SLC30a8 protect against type 2 diabetes. Nat Genet 46(4):357–363. doi:10.1038/ng.2915, URL http://dx.doi.org/10.1038/ng.2915

    Google Scholar 

  • Foucart C (2013) The impact of selection in the λ-wright-fisher model. Electron Commun Probab 18:1–10

    Article  Google Scholar 

  • Fu Y (1995) Statistical properties of segregating sites. Theor Popul Biol 48:172–197

    Article  CAS  PubMed  Google Scholar 

  • Fu Y (1996) New statistical tests of neutrality for DNA samples from a population. Genetics 143:557–570

    CAS  PubMed  PubMed Central  Google Scholar 

  • Fu Y (2006) Exact coalescent for the Wright-Fisher model. Theor Popul Biol 69:385–394

    Article  PubMed  Google Scholar 

  • Griffiths R, Tavaré S (1994a) Ancestral inference in population genetics. Stat Sci 9:307–319

    Google Scholar 

  • Griffiths R, Tavaré S (1994b) Sampling theory for neutral alleles in a varying environment. Phil Trans R Soc London B 344:403–410

    Google Scholar 

  • Griffiths R, Tavaré S (1994c) Simulating probability distributions in the coalescent. Theor Popul Biol 46:131–159

    Google Scholar 

  • Griffiths R, Tavaré S (1995) Unrooted genealogical tree probabilities in the infinitely-many-sites model. Math Biosci 127:77–98

    Article  CAS  PubMed  Google Scholar 

  • Gronau I, Hubisz MJ, Gulko B, Danko CG, Siepel A (2011) Bayesian inference of ancient human demography from individual genome sequences. Nat Genet 43(10):1031–1034. doi:10.1038/ng.937, URL http://dx.doi.org/10.1038/ng.937

    Google Scholar 

  • Halldórsdóttir K, Árnason E (2015) Whole-genome sequencing uncovers cryptic and hybrid species among Atlantic and Pacific cod-fish. doi:10.1101/034926, http://dx.doi.org/10.1101/034926

  • Harris H (1966) Enzyme polymorphisms in man. Proc R Soc Lond B Biol Sci 164(995):298–310

    Article  CAS  PubMed  Google Scholar 

  • Hearn J, Stone GN, Bunnefeld L, Nicholls JA, Barton NH, Lohse K (2013) Likelihood-based inference of population history from low-coverage de novo genome assemblies. Mol Ecol 23(1):198–211. doi:10.1111/mec.12578, URL http://dx.doi.org/10.1111/mec.12578

    Google Scholar 

  • Hedgecock D, Pudovkin AI (2011) Sweepstakes reproductive success in highly fecund marine fish and shellfish: a review and commentary. Bull Marine Science 87:971–1002

    Article  Google Scholar 

  • Heuer B, Sturm A (2013) On spatial coalescents with multiple mergers in two dimensions. Theor Population Biol 87:90–104. doi:10.1016/j.tpb.2012.11.006, URL http://dx.doi.org/10.1016/j.tpb.2012.11.006

    Google Scholar 

  • Hobolth A, Uyenoyama M, Wiuf C (2008) Importance sampling for the infinite sites model. Stat Appl Genet Mol Biol 7, article 32

    Google Scholar 

  • Hubby J, Lewontin R (1966) A molecular approach to the study of genic heterozygosity in natural populations. I. The number of alleles at different loci in Drosophila pseudoobscura. Genetics 54:577–594

    CAS  PubMed  PubMed Central  Google Scholar 

  • Hudson RR (1983) Properties of a neutral allele model with intragenic recombination. Theor Popul Biol 23:183–201

    Article  CAS  PubMed  Google Scholar 

  • Huillet TE (2014) Pareto genealogies arising from a Poisson branching evolution model with selection. J Math Biol 68(3):727–761

    Article  PubMed  Google Scholar 

  • Huillet T, Möhle M (2011) Population genetics models with skewed fertilities: forward and backward analysis. Stoch Models 27:521–554

    Article  Google Scholar 

  • Huillet T, Möhle M (2013) On the extended Moran model and its relation to coalescents with multiple collisions. Theor Popul Biol 87:5–14

    Article  PubMed  Google Scholar 

  • Ingvarson PK (2010) Nucleotide polymorphism, linkage disequilibrium and complex trait dissection in Populus. In: Genetics and genomics of Populus. Springer, Berlin, pp 91–111

    Google Scholar 

  • Johnson M, Black R (1982) Chaotic genetic patchiness in an intertidal limpet, Siphonaria sp. Mar Biol 70:157–164

    Article  Google Scholar 

  • Johnson M, Black R (1984) Pattern beneath the chaos: the effect of recruitment on genetic patchiness in an intertidal limpet. Evolution 38:1371–1383

    Article  Google Scholar 

  • Karlin S, McGregor J (1972) Addendum to paper of W. Ewens. Theor Popul Biol 3:113–116

