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B I O L O G I CA L C O N S E RVAT I O N 13 1 ( 20 0 6) 2 4 4–25 4 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/biocon Assessing risks of disease transmission between wildlife and livestock: The Saiga antelope as a case study E.R. Morgana,*, M. Lundervoldb, G.F. Medleyb, B.S. Shaikenovc, P.R. Torgersond, E.J. Milner-Gullande a School of Biological Sciences, University of Bristol, Woodland Road, Bristol BS8 1UG, UK Ecology and Epidemiology Group, Department of Biological Sciences, University of Warwick, Coventry CV4 7AL, UK c Institute of Zoology, Ministry of the Environment, Akademgorodok, Almaty, Kazakhstan d Institute of Parasitology, University of Zürich, Winterthurerstrasse 266a, CH-8057 Zürich, Switzerland e Division of Biology, Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, Berkshire SL5 7PY, UK b A R T I C L E I N F O A B S T R A C T Available online 5 June 2006 Disease transmission between wildlife and livestock can undermine conservation efforts, either by challenging the viability of threatened populations, or by eroding public tolerance Keywords: of actual or potential wildlife disease reservoirs. This paper describes the use of transmis- Model sion models to assess the risk of disease transfer across the wildlife–livestock boundary, Foot and mouth disease and to target control strategies appropriately. We focus on pathogens of the Saiga antelope Nematode (Saiga tatarica) and domestic ruminants in Central Asia. For both foot and mouth disease Migration and gastrointestinal nematodes, the main risk is associated with infection of saigas from Seasonality livestock, and subsequent geographical dissemination of infection through saiga migra- Kazakhstan tion. The chance of this occurring for foot and mouth disease is predicted to be highly dependent on saiga population size and on the time of viral introduction. For nematodes, the level of risk and predicted direction of transmission are affected by key parasite life history traits, such that prolonged off-host survival of Marshallagia in autumn enables infection of saigas and transfer northwards in spring. Field estimates of parasite abundance provide qualitative support for model predictions. The application of models as tools for the early evaluation of disease transmission between wildlife and livestock is discussed. Ó 2006 Elsevier Ltd. All rights reserved. 1. Introduction Many pathogens and parasites of wildlife also infect sympatric domestic animals. The role of different host populations in the maintenance and spread of infection then becomes important to conservation. Disease transmission from a domestic animal reservoir to wildlife can directly threaten population viability, as for rabies in Ethiopian wolves (Randall et al., 2006). Where wildlife is the reservoir of infection for domestic animals, on the other hand, control strategies might include culling or curtailing the movement of wildlife, which itself could have conservation implications. The relatively free movement of wild animals gives them the potential to act as vectors for the geographical spread of disease, even if infection does not persist for a long time in the wildlife population. In Africa, the importance of buffalo Syncerus caffer as a source of foot and mouth disease virus (FMDV) for livestock is enhanced by its ability to persist in this species (Vosloo et al., 2002), but other wild ruminants such as impala Aepyceros melampus might also act as a vector for transmission * Corresponding author: Tel.: +44 1179 287485; fax: +44 1179 257374. E-mail address: [email protected] (E.R. Morgan). 0006-3207/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.biocon.2006.04.012 B I O L O G I C A L C O N S E RVAT I O N between buffalo and cattle (Bastos et al., 2000; Hargreaves et al., 2004). Many other important infectious diseases including rift valley fever, malignant catarrhal fever and tuberculosis infect both wild and domestic ruminants and may be transmitted between them (Worthington and Bigalke, 2001). The willingness of landowners and other agricultural stakeholders to support wildlife conservation efforts is likely to be affected by assessment of the risk of disease transmission to livestock, and on the control strategies available should this risk be high. Unfortunately, assessing the risk of disease transmission between wildlife and livestock is usually extremely difficult. Data on levels of infection in wildlife are often scarce and open to bias, and are not in themselves sufficient for assessment of cross-species transmission. Thus, wild animals can be infected at a high level, but if most infection is from surrounding livestock, and there are limited opportunities for onward transmission, their role as a reservoir of disease might be negligible. The conclusion that high point prevalence indicates a source of infection is then incorrect (Haydon et al., 2002a). Crab-eating foxes in Brazil, for instance, have high seroprevalence for Leishmania infantum, but are not infective to the insect vector, and do not therefore contribute to infection of dogs and humans (Courtenay et al., 2002). Even if wild animals are infective to their domestic counterparts, the extent of cross-species transmission will depend on contact patterns, which are rarely straightforward. Where contact is seasonal or sporadic, for instance, its timing might be more important than relative levels of infection to the direction of disease transmission (Morgan et al., 2004). Climatic factors can significantly affect contact rates, for example through increased density and species range of ungulates around water holes in droughts (Redfern et al., 2005), as well as directly affecting the persistence of pathogens outside the host, and the development of parasites to the infective stage in the environment or in invertebrate intermediate hosts. Variation in the weather within and between years is then likely to influence risks of disease transfer between species. Disease data restricted to short sampling periods might miss key events in disease dynamics, and give an inaccurate picture of cross-species infection. 