  In 1990, Bertoin constructed a measure-valued Markov process in the framework
of a Bessel process of dimension between 0 and 1. In the present paper, we
represent this process in a space of interval partitions. We show that this is
a member of a class of interval partition diffusions introduced recently and
independently by Forman, Pal, Rizzolo and Winkel using a completely different
construction from spectrally positive stable L\'evy processes with index
between 1 and 2 and with jumps marked by squared Bessel excursions of a
corresponding dimension between $-2$ and 0.
