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

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.

扩散生态学（dispersal ecology）是一门热点学科，其核心在于理解并预测植物群落对全球变化多重驱动因子的响应。涉及长距离扩散（long-distance dispersal, LDD）事件的繁殖体运动，对于植物抵达并定植于破碎化景观中的适宜生境至关重要。然而，LDD事件极为罕见，因此准确估算繁殖体的最大扩散距离及其发生频率，长期以来都是植物生态学领域的一大挑战。近年来扩散生态学领域的进展虽已获得可靠的扩散距离记录，但这些记录仅局限于目标种群（focal population），这限制了我们推断景观尺度下LDD事件的发生频率与实际波及范围的能力。

本研究将LDD事件视为扩散函数的极值，通过极值统计学（statistics of extremes）推导模拟数据集与实测数据集的LDD事件发生频率与波及范围。我们首先简要阐释极值统计学背后的理论逻辑，随后阐明扩散生态学如何从极值分析的概念与分析层面获益。我们将分块极大值法（block maxima approach）应用于模拟种子扩散影区，将超阈值峰值法（peak over a threshold method）应用于包含马哈利樱桃（Prunus mahaleb，一种虫媒传粉、脊椎动物传播种子的树种）种群花粉与种子扩散距离的实测数据集。

诊断图显示，花粉的扩散距离阈值为υ=80米，种子的扩散距离阈值为υ=170米。超出阈值的花粉扩散距离符合轻尾分布函数，而种子扩散距离则符合重尾帕累托分布（Pareto distribution）。两种分布函数均估算出，植物抵达远超目标种群范围的远端生境的条件概率较低（但非零），具体数值如下：花粉的Pr(X≥1km)=9×10^-5，种子的Pr(X≥10km)=7×10^-5。

综合与启示：扩散生态学家可通过应用极值统计学，充分利用已有的扩散距离记录，推断那些极为罕见却至关重要的、能抵达远超目标种群范围生境的长距离扩散事件的发生概率。