General selection models: Bernstein duality and minimal ancestral structures

Cordero F, Hummel S, Schertzer E (2022)
Annals of Applied Probability 32(3): 1499-1556.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Lambda-Wright-Fisher processes provide a robust framework to describe the type-frequency evolution of an infinite neutral population. We add a polynomial drift to the corresponding stochastic differential equation to incorporate frequency-dependent selection. A decomposition of the drift allows us to approximate the solution of the stochastic differential equation by a sequence of Moran models. The genealogical structure underlying the Moran model leads in the large population limit to a generalisation of the ancestral selection graph of Krone and Neuhauser. Building on this object, we construct a continuous-time Markov chain and relate it to the forward process via a new form of duality, which we call Bernstein duality. We adapt classical methods based on the moment duality to determine the time to absorption and criteria for the accessibility of the boundaries; this extends a recent result by Gonzalez Casanova and Spano. An intriguing feature of the construction is that the same forward process is compatible with multiple backward models. In this context we introduce suitable notions for minimality among the ancestral processes and characterise the corresponding parameter sets. In this way we recover classic ancestral structures as minimal ones.
Stichworte
Lambda-Wright-Fisher process; duality; frequency-dependent selection; branching-coalescing system; ancestral selection graph; absorption; probability; coming down from infinity
Erscheinungsjahr
2022
Zeitschriftentitel
Annals of Applied Probability
Band
32
Ausgabe
3
Seite(n)
1499-1556
ISSN
1050-5164
Page URI
https://pub.uni-bielefeld.de/record/2964053

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Cordero F, Hummel S, Schertzer E. General selection models: Bernstein duality and minimal ancestral structures. Annals of Applied Probability. 2022;32(3):1499-1556.
Cordero, F., Hummel, S., & Schertzer, E. (2022). General selection models: Bernstein duality and minimal ancestral structures. Annals of Applied Probability, 32(3), 1499-1556. https://doi.org/10.1214/21-AAP1683
Cordero, F., Hummel, S., and Schertzer, E. (2022). General selection models: Bernstein duality and minimal ancestral structures. Annals of Applied Probability 32, 1499-1556.
Cordero, F., Hummel, S., & Schertzer, E., 2022. General selection models: Bernstein duality and minimal ancestral structures. Annals of Applied Probability, 32(3), p 1499-1556.
F. Cordero, S. Hummel, and E. Schertzer, “General selection models: Bernstein duality and minimal ancestral structures”, Annals of Applied Probability, vol. 32, 2022, pp. 1499-1556.
Cordero, F., Hummel, S., Schertzer, E.: General selection models: Bernstein duality and minimal ancestral structures. Annals of Applied Probability. 32, 1499-1556 (2022).
Cordero, Fernando, Hummel, Sebastian, and Schertzer, Emmanuel. “General selection models: Bernstein duality and minimal ancestral structures”. Annals of Applied Probability 32.3 (2022): 1499-1556.

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