Essay: Potential influence of mammal species diversity on pathogen prevalence

Introduction
Emerging and re-emerging diseases of wildlife increasingly pose threats to animal and human health. Studies across a range of host-pathogen systems indicate that host species’ diversity can regulate the ability for a pathogen to establish Johnson et al. (2015). Studies of natural populations have also examined correlations between the spatial distribution of disease and environmental variables, particularly those that can encourage immunologic susceptibility in a population (Buskirk and Ostfeld 1998, Giraudoux et al. 2003). However there may be tradeoffs between species diversity and environmental conditions (Moore and Borer 2012). The interaction of environmental conditions influencing the host or pathogen may operate at scales different than those of species diversity generating asymmetric effects on pathogen transmission (Huang et al. 2016). These effects may also be different for pathogens with a narrow versus large host range. Yet studies investigating relationships between pathogen persistence, environmental factors, and species diversity for pathogens with narrow and wide host ranges are still relatively limited, particularly at the macro-scale and for mammal species in North America.
Studies of host–pathogen systems suggest that the species diversity of ecological communities can moderate the prevalence of pathogens through several mechanisms generally referred to as dilution and amplification effects (Keesing et al. 2006, Ostfeld and Keesing 2012, Salkeld et al. 2013, Johnson et al. 2015, Huang et al. 2016). Dilution effects have been proposed to result primarily from increased species diversity that lowers encounter rates and in turn transmission (Johnson et al. 2015, Huang et al. 2016). Often termed the ‘diversity-disease hypothesis’, its origins can be traced back to Charles Elton (Elton 2000). Conversely amplification effects of species diversity are predicted to occur when increased diversity of competent hosts leads to an intensification of transmission in a community (Keesing et al. 2006). Empirical studies from a range of systems have found that high species diversity is often associated with lowered disease risk (Knops et al. 1999, Mitchell et al. 2002, Pautasso et al. 2005). However, the role of diversity in multi-host systems may be complex, especially when asymmetric transmission competency among hosts exists, leading some to conclude that the effect of species diversity is idiosyncratic and highly variable among systems (Keesing et al. 2010, Salkeld et al. 2013). Recently others have proposed that there may be common underlying ecological phenomena that give rise to the perceived idiosyncratic differences in the effect of species diversity. Johnson et al. (2015), Huang et al. (2016), and others have proposed that dilution and amplification may result from non-linear relationships among density and diversity of competent and non-competent hosts, environmental conditions experienced by host and pathogen, scale of both measurement and species interactions, and the metric used to measure the effect (e.g. prevalence versus incidence). To date few studies have attempted to investigate these relationships and additional variables, particularly at broad scales, because the data required are generally unavailable or difficult to collect. A further complication for conducting these studies is observation error.
Detection probabilities (true and false) for both the pathogen and the wildlife host are typically not included in wildlife disease ecology studies (McClintock et al. 2010). Several recent studies have provided evidence that failing to account for observation error can bias even the simplest estimators in a significant way or even change inference about species occupancy (Royle and Link 2006, McClintock et al. 2010, Lahoz‐Monfort et al. 2014). Accounting for observation errors may be even more important when investigating community level processes that are often difficult to detect (Salkeld et al. 2013). In the case of invading species – host or pathogen – this maybe particularly important, especially if the pathogen or host invasion is recent where observation error rates, either true or false detection, can be larger (MacKenzie et al. 2003). For pathogens this may result from individual heterogeneity in immunity, heterogeneity in population immunity and heterogeneity in infection rates across host populations (Pepin et al. 2017). While for invasive host species that by nature are not in an equilibrium state, this may result from heterogeneous distribution of individuals or difficulty in observing the host species due to low densities. Together uncertainty in detection for host and pathogen may obscure effects of ecological processes, and accounting for these errors may provide insight when investigating species diversity-disease relationships.
Wild pigs are one of the most successful invasive mammal species globally and the most abundant free-ranging, exotic ungulate in the United States (Lewis et al. 2017). They are a generalist species, successfully inhabiting a wide range of ecosystems globally and in North America that represent a large gradient of species diversity (e.g. boreal plain in Canada to South Western deserts of the United States) (Brook and van Beest 2014, Lewis et al. 2017). Wild pigs are also a host for over 40 pathogens of concern for human and animal health (Bevins et al. 2014, Miller et al. 2017). The generalist nature of wild pigs and the large number of pathogens they can be a host for makes wild pigs a good study system to investigate species diversity-disease relationships. The processes that facilitate or inhibit introduction and establishment of pathogens in invasive wild pig populations is largely unstudied in North America with most studies reporting apparent prevalence or demographic risk factors (Leiser et al. 2013, Miller et al. 2017, Pedersen et al. 2017). In North America the spatial distribution of pathogens of wild pigs has only been investigated for a small subset of pathogens primarily of importance for human or domestic animal health. Few have investigated environmental correlates of pathogen prevalence, and none have investigated disease-diversity relationships. However, the well-documented alternative hosts of wild swine pathogens makes them an ideal species in which to investigate complex disease-diversity relationships.
