Skip to content

Research at St Andrews

Using density surface models to estimate spatio-temporal changes in population densities and trend

Research output: Contribution to journalArticlepeer-review


Open Access permissions



Precise measures of population abundance and trend are needed for species conservation; these are most difficult to obtain for rare and rapidly changing populations. We compare uncertainty in densities estimated from spatio–temporal models with that from standard design‐based methods. Spatio–temporal models allow us to target priority areas where, and at times when, a population may most benefit. Generalised additive models were fitted to a 31‐year time series of point‐transect surveys of an endangered Hawaiian forest bird, the Hawai'i ‘ākepa Loxops coccineus. This allowed us to estimate bird densities over space and time. We used two methods to quantify uncertainty in density estimates from the spatio–temporal model: the delta method (which assumes independence between detection and distribution parameters) and a variance propagation method. With the delta method we observed a 52% decrease in the width of the design‐based 95% confidence interval (CI), while we observed a 37% decrease in CI width when propagating the variance. We mapped bird densities as they changed across space and time, allowing managers to evaluate management actions. Integrating detection function modelling with spatio–temporal modelling exploits survey data more efficiently by producing finer‐grained abundance estimates than are possible with design‐based methods as well as producing more precise abundance estimates. Model‐based approaches require switching from making assumptions about the survey design to assumptions about bird distribution. Such a switch warrants carefully considered. In this case the model‐based approach benefits conservation planning through improved management efficiency and reduced costs by taking into account both spatial shifts and temporal changes in population abundance and distribution.


Original languageEnglish
Pages (from-to)1079-1089
Number of pages11
Issue number7
Early online date9 Apr 2020
Publication statusPublished - Jul 2020

    Research areas

  • Density estimation, Distance sampling, Point-transect sampling, Spatio–temporal smoother, Variance propagation

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. dsmextra: extrapolation assessment tools for density surface models

    Bouchet, P., Miller, D. L., Roberts, J., Mannocci, L., Harris, C. M. & Thomas, L., Nov 2020, In: Methods in Ecology and Evolution. 11, 11, p. 1464-1469 6 p.

    Research output: Contribution to journalArticlepeer-review

  2. From here and now to there and then: practical recommendations for extrapolating cetacean density surface models to novel conditions

    Bouchet, P. J-F., Miller, D. L., Roberts, J., Mannocci, L., Harris, C. M. & Thomas, L., 4 Sep 2019, University of St Andrews. 59 p. (CREEM Technical Report; no. 2019-1)

    Research output: Book/ReportOther report

  3. Distance sampling in R

    Miller, D. L., Rexstad, E., Thomas, L., Marshall, L. & Laake, J. L., 9 May 2019, In: Journal of Statistical Software. 89, 1, 28 p.

    Research output: Contribution to journalArticlepeer-review

  4. Distance sampling

    Buckland, S. T., Miller, D. L. & Rexstad, E., 2019, Quantitative Analyses in Wildlife Science. Brennan, L., Marcot, B. & Tri, A. (eds.). Johns Hopkins University Press, p. 97-112

    Research output: Chapter in Book/Report/Conference proceedingChapter

  5. Model-based approaches to deal with detectability: a comment on Hutto (2016a)

    Marques, T. A., Thomas, L., Kery, M., Buckland, S. T., Borchers, D. L., Rexstad, E., Fewster, R. M., Mackenzie, D. I., Royle, J. A., Guillera-Arroita, G., Handel, C. M., Pavlacky, D. C. & Camp, R. J., Jul 2017, In: Ecological Applications. 27, 5, p. 1694-1698 5 p.

    Research output: Contribution to journalLetterpeer-review

Related by journal

  1. Ecography (Journal)

    Maria Dornelas (Member of editorial board)


    Activity: Publication peer-review and editorial work typesEditor of research journal

Related by journal

  1. A standard protocol for reporting species distribution models

    Zurell, D., Franklin, J., König, C., Bouchet, P. J., Dormann, C. F., Elith, J., Fandos, G., Feng, X., Guillera-Arroita, G., Guisan, A., Lahoz-Monfort, J. J., Leitão, P. J., Park, D. S., Peterson, A. T., Rapacciuolo, G., Schmatz, D. R., Schröder, B., Serra-Diaz, J. M., Thuiller, W., Yates, K. L. & 2 others, Zimmermann, N. E. & Merow, C., 1 Jun 2020, (E-pub ahead of print) In: Ecography. Early View, 17 p.

    Research output: Contribution to journalArticlepeer-review

  2. A standardized assessment of forest mammal communities reveals consistent functional composition and vulnerability across the tropics

    Rovero, F., Ahumada, J., Jansen, P. A., Sheil, D., Alvarez, P., Boekee, K., Espinosa, S., Lima, M. G. M., Martin, E. H., O'Brien, T. G., Salvador, J., Santos, F., Rosa, M., Zvoleff, A., Sutherland, C. & Tenan, S., Jan 2020, In: Ecography. 43, 1, p. 75-84 10 p.

    Research output: Contribution to journalArticlepeer-review

  3. Assessing the effectiveness of foraging radius models for seabird distributions using biotelemetry and survey data

    Critchley, E. J., Grecian, W. J., Bennison, A., Kane, A., Wischnewski, S., Canadas, A., Tierney, D., Quinn, J. L. & Jessopp, M. J., 1 Nov 2019, (E-pub ahead of print) In: Ecography. Early View, 13 p.

    Research output: Contribution to journalArticlepeer-review

  4. β-diversity scaling patterns are consistent across metrics and taxa

    Antão, L. H., McGill, B., Magurran, A. E., Soares, A. & Dornelas, M., May 2019, In: Ecography. 42, 5, p. 1012-1023

    Research output: Contribution to journalArticlepeer-review

ID: 267831841