Biometrics & Modeling III

Contributed Oral

All Species Distribution and Abundance Models Are Wrong, Which Are Useful?
Sara Stoudt, Perry de Valpine, William Fithian

Many questions ecologists face require hard-won data, and limited resources make it tempting to try to do more with less. There have been continued debates about which models we can trust to provide reliable information about species prevalence, occupancy, detection, and abundance, especially in the face of inevitable model mis-specification. We leverage econometrics literature to consider different levels of identifiability and the consequences of broken parametric assumptions that have been at the heart of these debates in the species distribution and abundance literature.

A stronger form of identifiability, non-parametric identifiability, exists when a model could, in principle, be estimated without parametric assumptions. The potential to fit a non-parametric model, even if one would not fit it in practice, means the data is truly informative of our quantities of interest.

We propose a method for investigating whether non-parametric identifiability holds in targeted parts of the model. We relax particular parametric assumptions and approximate a non-parametric relationship as a flexible, unpenalized spline fit to simulated data with increasing sample sizes. This approach reveals the importance of semi-parametric identifiability, non-parametric identifiability achieved in part of a species distribution or abundance model.  

We argue that ecologists should be most confident in results when the stronger non-parametric identifiability holds. When non-parametric identifiability holds in a regression relationship, a parametric model, even if mis-specified, may provide a useful approximation to the truth. When semi-parametric identifiability does not hold, parametric assumptions create identifiability by fiat, and the data cannot distinguish alternative models. Box’s adage that all models are approximations then has very different implications.

Efficacy of Positional and Behavioral Change-Point Models to Determine Ungulate Parturition Events
Katie Gundermann, Christopher Rosenberry, Duane Diefenbach, Jeremiah Banfield, Avery Corondi, W. David Walter, Frances Buderman

Animal behavior can be difficult, time-consuming, and costly to directly observe in the field. There is a rapidly expanding volume of innovative modelling methods that allow researchers to make inference about unobserved animal behaviors from movement data. For example, hidden Markov models fit to step-lengths and turning angles have become one of the primary ways that researchers identify behavioral states from movement data. However, we can frame behavioral state identification in a number of ways, and the optimal framework will depend on the behavioral ecology of the species in question and the amount of individual variation. We present two methods for identifying changes in movement behavior: a behavioral change-point model and a positional change-point model. We applied these models to two ungulate species, white-tailed deer (Odocoileus virginianus, n = 21) and elk (Cervus canadensis nelsoni, n = 37) in central Pennsylvania equipped with global positioning system (GPS) collars and vaginal implant transmitters (VITs) and compared the ability of each model to detect parturition events. We formulated these models in a Bayesian framework to easily compare the efficacy of each model across different species. To summarize the ability of each model to estimate the true parturition date, we calculated the posterior difference between the estimated parturition event and the parturition date determined by vaginal implant transmitters for each individual across species. On average, the behavioral change-point model detected the parturition event more consistently than the positional change-point model. We also did a simulation study to determine the frequency and duration of data after a parturition event has occurred influences the ability of the models to correctly identify the change-point.  Our framework can be used to make inference on parturition behavioral ecology and accurately determine parturition events, allowing managers make informed decisions for ungulate species of interest.

Identifying Behaviours with Orientation Bias Using Hidden Markov Models
Ron Togunov, Andrew Derocher, Nicholas Lunn, Marie Auger-Méthé

Animal movement is the primary means by which animals obtain resources and avoid hazards. Most movement exhibits directional bias that is related to environmental features (taxis), such as the location of food patches, predators, ocean currents, or wind. Numerous behaviours with directional bias can be characterised by maintaining orientation at an angle relative to the environmental stimuli (menotaxis), including navigation relative to sunlight or magnetic fields and energy-conserving flight across wind, however, no statistical methods exist to classify and characterise such behaviours.

We propose a flexible biased correlated random walk model that can identify menotactic behaviours without making a priori assumptions about the angle of bias. We apply the model within the framework of a multi-state hidden Markov model and describe methods to remedy information loss associated with coarse environmental data to improve characterisation of menotactic behaviours.

We illustrate the application of these methods by identifying cross wind olfactory foraging and drifting behaviour mediated by wind-driven sea ice drift in polar bears (Ursus maritimus) from remote tracking data.

The extensions we propose can be readily applied to movement data to identify and characterise menotactic behaviours and open up new avenues to investigate more mechanistic relationships between animal movement and the environment.

Modeling Spatio-Temporal Activity Patterns with Camera-Trap Data: An Integrated Approach
Fabiola Iannarilli, John Erb, John Fieberg

In a world under increasing human disturbance, species may have to modify their behavior to adapt to new conditions. Estimates of diel activity patterns from camera-trap data provide insights into the capacity of a species to adapt to natural and anthropogenic changes and the consequences of shifts in activity. The Kernel Density Estimators (KDEs) commonly used to estimate activity patterns ignore site-to-site variability intrinsic to camera-trap data collected at multiple sites, and may lead to biased estimates of uncertainty and misleading conclusions regarding the main drivers of activity patterns. Trigonometric terms and cyclic cubic splines paired with hierarchical models (i.e., Generalized Linear Mixed Models, GLMMs) can provide a valuable alternative. Like KDEs, these models accommodate circular data, but they also account for site-to-site and other sources of variability, correlation among repeated measures, and can more readily quantify and test hypotheses related to effects of covariates on activity patterns. Using empirical data, we illustrate how GLMM-based methods can quantify changes in activity levels in response to site-specific characteristics (e.g., environmental or sampling design features), seasonality, and co-occurring species.  Through simulations, we also show that 1. GLMMs with random-intercepts provide more accurate estimates of activity patterns compared to KDEs when sites vary in their frequency of use; 2. like KDEs, GLMMs with random-intercepts correctly identify the timing of peaks, but fail to estimate their magnitude when sites vary in the timing of peak levels of activity; and 3. GLMMs that also include random coefficients accommodate both variability in frequency of use and peak timing and provide the more accurate estimates. We conclude that GLMMs offer a viable and effective alternative to KDEs when modeling activity patterns.

