Abstract: A stick-breaking construction of the (two-parameter) Poisson-Dirichlet random measure yields the masses arranged in the size-biased order. Another order, which may be called `regenerative', appears when the masses are associated with jumps of a transformed increasing Levy process. For Ewens' subfamily these orders coincide, but in general the relation is more delicate. In this talk we show how the orders can be constructively linked to one another by means of a parametric family of infinite random permutations. A similar problem is also discussed in terms of integer partitions induced by drawing a finite sample from the Poisson-Dirichlet distribution.