We use a hierarchical Bayesian approach that accounts for imperfect detection probability to investigate the influence of species diversity on the infection probability in wild pigs for pathogens with broad and narrow host ranges. We use these pathogens to investigate if amplification or dilution effects of species diversity might contribute to pathogen prevalence and if environmental conditions that commonly cause stress in mammal populations may contribute to or dampen the effect of species diversity. Because true and false detection probabilities can influence inference and have rarely been included in studies of diversity-disease relationships, we further investigate the potential magnitude of the effect on parameter predictions for the ecological variables of interest. We discuss our results in terms of the diversity-disease hypothesis for pathogen invasion into an invasive species and species that are colonizing new habitats. We highlight the impact of accounting for imperfect detection probabilities on inference. We also discuss how including both ecological processes and imperfect detection can be used to improve predictions of wildlife disease prevalence ultimately improving management of these pathogens.
Methods
Pathogen Data
We used data collected from January 2007 through December 2015 as part of the US Department of Agriculture, Wildlife Services’ National Wildlife Disease Program (NWDP) – a national surveillance program of feral swine. These data have been previously described for various pathogens (Pedersen et al. 2012, Pedersen et al. 2013). Briefly they are collected as part of routine surveillance for a diversity of pathogens of concern for human and animal health. The data include the location (longitude-latitude coordinates), sex, and age of the animal along with serological assay results for a diversity of pathogens. Age class is determined based on lower jaw tooth eruption using an approach commonly used for wild pigs (Matschke 1967) and categorizes animals as juvenile (<2months), subadult (>2 months and ≤ 1 yr), and adult (≥1 yr). Testing for pathogens is limited to serological assays.
We selected two wild pig pathogens, pseudorabies virus (Suid herpesvirus) and swine brucellosis (Brucella suis), to investigate our hypotheses about dilution and amplification effects. The dilution effect of species diversity has been proposed to reduce disease risk in a community primarily by reducing transmission when low-competence hosts are present (Keesing et al. 2006, Ostfeld and Keesing 2012, Johnson et al. 2015). To investigate potential dilution effects, we selected pseudorabies virus, often termed Aujeszky\’s disease, which is an economically important disease of domestic swine. Pseudorabies virus is easily transmitted typically through direct contact via the venereal route (Romero et al. 2001) or horizontal (nonsexual) transmission (Smith 2012). A broad range of species are known to be susceptible to pseudorabies virus with the pathogen being highly virulent and typically fatal in non-porcine hosts (see Appendix Tables A3.1 and A3.2). Pseudorabies virus apparent prevalence in wild pigs in the United States is estimated to range from 0% to 61% (Müller et al. 2011, Pedersen et al. 2013). We expected increases in susceptible hosts that have low-competence for this virus to reduce prevalence while accounting for host density and environmental conditions influencing host survival.
In contrast species diversity has been proposed to amplify disease transmission in communities that have a large number of competent host species (Keesing et al. 2006, Huang et al. 2016). That is increasing competent host diversity in a community amplifies transmission and in turn disease prevalence. We used swine brucellosis to investigate potential amplification effects of species diversity. Swine brucellosis is easily transmitted through damaged skin or through mucosal membranes in the respiratory, reproductive, and gastrointestinal tracts (Olsen et al. 2011, Leiser et al. 2013). Routes of transmission in wild pigs are thought to occur through direct contact during intercourse, fighting, or via contact with contaminated aborted fetuses. Swine brucellosis has a large host range and is known to have competent non-porcine maintenance hosts (see supplemental). Swine brucellosis is common in North American wild pigs with apparent prevalence reported to range from 0.3% to 53% (Pedersen et al. 2012, Leiser et al. 2013). With regard to amplification effects, we expected increasing competent-host diversity to be associated with increased prevalence in wild pigs and that environmental conditions influencing host survival would have reduced effects on prevalence due to the differences in host survival relative to environmental conditions.
