1. Surveillance is critical for early detection of emerging and re-emerging infectious diseases. Weighted surveillance leverages heterogeneity in infection risk to increase sampling efficiency. 2. Here, we apply a Bayesian approach to estimate weights for 16 surveillance classes of white-tailed deer in Wisconsin, USA, relative to hunter-harvested yearling males. We used these weights to conduct a surveillance programme for detecting chronic wasting disease (CWD) in white-tailed deer at Shenandoah National Park (SHEN) in Virginia, USA. 3. Generally, for surveillance, risk of infection increased with age and was greater in males. Clinical suspect deer had the highest risk, with weight estimates of 33.33 and 9.09 for community-reported and hunter-reported suspect deer, respectively. Fawns had the lowest risk with an estimated weight of 0.001. 4. We used surveillance weights for Wisconsin deer to determine sampling effort required to detect a CWD-positive case in SHEN if prevalence in yearling males >= 0.025. The sampling required to detect CWD was 37-91 adult deer, depending on the adult male: female ratio in the surveillance stream. We collected rectal biopsies from 49 female and 21 male adult deer, and 10 additional samples from vehicle-killed deer. CWD was not detected and we concluded with 95% probability that prevalence in the reference population (yearling males) was between 0.0% and 3.6%. 5. Synthesis and applications. Our approach allows managers to estimate relative surveillance weights for different host classes and quantify limits of disease detection in real time when only a sample of animals from a population can be tested, resulting in considerable cost savings for agencies performing wildlife disease detection surveillance. Additionally, it provides a rigorous means of estimating prevalence limits when a disease/pathogen is not detected in a sample set. It is therefore applicable to other wildlife, domestic animal and human disease systems, which can be characterized by surveillance classes with heterogeneous probability of infection. This methodology is also extendable to other disciplines such as invasive species, environmental toxicology, and generally, any ecological question seeking to efficiently use scarce financial and human resources to maximize the detection probability of a rare event.

AbstractImplicit and explicit use of expert knowledge to inform ecological analyses is becoming increasingly common because it often represents the sole source of information in many circumstances. Thus, there is a need to develop statistical methods that explicitly incorporate expert knowledge, and can successfully leverage this information while properly accounting for associated uncertainty during analysis. Studies of cause‐specific mortality provide an example of implicit use of expert knowledge when causes‐of‐death are uncertain and assigned based on the observer's knowledge of the most likely cause. To explicitly incorporate this use of expert knowledge and the associated uncertainty, we developed a statistical model for estimating cause‐specific mortality using a data augmentation approach within a Bayesian hierarchical framework. Specifically, for each mortality event, we elicited the observer's belief of cause‐of‐death by having them specify the probability that the death was due to each potential cause. These probabilities were then used as prior predictive values within our framework. This hierarchical framework permitted a simple and rigorous estimation method that was easily modified to include covariate effects and regularizing terms. Although applied to survival analysis, this method can be extended to any event‐time analysis with multiple event types, for which there is uncertainty regarding the true outcome. We conducted simulations to determine how our framework compared to traditional approaches that use expert knowledge implicitly and assume that cause‐of‐death is specified accurately. Simulation results supported the inclusion of observer uncertainty in cause‐of‐death assignment in modeling of cause‐specific mortality to improve model performance and inference. Finally, we applied the statistical model we developed and a traditional method to cause‐specific survival data for white‐tailed deer, and compared results. We demonstrate that model selection results changed between the two approaches, and incorporating observer knowledge in cause‐of‐death increased the variability associated with parameter estimates when compared to the traditional approach. These differences between the two approaches can impact reported results, and therefore, it is critical to explicitly incorporate expert knowledge in statistical methods to ensure rigorous inference.

