IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v359y2017icp311-319.html
   My bibliography  Save this article

Using Optimal Transport Theory to Estimate Transition Probabilities in Metapopulation Dynamics

Author

Listed:
  • Nichols, J.M.
  • Spendelow, J.A.
  • Nichols, J.D.

Abstract

This work considers the estimation of transition probabilities associated with populations moving among multiple spatial locations based on numbers of individuals at each location at two points in time. The problem is generally underdetermined as there exists an extremely large number of ways in which individuals can move from one set of locations to another. A unique solution therefore requires a constraint. The theory of optimal transport provides such a constraint in the form of a cost function, to be minimized in expectation over the space of possible transition matrices. We demonstrate the optimal transport approach on marked bird data and compare to the probabilities obtained via maximum likelihood estimation based on marked individuals. It is shown that by choosing the squared Euclidean distance as the cost, the estimated transition probabilities compare favorably to those obtained via maximum likelihood with marked individuals. Other implications of this cost are discussed, including the ability to accurately interpolate the population's spatial distribution at unobserved points in time and the more general relationship between the cost and minimum transport energy.

Suggested Citation

  • Nichols, J.M. & Spendelow, J.A. & Nichols, J.D., 2017. "Using Optimal Transport Theory to Estimate Transition Probabilities in Metapopulation Dynamics," Ecological Modelling, Elsevier, vol. 359(C), pages 311-319.
    • Handle: RePEc:eee:ecomod:v:359:y:2017:i:c:p:311-319
    DOI: 10.1016/j.ecolmodel.2017.06.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380017303253
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2017.06.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Raimund Kovacevic & Alois Pichler, 2015. "Tree approximation for discrete time stochastic processes: a process distance approach," Annals of Operations Research, Springer, vol. 235(1), pages 395-421, December.
    2. LaRue, Michelle A. & Nielsen, Clayton K., 2008. "Modelling potential dispersal corridors for cougars in midwestern North America using least-cost path methods," Ecological Modelling, Elsevier, vol. 212(3), pages 372-381.
    3. P. Besbeas & J.‐D. Lebreton & B. J. T. Morgan, 2003. "The efficient integration of abundance and demographic data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 95-102, January.
    4. P. Besbeas & S. N. Freeman & B. J. T. Morgan & E. A. Catchpole, 2002. "Integrating Mark–Recapture–Recovery and Census Data to Estimate Animal Abundance and Demographic Parameters," Biometrics, The International Biometric Society, vol. 58(3), pages 540-547, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dennis, Emily B. & Kéry, Marc & Morgan, Byron J.T. & Coray, Armin & Schaub, Michael & Baur, Bruno, 2021. "Integrated modelling of insect population dynamics at two temporal scales," Ecological Modelling, Elsevier, vol. 441(C).
    2. Mosnier, A. & Doniol-Valcroze, T. & Gosselin, J.-F. & Lesage, V. & Measures, L.N. & Hammill, M.O., 2015. "Insights into processes of population decline using an integrated population model: The case of the St. Lawrence Estuary beluga (Delphinapterus leucas)," Ecological Modelling, Elsevier, vol. 314(C), pages 15-31.
    3. Gimenez, Olivier & Rossi, Vivien & Choquet, Rémi & Dehais, Camille & Doris, Blaise & Varella, Hubert & Vila, Jean-Pierre & Pradel, Roger, 2007. "State-space modelling of data on marked individuals," Ecological Modelling, Elsevier, vol. 206(3), pages 431-438.
    4. Besbeas, P.T. & McCrea, R.S. & Morgan, B.J.T., 2022. "Selecting age structure in integrated population models," Ecological Modelling, Elsevier, vol. 473(C).
