The population dynamics of Brucellosis in the Yellowstone National Park
Ecologists are beginning to show interest in models for pathogens that infect more than one host species. This work develops from the earlier studies of Holt and Pickering (Holt and Pickering 1985, Begon et al. 1992) and Anderson and May (Anderson and May 1986) and has more recently been developed by Begon, Bowers, and their colleagues (Begon et al. 1992) and Hochberg and Holt (1990). Less attention has been paid to the role that pathogens play in structuring ecological communities (Anderson and May 1986, Dobson and Hudson 1986). This lacuna is unfortunate as pathogens that infect both wildlife and domestic animals will cause problems around the edge of parks and wildlife reserves where wild and domestic host species interact (Dobson and May 1986, Dobson and Miller 1989). The transmission of pathogens between host species with different evolutionary histories of exposure to pathogens will thus create a special class of problems that conservation biologists interested in disease will have to face.
Yellowstone National Park was the first national park in the United States. The park contains nearly a complete fauna for the Northern Rocky Mountain region. It is situated in the north-western corner of Wyoming, and the greater Yellowstone ecosystem extends into Montana and Wyoming. The presence of Brucella in bison in Yellowstone National Park is a cause of concern to the cattle owners in Montana, Wyoming, and Idaho. If bison or elk move out of the park in winter it is important to know if they can transmit Brucella to cattle. At present a hazing and removal operation is used in areas to the north and west of the park whenever bison herds cross the park boundaries and encroach on neighboring grazing lands.
In this paper we use a mixture of long-term ecological data and mathematical models to examine the epidemiology of brucellosis in the Greater Yellowstone ecosystem. The paper emphasizes not only how pathogens affect the ecology of wild species, but also how ecological considerations can help in the development of epidemiological models.
HISTORY OF BISON AND BRUCELLOSIS IN YELLOWSTONE
The original herds of bison in the great plains east of the Rocky Mountains were reduced to a herd of [approximately equal to] 25 animals within Yellowstone National Park by the beginning of the present century. With protection, the wild bison increased and intermixed and interbred during summer with captive bison brought to the park in 1902. These bison formed two distinct wintering sub-populations; a third formed after 71 bison from the managed subpopulation were released in 1936 on historic, but vacant, winter range (Meagher 1973). The three subpopulations remained distinct in winter until the early 1980s (Meagher 1973, 1989). The subpopulations were managed variously, with population control a regular occurrence only on the northern range. Population regulation by human interference ceased in 1966 (Meagher 1973).
Detailed records of bison numbers exist for most of the last 90 yr [ILLUSTRATION FOR FIGURE 1 OMITTED]. The size of the population has been increasing steadily for the last 20 yr; and total population size has varied over two orders of magnitude at different times this century. Similar data are available for elk; the estimated size of the Northern Yellowstone elk population between 1920 and the present is illustrated in Fig. 1B (Huston 1982, and Yellowstone park records). The major determinants of population size over this period have been management removals, hunting pressure, and variability in climate (Huston 1982). After removals ceased in 1968, elk numbers increased rapidly and the population now numbers around 18 000-20 000 elk (J. Mack, personal communication).
Brucellosis in bison and elk
Brucellosis is a disease of ungulates caused by bacteria in the genus Brucella. It has been present in Yellowstone National Park in Wyoming for over 75 yr (Thorne et al. 1991); it was first diagnosed serologically in the park in 1917 from two bison that aborted their fetuses (Mohler 1917). Since then, the bison and elk herds have been tested opportunistically, and occasionally systematically, for the presence of brucellosis (Meyer 1992, Meagher and Meyer 1994, Meyer and Meagher 1995). Brucella abortus is essentially a pathogen of the reproductive tract, but most transmission occurs directly by the licking of aborted foetuses and grazing contaminated forage.
There are pronounced differences in the levels of pathology associated with brucellosis in elk, bison, cattle, and other hosts. Among experimental elk, [approximately equal to] 50% of infected cows aborted their first calf, and sometimes the second (Thorne et al. 1978); this may approximate the situation on the elk feed grounds in Wyoming. In contrast B. abortus in the Yellowstone bison does not appear to cause any discernible pathology (Meyer and Meagher 1995). Indeed, as the bison herd is growing at close to its maximal rate, the impact of the pathogen on fecundity would seem to be minimal. In contrast, brucellosis produces abortion in both elk and bison in the herds present on the National Elk Refuge adjacent to Grand Teton National Park to the south of Yellowstone. The winter feed ground for elk produce very high densities of hosts at the crucial time of year when Brucella-induced abortions occur. Infected animals are likely to have been exposed to high dosages of the pathogen and this may significantly increase the observed pathology (Meyer and Meagher 1995). In moose, brucellosis apparently is almost always fatal for the infected animal (Moore 1947). Efforts to detect differences in causative strains of B. abortus biovar 1 have so far proved futile (Meyer and Meagher 1995). It would appear that virulence differs depending upon the host species and the intensity of exposure.