1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4 245 It is clear that existing field data on wildlife disease will, in most cases, not enable reliable assessment of future risks of transmission from and to sympatric livestock populations. This will be particularly true for new and emerging disease threats, for which data are especially scarce, or when perturbations to host populations or the environment might affect disease dynamics in unknown ways. In these situations, understanding of general disease dynamics, formalised as mathematical models, could be applied to the specific system in question in order to predict likely transmission patterns, and investigate potential control strategies. Models have been used successfully in this way for several important livestock diseases (e.g., French et al., 1999; O’Callaghan et al., 1999; MacKenzie and Bishop, 2001; Smith, 2001; Keeling, 2005). However, additional complexities in wildlife systems limit the applicability of livestock-based models. These include host movement, variation in host population size, density and contact rates, unpredictable variation in climate, and species differences in the host–parasite relationship. Considerable adaptation is therefore necessary before such models can be successfully applied to disease transmission across the wildlife–livestock boundary. Nevertheless, mathematical modelling could be a useful first step in the investigation of risks of disease transmission between wild and domestic animals, if it is able to focus attention on likely drivers of disease dynamics, and on key areas of data scarcity. This paper attempts to illustrate the benefits and limitations of such an approach with respect to saiga antelopes and domestic ruminants in Kazakhstan, a system which includes many complexities that are common in other wildlife situations. 2. Saiga antelopes and livestock in Kazakhstan Until recently, the saiga antelope (Saiga tatarica) was common in Kazakhstan, reaching total numbers of around one million in the 1970s. It is a commercially valuable species, supplying meat, horns and hides to domestic and international markets (Fadeev and Sludskii, 1982; Bekenov et al., 1998). The species is nomadic, undertaking extensive seasonal migrations (Fig. 1). Large aggregations form in the spring, when females give birth over a 10 day period (Bekenov et al., 1998). Saigas Fig. 1 – Migrations of the saiga antelope in the Betpak-Dala region of Kazakhstan. Saigas spend the winter in the south (1), calve on the northward migration (2), and graze northern pastures in the summer (3), before migrating south in autumn (4). The other saiga populations are not shown. 246 B I O L O G I C A L C O N S E RVAT I O N graze on the open plains, and come into contact with domestic livestock by sharing pasture and water sources. This contact is uneven because of the patchy distribution of both livestock and saigas. In the Betpak-dala population of Central Kazakhstan, contact is likely to be closest in the winter, when saigas and livestock are concentrated on limited pasture in the south, and also occurs in the summer in the north. During the spring and autumn, saigas migrate through the central part of their range, which has become denuded of livestock in recent years. Additionally, most livestock is grazed close to villages at this time of year, and contact is less likely, although much of the pasture used by saigas will have been previously grazed by livestock. Saiga herds vary in size through the year, from huge aggregations during calving to small groups during summer grazing, with intermediate group size during migration and mating. Herd structure is also quite labile, and individuals can leave and join different groups through the year (Grachev and Bekenov, 1993). Total saiga population size is highly variable between years, and even in the absence of hunting severe winters can cause up to 50% mortality, with recovery over the next 2–3 years (Bekenov et al., 1998). Cattle, sheep, goats, camels and horses are present in the saiga range, but sheep are by far the most numerous and tend to graze the more remote pastures, and are therefore the most likely to share parasites and diseases with saigas. Recent changes have affected the numbers and grazing patterns of both saigas and livestock. Excessive hunting has pushed saiga numbers down to critical levels in much of its range (Milner-Gulland et al., 2001), while collapse of the agricultural economy in the 1990s has decimated livestock numbers and dramatically reduced grazing on the remote open plains, as well as inhibiting veterinary care and disease prevention (Lundervold et al., 2004). Impoverishment linked with reduced livestock production has been a major cause of increased saiga poaching (Robinson and Milner-Gulland, 2003). The likely effect of these changes on disease transmission between saigas and livestock, and the risks of disease to a declining saiga population, are unknown. Saigas and domestic ruminants are susceptible to many of the same parasites and diseases. Foot and mouth disease virus (FMDV) is known to infect saigas and appears to cause more severe disease than in domestic ruminants. Mortality in saigas experimentally infected with FMDV can be up to 75%, and as much as 10% of the free-living population has died during natural outbreaks (Sokolov and Zhirnov, 1998). Outbreaks of FMD in domestic ruminants involving viral types A and O have occurred regularly in Kazakhstan over the past few decades, with increasing frequency in border areas in recent years as veterinary controls and vaccine coverage have deteriorated (Lundervold, 2001). Brucella melitensis, a common cause of ovine abortion in Kazakhstan, can also infect saigas, though its clinical consequences in this species