Ecology | Statistics

New Concepts & Synthesis paper accepted in Ecology on optimal dynamic monitoring

Williams, P. J., M. B. Hooten, J. N. Womble, G. G. Esslinger, and M. R. Bower. In Press. Monitoring dynamic spatio-temporal ecological processes optimally. Ecology (pdf)


Population dynamics varies in space and time. Survey designs that ignore these dynamics may be inefficient and fail to capture essential spatio-temporal variability of a process. Alternatively, dynamic survey designs explicitly incorporate knowledge of ecological processes, the associated uncertainty in those processes, and can be optimized with respect to monitoring objectives. We describe a cohesive framework for monitoring a spreading population that explicitly links animal movement models with survey design and monitoring objectives. We apply the framework to develop an optimal survey design for sea otters in Glacier Bay. Sea otters were first detected in Glacier Bay in 1988 and have since increased in both abundance and distribution; abundance estimates increased from 5 otters to >5,000 otters, and they have spread faster than 2.7 km per year. By explicitly linking animal movement models and survey design, we were able to reduce uncertainty associated with predicted occupancy, abundance, and distribution. The framework we describe is general, and we outline steps to applying it to novel systems and taxa.

A pre-print of “A guide to Bayesian model checking for ecologists” available online

The manuscript is currently in review at Ecological Monographs and a pre-print is available via PeerJ Preprints.


Conn P, Johnson D, Williams P, Melin S, Hooten M. (2017) A guide to Bayesian model checking for ecologists. PeerJ Preprints 5:e3390v1


Checking that models adequately represent data is an essential component of applied statistical inference. Ecologists increasingly use hierarchical Bayesian statistical models in their research. The appeal of this modeling paradigm is undeniable, as researchers can build and fit models that embody complex ecological processes while simultaneously controlling observation error. However, ecologists tend to be less focused on checking model assumptions and assessing potential lack-of-fit when applying Bayesian methods than when applying more traditional modes of inference such as maximum likelihood. There are also multiple ways of assessing the fit of Bayesian models, each of which has strengths and weaknesses. For instance, Bayesian p-values are relatively easy to compute, but are well known to be conservative, producing p-values biased toward 0.5. Alternatively, lesser known approaches to model checking, such as prior predictive checks, cross-validation probability integral transforms, and pivot discrepancy measures may produce more accurate characterizations of goodness-of-fit but are not as well known to ecologists. In addition, a suite of visual and targeted diagnostics can be used to examine violations of different model assumptions and lack-of-fit at different levels of the modeling hierarchy, and to check for residual temporal or spatial autocorrelation. In this review, we synthesize existing literature to guide ecologists through the many available options for Bayesian model checking. We illustrate methods and procedures with several ecological case studies, including i) analysis of simulated spatio-temporal count data, (ii) N-mixture models for estimating abundance and detection probability of sea otters from an aircraft, and (iii) hidden Markov modeling to describe attendance patterns of California sea lion mothers on a rookery. We find that commonly used procedures based on posterior predictive p-values detect extreme model inadequacy, but often do not detect more subtle cases of lack of fit. Tests based on cross-validation and pivot discrepancy measures (including the sampled predictive p-value”) appear to be better suited to model checking and to have better overall statistical performance. We conclude that model checking is an essential component of scientific discovery and learning that should accompany most Bayesian analyses presented in the literature.

Upcoming short course entitled “Introductory R” at The Wildlife Society annual meeting in Albuquerque, New Mexico

This workshop, aimed at new R users, provides an introduction to object manipulation, data visualization and analysis, and basic programming in R. The R computing environment is a free, flexible, and open-source tool for data management, visualization, and analysis. We will cover a broad spectrum of topics including: how to import and export data, data types and object classes, simple R functions for querying, summarizing, plotting, and analyzing data, exploring spatial data, basic programming (e.g., for loops, writing R functions), and how to find and use R help resources. No prior experience with R is necessary, but participants should be comfortable with introductory statistics. The workshop will alternate between interactive instruction and guided exercises where participants will implement their new skills. Participants should bring their own laptop and have recent versions of R and RStudio installed prior to the workshop.

Co-taught with Drs. Frances Buderman and Brittany Mosher

Upcoming short course entitled “Spatio-temporal dynamic statistical modeling in practice”

Short course on spatio-temporal dynamic statistical modeling at the Western North American Region of the International Biometric Society. The course is scheduled for June 25th, in Santa Fe, New Mexico from 1-5 pm. The course will provide an overview  spatio-temporal statistical modeling,
efficient computation and implementation of ecological diffusion models, and embedding S-T dynamic models into integrated population models for ecological data.

Co-taught  with Drs. Mevin Hooten and Trevor Hefley.

New manuscript accepted in Methods in Ecology and Evolution

Williams, P. J., M. B. Hooten, J. N. Womble, and M. R. Bower. In Press. Estimating occupancy and abundance using aerial images with imperfect detection. Methods in Ecology and Evolution 00:00–00.


Species distribution and abundance are critical population characteristics for efficient management, conservation, and ecological insight. Point process models are a powerful tool for modeling distribution and abundance, and can incorporate many data types, including count data, presence-absence data, and presence-only data. Aerial photographic images are a natural tool for collecting data to fit point process models, but aerial images do not always capture all animals that are present at a site. Methods for estimating detection probability for aerial surveys usually include collecting auxiliary data to estimate the proportion of time animals are available to be detected.

We developed an approach for fitting point process models using an N-mixture model framework to estimate detection probability for aerial occupancy and abundance surveys. Our method uses multiple aerial images taken of animals at the same spatial location to provide temporal replication of sample sites. The intersection of the images provide multiple counts of individuals at different times. We examined this approach using both simulated and real data of sea otters (Enhydra lutris kenyoni) in Glacier Bay National Park, southeastern Alaska.

Using our proposed methods, we estimated detection probability of sea otters to be 0.80, which was an improvement compared to visual aerial surveys that have been used in the past (p=0.76). Further, simulations demonstrated that our approach is a promising tool for estimating occupancy, abundance, and detection probability from aerial photographic surveys.

Our methods can be readily extended to data collected using unmanned aerial vehicles, as technology and regulations permit. The generality of our methods for other aerial surveys depends on how well surveys can be designed to meet the assumptions of N-mixture models.