ABSTRACTWe developed models and provide computer code to make carcass recovery data more useful to wildlife managers. With these tools, wildlife managers can understand the spatial, temporal (e.g., across time periods, seasons), and demographic patterns in mortality causes from carcass recovery datasets. From datasets of radio‐collared and non‐collared carcasses, managers can calculate the detection bias by mortality cause in a non‐collared carcass dataset compared to a collared carcass dataset. As a first step, we provide a standard procedure to assign mortality causes to carcasses. We provide an example of these methods for radio‐collared wolves (n = 208) and non‐collared wolves (n = 668) found dead in Wisconsin (1979–2012). We analyzed differences in mortality cause relative to season, age and sex classes, wolf harvest zones, and recovery phase (1979–1995: initial recovery, 1996–2002: early growth, 2003–2012: late growth). Seasonally, illegal kills and natural deaths were proportionally higher in winter (Oct–Mar) than summer (Apr–Sep) for collared wolves, whereas vehicle strikes and legal kills were higher in summer than winter. Spatially, more illegally killed collared wolves occurred in eastern wolf harvest zones where wolves reestablished more slowly and in the central forest region where optimal habitat is isolated by agriculture. Natural mortalities of collared wolves (e.g., disease, intraspecific strife, or starvation) were highest in western wolf harvest zones where wolves established earlier and existed at higher densities. Calculating detection bias in the non‐collared dataset revealed that more than half of the non‐collared carcasses on the landscape are not found. The lowest detection probabilities for non‐collared carcasses (0.113–0.176) occurred in winter for natural, illegal, and unknown mortality causes. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

Meadow voles (Microtus pennsylvanicus) are permissive to chronic wasting disease (CWD) infection, but their susceptibility to other transmissible spongiform encephalopathies (TSEs) is poorly characterized. In this initial study, we intracerebrally challenged 6 meadow voles with 2 isolates of sheep scrapie. Three meadow voles acquired a TSE after the scrapie challenge and an extended incubation period. The glycoform profile of proteinase K-resistant prion protein (PrPres) in scrapie-sick voles remained similar to the sheep inocula, but differed from that of voles clinically affected by CWD. Vacuolization patterns and disease-associated prion protein (PrPSc) deposition were generally similar in all scrapie-affected voles, except in the hippocampus, where PrPSc staining varied markedly among the animals. Our results demonstrate that meadow voles can acquire a TSE after intracerebral scrapie challenge and that this species could therefore prove useful for characterizing scrapie isolates.

Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.

Understanding the seasonal timing of disease transmission can lead to more effective control strategies, but the seasonality of transmission is often unknown for pathogens transmitted directly. We inserted vaginal implant transmitters (VITs) in 575 elk (Cervus elaphus canadensis) from 2006 to 2014 to assess when reproductive failures (i.e., abortions or still births) occur, which is the primary transmission route of Brucella abortus, the causative agent of brucellosis in the Greater Yellowstone Ecosystem. Using a survival analysis framework, we developed a Bayesian hierarchical model that simultaneously estimated the total baseline hazard of a reproductive event as well as its 2 mutually exclusive parts (abortions or live births). Approximately, 16% (95% CI=0.10, 0.23) of the pregnant seropositive elk had reproductive failures, whereas 2% (95% CI=0.01, 0.04) of the seronegative elk had probable abortions. Reproductive failures could have occurred as early as 13 February and as late as 10 July, peaking from March through May. Model results suggest that less than 5% of likely abortions occurred after 6 June each year and abortions were approximately 5 times more likely in March, April, or May compared to February or June. In western Wyoming, supplemental feeding of elk begins in December and ends during the peak of elk abortions and brucellosis transmission (i.e., Mar and Apr). Years with more snow may enhance elk-to-elk transmission on supplemental feeding areas because elk are artificially aggregated for the majority of the transmission season. Elk-to-cattle transmission will depend on the transmission period relative to the end of the supplemental feeding season, elk seroprevalence, population size, and the amount of commingling. Our statistical approach allowed us to estimate the probability density function of different event types over time, which may be applicable to other cause-specific survival analyses. It is often challenging to assess the cause of death, or in this case whether the reproductive event was an abortion or live birth. Accounting for uncertainty in the event type is an important future addition to our methodological approach. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

