Skip to main content

Joint Temporal Point Pattern Models for Proximate Species Occurrence in a Fixed Area Using Camera Trap Data

Abstract

The distinction between an overlap in species daily activity patterns and proximate co-occurrence of species for a location and time due to behavioral attraction or avoidance is critical when addressing the question of species co-occurrence. We use data from a dense grid of camera traps in a forest in central North Carolina to inform about proximate co-occurrence. Camera trigger times are recorded when animals pass in front of the camera’s field of vision. We view the data as a point pattern over time for each species and model the intensities driving these patterns. These species-specific intensities are modeled jointly in linear time to preserve the notion of co-occurrence. We show that a multivariate log-Gaussian Cox process incorporating both circular and linear time provides a preferred choice for modeling occurrence of forest mammals based on daily activity rhythms. Model inference is obtained under a hierarchical Bayesian framework with an efficient Markov chain Monte Carlo sampling algorithm. After model fitting, we account for imperfect detection of individuals by the camera traps by incorporating species-specific detection probabilities that adjust estimates of occurrence and co-occurrence. We obtain rich inference including assessment of the probability of presence of one species in a particular time interval given presence of another species in the same or adjacent interval, enabling probabilities of proximate co-occurrence. Our results describe the ecology and interactions of four common mammals within this suburban forest including their daily rhythms, responses to temperature and rainfall, and effects of the presence of predator species. Supplementary materials accompanying this paper appear online.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  • Ahumada, J. A., Silva, C. E., Gajapersad, K., Hallam, C., Hurtado, J., Martin, E., McWilliam, A., Mugerwa, B., O’Brien, T., Rovero, F., Sheil, D., Spironello, W. R., Winarni, N., and Andelman, S. J. (2011). Community structure and diversity of tropical forest mammals: data from a global camera trap network. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 366(1578):2703–2711.

    Article  Google Scholar 

  • Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2014). Hierarchical modeling and analysis for spatial data. Chapman & Hall/CRC Press, Boca Raton, FL.

    MATH  Google Scholar 

  • Carlin, B. P. and Louis, T. A. (2008). Bayesian methods for data analysis. Chapman & Hall/CRC Press, Boca Raton, FL.

    MATH  Google Scholar 

  • Cusack, J. J., Dickman, A. J., Kalyahe, M., Rowcliffe, J. M., Carbone, C., Macdonald, D. W., and Coulson, T. (2017). Revealing kleptoparasitic and predatory tendencies in an African mammal community using camera traps: a comparison of spatiotemporal approaches. Oikos, 126(6):812–822.

    Article  Google Scholar 

  • Daley, D. J. and Vere-Jones, D. (2007). An introduction to the theory of point processes: volume II: general theory and structure. Springer Science & Business Media, New York, NY.

    MATH  Google Scholar 

  • Diete, R. L., Meek, P. D., Dickman, C. R., Lisle, A., and Leung, L. K.-P. (2017). Diel activity patterns of northern Australian small mammals: variation, fixity, and plasticity. Journal of Mammalogy, 98(3):848–857.

    Article  Google Scholar 

  • Ferreira, M., Filipe, A. F., Bardos, D. C., Magalhaes, M. F., and Beja, P. (2016). Modeling stream fish distributions using interval-censored detection times. Ecology and evolution, 6(15):5530–5541.

    Article  Google Scholar 

  • Gehrt, S. D. and Prange, S. (2007). Interference competition between coyotes and raccoons: a test of the mesopredator release hypothesis. Behavioral Ecology, 18(1):204–214.

    Article  Google Scholar 

  • Gelfand, A. E., Schmidt, A. M., Banerjee, S., and Sirmans, C. (2004). Nonstationary multivariate process modeling through spatially varying coregionalization. Test, 13(2):263–312.

    MathSciNet  Article  MATH  Google Scholar 

  • Gompper, M. E., Lesmeister, D. B., Ray, J. C., Malcolm, J. R., and Kays, R. (2016). Differential habitat use or intraguild interactions: what structures a carnivore community? PloS one, 11(1):e0146055.

    Article  Google Scholar 

  • Hanks, E. M., Schliep, E. M., Hooten, M. B., and Hoeting, J. A. (2015). Restricted spatial regression in practice: geostatistical models, confounding, and robustness under model misspecification. Environmetrics, 26(4):243–254.