are not well known (Lundervold, 2001). Of the 38 helminth species found in saigas in Kazakhstan, 35 have also been found in domestic ruminants (Morgan et al., 2005). These organisms are important causes of lost agricultural production in Kazakhstan, and have also been shown to adversely affect wildlife populations in other parts of the world. Previous work catalogued nematode species in saigas and high- 1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4 lighted the possibility of infection across the wildlife– livestock boundary, but did not quantify this risk (Berkinbaev et al., 1994). Evidence of mutual susceptibility gives us no indication of how important transmission between saigas and livestock actually is in nature, or how it might be prevented. However, the biology of the main pathogens and parasites of saigas is fairly well known, albeit in other host species, and we should be able to make sensible predictions about their behaviour in this more complex epidemiological setting. In this paper we use exploratory mathematical models to predict patterns of disease transmission within and between saiga and livestock populations. We focus on FMDV and gastrointestinal nematodes because they are important pathogens, and also because they illustrate the contrasting approaches to modelling infection patterns in microparasites (e.g., viruses) and macroparasites (e.g., helminths). The details of the models are published elsewhere: here we use them to illustrate how established model frameworks have to be adapted to take account of the additional complexities of the saiga– domestic ruminant (and, in general, the wildlife–livestock) interface. 3. Model 1: Foot and mouth disease (FMD) Saigas are known to be susceptible to FMD, and to excrete the virus for some days after infection. It has been widely assumed that saigas become infected from domestic ruminants, and there is also anecdotal evidence suggesting transmission from saigas to livestock. This is of particular concern because saigas could promote geographical dissemination of infection through their seasonal migrations. It is not known when saigas are most likely to be infected from livestock, how long the virus could persist in saiga populations, or under what conditions there is a significant risk of onward transmission to livestock. The model was designed to address these questions using existing knowledge of FMD epidemiology. 3.1. Model structure The model is based on the established SLIR framework (Anderson and May, 1991), whereby individuals are placed into mutually exclusive categories representing susceptible, latent infected, infectious and recovered (immune) states. The model architecture is shown in Fig. 2, and a detailed description can be found in Lundervold (2001). Similar models have been used to assess control strategies for FMD in domestic ruminants (Keeling, 2005), and to predict risks of FMDV establishment in wild pig populations (Pech and Hone, 1988; Pech and McIlroy, 1990). Additional complexities that might be important in the saiga–domestic ruminant system but are generally ignored in previous models include multiple host species, complex host movement patterns, and dramatic fluctuations in population size and density. These give rise to regional and seasonal differences in contact rates between saigas, and between saigas and domestic ruminants. Key points of infection risk are therefore likely to vary widely between different geographical locations and times of year. Fluctuations in saiga population size B I O L O G I C A L C O N S E RVAT I O N Nat_Death Ra Ω Adults Sa Calves Sc ν β La Ia σ Lc α FMD_Death FMDDeath_C Ic Births IM c Rc Nat_DeathC Fig. 2 – Schematic representation of the flow of hosts between classes, which records the dynamic interaction between the directly transmitted microparasite FMDV and its host population, the saiga antelope. Compartments represent susceptible (S), latently infected (L), infective (I) and recovered immune (R) individuals. Infection can lead to recovery or death (FMD__Death) at rate a, and all classes are subject to natural background mortality (Nat__Death). Suffix a = adult, c = calf. b represents the transmission function, r the latent period, m the infectious period, and X the duration of immunity. Calves may be born susceptible (Sc) or immune through maternal antibodies (IMc) (Lundervold, 2001). and density will also cause infection risk to vary greatly within and between years. These complexities were addressed by adaptations to the basic SLIR model. Most models of FMD in domestic ruminants focus on inter-herd spread, and consider each herd to be a unit. Because of variation in saiga herd size and structure, it is more appropriate to consider the individual saiga as the unit. Previous models of FMD and many other viruses also assume a linear relationship between population density and virus transmission. If the range of a population is fixed, then an increase in population size will lead to an increase in population density and increased contact rates. However, there is no fixed edge to the saiga range, which can expand when numbers increase, so the relationship between population size and density is not straightforward. Additionally, saigas 247 1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4 come together into groups to mate, calve and migrate even at low population density, and so the chances of an individual encountering other saigas (and passing on or contracting infection) is unlikely to vary linearly with population density. Consequently, we assume frequency-dependent rather than density-dependent transmission (McCallum et al., 2001). The seasonal dynamics of saiga populations present further challenges. Saigas give birth over a period of around 10 days, leading to a massive influx of susceptible individuals into the population. These large fluctuations in available hosts mean that infectious disease may spread more rapidly at certain times of