Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

Mevin Hooten


Mevin Hooten


David Koons


James Powell


In ecological studies, the goal is often to describe and gain further insight into ecological processes underlying the data collected during observational studies. Because of the nature of observational data, it can often be difficult to separate the variation in the data from the underlying process or 'state dynamics.' In order to better address this issue, it is becoming increasingly common for researchers to use hierarchical models. Hierarchical spatial, temporal, and spatio-temporal models allow for the simultaneous modeling of both first and second order processes, thus accounting for underlying autocorrelation in the system while still providing insight into overall spatial and temporal pattern. In this particular study, I use two species of interest, the lesser and greater scaup (Aythya affinis and Aythya marila), as an example of how hierarchical models can be utilized in wildlife management studies. Scaup are the most abundant and widespread diving duck in North America, and are important game species. Since 1978, the continental population of scaup has declined to levels that are 16% below the 1955-2010 average and 34% below the North American Waterfowl Management Plan goal. The greatest decline in abundance of scaup appears to be occurring in the western boreal forest, where populations may have depressed rates of reproductive success, survival, or both. In order to better understand the causes of the decline, and better understand the biology of scaup in general, a level of high importance has been placed on retrospective analyses that determine the spatial and temporal changes in population abundance. In order to implement Bayesian hierarchical models, I used a method called Integrated Nested Laplace Approximation (INLA) to approximate the posterior marginal distribution of the parameters of interest, rather than the more common Markov Chain Monte Carlo (MCMC) approach. Based on preliminary analysis, the data appeared to be overdispersed, containing a disproportionately high number of zeros along with a high variance relative to the mean. Thus, I considered two potential data models, the negative binomial and the zero-inflated negative binomial. Of these models, the zero-inflated negative binomial had the lowest DIC, thus inference was based on this model. Results from this model indicated that a large proportion of the strata were not decreasing (i.e., the estimated slope of the beta parameter was not significantly different from zero). However, there were important exceptions with strata in the northwest boreal forest and southern prairie parkland habitats. Several strata in the boreal forest habitat had negative slope estimates, indicating a decrease in breeding pairs, while some of the strata in the prairie parkland habitat had positive slope estimates, indicating an increase in this region. Additionally, from looking at plots of individual strata, it seems that the strata experiencing increases in breeding pairs are experiencing dramatic increases. Overall, my results support previous work indicating a decline in population abundance in the northern boreal forest of Canada, and additionally indicate that the population of scaup has increased rapidly in the prairie pothole region since 1957. Yet, by accounting for spatial and temporal auto-correlation in the data, it appears that declines in abundance are not as widespread as previously reported.


This work made publicly available electronically on April 12, 2012.