Estimating extreme displacements under a Lomax generalized linear model framework: the role of sample size and threshold choice

Understanding ecological variation is fundamental to predicting the dynamics of natural systems, and it becomes increasingly more complex when rare or extreme events are involved. Extreme value statistics are a useful but underutilized tool in ecological analysis, and in this paper we showcase a simulation based study that uses extreme value distributions to estimate rare events. Focused on long-distance dispersal events, we simulate individual variation in seed dispersal events within heterogeneous populations by using finite mixture models. We employ three different approaches to model fitting extreme value distributions, and we particularly incorporate the special case of a Lomax distribution. Using a modified generalized extreme value distribution and comparing to a peak over threshold model fitting approach, we assess which models are able to capture the true underlying parameters. Additionally, we used a well-known linear bootstrap bias-corrrection and evaluate its utility to correct the bias in the estimation. Our results show that threshold models are the best at capturing the true underlying probability of long-distance dispersal models, and that the bias correction is somewhat useful, depending on the sample size. Estimating rare events in ecology is an important and statistically challenging process and in this study we provide a simple probabilistic approach to doing so.