Amplicon-sequence data from environmental DNA (eDNA) and microbiome studies provide important information for ecology, conservation, management, and health. At present, amplicon-sequencing studies-known also as metabarcoding studies, in which the primary data consist of targeted, amplified fragments of DNA sequenced from many taxa in a mixture-struggle to link genetic observations to the underlying biology in a quantitative way, but many applications require quantitative information about the taxa or systems under scrutiny. As metabarcoding studies proliferate in ecology, it becomes more important to develop ways to make them quantitative to ensure that their conclusions are adequately supported. Here we link previously disparate sets of techniques for making such data quantitative, showing that the underlying polymerase chain reaction mechanism explains the observed patterns of amplicon data in a general way. By modeling the process through which amplicon-sequence data arise, rather than transforming the data post hoc, we show how to estimate the starting DNA proportions from a mixture of many taxa. We illustrate how to calibrate the model using mock communities and apply the approach to simulated data and a series of empirical examples. Our approach opens the door to improve the use of metabarcoding data in a wide range of applications in ecology, public health, and related fields.