year. Additionally, saiga migration leads to seasonal contact with different livestock populations, and consequently variation in the risk of cross-species transmission. Rather than attempting to simulate spatial variations in saiga–livestock contact explicitly, they are subsumed into temporal variation in the contact rate, b. This is possible because saigas generally migrate en masse and so geographical variation in infection risk is implicitly included by varying b (the effective contact rate) in time. b is split into saiga and livestock components to reflect the two sources of infection, and the livestock component is weighted according to livestock density at different times of year (=different parts of the saiga range) and monthly relative humidity (=ability of the virus to survive in the air). The seasonal forcing effect of mass saiga calving is included by splitting the saiga population into separate adult and juvenile compartments, with transfer from juvenile to adult compartments occurring at 6 months of age. Calves are assumed to carry maternal antibodies for the first 5 months of life, based on estimates of 3–7 months for the duration of maternal immunity in domestic cattle and buffalo (Lundervold, 2001). 3.2. Results The aim of the model is to predict the conditions necessary for FMD establishment and persistence in the saiga population, and hence the risk of onward transmission to livestock. Infection is introduced to the model by adding two infected Number of infected saigas 250000 200000 150000 100000 50000 0 0 52 104 156 208 260 312 364 416 468 Weeks Fig. 3 – The predicted size and frequency of FMD epidemic peaks when both population size (2,300,000) and contact rate (b) are high. The initial spike is on a much larger scale than the others; however, this is not seen on the graph as the y-axis has been truncated for clarity. Two peaks of infection are predicted to occur each year: the first when saigas come together for calving, and the second, higher peak when new susceptible juveniles enter the system after maternal immunity has waned in autumn. Week 0 = January. 248 B I O L O G I C A L C O N S E RVAT I O N 1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4 Table 1 – The predicted effect of varying the time of year that infection is introduced into the saiga population Value of b Spring Summer Autumn Winter High (5 x 10-6) Medium (9.3 x 10-7) Low (5 x 10-7) Initial population size in week 0 is at equilibrium (N = 2.3 million). Dark shading indicates cyclical epidemics, light shading one epidemic. b is the effective contact rate. adults to the population, and the main model output is the predicted number of infected saiga individuals through time. There are three possible consequences: no epidemic (the virus does not propagate successfully within the population and dies out), a single epidemic peak which is unsustainable and then dies out, or sustained cycles of infection. From the point of view of disease management in livestock, cyclical epidemics in saigas are the most dangerous because the virus can then persist until contact with other livestock populations occurs. We first explore the behaviour of a simple version of the model, with contact rate constant throughout the year. In this case, the outcome of a single infection event in saigas is strongly affected by the effective contact rate (b), as well as population size (N). When both parameters are high and constant, cyclical epidemics are predicted to occur, regardless of the time of year at which infection is introduced (Fig. 3). However, when N is reduced below 1.5 million, or b is set at a medium value, epidemics occur only if infection is introduced in autumn (Table 1). This is because at other times of year, infection ‘burns out’ by depleting the pool of susceptible animals, after which it cannot keep circulating until the introduction of new susceptible animals. When the population size is low (<750,000), there is predicted to be no epidemic unless b is at the upper end of its range. Thus there is a threshold minimum number of susceptible animals required to propagate an epidemic. The value of the contact rate b is therefore critical to model predictions. In a more realistic refinement of the model, b is varied seasonally to simulate fluctuating saiga herd size (largest in spring) and contact with livestock (closest in winter). The refined model predicts that just a single epidemic peak occurs if infection is introduced in spring. This is because such a high proportion (up to 92%) of the population is infected in the initial outbreak that there are insufficient susceptible animals left for the virus to persist through the rest of the year when b is much lower. Introduction of the virus at other times of year results in fewer than 70% of the population becoming infected, leaving enough susceptible animals for the virus to persist. If overall values of b are very low, the dip in contact rates in summer and autumn is such that the virus is unable to persist through the year. Virus introduced in winter is least likely to trigger an epidemic in saigas, as the population size at this time of year is at its lowest. This is fortunate, because saigas and livestock are in closest contact in winter, and infection of saigas from livestock is perhaps most likely then, but under these conditions the virus would disappear from saigas by the time they moved north in spring. Validation of model predictions is troublesome, because few quantitative data are available from past FMD epidemics. However, between 1955 and 1974, when saigas were relatively abundant, 9 separate FMD outbreaks were observed in saigas (Lundervold, 2001). Typically, large epidemics were observed in spring and summer, which died out in summer and autumn. This matches model predictions when seasonal variation in b is included. 