Scale of analysis
We used hydrologic units described by the United States Geological Survey\’s (USGS) Hydrologic Unit Codes (HUC) database as the analysis unit (USGS 2011). Hydrologic units, commonly referred to as watersheds, are a hierarchical classification system that are considered to be ecologically relevant landscape-level sampling units for large scale studies (Odum et al. 1971). They have been used as biologically representative sampling units for modeling species occurrence (Collins and Glenn 1990, Peterson et al. 2009) and have previously been used to model invasive wild pig occurrence probability in the United States (McClure et al. 2015). Watersheds are expected to represent a more discrete set of biotic and abiotic factors and to serve as a more ecologically relevant unit for aggregating covariates than an arbitrary grid. We chose a watershed size (HUC8 referred to as subbasin) that was much larger (mean=1,800 km2) than the mean home range size estimated for wild pigs in the U.S. (4.92±6.37 km2) and thus was expected to be capable of encompassing an entire population of pigs (McClure et al. 2015). In addition the subbasin scale represented a balance between data density within each subbasin and also being large enough to encompass a population of pigs. Surveillance data were assigned to each subbasin using their location (longitude-latitude coordinates). Hydrologic units have the advantage of being a hierarchical system allowing watersheds to be aggregated or disaggregated while preserving the ecological relationships. Using this characteristic we also considered hydrologic basins (HUC6), and subregions (HUC4) for validation (see Model implementation and performance) and hydrologic regions (HUC2) for observation processes (see Observation model).
Hydrologic subbasin-level environmental data
We evaluated four climatic covariates available from WorldClim (Hijmans et al. 2005) that represent environmental gradients that have been found to be important for limiting the geographic distribution (McClure et al. 2015), the density (Lewis et al. 2017) and the invasion probability (Snow et al. 2016) of wild pigs. The subbasin-level mean for each climatic variable was calculated using methods described in McClure et al. (2015). Pigs are known to have physiological characteristics making them sensitive to both high and low temperatures (Geisser and Reyer 2005, Acevedo et al. 2006). Pig mortality increases when ambient temperatures exceed 23°C (Porter and Gates 1969) and when temperatures fall below -4°C (Thompson et al. 1996). To represent these temperature gradients, we used the long term annual mean temperature in the coldest quarter of the year (WorldClim variable BIO11) and the long term annual mean temperature in the driest quarter of the year (WorldClim variable BIO9). We expected increasing temperature in the coldest quarter to be positively associated with pig survival and thus also positively associated with pathogen prevalence. Wild pigs thermo-regulate by accessing water resources (Choquenot and Ruscoe 2003) and require cooling when temperatures exceed 35°C. We used the mean annual temperature of the driest quarter to represent this gradient and expected pig mortality and pathogen prevalence to be negatively correlated as this gradient increased.
Wild pig survival at low temperatures is expected to be exacerbated by precipitation, which in northern climates equates to snow accumulation (Jedrzejewska et al. 1997, Melis et al. 2006, Honda 2009, Danilov and Panchenko 2012). Winter temperature and snow depth have been associated with wild pig occurrence probability (McClure et al. 2015) and wild pig density (Melis et al. 2006, Pedersen et al. 2017). We used the mean amount of precipitation in the coldest quarter (WorldClim variable BIO19) to represent winter precipitation expecting pig mortality to increase and pathogen prevalence to decline with increasing winter precipitation. Conversely, increasing precipitation during the warmest months of the year is expected to decrease the effects of increasing temperature, improving survival (Fraser and Phillips 1989) and has been linked to pig probability of occurrence. To represent this precipitation gradient that is somewhat orthogonal to temperature in the driest quarter, we used precipitation in the driest quarter (WorldClim variable BIO17). We expected wild pig survival and pathogen prevalence to increase as precipitation increased in the driest period of the year.
