William Link, Ph.D.
Dr. William Link has been Mathematical Statistician at the Patuxent Wildlife Research Center since 1987.
- University of Massachusetts at Amherst; M.A. (1983), Ph.D. (1986). Thesis: Contributions to Reliability Theory and Survival Analysis. Advisors: Profs. Ramesh Korwar, Hui-Kuang Hsieh, Constantine Gatsonis, and David Hosmer
- Western Maryland College; B.A. (mathematics)
- USGS Patuxent Wildlife Research Center; Laurel, Maryland. Mathematical Statistician. 1987-present
- University of Otago; Dunedin, New Zealand. Visiting Professor of Statistics. 2001
- Towson University; Towson, Maryland. Associate Professor of Mathematics. 1986-1987
Mark-recapture, count surveys, demographic analysis, Bayesian methods, multimodel inference
Science and Products
The Challenge: Many critical wildlife surveys, such as the North American Breeding Bird Survey (BBS), are analyzed using complex hierarchical models. These models are generally multi-scale and contain random effects; the standard approaches to model selection and assessment of model fit are often inappropriate and no simple way exists to compare alternative models. However, a clear need exists for these assessments. Many alternative models new exist for analysis of BBS data, and simply presenting multiple results without clear guidance on which model is most appropriate will lead to confusion among users of BBS data and limit use of this important survey.
The Challenge: Over the last half of the 20th century, the breeding range of American black duck (Anas rubripes) has contracted from central Canada and the Northeastern United States toward eastern Canada. This reduction in size of the breeding range has been reflected in a steady decline of black ducks counted during winter surveys, both the midwinter Waterfowl Survey conducted by the U. S. Fish and Wildlife Service and the Christmas Bird Count. The causes of the declines are unclear. Hunting regulations have been restricted to decrease the harvest. To improve our understanding of black duck population dynamics and of the role of harvest in population change, a variety of surveys, banding studies, and research activities have been conducted for this economically important species. Patuxent staff have been active participants in these activities, and have served on the Technical Committee and Management Board of the Black Duck Joint Venture of the North American Waterfowl Management Plan. Here, we describe Patuxent’s role in assisting with development and analysis of surveys for black ducks in eastern Canada.
The Challenge: Population status information is required for management of migratory bird populations, and structured decision making and adaptive anagement place additional emphasis on the need for rigorous survey designs and robust estimation methods. The North American Breeding Bird Survey (BBS) and Christmas Bird Count (CBC) provide continent-scale information on breeding and wintering populations of >450 species of North American birds, and for many species these two surveys are our only data source for population status and trend information. Appropriate analyses of these important surveys require sophisticated methods to accommodate variation in survey efficiency over the large areas covered by the surveys and to control for factors that influence detection of birds. Factors such as observer quality and effort, if not appropriately controlled for in the analysis, can lead to biased estimates of population change.
The Challenge: Much of wildlife research consists of the description of variation in data. Some of the variation results from spatial and temporal change in populations, while some results from biologically irrelevant sampling variation induced by the process of data collection. Distinguishing relevant from irrelevant variation is the first task of statistical analysis, but the job does not end there. Even if the true values of population parameters were known, without the contamination of sampling variation, the investigation of population processes would require an evaluation of pattern among parameters.
The Challenge: Wildlife science and management are guided by data, and it is unquestionably the case that the greatest success occurs when good data are analyzed by good statistical methods.
The Challenge: Diclofenac is a non-steroidal anti-inflammatory drug that has been used by veterinarians for the treatment of inflammation, fever and pain in domestic livestock. This drug appears to have been the principal cause of a severe population crash of vultures of the genus Gyps in India and Pakistan. Vultures unintentionally ingested diclofenac when scavenging livestock treated shortly before death. This is perhaps the only well-documented instance of a veterinary drug resulting in an adverse population-level effect in non-target free-ranging birds. Diclofenac is registered for veterinary use in many Western hemisphere countries (e.g., Chile, Argentina, Peru, Ecuador, and provisional use in the United States), and there is potential for non-target exposure of birds of prey, including endangered California condors (Gymnogyps californianus) in the western U.S.