3.3. Discussion The most important conclusions of the model, as it stands, are firstly that introduction of infection into the saiga population is most dangerous in autumn because establishment of cyclical epidemics is most likely at this time of year, and secondly that persistence of the virus in saigas is most likely when the population is large. These insights could be useful when planning vaccination of livestock to prevent infection of saigas. Thus, vaccination of livestock in saiga over-wintering areas might be preferred because contact rates are relatively high and exposure of saigas to the virus is arguably most likely here. However, because the risk of viral persistence in the saiga population is predicted to be higher if it is introduced in autumn, there is an argument for prioritising vaccination of livestock in those areas through which saigas pass at this time of year, i.e., on their southward migration. Large scale livestock vaccination campaigns have been used in the past in order to prevent infection of saigas. However, changes in the agricultural economy are likely to decrease the feasibility of such centrally funded blanket vaccination strategies in the future, and a strategic decision on where to best target limited resources will have to be made. The default saiga population size used in the model was the estimated carrying capacity. However, the results suggest that when saiga populations are small, as they are at present, the risk they present to livestock as a reservoir of infection for FMD is extremely low, and specific control strategies are unlikely to be needed. These results are for simulations with a constant contact rate regardless of population size. However, population fragmentation could lead to this assumption being violated. Furthermore, the effects of an outbreak of FMD are potentially more devastating from a population viability perspective if the saiga population is already low. Since B I O L O G I C A L C O N S E RVAT I O N agricultural economic reform and the cessation of effective vaccination schemes in much of Kazakhstan, localised outbreaks of FMD in domestic ruminants have become common (Lundervold et al., 2004), and the chance of spread to saigas has probably increased. This could be mitigated in part by the decrease in numbers of livestock grazing the open steppe (Robinson and Milner-Gulland, 2003). The model can be used to investigate alternative scenarios by weighting the relative contribution of saigas and livestock to b, and by manipulating its seasonal variation. The model also illustrates several points important to our understanding of disease dynamics in wildlife populations. The dominant features in the behaviour of the saiga-FMD model are the strong seasonal forcing effect of saiga population dynamics, and seasonal contact with livestock populations. Predictions using seasonally varying effective contact rates are qualitatively different to those using constant values. However, it is extremely difficult to obtain accurate estimates of contact rates in wildlife populations. This leaves us with a dilemma: the complexities which we really ought to include in our models are the very ones that are hardest to quantify. As a result, although model output can give us real insight into the possible behaviour of FMDV in saigas, parameterisation and validation are too tentative to allow us to place much confidence in practical recommendations for control. The alternative, however, is to omit factors about which we have little information, leading to simple, tractable models which are liable to completely miss fundamental drivers of system dynamics. The strong effect of contact rate (b) on the qualitative output of the model suggests that more accurate estimation of contact rates between saigas and between saigas and livestock is a priority if we are to accurately predict the course of disease in saiga populations. This will be difficult, although satellite tracking studies could make an important contribution. Serological studies of endemic viruses transmitted by similar routes could also help to estimate b without having to wait for the next FMD outbreak, although there are no obvious candidate viruses in saigas. 4. Model 2: Gastrointestinal nematodes The model of nematode dynamics considers three closely related but contrasting genera: Haemonchus, Nematodirus and Marshallagia. The adults live in the abomasum and lay eggs that pass out in the faeces. Larvae hatching from these eggs undergo further development before climbing onto the herbage to be ingested by the next host. Rates of development, mortality and migration onto herbage are dependent on climate, especially ambient temperature and moisture provided by recent rainfall. As a result, transmission is highly seasonal. The exact timing and extent of transmission within and between populations is also likely to differ between years according to the weather. Data on parasite abundance and epidemiology collected over a small number of years might not therefore be representative of typical patterns, and such field data cannot be relied on to guide control strategies in the future. The purpose of this model is to use existing understanding of the relationships between climate and parasite vital rates to predict the times of year when transmission is greatest. 249 1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4 This is important because it will enable control strategies to be focused appropriately. Additionally, the model can predict how regularly significant parasite transmission is expected to occur between saigas and domestic livestock. 4.1. Model structure The model is based on a framework that is well established for domestic ruminants (Coyne and Smith, 1994; Smith and Grenfell, 1994), and its basic structure is shown in Fig. 4. The total abundance of parasites in each life cycle stage is calculated in successive daily time steps. There are separate parasite populations in adult and juvenile saigas, and in sheep and lambs in the north, centre and south of the saiga range. These populations are linked by access of the hosts to common pools of free-living stages in each area. Migrating hosts infected by parasites transfer them to other areas and host populations through contamination of pasture with eggs. The model is deterministic, but the effect of climate is included as run-time variation in parasite vital rates, which are drawn from probability distributions within and between years (Table 2). Further details of the model are given in Morgan (2003). 