Works matching IS 00219002 AND DT 2020 AND VI 57 AND IP 4

Results: 19
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    Synchronized Lévy queues.

    Published in:
    Journal of Applied Probability, 2020, v. 57, n. 4, p. 1222, doi. 10.1017/jpr.2020.75
    By:
    • Kella, Offer;
    • Boxma, Onno
    Publication type:
    Article
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    Zipf's law for atlas models.

    Published in:
    Journal of Applied Probability, 2020, v. 57, n. 4, p. 1276, doi. 10.1017/jpr.2020.64
    By:
    • Fernholz, Ricardo T.;
    • Fernholz, Robert
    Publication type:
    Article
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    On Λ-Fleming–Viot processes with general frequency-dependent selection for general selective interactions as well as extreme reproductive events. Our multidimensional model aims for the generality of adaptive dynamics and the tractability of population genetics. It generalises the idea of Krone and Neuhauser [39] and González Casanova and Spanò [29], who represented the selection by allowing individuals to sample several potential parents in the previous generation before choosing the 'strongest' one, by allowing individuals to use any rule to choose their parent. The type of the newborn can even not be one of the types of the potential parents, which allows modelling mutations. Via a large population limit, we obtain a generalisation of $\Lambda$ -Fleming–Viot processes, with a diffusion term and a general frequency-dependent selection, which allows for non-transitive interactions between the different types present in the population. We provide some properties of these processes related to extinction and fixation events, and give conditions for them to be realised as unique strong solutions of multidimensional stochastic differential equations with jumps. Finally, we illustrate the generality of our model with applications to some classical biological interactions. This framework provides a natural bridge between two of the most prominent modelling frameworks of biological evolution: population genetics and eco-evolutionary models.

    Published in:
    Journal of Applied Probability, 2020, v. 57, n. 4, p. 1162, doi. 10.1017/jpr.2020.55
    By:
    • Gonzalez Casanova, Adrian;
    • Smadi, Charline
    Publication type:
    Article
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    Skeletal stochastic differential equations for superprocesses in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which initiates subcritical superprocesses. The Markov branching process corresponds to the genealogical description of prolific individuals, that is, individuals who produce eternal genealogical lines of descent, and is often referred to as the skeleton or backbone of the original superprocess. The Poissonian dressing along the skeleton may be considered to be the remaining non-prolific genealogical mass in the superprocess. Such skeletal decompositions are equally well understood for continuous-state branching processes (CSBP). In a previous article [16] we developed an SDE approach to study the skeletal representation of CSBPs, which provided a common framework for the skeletal decompositions of supercritical and (sub)critical CSBPs. It also helped us to understand how the skeleton thins down onto one infinite line of descent when conditioning on survival until larger and larger times, and eventually forever. Here our main motivation is to show the robustness of the SDE approach by expanding it to the spatial setting of superprocesses. The current article only considers supercritical superprocesses, leaving the subcritical case open.

    Published in:
    Journal of Applied Probability, 2020, v. 57, n. 4, p. 1111, doi. 10.1017/jpr.2020.53
    By:
    • Fekete, Dorottya;
    • Fontbona, Joaquin;
    • Kyprianou, Andreas E.
    Publication type:
    Article