Skip to main content

Advertisement

SpringerLink
Log in

Models for Jointly Estimating Abundances of Two Unmarked Site-Associated Species Subject to Imperfect Detection

  • Published:
Journal of Agricultural, Biological and Environmental Statistics Aims and scope Submit manuscript

Abstract

In ecological field surveys, it is often of interest to estimate the abundance of species. It is frequently the case that unmarked animals are counted on different sites over several time occasions. A natural starting point to model these data, while accounting for imperfect detection, is by using Royle’s N-mixture model (Biometrics 60:108–115, 2004). Subsequently, many multivariate extensions have been proposed to model communities as a whole. However, these approaches are used to study species richness and other community-level variables and do not focus on the relationship between two site-associated species. Here, we extend the N-mixture modelling framework to model two site-associated species abundances jointly and propose to measure the influence of one species’ abundance on the populations of the other and study how this changes over time and space. By including a new parameter in the abundance distribution of one of the species, linking it to abundance of the other, our proposed model treats extra variability as an effect induced by an associated species’ abundance and allows one to study how environmental covariates may affect this. Using results from simulation studies, we show that the model is able to recover true parameter estimates. We illustrate our approach using data from bald eagles and mallards obtained in the 2015 survey of the North American Breeding Bird Survey. By using the joint model, we were able to separate overdispersion from mallard-induced variability and hence what would be accounted for with a dispersion parameter in the univariate framework for the eagles was explained by covariates related to mallard abundance in the joint model. Our approach represents an attractive, yet simple, way of modelling site-associated species populations jointly. Conservation ecologists can use the approach to devise management strategies based on the strength of association between species, which may be due to direct interactions and/or environmental effects affecting both species’ populations. Also, mathematical ecologists can use this framework to develop tools for studying population dynamics under different scenarios. Supplementary materials accompanying this paper appear on-line.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Begon, M., Townsend, C.R. & Harper, J.L. (2005) Ecology: from individuals to ecosystems. Blackwell Publishing, Oxford.

    Google Scholar 

  • Berlow, E.L., Neutel, A., Cohen, J.E., De Ruiter, P.C., Ebenman, B., Emmerson, M., Fox, J.W., Jansen, V.A.A., Jones, J.I., Kokkoris, G.D., Logofet, D.O., Mckane, A.J., Montoya, J.M. & Petchey, O. (2004) Interaction strengths in food webs: issues and opportunities. Journal of Animal Ecology, 75, 585–598.

    Article  Google Scholar 

  • Brodie, J.F. & Giordano, A. (2013) Lack of trophic release with large mammal predators and prey in Borneo. Biological Conservation, 163, 58–67.

    Article  Google Scholar 

  • Brommer, J.E., Alakoski, R., Selonen, V. & Kauhala, K. (2017) Population dynamics of two beaver species in Finland inferred from citizen-science census data. Ecosphere, 8, e01947.

    Article  Google Scholar 

  • Broms, K.M., Hooten, M.B. & Fitzpatrick, R.M. (2016) Model selection and assessment for multi-species occupancy models. Ecology, 97, 1759–1770.

    Article  Google Scholar 

  • Carvalheiro, L.G., Buckley, Y.M. & Memmott, J. (2010) Diet breadth influences how the impact of invasive plants is propagated through food webs. Ecology, 91, 1063–1074.

    Article  Google Scholar 

  • Dail, D. & Madsen, L. (2011) Models for estimating abundance from repeated counts of an open metapopulation. Biometrics, 67, 577-587.

    Article  MathSciNet  MATH  Google Scholar 

  • Demétrio, C.G.B., Hinde, J. & Moral, R.A. (2014) Models for overdispersed data in entomology. In: Ferreira, C.P. & Godoy, W.A.C. (2014) Ecological modelling applied to entomology. Springer International Publishing.

  • Dénes, F.V., Silveire, L.F. & Beissinger, S.R. (2015) Estimating abundance of unmarked animal populations: accounting for imperfect detection and other sources of zero inflation. Methods in Ecology and Evolution, 6, 543–556.

    Article  Google Scholar 

  • Dennis, E.B., Morgan, B.J.T. & Ridout, M.S. (2015) Computational aspects of N-mixture models. Biometrics, 71, 237–246.

    Article  MathSciNet  MATH  Google Scholar 

  • Dorazio, R.M. & Connor, E.F. (2014) Estimating abundances of interacting species using morphological traits, foraging guilds, and habitat. PloS one, 9, e94323.

    Article  Google Scholar 

  • Ehrlén, J. & Morris, W.F. (2015) Predicting changes in the distribution and abundance of species under environmental change. Ecology Letters, 18, 303–314.

    Article  Google Scholar 

  • Flesch, A.D., Rosen, P.C. & Holm, P. (in press) Long-term changes in abundances of Sonoran Desert lizards reveal complex responses to climatic variation. Global Change Biology.

