Estimating the phenology of elk brucellosis transmission with hierarchical models of cause-specific and baseline hazards

Cross, Paul C.; Maichak, Eric J.; Rogerson, Jared D.; Irvine, Kathryn M.; Jones, Jennifer D.; Heisey, Dennis M.; Edwards, William H.; Scurlock, Brandon M.

doi:10.1002/jwmg.883

Cited by 34 publications

(58 citation statements)

References 32 publications

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“…In this study, we borrow spatial modelling frameworks from animal ecology and apply them to a chronic disease of wildlife and livestock. Brucellosis transmission occurs during spring when animals leave winter range and migrate to higher elevations (Cross et al., ; Jones et al., ), and our results demonstrate how annual weather variability can influence the phenology of host movement and thus the spatial dynamics of brucellosis transmission risk (Figures and ). As climate change continues to alter weather patterns, host movements and spatial distribution will inevitably change, resulting in novel disease dynamics in the future.…”

Section: Discussionsupporting

confidence: 60%

“…To translate probability of elk use to disease transmission risk, we calculated the predicted number of abortion events a xt per 500 m pixel x , per time step t (in days), for each of our five scenarios as

a_{x t} = u false(x, t false) \times N_{x} \times S_{x} \times y \times p false(a_{t} false)

where u ( x, t ) is the daily predicted probability of elk use, N x is the number of female adult and yearling elk counted at each feedground (Appendix ), S x is the average brucellosis seroprevelance estimated on each feedground (Appendix ), y is a mean pregnancy rate of 86.8% estimated based on ultrasonography of 871 adult and yearling female elk in winter across all feedgrounds from 1995 to 2012 (Wyoming Game and Fish Department, Unpubl. data), and p ( a t ) is the predicted daily probability of aborting given an individual is seropositive and pregnant (empirically estimated from Cross et al., ). The predicted number of abortion events a xt per 500 m pixel was calculated for each subpopulation separately and then summed together across the entire study area.…”

Section: Methodsmentioning

confidence: 99%

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Linking spring phenology with mechanistic models of host movement to predict disease transmission risk

Merkle

Cross

Scurlock

et al. 2017

Journal of Applied Ecology

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Disease models typically focus on temporal dynamics of infection, while often neglecting environmental processes that determine host movement. In many systems, however, temporal disease dynamics may be slow compared to the scale at which environmental conditions alter host space‐use and accelerate disease transmission. Using a mechanistic movement modelling approach, we made space‐use predictions of a mobile host (elk [Cervus Canadensis] carrying the bacterial disease brucellosis) under environmental conditions that change daily and annually (e.g., plant phenology, snow depth), and we used these predictions to infer how spring phenology influences the risk of brucellosis transmission from elk (through aborted foetuses) to livestock in the Greater Yellowstone Ecosystem. Using data from 288 female elk monitored with GPS collars, we fit step selection functions (SSFs) during the spring abortion season and then implemented a master equation approach to translate SSFs into predictions of daily elk distribution for five plausible winter weather scenarios (from a heavy snow, to an extreme winter drought year). We predicted abortion events by combining elk distributions with empirical estimates of daily abortion rates, spatially varying elk seroprevelance and elk population counts. Our results reveal strong spatial variation in disease transmission risk at daily and annual scales that is strongly governed by variation in host movement in response to spring phenology. For example, in comparison with an average snow year, years with early snowmelt are predicted to have 64% of the abortions occurring on feedgrounds shift to occurring on mainly public lands, and to a lesser extent on private lands. Synthesis and applications. Linking mechanistic models of host movement with disease dynamics leads to a novel bridge between movement and disease ecology. Our analysis framework offers new avenues for predicting disease spread, while providing managers tools to proactively mitigate risks posed by mobile disease hosts. More broadly, we demonstrate how mechanistic movement models can provide predictions of ecological conditions that are consistent with climate change but may be more extreme than has been observed historically.

