Genealogical structures under interactive neutral reproduction: factorial moment duality via a Frankenstein process
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913086089199616 |
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| author | Baake, Ellen Cordero, Fernando Dopmeyer, Hannah |
| author_facet | Baake, Ellen Cordero, Fernando Dopmeyer, Hannah |
| contents | We establish a genealogical framework for an existing analytical moment duality between a Wright--Fisher type SDE and a counting process with interaction. To achieve this, we construct a finite-population Moran model featuring interactive neutral reproduction as a novel mechanism. In the corresponding events, an individual, regardless of its own type, can only reproduce if a randomly encountered partner is of the ``fit'' type. This Moran model has a relatively simple counting process as its factorial moment dual, whose genealogical meaning appears to be cryptic: after all, the line-counting process of the natural genealogical process of the model, namely the ancestral influence graph (AIG), exhibits a complex hierarchical structure not reflected in the factorial moment dual. Since moment duality is a property in expectation, we are allowed to systematically remove information from the AIG and merge different realizations of the ancestry. We call the result the \emph{Frankenstein process}. Based on this, we establish the factorial moment duality from a genealogical perspective. The moment duality in the diffusion limit follows in a natural way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02499 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Genealogical structures under interactive neutral reproduction: factorial moment duality via a Frankenstein process Baake, Ellen Cordero, Fernando Dopmeyer, Hannah Probability Populations and Evolution 60K35, 92D15, 60J25, 60J27, 60J70 We establish a genealogical framework for an existing analytical moment duality between a Wright--Fisher type SDE and a counting process with interaction. To achieve this, we construct a finite-population Moran model featuring interactive neutral reproduction as a novel mechanism. In the corresponding events, an individual, regardless of its own type, can only reproduce if a randomly encountered partner is of the ``fit'' type. This Moran model has a relatively simple counting process as its factorial moment dual, whose genealogical meaning appears to be cryptic: after all, the line-counting process of the natural genealogical process of the model, namely the ancestral influence graph (AIG), exhibits a complex hierarchical structure not reflected in the factorial moment dual. Since moment duality is a property in expectation, we are allowed to systematically remove information from the AIG and merge different realizations of the ancestry. We call the result the \emph{Frankenstein process}. Based on this, we establish the factorial moment duality from a genealogical perspective. The moment duality in the diffusion limit follows in a natural way. |
| title | Genealogical structures under interactive neutral reproduction: factorial moment duality via a Frankenstein process |
| topic | Probability Populations and Evolution 60K35, 92D15, 60J25, 60J27, 60J70 |
| url | https://arxiv.org/abs/2605.02499 |