Parsing the effects of demography, climate and management on recurrent brucellosis outbreaks in elk

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2019 The Authors. Journal of Applied Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society 1Department of Wildland Resources, Utah State University, Logan, UT, USA 2U.S. Geological Survey, Northern Rocky Mountain Science Center, Bozeman, MT, USA 3Wyoming Cooperative Fish and Wildlife Research Unit, Department of Zoology and Physiology, University of Wyoming, Laramie, WY, USA 4Wyoming Game and Fish Department, Pinedale, WY, USA

influenced by climate and population size (Kilpatrick, Gillin, & Daszak, 2009). Elk, however, are widely distributed inside and outside the park, and brucellosis periodically spills back from elk to cattle (Kamath et al., 2016) at significant cost to the affected cattle industry. The pathogen is transmitted by direct contact with fetal tissues and fluids resulting from diseaseinduced abortions (National Research Council, 1998). Live births from infected mothers can also cause horizontal transmission if other herd members inspect the newborn calf or birth tissues, although parturient elk sequester themselves and their newborn calves (Van Campen & Rhyan, 2010). Vertical transmission is not thought to be important. Bison and elk born to seropositive mothers can have detectable antibodies, but these disappear after several months and do not provide lifelong immunity (Rhyan et al., 2009;Thorne, Morton, Blunt, & Dawson, 1978). Thus elk-to-elk and elk-to-cattle transmissions are most likely during and after abortion events, which primarily occur between March and May (Cross et al., 2015) and in the first year following infection (Thorne et al., 1978).
Elk-to-elk transmission of brucellosis is facilitated by 23 feedgrounds in Wyoming that aggregate large herds during part of the transmission season. Hay is provided daily at these diversionary locations to reduce depredation of private haystacks and minimize comingling with cattle in winter as part of a disease-risk mitigation strategy. Feedgrounds reduce local spillover risk to cattle in the short term (Brennan, Cross, Portacci, Scurlock, & Edwards, 2017), yet simultaneously contribute to disease persistence .
The seasonality of transmission, coinciding with winter feeding and high site fidelity of elk to particular feedgrounds, creates a metapopulation structure where feedground herds are subpopulations within which brucellosis circulates. This presents a fortuitous study system for investigating the drivers of pathogen transmission. Drivers can be broadly categorized as those that are exogenous, or 'external' to the host and pathogen, like climatic variables, and those that are endogenous, or 'internal', like vital rates or epidemiological processes.

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This article is protected by copyright. All rights reserved Interactions between the two can make it difficult to infer the underlying processes from the observed serological patterns (Koelle & Pascual, 2004;Paull et al., 2017). In the context of a metapopulation, strong environmental forcing might generate a Moran effect, with strong synchrony in outbreak size or timing across subpopulations (Moran, 1953). Yet, if disease trends are sensitive to stochasticity, vital rates, or epidemiological rates, then we might instead expect asynchrony despite common external forcing (Rohani et al. 1999).
Exogenous effects also depend on conditions within the host population. Strong forcing could facilitate pathogen transmission, but not if herd immunity is already high.
Previous work suggested that deep snowpack increases elk-to-elk brucellosis transmission (Cross, Edwards, Scurlock, Maichak, & Rogerson, 2007) and that dispersing haypiles across greater area on the feedground could reduce elk density by 83% and contagious contacts by 91% (Creech et al., 2012). The Wyoming Game and Fish Department (WGFD) has thus experimented with "low-density feeding" in addition to a test-and-slaughter program during late winter from 2006 to 2010 at three feedgrounds. The effectiveness of these actions had not been fully evaluated, which motivated our current work. We modeled the underyling infection dynamics of brucellosis in free-ranging, winter-fed elk using compartmental SIR models and explored the relative influences of demographic and environmental drivers on transmission. This provided a baseline understanding of seroprevalence trends within a metapopulation context while accounting for the ambiguity of serological status. Against this backdrop we assessed two management interventions in relation to their intended effectiveness in reducing disease prevalence: 'low-density' feeding and test-and-slaughter.

