| Abstract: |
| 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. |
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