Model selection for the North American Breeding Bird Survey: A comparison of methods
The North American Breeding Bird Survey (BBS) provides data for >420 bird species at multiple geographic scales over 5 decades. Modern computational methods have facilitated the fitting of complex hierarchical models to these data. It is easy to propose and fit new models, but little attention has been given to model selection. Here, we discuss...Link, William; Sauer, John; Niven, Daniel
The first 50 years of the North American Breeding Bird Survey
The vision of Chandler (Chan) S. Robbins for a continental-scale omnibus survey of breeding birds led to the development of the North American Breeding Bird Survey (BBS). Chan was uniquely suited to develop the BBS. His position as a government scientist had given him experience with designing and implementing continental-scale surveys, his...Sauer, John; Ziolkowski, David; Pardieck, Keith L.; Smith, Adam C.; Hudson, Marie-Anne R.; Rodriguez, Vicente; Berlanga, Humberto; Niven, Daniel; Link, William
Expanding the North American Breeding Bird Survey analysis to include additional species and regions
The North American Breeding Bird Survey (BBS) contains data for >700 bird species, but analyses often focus on a core group of ∼420 species. We analyzed data for 122 species of North American birds for which data exist in the North American Breeding Bird Survey (BBS) database but are not routinely analyzed on the BBS Summary and Analysis...Sauer, John; Niven, Daniel; Pardieck, Keith L.; Ziolkowski, David; Link, William
The North American Breeding Bird Survey, results and analysis 1966 - 2015
This website presents population change information for more than 400 species of North American birds, as estimated from the North American Breeding Bird Survey. Estimates of trend (interval-specific estimates of population change), annual indices of abundance, and maps of abundance and population change for these species are presented for a...Sauer, John; Niven, Daniel; Hines, James; Ziolkowski, David; Pardieck, Keith L.; Fallon, J.E.; Link, William
Bayesian cross-validation for model evaluation and selection, with application to the North American Breeding Bird Survey
The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty....Link, William; Sauer, John R.
Tarangire revisited: Consequences of declining connectivity in a tropical ungulate population
The hyper-abundance of migratory wildlife in many ecosystems depends on maintaining access to seasonally available resources. In Eastern and Southern Africa, land-use change and a loss of connectivity have coincided with widespread declines in the abundance and geographic range of ungulate populations. Using photographic capture-mark-recapture, we...Morrison, Thomas A.; Link, William; Newmark, William D.; Foley, Charles A.H.; Bolger, Douglas T.
Individual heterogeneity in growth and age at sexual maturity: A gamma process analysis of capture–mark–recapture data
Knowledge of organisms’ growth rates and ages at sexual maturity is important for conservation efforts and a wide variety of studies in ecology and evolutionary biology. However, these life history parameters may be difficult to obtain from natural populations: individuals encountered may be of unknown age, information on age at sexual maturity...Link, William; Hesed, Kyle Miller
Combining waterfowl and breeding bird survey data to estimate wood duck breeding population size in the Atlantic Flyway
We combined data from the Atlantic Flyway Breeding Waterfowl Survey (AFBWS) and the North American Breeding Bird Survey (BBS) to estimate the number of wood ducks (Aix sponsa) in the United States portion of the Atlantic Flyway from 1993 to 2013. The AFBWS is a plot-based survey that covers most of the northern and central portions of the Flyway;...Guthrie Zimmerman; Sauer, John; Fleming, Kathy; Link, William; Pamela R. Garrettson
Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective
Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the...Barker, Richard J.; Link, William A.
Modeling participation duration, with application to the North American Breeding Bird Survey
We consider “participation histories,” binary sequences consisting of alternating finite sequences of 1s and 0s, ending with an infinite sequence of 0s. Our work is motivated by a study of observer tenure in the North American Breeding Bird Survey (BBS). In our analysis, j indexes an observer’s years of service and...Link, William; Sauer, John
Hierarchical model analysis of the Atlantic Flyway Breeding Waterfowl Survey
We used log-linear hierarchical models to analyze data from the Atlantic Flyway Breeding Waterfowl Survey. The survey has been conducted by state biologists each year since 1989 in the northeastern United States from Virginia north to New Hampshire and Vermont. Although yearly population estimates from the survey are used by the United States Fish...Sauer, John R.; Zimmerman, Guthrie S.; Klimstra, Jon D.; Link, William A.
Insights into the latent multinomial model through mark-resight data on female grizzly bears with cubs-of-the-year
Mark-resight designs for estimation of population abundance are common and attractive to researchers. However, inference from such designs is very limited when faced with sparse data, either from a low number of marked animals, a low probability of detection, or both. In the Greater Yellowstone Ecosystem, yearly mark-resight data are collected for...Higgs, Megan D.; Link, William; White, Gary C.; Haroldson, Mark A.; Bjornlie, Daniel D