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Short-read sequencing technologies have in principle made it feasible to draw detailed inferences about the recent history of any organism. In practice, however, this remains challenging due to the difficulty of genome assembly in most organisms and the lack of statistical methods powerful enough to discriminate among recent, non-equilibrium histories. We address both the assembly and inference challenges. We develop a bioinformatic pipeline for generating outgroup-rooted alignments of orthologous sequence blocks from de novo low-coverage short-read data for a small number of genomes, and show how such sequence blocks can be used to fit explicit models of population divergence and admixture in a likelihood framework. To illustrate our approach, we reconstruct the Pleistocene history of an oak-feeding insect (the oak gallwasp Biorhiza pallida) which, in common with many other taxa, was restricted during Pleistocene ice ages to a longitudinal series of southern refugia spanning theWestern Palaearctic. Our analysis of sequence blocks sampled from a single genome from each of three major glacial refugia reveals support for an unexpected history dominated by recent admixture. Despite the fact that 80% of the genome is affected by admixture during the last glacial cycle, we are able to infer the deeper divergence history of these populations. These inferences are robust to variation in block length, mutation model, and the sampling location of individual genomes within refugia. This combination of de novo assembly and numerical likelihood calculation provides a powerful framework for estimating recent population history that can be applied to any organism without the need for prior genetic resources. This article is protected by copyright. All rights reserved.