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

  • Erin M. SchliepEmail author
  • Alan E. Gelfand
  • James S. Clark
  • Roland Kays


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.


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



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.

Supplementary material

13253_2018_327_MOESM1_ESM.rdata (65 kb)
Supplementary material 1 (Rdata 64 KB)


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Copyright information

© International Biometric Society 2018

Authors and Affiliations

  • Erin M. Schliep
    • 1
    Email author
  • Alan E. Gelfand
    • 2
  • James S. Clark
    • 2
    • 3
  • Roland Kays
    • 4
    • 5
  1. 1.Department of StatisticsUniversity of MissouriColumbiaUSA
  2. 2.Department of Statistical ScienceDuke UniversityDurhamUSA
  3. 3.Nicholas School of the EnvironmentDuke UniversityDurhamUSA
  4. 4.North Carolina Museum of Natural SciencesRaleighUSA
  5. 5. Department of Forestry and Environmental ResourcesNorth Carolina State UniversityRaleighUSA

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