Subbasin-level host species diversity data
To investigate the potential influence of mammal species diversity on pathogen prevalence, we used Shannon–Weaver species richness index as a proxy for species diversity (Shannon 1949). Species richness is often used as a proxy for species diversity when studying potential dilution or amplification effects of pathogen prevalence (Salkeld et al. 2013). We considered two cases for mammal species richness that have been debated to influence pathogen prevalence in different ways (Johnson et al. 2015) – changes in low-competence hosts (Keesing et al. 2006, Huang et al. 2016) and changes in competent hosts (Huang et al. 2013a). To identify these species we used the results of two meta-analyses by Miller et al. (2017) and Miller et al. (2013) that investigated the transmission potential of 86 pathogens between wild pigs, livestock and wildlife. Based on these studies, we considered competent hosts as those that could be clinically or sub-clinically infected and also demonstrated the ability to shed virus, while non-competent hosts are those that are susceptible but unable to transmit the pathogen. Using these constraints, 28 species from ten families were included as competent hosts for swine brucellosis and 34 non-competent species from 21 families for pseudorabies virus (See supplemental for tables listing species with supporting citations). Because experimental infection studies often use a similar set of species that are easy to work with in the laboratory, we assumed that experimental infection study results were broadly applicable at the taxonomic family level. To develop a measure of species richness, we obtained geographic range data for mammal species from the Nature Serve digital map library of the distributions of the terrestrial mammals of the Western Hemisphere that contains distribution data for over 1,700 species (Patterson et al. 2007). Using these range data, the presence / absence of each species was aggregated to hydrologic subbasins as described in McClure et al. (2015), and the subbasin-level Shannon–Weaver species richness index was calculated.
Wild pig abundance data
Disease transmission often demonstrates density dependence (Begon et al. 1999), and this relationship can influence intra- and inter-species interactions, influence transmission rates and also alter the effect of species diversity on pathogen prevalence (Johnson et al. 2015). Because we were interested in the influence of species richness on the prevalence of pathogens in wild pigs, we accounted for population density only in the focal species in our analysis. Currently there are no available national scale estimates of wild pig abundance at a resolution (subbasin) useful for our analysis. To account for density dependence of the focal host species (wild pigs), we used the mean subbasin-level relative occurrence probability described by McClure et al. (2015) as a proxy measure of population density. Relative occurrence probability is expected to be proportional to population abundance (Brown 1984) and offered the only available national scale data for our purposes.
Hierarchical model of pathogen infection
We constructed an occupancy model using a hierarchical formulation (Royle and Kéry 2007) for modeling individual infection probability and for estimating subbasin-level prevalence (Figure 3.1). We express the model by its two component processes that are the observations, y_ij, conditional on the unobserved state process (i.e., y_ij |z_ij) and, the unobserved or partially observed state process, z_ij,where i indexes the individual pigs sampled for the pathogen and j indexes the subbasin that they were located. This formulation allowed us to investigate multiple levels of pathogen infection probability (e.g. individual and subbasin) and allowed us to investigate the relationship between environmental gradients, species diversity, wild pig host density, and the infection state, z_ij, that was the primary focus of our investigation.
State model
The state model relates the probability of infection for each individual to the hypothesized demographic and environmental processes influencing the infection state. The state of individual, z_ij, is a Bernoulli process
z_ij ~ Bernoulli(ψ_ij ) Eq. 1
where ψ_ij is the probability of infection for individual i in subbasin j conditional on environmental and demographic processes. z_ij has the possible states of ‘positive’ (z_ij=1) or ‘negative’ (z_ij=0). We modeled the relationship of demographic and environmental processes to infection state as a linear process on the logit scale as,
logit(ψ_ij )=β_(0,j)+〖x^\’〗_ij β Eq. 2
where β is a vector of regression coefficients corresponding to 〖x^\’〗_ij, the transpose for the vector of demographic covariates of sex and age (juvenile, yearling, adult). We used index variables for both sex and age assuming that both are observed without error. Sex was coded relative to males and centered on zero with values -0.5 for males and 0.5 for females. This results in a one unit difference in males and females allowing the predicted posterior regression coefficient to be interpreted as the mean difference between males and females (Gelman and Hill 2006). Age class was coded one for juvenile, two for yearling, and three for adult. A standard normal distribution with precision of 0.01 was used as a prior for both age and sex regression coefficients (β).
The intercept of Eq. 2, β_(0,j), is the influence of subbasin-level factors on the probability of infection common to all individuals in the subbasin and is modeled as
β_(0,j) ~ normal(η_0+〖w^\’〗_j η,σ_(β_0)^2 ) Eq. 3
where η is a vector of regression coefficients corresponding to the subbasin-level predictors and η_0 is the background infection probability common across all subbasins. We used a vaguely informative inverse gamma prior distribution (α=0.5, β=0.5) to model the precision, 1/σ_(β_0)^2, of subbasin-level factors contributing to the infection state. A standard normal prior distribution with precision of 0.01 was used for all subbasin-level regression coefficients (η) and the intercept η_0. We chose not to include uncertainty in the subbasin-level covariates assuming that they are observed without error. The environmental and pig occurrence probability covariates are estimated from other models with unknown error. Similarly the species richness covariate is derived from sixty-two species range estimates that arise from an aggregate of scientific literature sources. Because the error is unknown for these covariates and inclusion of data models that would account for the error would likely be inaccurate, we did not include a data model for these covariates.