4.2. Results We focus here on Marshallagia, the most common of the three genera. The model predicts that saigas acquire Marshallagia primarily in the winter, from the south of their range H (i=1 to 10) μP (1-pe) pe β μLh Area (j=1 to 3) P λ Lh dm L3 μL3 dL L μL dh EL μel de E μe Fig. 4 – Schematic representation of the nematode model. Adult parasites (P) lay eggs (E) that pass out in the faeces and develop through successive embryonated egg (EL), early larval (L) and infective larval (L3) stages before becoming available to hosts on the herbage (Lh). The model tracks losses from each stage through development (d) and mortality (l). b represents the rate of uptake of larvae by grazing saigas or livestock, pe the proportion of larvae that establish successfully in the host after ingestion, and k the rate of egg production of adult worms. The part of the parasite life cycle that takes place within the host is duplicated for each host population, and the part that takes place on the ground is duplicated three times, once for each part of the saiga range. More details are given in Morgan (2003). 250 B I O L O G I C A L C O N S E RVAT I O N 1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4 Table 2 – Stochastic elements of the nematode transmission model, with range of run-time variation in parameter values Element Governed by Variation Form Time of year at which development of the freeliving stages can begin Time of year at which development of the freeliving stages must end Probability that a given dekad is sufficiently wet for development to take place Peak herbage biomass Range Timescale Air temperature in spring Normal, rounded off to whole dekad Annual End March–end May Air temperature in autumn Normal, rounded off to whole dekad Annual Start September–end October Rainfall in each dekad Uniform Dekadal 0.07–0.61 Cumulative early year precipitation Lognormal Annual 200–2000 kg/Ha Parameters were different for each of the three areas of the saiga range and for each of the three nematode species. Marshallagia Saigas and sheep S J F M C A N M J J C S A S O N D A S O N D Saigas alone J F M A M J J Fig. 5 – The peak times of Marshallagia acquisition by saigas predicted by the model. The vertical axis represents the daily change in the total parasite population in saigas: shading above the horizontal axis means net parasite acquisition, and shading below the axis net parasite loss. Letters on the horizontal axis are months of the year, and N, C and S indicate the periods during which saigas are in the northern, central or southern part of their range, respectively. In the top plot, saiga and sheep populations were included in the model, whereas in the bottom plot only saigas were present. The vertical axis on the lower plot is scaled to 1/100 of that in the upper plot: at the same scale, no parasite acquisition is discernible. The plots represent output of simulation for a single year, but climatic parameters typical for the region were chosen, and the winter peak of acquisition when sheep are included was consistently repeated. Marshallagia eggs deposited in autumn are able to develop to the infective stage and survive until saigas arrive in winter. When sheep are excluded from the model, this winter peak of larval ingestion is greatly reduced, suggesting that sheep are the main source of infection for saigas. By tracking the origin of ingested larvae, the model can partition infection according to the source population (Fig. 6). It appears that saigas indeed acquire most of their parasites from sheep. However, sheep in northern Kazakhstan can acquire a significant proportion of total annual infection from saigas that arrive from the south in summer. This only occurs in some years, depending on the weather conditions in relation to saiga movement. The model predictions are therefore riskbased, and acknowledge that infection patterns differ between years. Control strategies will not have exactly the same results every year, but must simply aim to reduce the overall risk of excessive parasite transmission. Haemonchus transmission is even more strongly affected than Marshallagia by changes in the weather between years, and significant infection of saigas from sheep in the north 'Perc entage trans mis s ion' from s aigas (Fig. 5). At first glance this is surprising, because conditions at that time of year are too cold for parasite development. However, winter transmission occurs in the model because 100 80 60 40 20 0 Saigas Sheep Sheep (transhumant) North Sheep Centre Sheep South Fig. 6 – The predicted importance of saigas as a source of nematode infection for different host populations. For each population, the first column is the cumulative percentage of infective larvae ingested over the course of a year that come from eggs egested by saigas; the second column is the proportion of years in which more than 10% of ingested L3 come from saigas (proportion >50% from saigas shaded). All figures are averages from 1000 stochastic simulations. B I O L O G I C A L C O N S E RVAT I O N Table 3 – Mean burdens of Marshallagia in saigas culled in autumn, before visiting the winter range, and in spring, after visiting the winter range Autumn (n = 87, 46) Spring (n = 5, 6) Juvenile Adult p 8 178 143 160 <0.001 NS The autumn sample was taken from Betpak-Dala in November 1997, and the spring sample from Ustiurt in May 1998. Means were compared using the Mann–Whitney U-test (Morgan et al., 2005). and subsequent carriage to southern pastures is predicted to occur