Dispersal is a fundamental biological process that results in the redistribution of organisms due to the interplay between the mode of dispersal, the range of scales over which movement occurs, and the scale of spatial heterogeneity, in which patchiness may occur across a broad range of scales. Despite the diversity of dispersal mechanisms and dispersal length scales in nature, we posit that a fundamental scaling relationship should exist between dispersal and spatial heterogeneity. We present both a conceptual model and mathematical formalization of this expected relationship between the scale of dispersal and the scale of patchiness, which predicts that the magnitude of dispersal (number of individuals) among patches should be maximized when the scale of spatial heterogeneity (defined in terms of patch size and isolation) is neither too fine nor too coarse relative to the gap-crossing abilities of a species. We call this the “dispersal scaling hypothesis” (DSH). We demonstrate congruence in the functional form of this relationship under fundamentally different dispersal assumptions, using well-documented isotropic dispersal kernels and empirically derived dispersal parameters from diverse species, in order to explore the generality of this finding. The DSH generates testable hypotheses as to when and under what landscape scenarios dispersal is most likely to be successful. This provides insights into what management scenarios might be necessary to either restore landscape connectivity, as in certain conservation applications, or disrupt connectivity, as when attempting to manage landscapes to impede the spread of an invasive species, pest, or pathogen.

中文翻译：

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为什么应在中间度的异质性最大化分散。

分散是一种基本的生物学过程，由于分散的模式，运动发生的尺度范围和空间异质性尺度（可能在广泛的尺度范围内发生斑块）之间的相互作用而导致生物体的重新分布。尽管自然界中散布机制和散布长度尺度的多样性，我们认为散布和空间异质性之间应该存在基本的标度关系。我们给出了分散规模和斑块规模之间这种预期关系的概念模型和数学形式化，它预测，当空间异质性的规模（根据斑块的大小和隔离度来定义）相对于物种的穿越能力而言既不细也不粗时，应当最大化斑块之间的散布量（个体数） 。我们称其为“离散缩放假设”（DSH）。为了证明这一发现的普遍性，我们使用了有据可查的各向同性分散核和根据经验从不同物种得出的分散参数，在根本不同的分散假设下，证明了这种关系的函数形式的一致性。DSH产生了关于何时以及在何种情况下进行景观扩散最有可能成功的可检验的假设。