    MathSciNet  Article  Google Scholar 

  • Hodges, J. S. and Reich, B. J. (2010). Adding spatially-correlated errors can mess up the fixed effect you love. The American Statistician, 64(4):325–334.

    MathSciNet  Article  MATH  Google Scholar 

  • Hody, J. W., Parsons, A. W., and Kays, R. (2017). Empirical evaluation of the spatial scale and detection process of camera trap surveys. Submitted for publication.

  • Hughes, J. and Haran, M. (2013). Dimension reduction and alleviation of confounding for spatial generalized linear mixed models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75(1):139–159.

    MathSciNet  Article  Google Scholar 

  • Illian, J., Penttinen, A., Stoyan, H., and Stoyan, D. (2008). Statistical analysis and modelling of spatial point patterns, volume 70. John Wiley & Sons, Chichester, UK.

    MATH  Google Scholar 

  • Kays, R. (2016). Candid creatures: how camera traps reveal the mysteries of nature. Johns Hopkins University Press, Baltimore, MD.

    Google Scholar 

  • Leininger, T. J. and Gelfand, A. E. (2017). Bayesian inference and model assessment for spatial point patterns using posterior predictive samples. Bayesian Analysis, 12(1):1–30.

    MathSciNet  Article  MATH  Google Scholar 

  • Li, Z., Ding, B., Wu, F., Lei, T. K. H., Kays, R., and Crofoot, M. C. (2013). Attraction and avoidance detection from movements. Proceedings of the Very Large Data Bases Endowment, 7(3):157–168.

    Google Scholar 

  • MacKenzie, D. I., Bailey, L. L., and Nichols, J. (2004). Investigating species co-occurrence patterns when species are detected imperfectly. Journal of Animal Ecology, 73(3):546–555.

    Article  Google Scholar 

  • MacKenzie, D. I., Nichols, J. D., Royle, J. A., Pollock, K. H., Bailey, L., and Hines, J. E. (2017). Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence. Elsevier, San Diego, CA.

    MATH  Google Scholar 

  • McShea, W. J., Forrester, T., Costello, R., He, Z., and Kays, R. (2016). Volunteer-run cameras as distributed sensors for macrosystem mammal research. Landscape Ecology, 31(1):55–66.

    Article  Google Scholar 

  • Murray, I., Adams, R. P., and MacKay, D. J. (2010). Elliptical slice sampling. Journal of Machine Learning Research: Workshop and Conference Proceedings (AISTATS), 9:541–548.

    Google Scholar 

  • Oliveira-Santos, L., Zucco, C., and Agostinelli, C. (2013). Using conditional circular kernel density functions to test hypotheses on animal circadian activity. Animal Behaviour, 85(1):269–280.

    Article  Google Scholar 

  • Parsons, A. W., Bland, C., Forrester, T., Baker-Whatton, M. C., Schuttler, S. G., McShea, W. J., Costello, R., and Kays, R. (2016). The ecological impact of humans and dogs on wildlife in protected areas in eastern North America. Biological Conservation, 203:75–88.

    Article  Google Scholar 

  • Pollock, L. J., Tingley, R., Morris, W. K., Golding, N., O’Hara, R. B., Parris, K. M., Vesk, P. A., and McCarthy, M. A. (2014). Understanding co-occurrence by modelling species simultaneously with a joint species distribution model (jsdm). Methods in Ecology and Evolution, 5(5):397–406.

    Article  Google Scholar 

  • Richmond, O. M., Hines, J. E., and Beissinger, S. R. (2010). Two-species occupancy models: a new parameterization applied to co-occurrence of secretive rails. Ecological Applications, 20(7):2036–2046.

    Article  Google Scholar 

  • Ridout, M. S. and Linkie, M. (2009). Estimating overlap of daily activity patterns from camera trap data. Journal of Agricultural, Biological, and Environmental Statistics, 14(3):322–337.

    MathSciNet  Article  MATH  Google Scholar 

  • Rota, C. T., Wikle, C. K., Kays, R. W., Forrester, T. D., McShea, W. J., Parsons, A. W., and Millspaugh, J. J. (2016). A two-species occupancy model accommodating simultaneous spatial and interspecific dependence. Ecology, 97(1):48–53.

