  For neutral genealogy models in a finite, possibly non-constant population,
there is a convenient representation of the family trees, known as the lookdown
representation, that arranges descendant subtrees in size-biased order. We give
a simple, conceptual demonstration of the size-biasing property, and address
the problem of identifiability: under what conditions can we infer some or all
of the lookdown arrangement by examining the (unlabelled) descendant subtrees?
We explain how this question is connected to two important properties of the
graph: uniqueness of the infinite path, and existence of a dominant lineage,
and give sufficient and sometimes necessary conditions for each. We also
discuss connections to the spinal representation of size-biased Galton-Watson
trees.
