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.传播生态学是当前的热点研究学科，旨在理解并预测植物群落对全球变化多重驱动因子的响应。涉及长距离传播（long-distance dispersal, LDD）事件的繁殖体移动，对于植物能够抵达并定植于破碎化景观中的适宜生境至关重要。然而，LDD事件发生频率极低，因此，准确估算繁殖体的最大传播距离及其发生频率，长期以来都是植物生态学领域的一大难题。 近期传播生态学领域已取得进展，能够获取可靠的传播距离观测数据，但此类数据仍仅局限于研究种群范围内，这限制了我们对景观尺度下LDD事件发生频率与实际传播范围的推断能力。 本研究将LDD事件视为传播函数的极值，并运用极值统计（statistics of extremes）方法推导模拟数据集与实测数据集的LDD事件发生频率与传播范围。我们首先简要阐释极值统计的理论依据，随后从概念与分析层面说明，应用极值分析能够为传播生态学研究带来助益。我们对模拟种子扩散格局应用块极大值法，并对包含某种群马哈利樱桃（Prunus mahaleb）的花粉与种子传播距离的实测数据集应用阈值超额法；该树种为虫媒授粉、脊椎动物传播的乔木物种。 诊断图显示，花粉传播的距离阈值υ=80米，种子传播的距离阈值υ=170米。超出阈值的花粉传播距离符合轻尾分布函数，而种子传播距离则符合重尾帕累托分布。两种分布函数均估算出，植物抵达远超研究种群边界的远距离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。 综合分析。传播生态学家可通过应用极值统计方法，充分利用已有的传播距离观测数据，推算出那些发生概率极低但至关重要的、能够抵达研究种群边界之外的长距离传播事件的发生概率。