    Article  CAS  PubMed  Google Scholar 

  • Kelleher J, Etheridge AM, McVean G (2015) Efficient coalescent simulation and genealogical analysis for large sample sizes. Technical report, University of Oxford. doi:10.1101/033118, URL http://dx.doi.org/10.1101/033118

  • Kersting G (2012) The asymptotic distribution of the length of Beta-coalescent trees. Ann Appl Probab 22:2086–2107

    Article  Google Scholar 

  • Kersting G, Stanciu I (2015) The internal branch lengths of the Kingman coalescent. Ann Appl Probab 25:1325–1348

    Article  Google Scholar 

  • Kimura M (1969) The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations. Genetics 61:893–903

    CAS  PubMed  PubMed Central  Google Scholar 

  • Kingman JFC (1982a) The coalescent. Stoch Proc Appl 13:235–248

    Article  Google Scholar 

  • Kingman JFC (1982b) Exchangeability and the evolution of large populations. In: Koch G, Spizzichino F (eds) Exchangeability in probability and statistics. North-Holland, Amsterdam, pp 97–112

    Google Scholar 

  • Kingman JFC (1982c) On the genealogy of large populations. J App Probab 19A:27–43

    Article  Google Scholar 

  • Kingman J (2000) Origins of the coalescent: 1974–1982. Genetics 156:1461–1463

    CAS  PubMed  PubMed Central  Google Scholar 

  • Koskela J, Jenkins P, Spanò D (2015) Computational inference beyond Kingman’s coalescent. J Appl Probab 52:519–537

    Article  Google Scholar 

  • Kreitman M (1983) Nucleotide polymorphism at the alcohol dehydrogenase locus of Drosophila melanogaster. Nature 304:412–417

    Article  CAS  PubMed  Google Scholar 

  • Krone SM, Neuhauser C (1997) Ancestral processes with selection. Theor Popul Biol 51:210–237

    Article  PubMed  Google Scholar 

  • Lewontin R, Hubby J (1966) A molecular approach to the study of genic heterozygosity in natural populations. II. Amount of variation and degree heterozygosity in natural populations of Drosophila pseudoobscura. Genetics 54:595–609

    CAS  PubMed  PubMed Central  Google Scholar 

  • Li H, Durbin R (2011) Inference of human population history from individual whole-genome sequences. Nature 475(7357):493–496. doi:10.1038/nature10231, URL http://dx.doi.org/10.1038/nature10231

    Google Scholar 

  • Li G, Hedgecock D (1998) Genetic heterogeneity, detected by PCR-SSCP, among samples of larval Pacific oysters (Crassostrea gigas) supports the hypothesis of large variance in reproductive success. Can J Fish Aquat Sci 55(4):1025–1033. doi:10.1139/f97-312, URL http://dx.doi.org/10.1139/f97-312

    Google Scholar 

  • Li N, Stephens M (2003) Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data. Genetics 165:2213–2233

    CAS  PubMed  PubMed Central  Google Scholar 

  • Limic V, Sturm A (2006) The spatial Λ-coalescent. Electron J Probab 11:363–393

    Article  Google Scholar 

  • May AW (1967) Fecundity of Atlantic cod. J Fish Res Brd Can 24:1531–1551

    Article  Google Scholar 

  • McManus KF, Kelley JL, Song S, Veeramah KR, Woerner AE, Stevison LS, Ryder OA, Project GAG, Kidd JM, Wall JD, Bustamante CD, Hammer MF (2014) Inference of gorilla demographic and selective history from whole-genome sequence data. Mol Biol Evol 32(3):600–612. doi:10.1093/molbev/msu394, URL http://dx.doi.org/10.1093/molbev/msu394

    Google Scholar 

  • Möhle M (2011) Coalescent processes derived from some compound Poisson population models. Elect Comm Probab 16:567–582

    Article  Google Scholar 

  • Möhle M, Sagitov S (2001) A classification of coalescent processes for haploid exchangeable population models. Ann Probab 29:1547–1562

    Article  Google Scholar 

  • Möhle M, Sagitov S (2003) Coalescent patterns in diploid exchangeable population models. J Math Biol 47:337–352

    Article  PubMed  Google Scholar 

  • Nelson MR, Wegmann D, Ehm MG, Kessner D, Jean PS, Verzilli C, Shen J, Tang Z, Bacanu SA, Fraser D, Warren L, Aponte J, Zawistowski M, Liu X, Zhang H, Zhang Y, Li J, Li Y, Li L, Woollard P, Topp S, Hall MD, Nangle K, Wang J, Abecasis G, Cardon LR, Zollner S, Whittaker JC, Chissoe SL, Novembre J, Mooser V (2012) An abundance of rare functional variants in 202 drug target genes sequenced in 14,002 people. Science 337(6090):100–104. doi:10.1126/science.1217876, URL http://dx.doi.org/10.1126/science.1217876

