  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.