The serological tests used to determine the presence of Brucella abortus in elk and bison were originally developed for cattle. The tests are fairly reliable when applied to cattle. Unfortunately, they do not extrapolate readily to bison and elk. In particular, the tests tend to give large numbers of false positives and negatives. Thus serological tests on blood may indicate the presence of Brucella antibodies in bison, but it is only possible to positively identify an animal as infected if positive cultures are grown from tissue collected from that animal (Meyer 1992). Estimates of the incidence of Brucella should thus be treated with extreme caution unless accompanied by data from tissue culture.
A number of sets of data are available that describe the possible levels of Brucella infections in the Yellowstone bison herd; both serological and culture data have been collected from the bison at different times between 1917 and 1992 (Meyer 1992, Meyer and Meagher 1995). These historical data are complemented by data obtained opportunistically during two recent removals of bison on the boundary of the park in the winters of 1988-1989 (Pac and Frey 1991) and 1991-1992 (Meagher and Meyer 1994, Meyer and Meagher 1995). In the 1991-1992 survey, tissue from the same individuals were analyzed using both serological tests and culture results. These data provide an important opportunity to determine the sensitivity and specificity of the serology test and to compare matching rates between the serology and culture results.
The observed prevalence of sero-reactors in different historical surveys in Yellowstone is illustrated in Fig. 2. These surveys suggest that sero-prevalence has varied between [approximately equal to] 20 and 65-70%. Culture tests indicate a prevalence of [approximately equal to] 10%. This suggests that estimates of Brucella prevalence based on sero-reactors give a significant overestimate of the true level of infection.
RELATIONSHIP BETWEEN POPULATION SIZE AND BRUCELLOSIS SEROLOGY
The data on population size and Brucella sero-prevalence can be combined to examine the relationship between population size and brucellosis sero-prevalence. The data in Fig. 2 illustrate the proportion of samples that are sero-positive at different times during this century plotted against population size for the Yellowstone bison herd. Brucellosis is present whenever the herd size exceeds [approximately equal to] 200 animals and sero-prevalence rises slowly as buffalo numbers exceed this threshold for establishment. Data from similar surveys of bison populations in other national parks in the United States and Canada are also included in this figure (Moore 1947, Choquette et al. 1961, Tessaro 1986, 1989); they suggest a similar trend underlies the data for each herd. The pattern complements those observed in studies of measles in human populations where populations of [approximately equal to] 500 000 people are required to continuously sustain infections with measles (Bartlett 1960, Black 1966). Sustained infections of brucellosis require bison herds in excess of 200-300 animals. Once a herd drops below this number brucellosis tends not to be present.
The major exception to the observed general trend in the relationship between sero-reactors and population size is the case of bison in Grand Teton National Park, which is immediately to the south of Yellowstone. The bison in this park were introduced 20 yr ago from a stock of uninfected individuals. They have acquired brucellosis from elk on the adjacent National Elk refuge at Jackson, Wyoming. Brucellosis is endemic in the elk in the Jackson herd due to the concentration of elk on the winter feed grounds (Boyce 1990). Enhanced Brucella transmission from elk occurs when bison mix with elk on these feed grounds, where they are likely to acquire a high level of exposure to the infective stages of B. abortus.
THE WINTER REMOVALS OF 1988-1989 AND 1991-1992
In two recent winters movements of bison from the park into the areas north of Gardiner and west of West Yellowstone have led to a large removal operation, under the authority of Montana Fish, Wildlife, and Parks. These removals are controversial, but deemed necessary to prevent transmission of Brucella to domestic livestock. The removals provide important data on the epidemiological status of the bison herd. Where bison are removed lethally, it is important that all of the potential information be gathered and analyzed from as many different perspectives as possible. The two large removals in the winters of 1988-1989 (Pac and Frey 1991) and 1991-1992 (Aune and Schladweiler 1993) provided a wealth of epidemiological data. In 1988-1989 the only test to be undertaken was the serology test. In contrast, in 1991-1992, [approximately equal to] 500 animals provided serum for a serology test and a subsample of these also provided tissue that could be examined using a culture test for brucellosis. This allows positive identification of infected carcasses that harbor the organism. These additional data allow evaluation of the specificity and sensitivity of the serology test and more accurate classification of animals into infected and exposed individuals.