    Article  Google Scholar 

  • Rowcliffe, J. M., Kays, R., Kranstauber, B., Carbone, C., and Jansen, P. A. (2014). Quantifying levels of animal activity using camera trap data. Methods in Ecology and Evolution, 5(11):1170–1179.

    Article  Google Scholar 

  • Schuttler, S., Parsons, A., Forrester, T., Baker, M., McShea, W., Costello, R., and Kays, R. (2017). Deer on the lookout: how hunting, hiking and coyotes affect white-tailed deer vigilance. Journal of Zoology, 301(4):320–327.

    Article  Google Scholar 

  • Small, R. J., Brost, B., Hooten, M., Castellote, M., and Mondragon, J. (2017). Potential for spatial displacement of cook inlet beluga whales by anthropogenic noise in critical habitat. Endangered Species Research, 32:43–57.

    Article  Google Scholar 

  • Stokes, M. K., Slade, N. A., and Blair, S. M. (2001). Influences of weather and moonlight on activity patterns of small mammals: a biogeographical perspective. Canadian Journal of Zoology, 79(6):966–972.

    Article  Google Scholar 

  • Tanner, M. A. (1991). Tools for statistical inference, volume 3. Springer, New York, NY.

    Book  MATH  Google Scholar 

  • Vieira, E., Baumgarten, L., Paise, G., and Becker, R. (2010). Seasonal patterns and influence of temperature on the daily activity of the diurnal neotropical rodent Necromys lasiurus. Canadian Journal of Zoology, 88(3):259–265.

    Article  Google Scholar 

  • Yoccoz, N. G., Nichols, J. D., and Boulinier, T. (2001). Monitoring of biological diversity in space and time. Trends in Ecology & Evolution, 16(8):446–453.

    Article  Google Scholar 

Download references

Acknowledgements

The project was funded in part by the EAGER program of the National Science Foundation under Grants NSF-EF-1550907 and NSF-EF-1550911. Additionally, we thank Bene Bachelet, Chase Nuñez, Daniel Taylor-Rodrigues, Bradley Tomasek for useful discussion.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Erin M. Schliep.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (Rdata 64 KB)

A Appendix

A Appendix

We specified prior distributions for the parameters in the models outlined in Sect. 3.1. Samples from the joint posterior distribution were obtained by a customized Metropolis–Hastings algorithm. For models 1 and 2, each chain was run for 1,000,000 iterations and thinned to every 50th iteration to reduce dependence within the chain. The chain for model 3 was run for 2,000,000 iterations and thinned to every 100th iteration. The first half of the chain was discarded as burn-in and the remaining 10,000 iterations used for posterior inference.

Each species-specific coefficient vector, \(\varvec{\beta }^{(r)}\) for \(r = 1, \ldots , R\), was modeled as \(\varvec{\beta }^{(r)} \sim \text {MVN}(\mathbf {0}, \mathbf {I})\) and was updated in block using a Metropolis step. The diagonal elements of the coregionalization matrix \(\mathbf {A}\) were assigned log-normal priors where the mean of each \(A_{rr}\) was equal to 1. The off-diagonal element was assigned a mean 0 normal priors. Each element of the lower-triangular matrix of \(\mathbf {A}\) was updated univariately using a Metropolis–Hastings algorithm.

The temporal random effects were each modeled using a multivariate normal distribution and updated using an elliptical slice sampler (Murray et al. 2010). The elliptical slice sampler was constructed for sampling \(\mathbf {V}_r^*\), the temporal random effects orthogonal to the fixed effects in the model as defined in (4). The decay parameter of the exponential covariance model was fixed to \(\phi _r =1/48\) for each r, resulting in a rate of decay of 1/48 per hour or 24/48 per day. The effective range, or, rather, the temporal lag at which the correlation drops below 0.05, was approximately 6 days and was chosen such that it was not on the same scale as the periodic functions or other fixed effects.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Schliep, E.M., Gelfand, A.E., Clark, J.S. et al. Joint Temporal Point Pattern Models for Proximate Species Occurrence in a Fixed Area Using Camera Trap Data. JABES 23, 334–357 (2018). https://doi.org/10.1007/s13253-018-0327-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13253-018-0327-8

Keywords

  • Circular time
  • Fourier series representation
  • Hierarchical model
  • Linear time
  • Multivariate log-Gaussian Cox process
  • Nonhomogeneous Poisson process