approximately one year in five. The time of peak Nematodirus transmission is predicted to be in spring, when saigas are furthest from sheep pastures, and transmission between saigas and livestock is likely to be minimal. Interestingly, the most common Nematodirus species in saigas, Nematodirus gazellae, is rarely observed in sheep or cattle. The model is run using moderately high saiga numbers from the 1980s (240,000 saigas in the Betpak-Dala range); with the lower current population size, the contribution of saigas to contamination of livestock pasture with nematode larvae is predicted by the model to be negligible, and so no specific control strategies to counter this are indicated. Validation of the model would require extensive field sampling of saigas and livestock over a long period of time. However, the most interesting prediction is winter infection of saigas with Marshallagia. Analysis of parasite count data revealed that in autumn, juvenile saigas – which have not yet visited the winter range – were observed to carry far fewer Marshallagia worms than adults, whereas in spring, there was little difference in parasite burden between old and young saigas (Table 3), suggesting that both age classes have been exposed to a similar level of infection. These field data provide support for the winter transmission hypothesis. To directly test the hypothesis that sheep are the main source of this infection, an intervention study could be developed in which sheep are treated during the autumn to decrease their output of eggs, and a reduction in worm burdens in saigas moving north is assessed. If burdens are reduced, treatment of sheep in autumn in the south of the saiga range could decrease the risk of onward transmission to sheep in the north via migrating saigas. 4.3. Discussion The model helps to explain observed patterns of parasite transmission, and to focus analysis of field data (and potentially future sampling effort) onto the most important times and places for parasite transmission. The model also allows us to extrapolate our expectations regarding parasite epidemiology between years, in a way we could not attempt using field data alone. To take an extreme example, saigas are predicted to provide the majority of Marshallagia infection for sheep in the south of their range just one year in a hundred, but if we happened to sample only in this year, we would have a distorted view of transmission dynamics and might be tempted to instigate inappropriate control strategies. Transmission in the other direction – from sheep in the south via 1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4 251 saigas to sheep in the north – is predicted to occur quite consistently, and would be a more suitable target for control. The effect of control strategies can be investigated by manipulating the model, before submitting to the risk and expense of trying them out in the field. The model output is stochastic and the expected effect of control strategies is expressed in terms of risk of significant transmission, rather than parasite burdens per se. This makes more sense; other factors such as host nutrition and immunity confound predictions of parasite burdens, whereas what managers need to know is the chance that parasite control in livestock will fail as a result of introduction of infection from saigas. The nematode model is not without problems. Even though it predicts over-winter transmission of Marshallagia, for instance, this results from a combination of parasite life history characteristics, weather and saiga movement patterns. Changing any of these affects the magnitude and/or timing of the predicted transmission peak. The more complex a model is, the less transparent are the mechanisms behind its predictions, and the less sure we can be about what aspects of the model generate the key infection patterns. In this case, detailed sensitivity analysis could be used not only to identify key parameters, but also to determine the simplest model structure that still generates the observed epidemiology. A further limitation of the model is that it is specific to saigas, and of limited relevance to other systems. Extrapolation of its findings to other problem parasites of wildlife is not recommended, since movement patterns and host factors are likely to be different, and few general lessons about parasite epidemiology emerge. It is possible that parameters that have been extrapolated from sheep, such as parasite establishment and survival rates, are very different in saigas, leading to qualitative differences in model predictions. This is a common problem with models of wildlife disease, especially for threatened species for which estimation of parameters using experimental infection of captive individuals is both impractical and undesirable. Finally, validation of the model is difficult. The source population of ingested larvae, for instance, would be impossible to measure, although advancing techniques in molecular genetics might change this in future. Because transmission is influenced by stochastic variation in climate, parasite abundance data collected in a single year would be of limited relevance. Validation would therefore have to be a long term process, and recommendations might be needed before it is complete. The outcome of control strategies based on the model cannot be known until they are put into practice, and so recommendations can only be made tentatively pending thorough validation. Nevertheless, the model fulfils the aim of providing an initial indication of the likelihood of parasite transmission between saigas and livestock, and focusing research effort on the probable key times and places of parasite acquisition. 