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### Abstract

We construct extensions of the pure-jump $\Lambda $-Wright–Fisher processes with frequency-dependent selection ($\Lambda $-WF with selection) with different behaviors at their boundary $1$. Those processes satisfy some duality relationships with the block counting process of simple exchangeable fragmentation-coagulation processes (EFC processes). One-to-one correspondences are established between the nature of the boundaries $1$ and $\infty $ of the processes involved. They provide new information on these two classes of processes. Sufficient conditions are provided for boundary $1$ to be an exit boundary or an entrance boundary. When the coalescence measure $\Lambda $ and the selection mechanism verify some regular variation properties, conditions are found in order that the extended $\Lambda $-WF process with selection makes excursions out from the boundary $1$ before getting absorbed at $0$. In this case, $1$ is a transient regular reflecting boundary. This corresponds to a new phenomenon for the deleterious allele, which can be carried by the whole population for a set of times of zero Lebesgue measure, before vanishing in finite time almost surely.

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