Observation model
The observation model specified conditional on the infection state, z_ij, is given by
y_ij |z_ij ~ Bernoulli((z_ij ρ_k+(1-z_ij )(1-ϕ_k )) 1_(j∈k) ) Eq. 4
where ρ_k is the true positive detection probability and (1-ϕ_k ) is the false positive detection probability in hydrologic region k. An indicator variable, 1_(j∈k), is used to identify when subbasin j is contained within hydrologic region k by,
1_(j∈k)= {■(1 if j ∈k@0 otherwise)┤ Eq. 5
This formulation, which is common in epidemiology (McClintock et al. 2010, Christensen et al. 2011) and increasingly common in species occupancy models (Royle and Link 2006, Miller et al. 2011), provides an estimation of the true state of an individual, in our case infected or not infected, accounting for false positive and false negative errors.
The true positive detection probability, ρ_k (also referred to as true positive rate or sensitivity in some fields), and true negative detection probability (i.e. true negative rate or specificity), ϕ_k, can result from a diversity of processes including diagnostic test error (Branscum et al. 2005), population immunity (Pepin et al. 2017), and differences in detectability of the pathogen given infection status of the animal (Jennelle et al. 2007). The diagnostic tests used for pseudorabies virus and swine brucellosis were developed and validated for domestic animals and performance of diagnostic tests are often different for wildlife (Stallknecht 2007). The beta distribution was used as a prior to account for true positive and true negative detection error arising from diagnostic error and other processes. We used a parameterization common in epidemiological studies (Branscum et al. 2005, Christensen et al. 2011) that is often termed the expert beta. We parameterized ρ_k and ϕ_k with respect to the mean for the diagnostic error using,
ρ_k ~ beta( μ_(ρ_k ) σ_(ρ_k ),(1-μ_(ρ_k ) ) σ_(ρ_k ) )
Eq. 6
ϕ_k ~ beta(μ_(ϕ_k ) σ_(ϕ_k ),(1-μ_(ϕ_k ) ) σ_(ϕ_k ) )
Eq. 7
where μ_(ρ_k ) and μ_(ϕ_k ) are beta distributed hyper-priors for the detection means and σ_(ρ_k ) and σ_(ϕ_k ) are gamma distributed hyper-priors for the mean detection variances. This parameterization allows the mean and variance for each detection probability to be defined in terms of the confidence in the available data (Christensen et al. 2011). We assumed in the absence of other contributors to observation error that the true positive and true negative detection rates would approach those of the diagnostic test. Deviations from the diagnostic test values would indicate other contributions to detection errors are present. For this purpose, we assumed μ_(ρ_k ) and μ_(ϕ_k ) were the reported diagnostic test error rate with 65% confidence, and we assumed that the true value of μ_(ρ_k ) and μ_(ϕ_k ) was greater than 0.6 with 95% confidence. This parameterization allowed some uncertainty in the true value of μ_(ρ_k ) and μ_(ϕ_k ) with the null hypothesis that the mean value is the same as the diagnostic test (Appendix Table. A3.3).
Derived subbasin-level quantities
The parameters of the occupancy model of primary interest are the individual-level true infection state probability, ψ_ij, the true positive detection probability, ρ_k, the true negative detection probability, ϕ_k and the regression coefficients (β, η). To derive the subbasin-level true occurrence probability, which in our model is based on the individual-level true infection probability, we generated realizations from the posterior distribution of ψ_ij using,
π ̂_(〖true〗_j )=1/n_j ∑_(j=1)^J▒ψ_ij Eq. 8
where π ̂_(〖true〗_j ) is the derived true subbasin-level pathogen prevalence conditional on the demographic, environmental, species diversity, and wild pig occurrence probability parameters. Because π ̂_(〖true〗_j ) is generated from ψ_ij, it represents a subbasin-level posterior prediction that applies to a theoretically infinite population of individuals (Royle and Dorazio 2008) and can be interpreted as the probability of disease for any individual animal sampled from the subbasin (Royle and Kéry 2007).