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This article is protected by copyright. All rights reserved Our study area is western Wyoming, south of Yellowstone National Park, USA, at winter feedgrounds that are used by approximately 80% of the region's elk annually (Figure 1; Dean et al., 2004). Elk captures occurred principally in February of each year for the purpose of disease surveillance. Blood was drawn only from female elk because males are insignificant as vectors of infection (National Research Council, 1998). Serological testing was performed in accordance with National Veterinary Services Laboratory protocols as described by Maichak et al. (2017). Elk calves were excluded from serological testing.
Serologic test results were aggregated by site and year. Greys River, Dell Creek, and Muddy Creek feedgrounds each had 15-25 years of serology data with robust sample sizes, despite periodic gaps (Table S1). Demographic data included adult counts by sex and the number of calves present. Attendance at these feedgrounds ranged from 100-700 adult female elk per year. Counts and age/sex classifications were recorded during peak-winter along feedlines, when feedground attendance by elk is presumed highest. One additional feedground, Scab Creek, provided sufficient data with which to test our top model and parameter estimates.
Beginning in 2009 'low-density' feeding practices were adopted at Greys River feedground.
Reliable feed distribution and elk density data were unavailable and so we characterized the experimental treatment as a categorical (before-and-after) variable. Test-and-slaughter of seropositive female elk took place at Muddy Creek and Scab Creek, where capture and testing rates ranged from 29-62% of attending female elk per year (Table S2;

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Partially-observed Markov process models
Deterministic compartmental models are central to the study of disease dynamics. Although statistical inference is simpler with deterministic models, "many infectious systems are fundamentally individual-based stochastic processes, and are more naturally described by stochastic models" (Roberts, Andreasen, Lloyd, & Pellis, 2015). Partially-observed Markov process (POMP) models combine the mechanistic processes in compartmental SIR models with probabilistic models linking the observed data to the latent process (King, Nguyen, & Ionides, 2016). Our latent process was a four-compartment model (Figure 2), alternatively described as a series of discretized equations (Supplement). We modeled a discrete-time process at annual intervals because disease transmission and birth pulses are seasonal and infected females are likely to abort, and thus transmit infection, in the following year.

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This article is protected by copyright. All rights reserved Additionally, 90% of our data were collected in February, a length of time less than the average time to seroconvert following exposure (Thorne et al., 1978) and prior to peak transmission season (Cross et al., 2015).
The compartments of our models include susceptible and seronegative (S), infected, infectious, and seropositive (I), seropositive but no longer abortive (R 1 ), and serorevertedseronegative and recovered with immunity (R 2 ). Entry occurs via calf recruitment. Because we modeled female elk only, the number of calves (C) in year t was the number observed divided by two under the assumption of equal sex ratio in calves (Johnson, 1951). Hunting is the dominant source of mortality in this population and so individuals across all compartments experienced an equal probability of mortality μ j within each defined period of the timeseries (j = 1-3 periods depending on feedground) when there was a new management objective for that hunt unit. Susceptibles are exposed at a rate corresponding to the force of infection (λ), but not all that are exposed and seroconvert become infectious (abort), which allows a proportion to transition straight from S to R 1 (ρ). Elk that do become infectious recover with probability σ and detectable antibodies are lost with probability ɣ.
Because serology does not distinguish between compartments I and R 1 , the test-andslaughter models (Muddy Creek and Scab Creek) included v, the probability of seropositives exiting I and R 1 in years with removals. Conditional on being in compartments I and R 1 , the probability of removal was equal to the proportion of females captured for testing at a feedground in a given year. This approach is integer-based, therefore probabilities and rates were incorporated into the process model using random draws from an eulermultinomial distribution within the software package 'pomp' (King et al., 2018) in R (R Core Team, 2018).

