Fast Radio Bursts (FRBs) are energetic, short, bright transients that occur frequently over the entire radio sky. The observational challenges following from their fleeting, generally one-off nature have prevented identification of the underlying sources producing the bursts. As the population of detected FRBs grows, the observed distributions of brightness, pulse width and dispersion measure now begin to take shape. Meaningful direct interpretation of these distributions is, however, made impossible by the selection effects that telescope and search pipelines invariably imprint on each FRB survey. Here we show that multi-dimensional FRB population synthesis can find a single, self-consistent population of FRB sources that can reproduce the real-life results of the major ongoing FRB surveys. This means that individual observed distributions can now be combined to derive the properties of the intrinsic FRB source population. The characteristics of our best-fit model for one-off FRBs agree with a population of magnetars. We extrapolate this model and predict the number of FRBs future surveys will find. For surveys that have commenced, the method we present here can already determine the composition of the FRB source class, and potentially even its subpopulations.
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