Previous work constructed Fleming–Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval
[
0
,
1
]
[0,1]
) that are stationary with respect to the Poisson–Dirichlet random measures with parameters
α
∈
(
0
,
1
)
\alpha \in (0,1)
and
θ
>
−
α
\theta > -\alpha
. In this paper, we complete the proof that these processes resolve a conjecture by Feng and Sun [Probab. Theory Related Fields 148 (2010), pp. 501–525] by showing that the processes of ranked atom sizes (or of ranked interval lengths) of these diffusions are members of a two-parameter family of diffusions introduced by Petrov [Funct. Anal. Appl. 43 (2009), pp. 279–296], extending a model by Ethier and Kurtz [Adv. in Appl. Probab. 13 (1981), pp. 429–452] in the case
α
=
0
\alpha =0
.