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This article is protected by copyright. All rights reserved experience an equal period-dependent probability of mortality (μ j ). Susceptible elk are exposed at a rate corresponding to the force of infection (λ), but not all elk that seroconvert will abort, which allows a proportion (ρ) to transition straight from S to R 1 . Recovery occurs with probability σ and detectable antibodies are lost with probability ɣ. Conditional on being seropositive, the probability of removal ν(t) for test-and-slaughter (TAS) models equaled the proportion of the herd captured for testing in a given year. The measurement model assumed that the number of positive tests (+) was a binomial draw and the probability of the observed female elk count was drawn from a normal distribution.
The force of infection, λ, took one of three basic forms each corresponding to a model where transmission was internally-driven (endogenous), driven by climate (exogenous), or driven by both factors (combination). In the endogenous model, we assumed λ 1 is equal to the product of a constant transmission parameter β, and the sum of the annual number of infecteds I and imported infections from outside the herd ι, divided by the population size N raised to a scaling parameter ϴ. The scaling parameter describes the degree to which the

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This article is protected by copyright. All rights reserved transmission process is density-dependent (ϴ = 0) or frequency-dependent (ϴ = 1) (Cross et al., 2013). In the exogenous forcing model, we assumed λ 2 is related to a winter severity covariate ψ that varied annually and by feedground. The final form was a combination of the previous two.
The observed process was the number of seropositive test results divided by the total number tested for a given feedground in a given year ('apparent seroprevalence'). The probability of the data (number of seropositive test results) in year t was binomially distributed and conditional on the probability p(t), which was the 'true seroprevalence' from the latent process and n(t), the total number of tests. We also modeled female elk counts to ensure that our model predictions conformed both to the observed disease and population trends. Observed counts were modeled as a draw from a normal distribution with a mean at the 'true population size' N (the sum of the four compartments), and a standard deviation of 20, which represents approximately 5% of an intermediate-sized feedground herd.

Incorporating winter severity
Based on previous studies we expected that environmental conditions causing larger elk aggregations for longer periods during late winter should result in more transmission (Creech et al., 2012;Cross et al., 2007). We thus tested models in which 'heavy snow' and 'late green-up' contributed to environmentally-driven transmission (ψ) via the force of infection. Snow-depth data were unavailable across the temporal and spatial extent of our study area so we used snowmelt water equivalent (SWE) values from nearby SNOTEL sites

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This article is protected by copyright. All rights reserved for each feedground between March and June. These values were strongly correlated with one another across sites within each year ( Figure S8). We summed the SWE values of the first day in each of these months to arrive at a single value per site and year.
Often the nearest SNOTEL stations are several kilometers from the feedground and hundreds of meters higher in elevation, so we also calculated green-up metrics using normalized difference vegetation index (NDVI) MODIS data and the 3x3 square of pixels around each feedground where each pixel was 250x250m. We excluded pixels that included roads or buildings. We fit double logistic curves to NDVI time series to calculate these metrics following the methods of Bischof et al. (2012)

Candidate models
All of our models follow the four-compartment plan ( Figure 2). Alternative models featuring no seroreversion or seroreversion without retained immunity did a poor job of describing the data and received less support using AIC in a preliminary analysis ( Figures S1, S2). The possibility of a 'low-density feeding' treatment effect was tested at Greys River feedground with models where λ was allowed to vary 'before' and 'after' treatment initiation in 2009.
Testing all possible combinations for a time-dependent low-density feeding treatment effect yielded 5 additional models (Table S3).

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Inference, comparison, and constraints
We used sequential Monte Carlo to obtain the log likelihood following the maximumlikelihood approach of Ionides et al. (2015), and iterated filtering in the software package 'pomp' (King et al., 2018). A broad exploration of parameter space was initiated using 100 sets of parameter values, with each value drawn from a uniform distribution. Likewise, initial starting conditions were generated for the 4 compartments (full details in Supplement).

