Supplementary materials for this article are available at https:// doi.org/ 10.1007/ s13253-018-0327-8.
Joint Temporal Point Pattern Models for
Proximate Species Occurrence in a Fixed Area
Using Camera Trap Data
Erin M. Schliep,AlanE.Gelfand, James S. Clark, and 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
Supplementary materials accompanying this paper appear online.
Key Words: Circular time; Fourier series representation; Hierarchical model; Linear
time; Multivariate log-Gaussian Cox process; Nonhomogeneous Poisson process.
Erin M. Schliep (
), Department of Statistics, University of Missouri, Columbia, MO 65211, USA
(E-mail: firstname.lastname@example.org). Alan E. Gelfand and James S. Clark, Department of Statistical Science, Duke
University, Durham, NC 27708, USA. James S. Clark, Nicholas School of the Environment, Duke University,
Durham, NC 27708, USA. Roland Kays, North Carolina Museum of Natural Sciences, Raleigh, NC, USA and
Department of Forestry and Environmental Resources, North Carolina State University, Raleigh, NC, USA.
© 2018 International Biometric Society
Journal of Agricultural, Biological, and Environmental Statistics, Volume 23, Number 3, Pages 334–357