The effective population size (Ne) is an important parameter in population genetics and evolutionary biology telling us about the expected amount of variability due to genetic drift. Although several methods have been developed, this parameter is known to be often difficult to estimate. In particular, appropriate estimators have not been available for experimental evolution experiments producing pool sequencing data. Therefore we propose a new estimator that relies on allele frequency changes in temporal data. Our approach corrects both for the variance due to sampling individuals and the random sampling of reads out of the DNA pool during sequencing. In our simulations, we obtained accurate estimates, as long as the drift variance is not too small compared to the sampling and sequencing variance. We also extend our method using a recursive partitioning approach to estimate Ne locally along a chromosome. Since type I error control is available, our method permits the identification of genomic regions that differ significantly in their effective population size. We present an application to Pool-Seq data from experimental evolution with Drosophila melanogaster and give recommendations for using our approach on whole-genome data. The estimator is computationally fast and available as an R-package at https://github.com/ThomasTaus/Nest .