ABSTRACT Understanding effects of location and timing of harvest seasons on mortality of ducks and geese from hunting is important in forming regulations that sustain viable waterfowl populations throughout their range. During 1990 and 1991 we alternately marked 80 hatching year (HY), female mallards along the Vermont–Quebec border; half with radio‐transmitters and bands and half with only aluminum leg bands. We monitored radio‐marked ducks daily and recorded survival status weekly for 15 weeks from August until December each year. Mallard mortalities began 25 September when the hunting season opened in the Province of Quebec, Canada. Overall survival of mallards at week 10 did not differ between years (0.51 in 1990 vs. 0.43 in 1991) or differ from that of HY American black ducks (0.44 females, 0.42 males) based on proportional hazard analysis in a Bayesian framework. The mortality rates for mallards from hunting (0.47) and causes unrelated to hunting (0.06) were similar between years and to those rates for HY black ducks at that same site. Hunter harvest accounted for most of the mortality recorded during this study and illegal feeding (i.e., baiting) at sites just before and during the hunting season was observed. Females with lower body condition index had greater mortality rates; a 1‐standard‐deviation increase in condition index would reduce mortality hazard by about 29%. Management options that may increase mallard survival in the area include lowering daily bag limit in Quebec and suspending split hunting seasons in Vermont that increase harvest, delaying opening date of hunting in Quebec to allow for increased body condition before hunting season opens, and improving enforcement of baiting restrictions. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

This article describes a method for quantifying blood flow distribution among lung alveoli. Our method is based on analysis of trapping patterns of small diameter (4 μm) fluorescent latex particles infused into lung capillaries. Trapping patterns are imaged using confocal microscopy, and the images are analyzed statistically using SAS subroutines. The resulting plots provide a quantifiable way of assessing interalveolar perfusion distribution in a way that has not previously been possible. Methods for using this technique are described, and the SAS routines are included. This technique can be an important tool for learning how this critical vascular bed performs in health and disease.

Many ecological and epidemiological studies occur in systems with mobile individuals and heterogeneous landscapes. Using a simulation model, we show that the accuracy of inferring an underlying biological process from observational data depends on movement and spatial scale of the analysis. As an example, we focused on estimating the relationship between host density and pathogen transmission. Observational data can result in highly biased inference about the underlying process when individuals move among sampling areas. Even without sampling error, the effect of host density on disease transmission is underestimated by approximately 50 % when one in ten hosts move among sampling areas per lifetime. Aggregating data across larger regions causes minimal bias when host movement is low, and results in less biased inference when movement rates are high. However, increasing data aggregation reduces the observed spatial variation, which would lead to the misperception that a spatially targeted control effort may not be very effective. In addition, averaging over the local heterogeneity will result in underestimating the importance of spatial covariates. Minimizing the bias due to movement is not just about choosing the best spatial scale for analysis, but also about reducing the error associated with using the sampling location as a proxy for an individual’s spatial history. This error associated with the exposure covariate can be reduced by choosing sampling regions with less movement, including longitudinal information of individuals’ movements, or reducing the window of exposure by using repeated sampling or younger individuals.

Read the Feature Paper: Bayesian shared frailty models for regional inference about wildlife survivalOther Commentaries on this paper: Combining information in hierarchical models improves inferences in population ecology and demographic population analyses; ‘Each site has its own survival probability, but information is borrowed across sites to tell us about survival in each site’: random effects models as means of borrowing strength in survival studies of wild vertebratesResponse from the authors: ‘Exciting statistics’: the rapid development and promising future of hierarchical models for population ecology

Recent technological advances, such as proximity loggers, allow researchers to collect complete interaction histories, day and night, among sampled individuals over several months to years. Social network analyses are an obvious approach to analyzing interaction data because of their flexibility for fitting many different social structures as well as the ability to assess both direct contacts and indirect associations via intermediaries. For many network properties, however, it is not clear whether estimates based upon a sample of the network are reflective of the entire network. In wildlife applications, networks may be poorly sampled and boundary effects will be common. We present an alternative approach that utilizes a hierarchical modeling framework to assess the individual, dyadic, and environmental factors contributing to variation in the interaction rates and allows us to estimate the underlying process variation in each. In a disease control context, this approach will allow managers to focus efforts on those types of individuals and environments that contribute the most toward super-spreading events. We account for the sampling distribution of proximity loggers and the non-independence of contacts among groups by only using contact data within a group during days when the group membership of proximity loggers was known. This allows us to separate the two mechanisms responsible for a pair not contacting one another: they were not in the same group or they were in the same group but did not come within the specified contact distance. We illustrate our approach with an example dataset of female elk from northwestern Wyoming and conclude with a number of important future research directions.

