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Multiple haplotype reconstruction from allele frequency data

A preprint version of the article is available at bioRxiv.


Because haplotype information is of widespread interest in biomedical applications, effort has been put into their reconstruction. Here, we propose an efficient method, called haploSep, that is able to accurately infer major haplotypes and their frequencies just from multiple samples of allele frequency data. Even the accuracy of experimentally obtained allele frequencies can be improved by re-estimating them from our reconstructed haplotypes. From a methodological point of view, we model our problem as a multivariate regression problem where both the design matrix and the coefficient matrix are unknown. Compared to other methods, haploSep is very fast, with linear computational complexity in the haplotype length. We illustrate our method on simulated and real data focusing on experimental evolution and microbial data.

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Fig. 1: Reconstruction results for three typical experimental evolution experiments.
Fig. 2: Simulation results on haplotype reconstruction errors.
Fig. 3: Improved allele frequency reconstruction using estimated haplotypes.
Fig. 4: Haplotype reconstruction from experimental data of ref. 11.
Fig. 5: Method comparison between haploSep, CliqueSNV and TenSQR.

Data availability

In the ‘Drosophila simulans’ section, we used published data11,58. We obtained allele frequency data and sequences of founder haplotypes from the authors (N. Barghi and C. Schlötterer). In the ‘Longshanks experiment in mice’ section, we used time-series data from the experiment described by Castro et al.40 (only partially published so far). We obtained the allele frequency data for the considered region from the authors (F. Chan, L. Hiramatsu and N. Barton). In the ‘Caenorhabditis elegans’ section, we used published data from Noble and others39. The raw data are available from NCBI SRA under BioProject PRJNA381203. We obtained allele frequency data and genotypes from the authors (L. Noble and H. Teotónio). In the ‘HIV’ section, we used published data from Zanini and others21. The data are available at Source data are provided with this paper.

Code availability

All our code is written in R. Our software, simulation functions and examples are available from Our code is also available in our Code Ocean repository59, where we also provide code to generate Figs. 1–5.


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We are grateful to the laboratories of N. Barton, C. Schlötterer and H. Teotonio for providing us with their experimental data. We also thank Q. Long, L. Mak and C. Cao for helping us with using PoolHapX. M.P. and A.F. acknowledge support of the Austrian Science Fund (FWF; DK W1225-B20). M.B. was supported by the Deutsche Forschungsgemeinschaft (DFG; German Research Foundation) Postdoctoral Fellowship BE 6805/1-1. M.B. acknowledges funding via DFG-GRK 2088. This work benefited from a research stay that was partially supported by the Simons Foundation and by Mathematisches Forschungsinstitut Oberwolfach. A.M. and M.B. acknowledge support via DFG-SFB 803 Z02. H.L. is funded and A.M. is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC 2067/1-390729940.

Author information




A.F. and A.M. conceived the project. M.P., M.B., H.L. and A.F. contributed to the design of the research and wrote the manuscript. M.P., M.B. and H.L. wrote the code for software, simulations and data analysis. All authors read and approved the manuscript.

Corresponding author

Correspondence to Andreas Futschik.

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The authors declare no competing interests.

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Peer review information Nature Computational Science thanks the anonymous reviewers for their contribution to the peer review of this work. Fernando Chirigati was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

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Pelizzola, M., Behr, M., Li, H. et al. Multiple haplotype reconstruction from allele frequency data. Nat Comput Sci 1, 262–271 (2021).

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