To understand the influence of including detection probabilities and the resulting influence on subbasin-level derived predictions of true pathogen prevalence, we contrast π ̂_(〖true〗_j ), the derived true subbasin-level prevalence, with the standard approach (often termed apparent prevalence) using a metric describing relative bias (%RB) (Jennelle et al. 2007). The bias metric is defined as
%RB= ((π_(〖obs〗_j )- π ̂_(〖true〗_j ) )*100)/π ̂_(〖true〗_j ) Eq. 9
Where π_(〖obs〗_j ) is the observed apparent prevalence in subbasin j defined as
π_(〖obs〗_j )= 1/n_j ∑_(j=1)^J▒y_ij Eq. 10
where y_ij (which when summed) is the observed number of positive animals in subbasin j, n_j is the total number of animals tested in subbasin j, and π ̂_(〖true〗_j ) is the derived true subbasin-level pathogen prevalence.
We were also interested in the ability of the model to accurately predict subbasin-level apparent prevalence so we could evaluate model performance. To derive the subbasin-level predicted apparent prevalence, we simulated new values of y_ij |z_ij using Eq. 4 and then calculated
π ̂_(〖pred〗_j )= 1/n_j ∑_(j=1)^J▒〖y_ij |z_ij 〗 Eq. 11
where π ̂_(〖pred〗_j ) is the predicted subbasin-level apparent prevalence conditional on the true positive and true negative detection errors and the individual and subbasin-level processes defined in Eq. 2 and 3.
Model implementation and performance
All environmental and demographic covariates were centered prior to model fitting, and effects were standardized to allow comparison between covariates and models. Posterior distributions of the infection states and parameters of interest were predicted using Markov chain Monte Carlo (MCMC) methods using three chains with diffuse initial conditions (Brooks and Gelman 1998). Each parameter and infection state was predicted by sampling from the posterior distribution using Gibbs sampling implemented in JAGS (Plummer 2014) and the runjags (Denwood 2016) package in the R computing environment (Team 2011). The MCMC procedure was run until convergence of all model parameters was achieved. Once convergence was assured, posterior inference was based on 20,000 samples from the MCMC chains. Convergence was evaluated by visual inspection of trace plots, the Gelman-Rubin diagnostic (Gelman and Rubin 1992), and the Heidelberg-Welch diagnostic (Heidelberger and Welch 1983). Convergence diagnostics and statistical analysis of the model output was performed using the R coda package (Plummer et al. 2006).
Out-of-sample prediction was used to assess model performance. Subbasins to withhold for model validation were identified using conditioned Latin hypercube sampling (Minasny and McBratney 2006) that allows ancillary data to be used to stratify sampling. We were interested in the predictive abilities of the model across three gradients important for invasive wild pigs in North America. These gradients included: 1) the range of observed apparent prevalence (0 to 1.0), 2) the range of latitudes that pigs occur in North America (N 26° to N 48°), and 3) the length of time wild pigs have been present in a subbasin (<1 year to >100 years). These ancillary data were used to identify approximately 10% of subbasins to use as out-of-sample validation data (Table 3.1).
Posterior predictive evaluations for the ability of the model to predict subbasin-level apparent prevalence were conducted to evaluate the fit of the model to the data (Gelman and Hill 2006, Gelman et al. 2014). Posterior predictive checks use a test statistic calculated from the observed data and from replicated data sets simulated from the posterior predictive distribution. To implement this procedure, we generated replicate data sets of the predicted subbasin-level apparent prevalence (Eq. 11) from the MCMC chains after obtaining convergence. We calculated Bayesian P-values for the mean discrepancy between π ̂_(〖pred〗_j ) and π_(〖obs〗_j ). Bayesian P-values provide a measure of how extreme the predicted data are in comparison to the observed data. Values near 0.5 indicate good fit, while values close to 0 indicate model predictions that are less than the observed data and values close to 1 indicate predictions that are greater than the observed data (Gelman et al. 2014). We also assessed out-of-sample prediction capacity by computing the mean square error (MSE) between observed apparent prevalence (π_(〖obs〗_j )) and the predicted apparent prevalence (π ̂_(〖pred〗_j )) across the three gradients to indicate discrepancies in dispersion of the predicted data relative to the observed data. Because models often predict better at a courser resolution, we evaluated Bayesian P-values at the subbasin (HUC8), basin (HUC6), and subregion (HUC4) hydrologic scales.
Results
Model evaluation
All diagnostics indicated model convergence for the pseudorabies virus and swine brucellosis models for all chains following a 1-million iteration burn-in. Model run times were long ranging from 2-2.5 hours for each 100,000 iterations and required several days to run for convergence. Convergence was easier to achieve for pseudorabies virus than for swine brucellosis, which required two million iterations. Trace plots indicated thorough mixing of all chains, and the upper 97.5% quantile of the Gelman-Rubin diagnostic was less than 1.01 for all parameters in both models after convergence. Chains passed the Heidelberger-Welch test for stationarity and mean half width.