AGE-PREVALENCE PROFILES FOR 1988-1989 AND 1991-1992
A large proportion of the samples were taken from animals for which age and sex could be determined. This allows us to examine the change in prevalence of both sero-reactor animals and culture-positive animals with age. These data are represented in Fig. 3. Both sets of data show an increase in exposure to brucellosis with age and both suggest that Brucella exhibits a higher level of exposure in males than in females. The slower rate of increase in the second survey may reflect the lowered force of infection due to the impact of the previous cull on bison numbers (approximately one-sixth of the herd was removed in the 1988-1989 cull). However, the difference may also reflect sampling from a different section of the population, so no major insights may be obtained from these data as to the efficacy of culling as a control technique.
TABLE 1. A comparison of the specificity and sensitivity of the
serology test using data from the 1991-1992 winter control
operation. The data are arranged so that the individuals that were
positive (+ve) or negative (-ve) in both tests are along the leading
diagonal of the array. Those that were positive in one and negative
in the other form the off-diagonal elements. The culture test
provides a highly accurate test of whether an animal is infected.
This has allowed us to calculate the sensitivity, specificity,
positive predictive value, and matching rate between the two tests.
Initially, let us consider a model for the dynamics of brucellosis in a single host population. The model assumes that calves born to uninfected mothers are brucellosis free. Susceptible individuals, S, may acquire infection from contact with infectious individuals, I, or a proportion of calves born to infected mothers will also be infected. There is thus some vertical transmission in the model. Here we also assume that infected mothers may exhibit some loss of fecundity, that transmission and pathogenicity of Brucella are low, and that transmission can be described by a simple mass action term [Beta]. This transmission rate can be either directly dependent upon the density of infected and susceptible animals, or upon the relative density of infected and susceptible individuals (Antonovics et al. 1995, Meyer and Meagher 1995, DeLeo and Dobson 1996).
Infected individuals are assumed to maintain the infection for [approximately equal to] 1-2 yr, when they recover and enter a resistant or immune class of hosts. The model can be expressed algebraically using three coupled differential equations:
dS/dt = (a – [Phi]N)[S + R + I[Rho](1 – e)] – bS + [Delta]R – [Lambda](I) (1)
dI/dt = [Lambda](I)S + I(a – [Phi]N)e[Rho] – ([Alpha] + b + v)I (2)
dR/dt = vI – (b + [Delta])R (3)
N = S + I + R. (4)
The parameters used in the model are host birth rate, a (bison 0.26, elk 0.25); host death rate, b (bison 0.1, elk 0.15); [Phi], density-dependent reduction in host births; [Beta], transmission rate of B. abortus; [Epsilon], proportion of infected females that produce infected offspring; [Rho], reduction of fecundity in infected individuals; v, recovery rate of infected individuals (1/v [right arrow] 2 yr); [Alpha], virulence (increase in mortality rate of infected hosts); [Delta], rate of loss of resistance. Estimates of their magnitude were made from studies of bison and elk demography (Meagher 1973, Houston 1982) and published epidemiological studies on brucellosis (Nicoletti 1980, Witter 1981). We have assumed that the bison herd will equilibrate at [approximately equal to] 4500 individuals (thus [Phi] = 0.00004), that elk may equilibrate at 25000 individuals (thus [Phi] = 0.000004); and that a high proportion of infected females will produce infected calves ([Epsilon] = 0.9) and that 50% of infected females fail to produce a calf ([Rho] = 0.5). There is very little evidence for increased mortality of bison or elk infected with Brucella. We have therefore set [Alpha] = 0.005 for each species. We also assume that an infected animal may transmit the disease for [approximately equal to] 2 yr (v = 0.5). As with any epidemiological study, estimating the transmission rate poses the greatest problems. We have assumed that the rate at which animals transfer from the susceptible to the infected class, the “force of infection” [Lambda](I), can take one of two forms that correspond to the two main types of transmission. When the probability of an animal becoming infected is a function of the density of infected individuals in the population then [Lambda](I) = [Beta]I. In contrast, frequency-dependent transmission will occur when transmission is a function of the proportion of individuals infected, in this case we use [Lambda](I) = [Beta]I/N. Because the threshold for establishment seems to be a herd size of between 200 and 500 individuals we can coarsely estimate transmission rate in the density-dependent case by deriving an expression for the threshold for establishment.
[H.sub.T] = [Alpha] + b + v – [Rho][center dot]a[center dot][Epsilon]/[Beta].