Chronic wasting disease (CWD) is a fatal disease of deer, elk, and moose transmitted through direct, animal-to-animal contact, and indirectly, via environmental contamination. Considerable attention has been paid to modeling direct transmission, but despite the fact that CWD prions can remain infectious in the environment for years, relatively little information exists about the potential effects of indirect transmission on CWD dynamics. In the present study, we use simulation models to demonstrate how indirect transmission and the duration of environmental prion persistence may affect epidemics of CWD and populations of North American deer. Existing data from Colorado, Wyoming, and Wisconsin's CWD epidemics were used to define plausible short-term outcomes and associated parameter spaces. Resulting long-term outcomes range from relatively low disease prevalence and limited host-population decline to host-population collapse and extinction. Our models suggest that disease prevalence and the severity of population decline is driven by the duration that prions remain infectious in the environment. Despite relatively low epidemic growth rates, the basic reproductive number, R(0), may be much larger than expected under the direct-transmission paradigm because the infectious period can vastly exceed the host's life span. High prion persistence is expected to lead to an increasing environmental pool of prions during the early phases (i.e. approximately during the first 50 years) of the epidemic. As a consequence, over this period of time, disease dynamics will become more heavily influenced by indirect transmission, which may explain some of the observed regional differences in age and sex-specific disease patterns. This suggests management interventions, such as culling or vaccination, will become increasingly less effective as CWD epidemics progress.

The relationship between host density and parasite transmission is central to the effectiveness of many disease management strategies. Few studies, however, have empirically estimated this relationship particularly in large mammals. We applied hierarchical Bayesian methods to a 19-year dataset of over 6400 brucellosis tests of adult female elk (Cervus elaphus) in northwestern Wyoming. Management captures that occurred from January to March were over two times more likely to be seropositive than hunted elk that were killed in September to December, while accounting for site and year effects. Areas with supplemental feeding grounds for elk had higher seroprevalence in 1991 than other regions, but by 2009 many areas distant from the feeding grounds were of comparable seroprevalence. The increases in brucellosis seroprevalence were correlated with elk densities at the elk management unit, or hunt area, scale (mean 2070 km(2); range = [95-10237]). The data, however, could not differentiate among linear and non-linear effects of host density. Therefore, control efforts that focus on reducing elk densities at a broad spatial scale were only weakly supported. Additional research on how a few, large groups within a region may be driving disease dynamics is needed for more targeted and effective management interventions. Brucellosis appears to be expanding its range into new regions and elk populations, which is likely to further complicate the United States brucellosis eradication program. This study is an example of how the dynamics of host populations can affect their ability to serve as disease reservoirs.

Underlying dynamic event processes unfolding in continuous time give rise to spatiotemporal patterns that are sometimes observable at only a few discrete times. Such event processes may be modulated simultaneously over several spatial (e.g., latitude and longitude) and temporal (e.g., age, calendar time, and cohort) dimensions. The ecological challenge is to understand the dynamic latent processes that were integrated over several dimensions (space and time) to produce the observed pattern: a so‐called inverse problem. An example of such a problem is characterizing epidemiological rate processes from spatially referenced age‐specific prevalence data for a wildlife disease such as chronic wasting disease (CWD). With age‐specific prevalence data, the exact infection times are not observed, which complicates the direct estimation of rates. However, the relationship between the observed data and the unobserved rate variables can be described with likelihood equations. Typically, for problems with multiple timescales, the likelihoods are integral equations without closed forms. The complexity of the likelihoods often makes traditional maximum‐likelihood approaches untenable. Here, using seven years of hunter‐harvest prevalence data from the CWD epidemic in white‐tailed deer (Odocoileus virginianus) in Wisconsin, USA, we develop and explore a Bayesian approach that allows for a detailed examination of factors modulating the infection rates over space, age, and time, and their interactions. Our approach relies on the Bayesian ability to borrow strength from neighbors in both space and time. Synthesizing a number of areas of event time analysis (current‐status data, age/period/cohort models, Bayesian spatial shared frailty models), our general framework has very broad ecological applicability beyond disease prevalence data to a number of important ecological event time analyses, including general survival studies with multiple time dimensions for which existing methodology is limited. We observed strong associations of infection rates with age, gender, and location. The infection rate appears to be increasing with time. We could not detect growth hotspots, or location by time interactions, which suggests that spatial variation in infection rates is determined primarily by when the disease arrives locally, rather than how fast it grows. We emphasize assumptions and the potential consequences of their violations.