Extended dispersal kernels in a changing world: insights from statistics of extremes

Abstract

Dispersal ecology is a topical discipline that involves understanding and predicting plant community responses to multiple drivers of global change. Propagule movements that entail long-distance dispersal (LDD) events are crucial for plants to reach and colonize suitable sites across fragmented landscapes. Yet, LDD events are extremely rare, and thus, obtaining reliable estimates of the maximum distances that propagules move across and of their frequency has been a long-lasting challenge in plant ecology. Recent advances in dispersal ecology have provided reliable records of dispersal distances, but they remain confined to focal populations, limiting our ability to infer the frequency and actual extent of LDD events across landscapes. In this study, we view LDD events as extreme values of a dispersal function, and we apply statistics of extremes to derive the frequency and extent of LDD events of simulated and empirical data sets. We first briefly explain the rationale behind statistics of extremes, and we then illustrate how dispersal ecology can benefit conceptually and analytically from applying extreme value analyses. We apply the block maxima approach to simulated seed shadows, and we apply the peak over a threshold method to empirical data sets that contain pollen and seed dispersal distances recorded for a population of Prunus mahaleb, an insect-pollinated and vertebrate-dispersed tree species. Diagnostic plots reveal a distance threshold of υ = 80 m for pollen grains and of υ = 170 m for dispersed seeds. Values that exceed the threshold fit a light-tailed distribution function for pollen and fit a fat-tailed Pareto distribution for seed dispersal distances. Both distribution functions estimate a low (but nonzero) conditional probability of reaching distant locations, extending well beyond the borders of our focal population as follows: Pr (X ≥ 1 km) = 9 × 10−5 for pollen grains and Pr (X ≥ 10 km) = 7 × 10−5 for dispersed seeds. Synthesis. Dispersal ecologists can take the most of their dispersal distance records by applying statistics of extremes to infer the probability of occurrence of extremely rare, but crucial, long distance dispersal events that reach locations well beyond focal populations.