We construct a multitype constant-size population model allowing 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.

中文翻译：

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关于具有一般频率相关选择的 Λ-Fleming-Viot 过程

我们构建了一个多类型恒定大小的种群模型，允许一般的选择性相互作用以及极端的生殖事件。我们的多维模型旨在适应动态的普遍性和群体遗传学的易处理性。它概括了 Krone 和 Neuhauser [39] 以及 González Casanova 和 Spanò [29] 的想法，他们通过允许个人在选择“最强”父母之前对上一代的几个潜在父母进行抽样来代表选择，允许个人使用任何规则来选择他们的父母。新生儿的类型甚至不能是潜在父母的类型之一，这允许对突变进行建模。通过大的人口限制，我们得到了一个概括$\Lambda$-Fleming-Viot 过程，具有扩散项和一般的频率相关选择，允许群体中存在的不同类型之间的非传递交互。我们提供了这些过程与消光和固定事件相关的一些性质，并给出了将它们实现为具有跳跃的多维随机微分方程的唯一强解的条件。最后，我们通过对一些经典生物相互作用的应用来说明我们模型的普遍性。该框架在两个最突出的生物进化建模框架之间提供了天然的桥梁：种群遗传学和生态进化模型。