Posterior predictive checks did not indicate significant lack of fit between model predictions and the data (Table 3.2). The mean Bayesian P-values for the difference in the mean observed apparent prevalence and mean predicted apparent prevalence among subbasins ranged from 0.768 to 0.573 pseudorabies virus and 0.869 to 0.694 for swine brucellosis. Bayesian P-values approached 0.5 for both pathogens as hydrologic unit became increasingly coarse (subbasin to basin to subregion) indicating our model predictions improved as hydrologic units were aggregated. Bayesian P-values greater than 0.5 indicated that the predicted apparent prevalence tended to be less than the observed apparent prevalence.
Comparison of out-of-sample data with model predictions of subbasin-level predicted apparent pathogen prevalence provided confidence that our model could accurately represent the observed apparent pathogen prevalence (Figure. 3.2). Our model accurately predicted subbasin-level observed apparent prevalence in the majority of subbasins, 96.3% for pseudorabies virus and 93.0% for swine brucellosis (Figures 3.2 and 3.3). The models performed well across the range of latitudes considered (26° to 48°) but differed for each pathogen. Latitudes from 26° to 42° had relatively similar amounts of prediction error for swine brucellosis, but an increase in prediction error occurred above 42°. Prediction error for pseudorabies virus was greatest at 26° to 28° latitude, declined through the majority of wild pig range, and then increased some at latitudes above 42°. Prediction errors remained below 0.08 for all latitudes. The prediction error by the length of time pigs have been present in a subbasin had no significant differences for pseudorabies virus and showed some differences for swine brucellosis but remained less than 0.03 across all subbasins (Figure 3.3). In aggregate these assessments indicate that our models had good predictive capacity across the majority of the observed prevalence distribution and across the majority of the wild pig range in the United States providing confidence in our predictions of true apparent prevalence.
Parameter predictions
Generally parameters were predicted with narrow credible intervals relative to the prior distribution and medians that were different than the prior distribution demonstrating that the data informed parameters beyond the information contained in the priors (Table 3.3, 3.4 and Figure 3.4). Derived subbasin-level true pathogen prevalence declined for both pseudorabies virus and swine brucellosis as species diversity increased (Table 3.4 and Figure 3.5). The posterior distribution for the effect of species diversity on pseudorabies virus had a much narrower range when compared to swine brucellosis.
Discussion
We found support for species richness dilution effects for pseudorabies virus and swine brucellosis after controlling for environmental gradients influencing host survival, host density, and pathogen detection errors. The results for pseudorabies virus align well with currently proposed theory in that increased diversity of non-competent hosts was associated with reduce pathogen prevalence (Keesing et al. 2006, Ostfeld and Keesing 2012, Young et al. 2013). In addition we also observed negative effects of environmental gradients that are associated with reduced host survival. However for swine brucellosis, we did not observe the expected species richness effect. Current species-diversity disease theory would have predicted amplification effects for swine brucellosis because the species richness index used was composed solely of competent species (Johnson et al. 2015, Huang et al. 2016). However, we observed a negative relationship with increasing species richness for swine brucellosis that is contrary to the amplification hypothesis.
There are several potential reasons why we did not observe the expected relationship for swine brucellosis. While our model predicted a negative effect for swine brucellosis, this negative effect had greater variance compared to pseudorabies virus indicating that there may be other processes involved that were not included in our model. These might include non-linear environmental relationships with alternate host survival or infection probability that obscure species-diversity effects on swine brucellosis prevalence for wild pigs. We also only accounted for host density for our focal species, wild pigs, and because swine brucellosis tends to occur at lower prevalence, there may be host density effects for alternate hosts that we did not include. These types of non-linear effects between species-diversity and infection probability have been termed identity effects (Hantsch et al. 2013, Huang et al. 2014) and have been observed for bovine tuberculosis in Africa (Huang et al. 2014). In the case of bovine tuberculosis in Africa, increasing mammal species richness had a negative effect on disease risk; however in regions with African buffalo, there was a positive effect because African buffalo presence is correlated with species richness (Huang et al. 2013b). Collectively, these relationships highlight the importance of distinguishing non-linear associations between environmental gradients and host density for multi-host pathogens.