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Section: Discussionsupporting

confidence: 60%

a_{x t} = u false(x, t false) \times N_{x} \times S_{x} \times y \times p false(a_{t} false)

Section: Methodsmentioning

confidence: 99%

Linking spring phenology with mechanistic models of host movement to predict disease transmission risk

Merkle

Cross

Scurlock

et al. 2017

Journal of Applied Ecology

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“…Our approach to estimate cause‐specific mortality expands on the two‐component model of Cross et al. (). For the first component, we modeled the overall event hazard using the conditional survival function (Kalbfleisch & Prentice, ) where we defined the overall event hazard as any death irrespective of the source of mortality, excluding known censoring events (e.g., survived to the end of study, dropped collar).…”

Section: Methodsmentioning

confidence: 99%

“…To account for the competing risks nature of various potential sources of mortality, we partitioned the overall event hazard by each source of mortality in the second component of our model. Conditional on death, we used the categorical distribution to estimate the probabilities the death was due to the various potential sources of mortality, hereafter called cause‐specific probabilities (Cross et al., ; Figure ). The probability an individual's death was associated with a specific source of mortality (π k ) was modeled as: cause i , u , k ~ Categorical[π u , k ], where cause i , u , k = indicator (1 or 0) if cause‐of‐death for the i th subject during the u th interval was assigned by the observer to the k th source of mortality.…”

Section: Methodsmentioning

confidence: 99%

Using expert knowledge to incorporate uncertainty in cause‐of‐death assignments for modeling of cause‐specific mortality

Walsh

Norton

Storm

et al. 2017

Ecology and Evolution

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Implicit 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.

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“…In the Wyoming portion of the southern GYE, there are 23 feedgrounds operating annually and, at times, local seroprevalence can reach as high as 60% (Cotterill et al., ). With such high exposure, one might expect that abortions should be frequent and readily observed, but on average, fewer than two fetuses were detected annually over a 50‐year period (Cross et al., ). Because of the difficulty of observation, a more rigorous approach for detecting abortions was undertaken using vaginal‐implant transmitters (VITs) which were cultured for B. abortus within days after being expelled due to abortion or parturition.…”

Section: Introductionmentioning

confidence: 99%

Hidden cost of disease in a free‐ranging ungulate: brucellosis reduces mid‐winter pregnancy in elk

Cotterill

Cross

Middleton

et al. 2018

Ecology and Evolution

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Demonstrating disease impacts on the vital rates of free‐ranging mammalian hosts typically requires intensive, long‐term study. Evidence for chronic pathogens affecting reproduction but not survival is rare, but has the potential for wide‐ranging effects. Accurately quantifying disease‐associated reductions in fecundity is important for advancing theory, generating accurate predictive models, and achieving effective management. We investigated the impacts of brucellosis (Brucella abortus) on elk (Cervus canadensis) productivity using serological data from over 6,000 captures since 1990 in the Greater Yellowstone Ecosystem, USA. Over 1,000 of these records included known age and pregnancy status. Using Bayesian multilevel models, we estimated the age‐specific pregnancy probabilities of exposed and naïve elk. We then used repeat‐capture data to investigate the full effects of the disease on life history. Brucellosis exposure reduced pregnancy rates of elk captured in mid‐ and late‐winter. In an average year, we found 60% of exposed 2‐year‐old elk were pregnant compared to 91% of their naïve counterparts (a 31 percentage point reduction, 89% HPDI = 20%–42%), whereas exposed 3‐ to 9‐year‐olds were 7 percentage points less likely to be pregnant than naïve elk of their same age (89% HPDI = 2%–11%). We found these reduced rates of pregnancy to be independent from disease‐induced abortions, which afflict a portion of exposed elk. We estimate that the combination of reduced pregnancy by mid‐winter and the abortions following mid‐winter reduces the reproductive output of exposed female elk by 24%, which affects population dynamics to a similar extent as severe winters or droughts. Exposing hidden reproductive costs of disease is essential to avoid conflating them with the effects of climate and predation. Such reproductive costs cause complex population dynamics, and the magnitude of the effect we found should drive a strong selection gradient if there is heritable resistance.

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Estimating the phenology of elk brucellosis transmission with hierarchical models of cause-specific and baseline hazards

Cited by 34 publications

References 32 publications

Linking spring phenology with mechanistic models of host movement to predict disease transmission risk

Linking spring phenology with mechanistic models of host movement to predict disease transmission risk

Using expert knowledge to incorporate uncertainty in cause‐of‐death assignments for modeling of cause‐specific mortality

Hidden cost of disease in a free‐ranging ungulate: brucellosis reduces mid‐winter pregnancy in elk

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