Substitution of our initial parameter estimates into this equation suggests that [Beta] in the density-dependent case is in the range 0.001-0.0005. Alternatively, DeLeo and Dobson (1996) have recently demonstrated that the transmission rates in models for different pathogens will scale allometrically with the body mass of the host species. Their work suggests that where transmission is density dependent, a good estimate of the minimum transmission rate necessary for the pathogen to establish, [[Beta].sub.min] is [[Beta].sub.min] = [0.0247w.sup.0.44]; in contrast, in the case of frequency-dependent transmission [[Beta].sub.min] = [0.4w.sup.-0.26], where w is the mass (in kilograms) of the host species. When we rescale these transmission rates to obtain estimates for transmission rates for bison herds on the entire Northern range we obtain values of [Beta] [approximately equal to] 0.002 for density-dependent transmission, and [Beta] [approximately equal to] 2.0 for frequency-dependent transmission. The two different versions of the model may then he used to run numerical simulations for brucellosis in the bison population [ILLUSTRATION FOR FIGURE 5 OMITTED]. Both simulations broadly capture the essential features of the interaction, however the frequency-dependent case produces levels of prevalence that more closely resemble those observed in the serological surveys. In contrast to the basic SIR model where disease prevalence is dependent upon population density, in the frequency-dependent transmission case, the proportion of the population infected is the same for all population sizes.
The dynamics of the model are very stable for the broad range of parameter values that correspond to brucellosis in wild and domestic ungulates. The pronounced stability of the interaction is primarily due to the long period of time for which animals are infected with the pathogen. Reducing this time period to a value that corresponds to weeks rather than years can produce epidemic outbreaks in the model (Anderson and May 1991). There is no evidence that this occurs with brucellosis. Introduction of the pathogen into a growing herd of bison results in a steady spread of the pathogen through the population, with [approximately equal to] 10% of the population being infected at any time and a further 30% of the population exhibiting a positive serology test reflecting past exposure to the pathogen [ILLUSTRATION FOR FIGURE 5 OMITTED]. The dynamics of the model are most sensitive to the equilibrium population density at which the herd would equilibrate (a – b)/[Phi], the transmission rate [Beta], and the pathological impact of the pathogen on host fecundity [Rho], and mortality [Alpha].
TWO-SPECIES BRUCELLOSIS MODEL
The model can be readily extended to include a second species of host:
[dS.sub.i]/dt = ([a.sub.i] – [[Phi].sub.i][N.sub.i])[[S.sub.i] + [R.sub.i] + [I.sub.i][[Rho].sub.i](1 – [e.sub.i])]
+ [[Delta].sub.i][R.sub.i] – [b.sub.i][S.sub.i] – [[Beta].sub.ii][S.sub.i][I.sub.i] – [[Beta].sub.ij][S.sub.i][I.sub.j] (6)
= [B.sub.ii][S.sub.i][I.sub.i] + [[Beta].sub.ij][S.sub.i][I.sub.j] + [I.sub.i]([a.sub.i] – [[Phi].sub.i][N.sub.i])[e.sub.i][[Rho].sub.i]
– ([[Alpha].sub.i] + [b.sub.i] + [v.sub.i]) [I.sub.i] (7)
[dR.sub.i]/dt = [v.sub.i][I.sub.i] – ([b.sub.i] + [[Delta].sub.i])[R.sub.i]. (8)
Here the [[Beta].sub.ii] terms represent within-species transmission and the [[Beta].sub.ij] terms reflect between-species transmission. As with any epidemiological model the main empirical problem is determining how to quantify transmission rates. This problem is greatly compounded in multihost models. We have attempted to reduce this inherent complexity by assuming that transmission has both an ecological and a physiological component, but that between-species transmission is dominated by the ecological component. Rates of transmission between species will thus be determined by the amount of range overlap and by the tendency of the different species to aggregate together while foraging and resting.
Range overlap for bison and elk in Yellowstone was quantified using data provided by the Yellowstone GIS (Geographic Information System) laboratory. The analysis suggests that only [approximately equal to] 7% of the elk winter range is occupied by bison. This implies that low levels of range overlap between the two species may be responsible for the low levels of prevalence observed in elk. Obviously, this result could be considerably biased if the species tend to aggregate together on the parts of their range that they both jointly occupy. Table 3 provides estimates of the density of bison and elk on their winter ranges in Yellowstone and in the National Elk Range in Jackson. Although overall elk and bison densities in Yellowstone are about the same, the density of elk in Jackson is a factor of 10 higher than in Yellowstone. Furthermore, the elk are highly aggregated in winter on feed grounds in the elk refuge. As the Jackson elk maintain endemic brucellosis infections at high levels of prevalence, this implies that the Yellowstone elk would have to increase considerably before they too could support Brucella at the levels of prevalence observed on the National Elk Refuge. As it is, elk are only likely to transmit Brucella when they are temporarily aggregated together in large herds during the winter.
TABLE 3. Estimates of the average density of bison and elk in 1970
and 1990 in Yellowstone National Park and on the National Elk Refuge
in Jackson, Wyoming. The data for bison and elk numbers were taken
from Meagher (1973, 1993) and Houston (1985); the data on range size
were taken from Boyce (1989).
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