Animals disperse in space through different movement behaviors, resulting in different displacement distances. This is often described with a displacement kernel where the long-distance dispersers are within the tail of the kernel. A displacement with a large proportion of long-distance dispersers may have impact on different aspects of spatial ecology such as invasion speed, population persistence, and distribution. It is, however, unclear whether the kurtosis of the kernel plays a major role since a fatter tail also influences the variance of the kernel. We modeled displacement in landscapes with different amounts and configurations of habitats and handled kurtosis and variance separately to study how these affected population distribution and transition time. We conclude that kurtosis is not important for any of these aspects of spatial ecology. The variance of the kernel, on the other hand, was of great importance to both population distribution and transition time. We argue that separating variance and kurtosis can cast new light on the way in which long-distance dispersers are important in ecological processes. Consequences for empirical studies are discussed.