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In Aldous and Shields (1988), a model for a rooted, growing random binarytree was presented. For some c>0, an external vertex splits at rate c^(-i) (andbecomes internal) if its distance from the root (depth) is i. For c>1, wereanalyse the tree profile, i.e. the numbers of external vertices in depthi=1,2,.... Our main result are concrete formulas for the expectation andcovariance-structure of the profile. In addition, we present the application ofthe model to cellular ageing. Here, we assume that nodes in depth h+1 aresenescent, i.e. do not split. We obtain a limit result for the proportion ofnon-senescent vertices for large h.

The Aldous-Shields model revisited (with application to cellular ageing)