Long-distance dispersal (LDD) has long been recognized as a key factor in determining rates of spread in biological invasions. Two approaches for incorporating LDD in mathematical models of spread are mixed dispersal and heavy-tailed dispersal. In this paper, I analyze integrodifference equation (IDE) models with mixed-dispersal kernels and fat-tailed (a subset of the heavy-tailed class) dispersal kernels to study how short- and long-distance dispersal contribute to the spread of invasive species. I show that both approaches can lead to biphasic range expansions, where an invasion has two distinct phases of spread. In the initial phase of spread, the invasion is controlled by short-distance dispersal. Long-distance dispersal boosts the speed of spread during the ultimate phase, and can have significant effects even when the probability of LDD is vanishingly small. For fat-tailed kernels, I introduce a method of characterizing the “shoulder” of a dispersal kernel, which separates the peak and tail.

长期以来，长距离扩散（LDD）是确定生物入侵扩散速率的关键因素。将LDD纳入扩散模型的两种方法是混合扩散法和重尾扩散法。在本文中，我分析了具有混合扩散核和肥尾（重尾类的子集）扩散核的积分差异方程（IDE）模型，以研究短距离和长距离扩散如何促进入侵物种的扩散。我证明了这两种方法都可以导致双相射程扩展，在这种情况下，入侵具有两个不同的扩散阶段。在扩散的初始阶段，入侵是由短距离扩散控制的。远程分散可以提高最终阶段的传播速度，即使LDD的可能性极小，也可能产生重大影响。对于胖尾仁，我介绍了一种表征分散仁“肩”的方法，该方法将峰和尾分开。