  A continuous-state branching process in varying environments is constructed
by the pathwise unique solution to a stochastic integral equation driven by
time-space noises. The process arises naturally in the limit theorem of
Galton--Watson processes in varying environments established by Bansaye and
Simatos (2015). In terms of the stochastic equation we clarify the behavior of
the continuous-state process at its bottlenecks, which are the times when it
arrives at zero almost surely by negative jumps.