For single-host pathogens such as pseudorabies virus, environmental gradients associated with host survival may limit the ability of pathogens to invade populations in more northern climates reducing risks related to disease in these populations. For pseudorabies virus, our model predicts lowered disease prevalence in regions experiencing colder winters with greater precipitation, and while posterior distributions for swine brucellosis contained zero, they were also in the same direction as pseudorabies virus. Presumably this is associated with reduced host survival that might be further aggravated when the host is immunologically compromised by active infection. These effects were greater for pseudorabies virus, which is a life-long persistent infection that commonly worsens under stress or during reproduction. This effect is supported by reported observed apparent prevalence in European wild boar, which generally declines with latitude (Müller et al. 2011).
These environmental effects may be exacerbated by age and sex. The effects of age on infection probability were similar to those previously reported for wild pigs in North America (Pedersen et al. 2012, Pedersen et al. 2013) and also for wild boar in Europe (Ruiz-Fons et al. 2008). However our model did predict different effects of sex on infection probability for both pathogens. We found females had a higher probability of pseudorabies virus infection than males, which is different from two previous studies in North America (Pirtle et al. 1989, Müller et al. 1998, Pedersen et al. 2013) but similar to findings for wild boar in Spain (Ruiz-Fons et al. 2008). There are several potential reason for the difference from previous studies in North America. Previous studies have not accounted for detection error, which may be different for males and females. These studies also used smaller sample sizes and did not include ecological covariates (e.g. environmental gradients, species diversity, or host density) when estimating effect sizes and hence may have obscured associations between infection probability and sex. Similar to our study, Ruiz-Fons et al. (2008) included environmental factors as covariates, supporting that there may be an interaction between sex and environmental factors in determining infection probability.
Our study has several implications for studies investigating relationships between pathogen prevalence, environmental risk factors, and species diversity. We observed large differences in detection errors that could not be solely explained by reported diagnostic test sensitivity and specificity. Studies that do not account for these types of errors, particularly at the macro-scale, might under estimate pathogen prevalence, and this may in turn influence estimated effect sizes for risk factors. This highlights not only the need to include these types of errors but also to further understand the underlying mechanisms responsible for these processes – both biological and measurement. Improvements to our approach might include explicitly modeling both biological and measurement processes that might contribute to true and false detection errors. This is commonly done in species occupancy models, however is rarely done in epidemiological models where true and false detection is generally assumed to arise solely from the diagnostic testing process (Branscum et al. 2005, Christensen et al. 2011). Of specific interest is investigating if individual and population level immunological processes may be important in understanding pathogen detection (Pepin et al. 2017) indicating that both biology and measurement may be important in observation processes.
Our study could be extended by including greater resolution in terms of host competency. We assumed that all hosts were equally competent or non-competent for the pathogens. In reality, competency likely occurs along a gradient that has non-linear relationships with host density and other ecological factors influencing host survival. We assumed that infection study results for species were representative of the taxonomic family’s host competence. This assumption may have included some species that are not competent due to heterogeneities within taxonomic families. Including greater detail for host competency may highlight host species that are important in the transmission process, either reducing or increasing pathogen transmission. Our model also assumed processes were stationary with respect to time, and there may be important nonlinear and potentially orthogonal effects of species richness on transmission during different seasons or they may change over time as host densities change. This may be particularly important for invasive species that are invading new communities potentially altering species assemblages and transmission processes and also for multi-host pathogens. Our model also did not explicitly include spatial auto-correlation in the model structure so our predictions may be overly optimistic. This may also be influenced by host density as there is an expectation that density of hosts is auto-correlated in space. Including spatial structure of both the focal host, wild pigs, and species richness could be an important extension of this work.
There are practical implications for management of disease risk in wild pig populations from our results. Our finding that environmental gradients are associated with changes in pathogen prevalence and may limit the ability of pathogens to invade populations experiencing stressful conditions may be useful for characterizing disease risk. Populations occurring in more stressful environments may be at lower risk for disease outbreaks or for pathogens to become established as endemic. This may aid national scale surveillance efforts by allowing more resources to be diverted to areas with greater risk of pathogen establishment. This may also indicate that transmission risk from wild pigs to humans, domestic animals or other wildlife may be reduced for some pathogens in more northern regions of North America.
Our study fills a gap in the current knowledge related to the drivers of macro-scale pathogen prevalence for an important invasive species in North America. There are several implications for studies investigating relationships between pathogen prevalence and species diversity, particularly for multi-host pathogens. Relationships between species-diversity and pathogen prevalence may be obscured if environmental factors are not taken into account.