BACKGROUND Rare long distance dispersal events impact the demography and the genetic structure of populations. When dispersal is modelled via a dispersal kernel, one possible characterisation of long-distance dispersal is given by the shape of the tail of the kernel, i.e. its type of decay. This characteristic is known to directly act on the speed and pattern of colonization, and on the spatial structure of genetic diversity during colonization. In particular, colonization waves behave differently depending on whether the kernel decreases faster or slower than an exponential (i.e. is thin-tailed vs. fat-tailed). To interpret and extend published results on the impact of long-distance dispersal on the genetic structure of populations, we examine a classification of dispersal kernels based on the shape of their tails and formally demonstrate qualitative differences among them that can influence the predicted diversity of a propagule pool sampled far from two distinct sources. RESULTS We show that a fat-tailed kernel leads asymptotically to a diverse propagule pool containing a balanced mixing of the propagules from the two sources, whereas a thin-tailed kernel results in all propagules originating from the closest source. We further show that these results hold for biologically relevant distances under certain circumstances, and in particular if the number of propagules is large enough, as would be the case for pollen or seeds. CONCLUSION To understand the impact of long-distance dispersal on the structure and dynamics of a metapopulation, it might be less important to precisely estimate an average dispersal distance than to determine if the tail of the dispersal kernel is fatter or thinner than that of an exponential function. Depending solely on this characteristic, a metapopulation will behave similarly to an island model with a diverse immigrant pool or to a stepping-stone model with migrants from closest populations. Our results further help to understand why thin-tailed dispersal kernels lead to a colonization wave of constant speed, whereas fat-tailed dispersal kernels lead to a wave of increasing speed. Our results also suggest that the diversity of the pollen cloud of a mother plant should increase with increasing isolation for fat-tailed kernels, whereas it should decrease for thin-tailed kernels.

中文翻译：

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来自离散源的繁殖体在远距离处的混合：比较分散尾部和指数尾部。

背景技术罕见的长距离传播事件影响人口统计学和种群的遗传结构。通过弥散核对弥散进行建模时，长距离弥散的一种可能的表征是核仁尾部的形状，即衰变的类型。已知该特征直接影响定殖的速度和模式，以及定殖期间遗传多样性的空间结构。特别是，定植波的行为会有所不同，具体取决于内核的下降速度是快于还是慢于指数下降（即，细尾与胖尾）。为了解释和扩展关于长距离扩散对种群遗传结构影响的已发表结果，我们根据它们的尾巴形状检查了分散核的分类，并正式证明了它们之间的质性差异可能会影响远离两个不同来源的繁殖池的预测多样性。结果我们显示，一个肥尾的谷粒渐近地导致一个多样化的繁殖体池，其中包含两种来源的繁殖体的平衡混合，而细尾的仁导致所有繁殖体都来自最接近的繁殖体。我们进一步表明，在某些情况下，特别是如果繁殖体的数量足够大时（与花粉或种子一样），这些结果适用于生物学上相关的距离。结论要了解远程分散对一个种群的结构和动力学的影响，精确估计平均分散距离比确定分散核的尾部比指数函数的尾部更胖或更细，可能没有那么重要。仅根据此特征，人口迁移的行为将类似于具有多样化移民池的岛屿模型，或具有来自最近人口的移民的垫脚石模型。我们的结果进一步有助于理解为什么细尾弥散的果粒会导致恒速的定居浪潮，而胖尾弥散的果仁会导致速增的浪潮。我们的结果还表明，对于胖尾仁，母本植物花粉云的多样性应随隔离度的增加而增加，而对于细尾仁则应降低。