1AbstractWe propose a new method that is able to accurately infer major haplotypes and their frequencies just from multiple samples of allele frequency data. Our approach seems to be the first that is able to estimate more than one haplotype given such data. Even the accuracy of experimentally obtained allele frequencies can be improved by re-estimating them from our reconstructed haplotypes.Reconstructing haplotypes from sequencing data is of interest to several areas of biological and medical research. In evolutionary genetics, for instance, haplotypes help to better understand the genetic architecture of adaptation. Here we consider genomic time series data from three evolve and re-sequence experiments as an application. However, the approach can in principle be used in a wider context, as only data from multiple samples are needed, not necessarily collected over time.