Testing expectations of synchrony
Assuming heavy snowfall causes elk to aggregate, thereby increasing transmission, we expected synchronous seroprevalence trends across feedgrounds because all feedgrounds experienced synchronous snowfall ( Figure S8)

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This article is protected by copyright. All rights reserved We found substantial temporal variability in seroprevalence within individual feedground herds suggesting recurrent outbreaks (Figure 3) that were asynchronous across subpopulations. At Greys River feedground, the site for which we had the most years of data, the endogenous model received the highest support by AIC, while at Dell Creek and Muddy Creek, exogenous models received similar model weight to the alternatives (Table   S5). Substituting vegetation green-up for snow data did not substantially alter these results (Table S6), except that the exogenous model received stronger support at Dell Creek. This might suggest that NDVI improved on SWE for modeling. The incorporation of a treatment effect from low-density feeding practices at Greys River failed to improve model fit. There were not sufficient data at Scab Creek to perform a formal model comparison, but the endogenous model and parameter estimates from other feedgrounds were in rough agreement ( Figure 3).
Because λ depends on the relative fraction of susceptible and infectious individuals, it can vary substantially over time despite a constant transmission term (Figure 4). By simulating with the parameter values at the MLE, it becomes apparent that relatively few infective elk are needed to achieve high levels of seroprevalence. This is consistent with the difficulty in detecting abortions at the feedgrounds and previous work which estimated that 16% of seropositive elk abort in any given year (95% CI: 0.10, 0.23; Cross et al., 2015). I, which we defined as abortive in our models, provided this additional point of comparison. Indeed, the sum of for the full time series of the endogenous models from 2000 stochastic /( + 1 ) simulations had a median of 16.6% at Greys River (90% prediction interval: 0.14, 0.19), 13.6% at Dell Creek (90% PI: 0.08, 0.18), and 17.0% at Muddy Creek (90% PI: 0.12, 0.20).
Our models consistently estimated quick transitions from I to R 1 , indicating that the majority of elk that do abort only do so in the first year following infection, consistent with work on At Muddy Creek we estimate that of 107 seropositive elk that were removed over 5 years, only 6 were infective, but this prevented an additional 20 infections in the following 8 years.
These effects translate to two fewer infectives in the remaining population per year compared to models without test-and-slaughter ( Figure 6). Annually removing 10% of female seronegative elk during the same 5-year period was predicted to generate a similar reduction to the number of infectives present during control efforts, but yield additional benefits over the remaining time period (37 fewer infectives compared to seropositive removal). The simulation of culling without regard to serostatus of 7.5% of female elk per year fell between the other two predictions: it achieved fewer infectives compared to slaughter of seropositive elk, but underperformed compared to seronegative slaughter.

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This article is protected by copyright. All rights reserved slaughter of 10% of seronegative female elk (blue); indiscriminate culling of 7.5% of female elk (orange).
Center: corresponding estimates for seroprevalence under the four regimes. Right: corresponding female count estimates. Colored dashed/dotted lines represent median estimates; shaded areas are 50% prediction intervals from 2000 simulations.