    5. Panagiotis Besbeas & Byron J. T. Morgan, 2017. "Variance estimation for integrated population models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 439-460, October.
    6. Raimund M. Kovacevic, 2019. "Valuation and pricing of electricity delivery contracts: the producer’s view," Annals of Operations Research, Springer, vol. 275(2), pages 421-460, April.
    7. Gurutzeta Guillera-Arroita & José J. Lahoz-Monfort, 2017. "Species occupancy estimation and imperfect detection: shall surveys continue after the first detection?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 381-398, October.
    8. Zhang, Hongmei & Ghosh, Kaushik & Ghosh, Pulak, 2012. "Sampling designs via a multivariate hypergeometric-Dirichlet process model for a multi-species assemblage with unknown heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2562-2573.
    9. Hannes Schwarz & Valentin Bertsch & Wolf Fichtner, 2018. "Two-stage stochastic, large-scale optimization of a decentralized energy system: a case study focusing on solar PV, heat pumps and storage in a residential quarter," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 265-310, January.
    10. Leo Polansky & Ken B. Newman & Lara Mitchell, 2021. "Improving inference for nonlinear state‐space models of animal population dynamics given biased sequential life stage data," Biometrics, The International Biometric Society, vol. 77(1), pages 352-361, March.
    11. Shaokun Zhou & Yuhong Song & Yijiao Li & Jing Wang & Lan Zhang, 2022. "Construction of Ecological Security Pattern for Plateau Lake Based on MSPA–MCR Model: A Case Study of Dianchi Lake Area," Sustainability, MDPI, vol. 14(21), pages 1-17, November.
    12. Blanca Sarzo & Ruth King & David Conesa & Jonas Hentati-Sundberg, 2021. "Correcting Bias in Survival Probabilities for Partially Monitored Populations via Integrated Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(2), pages 200-219, June.
    13. An, Yi & Liu, Shiliang & Sun, Yongxiu & Shi, Fangning & Liu, Yixuan & Beazley, Robert, 2021. "Determining the importance of core areas in the alpine shrub-meadow gradient zone of the Qinghai-Tibet Plateau," Ecological Modelling, Elsevier, vol. 440(C).
    14. LaRue, Michelle A. & Nielsen, Clayton K., 2016. "Population viability of recolonizing cougars in midwestern North America," Ecological Modelling, Elsevier, vol. 321(C), pages 121-129.
    15. Biljana Savić & Alevtina Evgrafova & Cenk Donmez & Filip Vasić & Michael Glemnitz & Carsten Paul, 2021. "Assessing the Role of Kettle Holes for Providing and Connecting Amphibian Habitats in Agricultural Landscapes," Land, MDPI, vol. 10(7), pages 1-22, June.
    16. Chiara Mazzetta & Steve Brooks & Stephen N. Freeman, 2007. "On Smoothing Trends in Population Index Modeling," Biometrics, The International Biometric Society, vol. 63(4), pages 1007-1014, December.
    17. Abadi, Fitsum & Gimenez, Olivier & Jakober, Hans & Stauber, Wolfgang & Arlettaz, Raphaël & Schaub, Michael, 2012. "Estimating the strength of density dependence in the presence of observation errors using integrated population models," Ecological Modelling, Elsevier, vol. 242(C), pages 1-9.
    18. Martin Glanzer & Georg Ch. Pflug, 2020. "Multiscale stochastic optimization: modeling aspects and scenario generation," Computational Optimization and Applications, Springer, vol. 75(1), pages 1-34, January.
    19. Stricker, Heather K. & Gehring, Thomas M. & Donner, Deahn & Petroelje, Tyler, 2019. "Multi-scale habitat selection model assessing potential gray wolf den habitat and dispersal corridors in Michigan, USA," Ecological Modelling, Elsevier, vol. 397(C), pages 84-94.
    20. José J. Lahoz-Monfort & Michael P. Harris & Sarah Wanless & Stephen N. Freeman & Byron J. T. Morgan, 2017. "Bringing It All Together: Multi-species Integrated Population Modelling of a Breeding Community," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(2), pages 140-160, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecomod:v:359:y:2017:i:c:p:311-319. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.