  • Gaston, K.J. (2000) Global patterns in biodiversity. Nature, 405, 220–227.

    Article  Google Scholar 

  • Guillera-Arroita, G. (2017) Modelling of species distributions, range dynamics and communities under imperfect detection: advances, challenges and opportunities. Ecography, 40, 281–295.

    Article  Google Scholar 

  • Haines, L.M. (2016) Maximum likelihood estimation for N-mixture models. Biometrics, 72, 1235–1245.

    Article  MathSciNet  MATH  Google Scholar 

  • — (2016) A note on the Royle-Nichols model for repeated detection-nondetection data. Journal of Agricultural, Biological, and Environmental Statistics, 21, 588–598.

  • Hanski, I. (1998) Metapopulation dynamics. Nature, 396, 41–49.

    Article  Google Scholar 

  • Hua, F., Fletcher Jr., R.J., Sieving, K.E. & Dorazio, R.M. (2013) Too risky to settle: avian community structure changes in response to perceived predation risks on adults and offspring. Proceedings of the Royal Society B, 280, 20130762.

    Article  Google Scholar 

  • Hostetler, J.A. & Chandler, R.B. (2015) Improved state-space models for inference about spatial and temporal variation in abundance from count data. Ecology, 96, 1713–1723.

    Article  Google Scholar 

  • Gerrard, J.M. & Bortolotti, G.R. (1988) The bald eagle: Haunts and habits of a wilderness monarch. Smithsonian books, Washington.

    Google Scholar 

  • Iknayan, K.J., Tingley, M.W., Furnas, B.J. & Beissinger, S.R. (2014) Detecting diversity: emerging methods to estimate species diversity. Trends in Ecology and Evolution, 29, 97–106.

    Article  Google Scholar 

  • Jakob, C., Ponce-Boutin, F. & Besnard, A. (2014) Coping with heterogeneity to detect species on a large scale: N-mixture modeling applied to red-legged partridge abundance. The Journal of Wildlife Management, 78, 540–549.

    Article  Google Scholar 

  • Johnson, D.H. (1995) Point counts of birds: What are we estimating? In: Ralph, C.J., Sauer, J.R. & Droege, S. (1995) Monitoring bird populations by point counts. United States Forest Service General Technical Report PSW-GTR-149.

  • Lyons, J.E., Royle, J.A., Thomas, S.M., Elliott-Smith, E., Evenson, J.R., Kelly, E.G., Milner, R.L., Nysewander, D.R. & Andres, B.A. (2012) Large-scale monitoring of shorebird populations using count data and N-mixture models: Black oystercatcher (Haematopus bachmani) surveys by land and sea. The Auk, 129, 645–652.

    Article  Google Scholar 

  • MacCan, K., Hastings, A. & Huxel, G.R. (1998) Weak trophic interactions and the balance of nature. Nature, 395, 794–798.

    Article  Google Scholar 

  • Moral, R., Demétrio, C.G.B. & Hinde, J. (2016) Joint N-mixture models for site-associated species. R package version 1.0.

  • Ovaskainen, O., Abrego, N., Halme, P., & Dunson, D. (2016a) Using latent variable models to identify large networks of species-to-species associations at different spatial scales. Methods in Ecology and Evolution, 7, 549–555.

    Article  Google Scholar 

  • Ovaskainen, O., Roy, D.B., Fox, R., & Anderson, B.J. (2016b) Uncovering hidden spatial structure in species communities with spatially explicit joint species distribution models. Methods in Ecology and Evolution, 7, 428–436.

    Article  Google Scholar 

  • Pardieck, K.L., Ziolkowski Jr., D.J., Hudson, M.-A.R. & Campbell, K. (2016) North American breeding bird survey dataset 1966 - 2015, version 2015.0. U.S. Geological Survey, Patuxent Wildlife Research Center. URL www.pwrc.usgs.gov/BBS/RawData/; https://doi.org/10.5066/F71R6NK8.

  • Popescu, V.D., Iosif, R., Pop, M.I., Chiriac, S., Bouro?, G. & Furnas, B.J. (2017) Integrating sign surveys and telemetry data for estimating brown bear (Ursus arctos) density in the Romanian Carpathians. Ecology and Evolution, 7, 7134–7144.

  • Priol, P., Mazerolle, M.J., Imbeau, L., Drapeau, P., Trudeau, C. & Jessica Ramire, J. (2017) Using dynamic N-mixture models to test cavity limitation on northern flying squirrel demographic parameters using experimental nest box supplementation. Ecology and Evolution, 4, 2165–2177.

    Google Scholar 

  • Quinn, J.E., Johnson, R.J. & Brandle, J.R. (2014) Identifying opportunities for conservation embedded in cropland anthromes. Landscape Ecology, 29, 1811–1819.