DISCUSSION:
We found brucellosis seroprevalence trends that were asynchronous across elk subpopulations despite their exposure to similar environmental forcing. Our mechanistic modeling tackled the 'inverse problem' of inferring the latent processes from the observed serological dynamics. Although brucellosis is widely considered a chronic ailment (Ahmed, Zheng, & Liu, 2016), our results suggest that disease transmission may be brief, followed by recovery. The time to seroconversion following exposure (approximately 1 month), the timing of testing (prior to disease-induced abortions), and the chances that a newly-infected elk will actually abort (approximately 50%), along with quick recovery time and lifelong immunity, all contribute to a situation in which targeting seropositives rarely removes infectious individuals. Though at first counterintuitive, it follows that removing seronegative elk would have longer-term protective effects. This is consistent with brucellosis work in bison suggesting that the loss of herd immunity created by removal of seropositive individuals can result in ricochet effects (Ebinger, Cross, Wallen, White, & Treanor, 2011). Timing of interventions is also paramount. It appears that test-and-slaughter at Muddy Creek coincided with a 'fadeout period' when seroprevalence was high, but declining. Therefore, the number of infectious elk was low (Figure 4). If removals instead targeted seronegative elk when seroprevalence is high, this would drive a spike in seroprevalence but a decline in newly infected elk, a longer period with reduced spillover risk, and thereafter a decline in seroprevalence. Achieving public support for such action might require substantial outreach.
Alternatively, sustained culling without regard to serostatus (through increased hunter harvest) might garner wider support. This result stands in contrast to a finding that hunting can increase disease prevalence (Choisy & Rohani, 2006), but which involved a region of Accepted Article the parameter space that is unlikely in our system (large annual fluctuations in host population size and rapid, explosive spikes in prevalence).
Based on the simulation results of our hypothetical herds we should not necessarily expect synchronous seroprevalence trends even in scenarios with strong climate forcing. Outbreaks might periodically align following severe winters, but intervening years exhibit asynchrony like that detected in the actual seroprevalence data. Severe winters can only trigger outbreaks if a large pool of susceptible female elk already exists. This underscores the importance of birth rate and population turnover to the disease dynamics of this system. These findings are consistent with existing literature (Lloyd & Sattenspiel, 2010), yet ours is the first application for long-lived, free-ranging wildlife. Lastly, we found no evidence that 'low-density feeding' has reduced the force of infection at Greys River feedground.
Additional data on elk density and feed distribution would permit more explicit modeling. The course of an outbreak for any one of our subpopulations appears to exceed a decade, and our longest time-series was 25 years. In that context, small treatment effects may be difficult to detect.
These findings prompt a review of the options for reducing brucellosis transmission among feedground elk. A vaccination program persisted at feedgrounds for decades, in part because its implementation coincided with a brief dip in seroprevalence, although it was later deemed ineffective (Maichak et al., 2017). Further vaccine development is hampered by the USDA's Select Agent Status for Brucella spp. (National Academies of Sciences, Engineering, and Medicine, 2017). Quarantine is infeasible for free-ranging elk and widescale fencing is problematic (Mysterud & Rolandsen, 2018). In general, removing infectives should reduce contagion in situations where 'infectiousness' can be accurately identified, rates of capture and monitoring are high, and mixing with other populations is minimal.
Although all these conditions can exist in some wildlife systems (Garwood, 2018), it is more Accepted Article common that the inability to meet one or all of them diminishes the efficacy of this practice (Wolfe, Watry, Sirochman, Sirochman, & Miller, 2018).
Managing brucellosis in elk is ultimately about limiting risk to cattle because the disease does not pose a major threat to elk abundance. This means minimizing the risk of cattle encountering elk fetuses from brucellosis-induced abortions. Although feedgrounds contribute to the persistence of this dilemma, suggestions of closing them have met with opposition. After all, the feedgrounds divert elk from areas of their winter range where they would comingle with cattle. Our models suggest that this seasonal sequestration has created subpopulations (different feedground herds) within which recurrent brucellosis outbreaks occur, and when local seroprevalence is high the period of greatest spillover risk has likely passed. This reframing of risk, combined with spatial modelling of resource selection, should help identify risky times and places for cattle (Merkle et al., 2018). Finally, scavengers are effective in removing infective tissues (Maichak et al., 2009) and so conserving the scavenger guild is likely beneficial for reducing brucellosis contagion on open rangeland.
Nevertheless, these options remain limited while brucellosis is spreading through the growing elk populations in the GYE. Also, chronic wasting disease (CWD) has recently arrived to the GYE and so management actions aimed at controlling one will necessitate consideration of the impacts on both. For example, CWD could create a younger age structure and reduce population growth, but any management efforts to maintain the total abundance of (younger) elk could increase the frequency and intensity of brucellosis outbreaks. Our findings emphasize a need to move beyond traditional control measures and should serve as a warning to agencies that face the possibility of increasing brucellosis infections in elk elsewhere in North America or red deer (Cervus elaphus) in other countries.
If infected subpopulations become interconnected then eradicating this troublesome disease could quickly become impossible without extremely costly and controversial culling campaigns.