Centroid-AME: An open-source software for estimating avian migration trajectories using population centroids movement in the annual cycle

Migration is a critical aspect of many birds' annual life cycles, with up to 40 % of bird species engaging in migratory behavior. However, understanding the migration dynamics, particularly in small birds, presents challenges due to both financial and physical constraints. The growth of citizen science observation databases is creating unique opportunities to estimate avian migration trajectories at the population level, across species and without the need for expensive additional data. Centroid-AME is a Python-based tool designed to estimate avian migration trajectories using the spatiotemporal locations of population centroids. In this paper, we propose a general framework for trajectory estimation, and explore the practicality of Centroid-AME as a tool for analyzing observation data at the population level. Our approach consists of three core components: data preprocessing, migration trajectory estimation, and the computation of dynamic indicators within the annual cycle. To address the inherent spatial and temporal biases of observations, the preprocessing steps include the interpolation of missing values, the application of sliding window, and the detection of outliers, which will address gaps and errors. We apply an unsupervised Mean-Shift clustering algorithm to extract dense clusters of observations and identify subgroups of the species population. The centroids are then grouped using a shortest path with the lowest cost and migration trajectories are estimated by fitting them respectively. Finally, we compute three key metrics to assess population-level migration dynamics: migration speed, migration offset distance, and population centroids distribution. The information provided by these metrics complements traditional individual-level assessments, enhancing our understanding of the migration process. To verify the feasibility of our estimation framework, we apply it to the observation data of Spragues' pipit ( Anthus spragueii , Audubon) from eBird, and analyze its moving dynamics during the migration cycle as a case study. • Open-source migration trajectory estimation software tool for citizen-science observation data at the population level • General framework for large-scale observations automated batch processing • Discover high-density avian subgroup migration trajectories and patterns in the annual cycle • Capture dynamic characteristics during bird migration process