    Article  Google Scholar 

  • R Core Team (2017) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna. URL http://www.R-project.org

  • Refaeilzadeh, P., Tang, L. & Liu, H. (2009) Cross-validation. Encyclopedia of Database Systems, 532–538.

  • Ridgely, R.S., Allnutt, T.F., Brooks, T., McNicol, D.K., Mehlman, D.W., Young, B.E. & Zook, J.R. 2003. Digital distribution maps of the birds of the Western hemisphere, version 1.0. NatureServe, Arlington, Virginia, USA.

  • Riffell, S.K., Monroe, A.P., Martin, J.A., Evans, K.O., Burger Jr., L.W. & Smith, M.D. (2015) Response of non-grassland avian guilds to adjacent herbaceous field buffers: testing the configuration of targeted conservation practices in agricultural landscapes. Journal of Applied Ecology, 52, 300–309.

    Article  Google Scholar 

  • Romano, A., Costa, A., Basile, M., Raimondi, R., Posillico, M., Roger, D.S., Crisci, A., Piraccini, R., Raia, P., Matteucci, G. & Cinti, B. (2017) Conservation of salamanders in managed forests: Methods and costs of monitoring abundance and habitat selection. Forest Ecology and Management, 400, 12–18.

    Article  Google Scholar 

  • Roth, T., Bühler & Amrhein, V. (2016) Estimating effects of species interactions on populations of endangered species. The American Naturalist, 187, 457–467.

  • Royle, J.A. (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics, 60, 108–115.

    Article  MathSciNet  MATH  Google Scholar 

  • Schmitz, O.J., Hamback, P.A. & Beckerman, A.P. (2000) Trophic cascades in terrestrial systems: a review of the effects of carnivore removals on plants. American Naturalist, 155, 141–153.

    Article  Google Scholar 

  • Shamoon, H., Saltz, D. & Dayan, T. (2017) Fine-scale temporal and spatial population fluctuations of medium sized carnivores in a Mediterranean agricultural matrix. Landscape Ecology, 32, 1243–1256.

    Google Scholar 

  • Stewart, D.R. & Long, J.M. (2016) Using hierarchical Bayesian multispecies mixture models to estimate tandem hoop-net-based habitat associations and detection probabilities of fishes in reservoirs. Transactions of the American Fisheries Society, 145, 450–461.

    Article  Google Scholar 

  • Wright, B.S. (1953) The relation of bald eagles to breeding ducks in New Brunswick. The Journal of Wildlife Management, 17, 55–62.

    Article  Google Scholar 

  • Yamaura, Y., Royle, J.A., Shimada, N., Asanuma, S., Sato, T., Taki, H. & Makino, S. (2012) Biodiversity of man-made open habitats in an underused country: a class of multispecies abundance models for count data. Biodiversity Conservation, 21, 1365–1380.

    Article  Google Scholar 

  • Yamaura, Y., Kéry, M. & Royle, J.A. (2016) Study of biological communities subject to imperfect detection: bias and precision of community N-mixture abundance models in small-sample situations. Ecological Research, 31, 289–305.

    Article  Google Scholar 

  • Yoccoz, N.G., Nichols, J.D. & Boulinier, T. (2001) Monitoring of biological diversity in space and time. Trends in Ecology and Evolution, 16, 446–453.

    Article  Google Scholar 

Download references

Acknowledgements

We thank the Associate Editor and two anonymous referees for their constructive comments which helped improve the manuscript.

Funding

RAM was funded by FAPESP (Grant No. 2014/12903-8). Exchange visits between CGBD and JH were partially supported by CNPq, FAPESP and SFI. CR and WACG were funded by CNPq.

Author information

Authors and Affiliations

  1. Departamento de Ciências Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade de São Paulo, Av. Pádua Dias, 11, Piracicaba, SP, Brazil

    Rafael A. Moral & Clarice G. B. Demétrio

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, University Rd., Galway, Ireland

    John Hinde

  3. Departamento de Ecologia e Biologica Evolutiva, Universidade Federal de São Carlos, Rod. Washington Luís km 235, São Carlos, SP, Brazil

    Carolina Reigada

  4. Departamento Entomologia e Acarologia, Escola Superior de Agricultura Luiz de Queiroz, Universidade de São Paulo, Av. Pádua Dias, 11, Piracicaba, SP, Brazil

    Wesley A. C. Godoy

Authors
  1. Rafael A. Moral
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John Hinde
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Clarice G. B. Demétrio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Carolina Reigada
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wesley A. C. Godoy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rafael A. Moral.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (zip 10 KB)

Supplementary material 2 (pdf 117 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moral, R.A., Hinde, J., Demétrio, C.G.B. et al. Models for Jointly Estimating Abundances of Two Unmarked Site-Associated Species Subject to Imperfect Detection. JABES 23, 20–38 (2018). https://doi.org/10.1007/s13253-017-0316-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13253-017-0316-3

Keywords

Search

Navigation