Using a Bayesian Model to Compare Viral Transmission of Inland and Coastal Hatchery Salmonids in Pacific Northwest States
Jeffrey Mattheiss, Paige Ferguson, Rachel Breyta, Gael Kurath, David Paez

Juvenile salmonid mortality due to infectious hematopoietic necrosis virus (IHNV) can be a major burden on hatcheries, yet questions remain about how viral transmission occurs within diverse aquatic systems. A dynamic susceptible-exposed-infected (SEI) epidemiological model, incorporating a Bayesian statistical framework, was used to apply historical viral testing records to estimate potential viral transmission routes. The model was applied to real data from 37 hatchery locations in the Snake River Basin, 24 hatcheries in the Lower Columbia River Basin, and 39 hatcheries along Coastal Washington and Oregon; each subset representing a unique aquatic habitat. The virology data was derived from an expansive database that contains IHNV records from 2000-2013. Model assumptions were adjusted to account for environmental disparities and anthropogenic impacts that exist within each region. The model generated posterior distributions for parameters and estimated probabilities of juvenile infection at hatcheries given exposure by various routes. While migrating adult salmonids were responsible for the most instances of exposure within all regions, infection probabilities for each possible transmission route varied by location. The model predicted that Coastal and Lower Columbia River hatcheries experienced greatest infection probabilities from exposure by infected juveniles of the previous cohort, but that the Snake River hatcheries had the greatest infection probability from exposure by migrating adults. This study demonstrates transmission potential that exists regionally and can lead to possible IHNV source-sink discussions. Additionally, this research provides more insight on viral transmission at hatcheries and suggests potential improvements to biosecurity techniques. Finally, the model structure is not exclusive to this specific case study and can be applied to a different dataset to determine transmission potential of other pathogens, with other hosts, or within different regions.

A Comparison of Alternative Basis Function Approaches for Bayesian Time-To-Event Age-Period Survival Models
Alison Ketz, Daniel Storm, Anthony Apa, Rachel Barker, Cristian Oliva-Aviles, Daniel Walsh

Many factors may influence survival throughout the life history of an individual, including environmental drivers, predation pressure, maternal care, and genetic and phenotypic traits. We developed a Bayesian age-period model of survival to account for variation in the survival hazard due to age and time. We developed 5 different semi-parametric hazard rate models that use alternative basis functions to obtain hazards for the age and period effects. These included the intrinsic-Conditional Auto-Regressive (ICAR) model, a kernel convolution process model, B-splines, natural splines, as well as shape-constrained generalized additive models (GAM). We used simulations to evaluate model performance, and generated survival data using two hazard functional forms over the ages to reflect different life history strategies. We generated data for a r-select strategy, where juvenile mortality was highest at youngest ages and decreased over time. We also generated data reflecting a k-select strategy, with high juvenile mortality, low mortality for intermediate ages, and increased mortality during senescence. To incorporate variation in the hazard through time, we used a cyclic function, reflecting changes in mortality occurring independent of age, such as seasonal mortality. We evaluated the performance of these different models to examine bias, efficiency and computation time for 100 simulated data sets and found that the least biased and fastest models relied on the shape-constrained GAMs and natural splines to capture the age effects, with a B-spline adequately modeling variation in the hazard through time. We used these models to obtain age-period mortality hazard rates for white-tailed deer (Odocoileus virginianus) in south-central Wisconsin, USA using data obtained from GPS collared adult and telemetry collared juveniles from 2017-2020. We also used these models to obtain age-period mortality hazards from telemetry collared sharp-tailed grouse (Tympanuchus phasianellus) chicks and juveniles in northern Colorado, USA from 2015-2017.

Using Piecewise Regression to Identify Biological Phenomena in Biotelemetry Datasets
David Wolfson, David Andersen, John Fieberg

Technological advances in the field of animal tracking have greatly expanded the potential to remotely monitor animals, opening the door to exploring how animals shift their behavior over time or respond to external stimuli.  Here, we demonstrate how piecewise regression can be used to identify the presence and timing of potential shifts in a variety of biological responses using GPS telemetry and other biologging data streams. Different biological latent states can be inferred by partitioning a time-series into multiple segments based on changes in modeled responses (e.g., their mean, variance, trend, degree of autocorrelation) and specifying a unique model structure for each interval.  We provide five example applications highlighting a variety of taxonomic species, data streams, timescales, and biological phenomena. These examples include identification of altered movement (flee and return) immediately following a GPS collar deployment; a physiological response (spike in heart-rate) to a stressful stimulus (presence of a drone); a mortality event signaled by changes in collar temperature and Overall Dynamic Body Acceleration; altered movement immediately preceding parturition; and an unsupervised method for identifying the onset, return, duration, and staging use of long-distance migration. We implement analyses using the mcp package in R, which provides functionality for specifying and fitting a wide variety of user-defined model structures in a Bayesian framework and methods for assessing and comparing models using information criterion and cross-validation measures. This approach improves on existing segmentation methods by allowing prior biological knowledge to be directly incorporated into the model structure and is a straightforward means of assessing a variety of biologically relevant changes in animal behavior.

Contributed Oral
Location: Virtual Date: November 4, 2021 Time: 1:00 pm - 2:00 pm