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Modeling First Arrival of Migratory Birds Using a Hierarchical Max-Infinitely Divisible Process

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Abstract

Humans have recorded the arrival dates of migratory birds for millennia, searching for trends and patterns. As the first arrival among individuals in a species is the realized tail of the probability distribution of arrivals, the appropriate statistical framework with which to analyze such events is extreme value theory. Here, for the first time, we apply formal extreme value techniques to the dynamics of bird migrations. We study the annual first arrivals of Magnolia Warblers using modern tools from the statistical field of extreme value analysis. Using observations from the eBird database, we model the spatial distribution of observed Magnolia Warbler arrivals as a max-infinitely divisible process, which allows us to spatially interpolate observed annual arrivals in a probabilistically coherent way and to project arrival dynamics into the future by conditioning on climatic variables. Supplementary materials accompanying this paper appear online.

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Acknowledgements

We acknowledge input by Dr. Viviana Ruiz Gutierrez and Dr. Daniel Fink of the Cornell Lab of Ornithology. We would also like to thank the two anonymous referees for their helpful comments and suggestions. The authors gratefully acknowledge support from the US National Science Foundation under NSF DMS-2001433, NSF DMS-2308680, and NSF DMS-2015273. Computations for this research were performed on the Pennsylvania State University’s Institute for CyberScience Advanced CyberInfrastructure (ICS-ACI). This content is solely the responsibility of the authors and does not necessarily represent the views of the Institute for CyberScience. This work has no connection to Microsoft Corporation and was conducted by D.A.W. during her doctoral studies, prior to joining Microsoft Corporation.

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Authors and Affiliations

  1. Microsoft Corporation, 1 Microsoft Way, Redmond, WA, 98052, USA

    Dhanushi A. Wijeyakulasuriya

  2. Department of Statistics, Pennsylvania State University, University Park, PA, 16802, USA

    Ephraim M. Hanks

  3. Department of Statistics, Colorado State University, Fort Collins, CO, 80523, USA

    Benjamin A. Shaby

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  1. Dhanushi A. Wijeyakulasuriya
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  2. Ephraim M. Hanks
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  3. Benjamin A. Shaby
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Correspondence to Benjamin A. Shaby.

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Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary Material:

Additional plots, model diagnostics, etc. (2.42 MB)

R-package stablemixEco for fitting the model:

A modified version of the package stablemix. To improve mixing, we have changed the way the spatially-varying fields are updated (see the Supplementary Materials for details). (2.65 MB)

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Wijeyakulasuriya, D.A., Hanks, E.M. & Shaby, B.A. Modeling First Arrival of Migratory Birds Using a Hierarchical Max-Infinitely Divisible Process. JABES (2024). https://doi.org/10.1007/s13253-024-00624-y

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  • DOI: https://doi.org/10.1007/s13253-024-00624-y

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