    Google Scholar 

  • Neuhauser C, Krone SM (1997) The genealogy of samples in models with selection. Genetics 145:519–534

    CAS  PubMed  PubMed Central  Google Scholar 

  • Oosthuizen E, Daan N (1974) Egg fecundity and maturity of North Sea cod, Gadus morhua. Neth J Sea Res 8(4):378–397

    Article  Google Scholar 

  • Pitman J (1999) Coalescents with multiple collisions. Ann Probab 27:1870–1902

    Article  Google Scholar 

  • Polanski A, Kimmel M (2003) New explicit expressions for relative frequencies of single-nucleotide polymorphisms with application to statistical inference on population growth. Genetics 165:427–436

    CAS  PubMed  PubMed Central  Google Scholar 

  • Sagitov S (1999) The general coalescent with asynchronous mergers of ancestral lines. J Appl Probab 36:1116–1125

    Article  Google Scholar 

  • Sagitov S (2003) Convergence to the coalescent with simultaneous mergers. J Appl Probab 40:839–854

    Article  Google Scholar 

  • Sargsyan O, Wakeley J (2008) A coalescent process with simultaneous multiple mergers for approximating the gene genealogies of many marine organisms. Theor Pop Biol 74:104–114

    Article  Google Scholar 

  • Schweinsberg J (2000) Coalescents with simultaneous multiple collisions. Electron J Probab 5:1–50

    Article  Google Scholar 

  • Schweinsberg J (2003) Coalescent processes obtained from supercritical Galton-Watson processes. Stoch Proc Appl 106:107–139

    Article  Google Scholar 

  • Spence JP, Kamm JA, Song YS (2016) The site frequency spectrum for general coalescents. Genetics 202(4):1549–1561. doi:10.1534/genetics.115.184101, URL http://www.genetics.org/content/202/4/1549, http://www.genetics.org/content/202/4/1549.full.pdf

    Google Scholar 

  • Stephens M, Donnelly P (2000) Inference in molecular population genetics. J R Stat Soc Ser B Stat Methodol 62:605–655

    Article  Google Scholar 

  • Tajima F (1983) Evolutionary relationships of DNA sequences in finite populations. Genetics 105:437–460

    CAS  PubMed  PubMed Central  Google Scholar 

  • Taylor J, Véber A (2009) Coalescent processes in subdivided populations subject to recurrent mass extinctions. Electron J Probab 14:242–288

    Article  Google Scholar 

  • Tellier A, Lemaire C (2014) Coalescence 2.0: a multiple branching of recent theoretical developments and their applications. Mol Ecol 23:2637–2652

    Article  PubMed  Google Scholar 

  • Wakeley J (2007) Coalescent theory. Roberts & Co

    Google Scholar 

  • Wakeley J, Takahashi T (2003) Gene genealogies when the sample size exceeds the effective size of the population. Mol Biol Evol 20:208–2013

    Article  CAS  PubMed  Google Scholar 

  • Wakeley J, King L, Low BS, Ramachandran S (2012) Gene genealogies within a fixed pedigree, and the robustness of Kingman’s coalescent. Genetics 190(4):1433–1445

    Article  PubMed  PubMed Central  Google Scholar 

  • Watterson GA (1975) On the number of segregating sites in genetical models without recombination. Theor Pop Biol 7:256–276

    Article  CAS  Google Scholar 

  • Zhao S, Zheng P, Dong S, Zhan X, Wu Q, Guo X, Hu Y, He W, Zhang S, Fan W, Zhu L, Li D, Zhang X, Chen Q, Zhang H, Zhang Z, Jin X, Zhang J, Yang H, Wang J, Wang J, Wei F (2012) Whole-genome sequencing of giant pandas provides insights into demographic history and local adaptation. Nat Genet 45(1):67–71. doi:10.1038/ng.2494, URL http://dx.doi.org/10.1038/ng.2494

    Google Scholar 

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Acknowledgements

I thank Einar Árnason for helpful comments. The financial support of the DFG Priority Programme SPP1590 ‘Probabilistic Structures in Evolution’ through grant BL 1105/3-1 to Jochen Blath at TU Berlin, and Matthias Birkner at JGU Mainz, is acknowledged. As is the support of the DFG Priority Programme SPP 1819 ‘Rapid Evolutionary Adaptation’ through DFG grant STE 325/17-1 to Wolfgang Stephan. The generous hospitality of TU Berlin is warmly acknowledged.

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  1. Museum Fuer Naturkunde, Leibniz Institut Fuer Evolutions- Und Biodiversitaetsforschung, Berlin, Germany

    Bjarki Eldon

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  1. CNRS, Laboratoire Evolution Biologique et Modélisation, Université d’Aix-Marseille, Marseille, France

    Pierre Pontarotti

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Eldon, B. (2016). Inference Methods for Multiple Merger Coalescents. In: Pontarotti, P. (eds) Evolutionary Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-41324-2_20

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