In this paper we consider a selection-mutation model with an advection term formulated on the space of finite signed measures on $ \mathbb{R}^d $. The selection-mutation kernel is described by a family of measures which allows the study of continuous and discrete kernels under the same setting. We rescale the selection-mutation kernel to obtain a diffusively rescaled selection-mutation model. We prove that if the rescaled selection-mutation kernel converges to a pure selection kernel then the solution of the diffusively rescaled model converges to a solution of an advection-diffusion equation.

中文翻译：

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测度空间上的小变异选择变异方程的扩散极限

在本文中，我们考虑带有对流项的选择变异模型，该对流项是在$ \ mathbb {R} ^ d $的有限符号度量空间上制定的。选择突变核通过一系列测量方法来描述，这些方法允许研究相同设置下的连续和离散核。我们重新缩放选择突变核，以获得扩散重新缩放的选择突变模型。我们证明，如果重新缩放的选择变异核收敛到纯选择核，那么扩散重新缩放的模型的解收敛到对流扩散方程的解。