5. General discussion For both FMD and gastrointestinal nematodes, mathematical models based on our understanding of disease dynamics in livestock were able to provide predictions concerning the role of saigas in the epidemiology of livestock disease, and vice 252 B I O L O G I C A L C O N S E RVAT I O N versa. However, this was only possible when additional complexities were included, in particular host movement and population dynamics, multiple host species, and temporal and spatial climatic variation. These complexities are also likely to be important in other free-living wildlife. Observed patterns of infection of house finches Carpodacus mexicanus with the bacterium Mycoplasma gallisepticum, for instance, can only be explained by transmission models that include seasonal breeding (Hosseini et al., 2004). Seasonal host absence, which can drive macroparasite dynamics in livestock (Roberts and Grenfell, 1991), is also likely to be a common feature in free-living wildlife populations that occupy habitat patches for only part of the year. For the saiga diseases discussed here, increased complexity of the transmission models radically affects their predictions, and cannot be left out without justification. However, the decision on whether and how to include these complexities is subjective, and they also make it more difficult to see what actually drives system dynamics. The act of constructing a model does at least force us to formalise our understanding in a logical way, highlighting the areas in which we know too little. These areas of uncertainty can then be made the focus of further research, and also warn us not to accept too readily the predictions of simpler models. There are many potentially important complexities that are too difficult to parameterise. Excretion of FMDV by wild ruminants is a good example: the virus has been found in many species, but data are observational and a transmission model would have to use livestock-derived data on important parameters such as duration of infectiousness (Thomson et al., 2003). In these circumstances, a complex model can still be justified. For example, if realistic population densities and movement patterns in a complex model produce similar qualitative results regardless of variation of some parameters within their plausible ranges, seeking to refine those parameter estimates is not a priority. Where parameter uncertainty is great, as in most wildlife situations, sensitivity analysis of transmission models can be valuable in focusing limited experimental and field resources (McCallum and Dobson, 1995). Model structure, and the key complexities involved in transmission, differ for micro- and macroparasites. In both cases, parasite persistence depends on host availability. However, microparasites generally survive for a limited period outside the host and are subject to strong host immunity, so patterns of contact between individual hosts, and the timecourse of immunity and re-supply of susceptible hosts, are crucial to parasite population dynamics. Macroparasites, by contrast, must usually undergo development outside the host and can survive for a period in the external environment. Parasite population growth and problems for the hosts depend on reinfection and the build-up of parasite numbers. The dynamics of transmission and persistence then depend on patterns of host movement in relation to infective stage development and availability in the environment (Morgan et al., 2004). Climatic stochasticity and its effect on parasite vital rates is likely to be important. In both cases, spatial factors including host distribution and movement, and variation in the environment, could influence rates of infection. However, modelling this spatial heterogeneity explicitly leads to complex simulations that are even more difficult to para- 1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4 meterise, explore and validate than the models presented here. Deciding on the level of complexity to include in models of parasite transmission is an important dilemma facing theoreticians of animal parasites in general (Cornell, 2005), but is perhaps an even greater issue when considering wildlife disease and associated conservation management issues. This paper aims to demonstrate that mathematical models of wildlife disease can be usefully applied to assess the risk of transmission across the wildlife–livestock boundary, and to guide control strategies accordingly. Earlier efforts at modelling wildlife disease largely focused on models that generate general patterns of disease dynamics using only a simple structure (e.g., Grenfell, 1992; Heesterbeek and Roberts, 1995; Roberts et al., 1995; Roberts and Heesterbeek, 1998). These models have the advantage that they are transparent and analytically tractable, and they hold lessons that can be applied to a wide range of systems. However, predictions are usually too vague to be used in relation to a specific system. The motivation behind this class of model is the discovery of determinants of general disease behaviour, and not the control of wildlife disease per se. As a result, a culture gap has grown between modellers and wildlife managers. The proceedings of an important meeting on wildlife disease targeted the narrowing of this gap as a priority for the research community (Grenfell and Dobson, 1995), but a follow-up meeting acknowledged that little progress had been made in this direction (Hudson et al., 2002). More recently, models have appeared that consider pathogen dynamics in multiple host species (e.g., Dobson, 2004), although few explicitly consider implications for control in specific systems (but see Haydon et al., 2002b; Caley and Hone, 2004; Cox et al., 2005; Randall et al., 2006; Vial et al., 2006). In order to persuade field veterinarians and others with responsibility for the control of wildlife disease of the merits of modelling as a tool in disease control, its output must be meaningful in terms of practical control strategies for specific systems. This will require models that are narrower and more applied in focus than many theoretical biologists are comfortable with. Greater biological realism will have to be incorporated. There is a danger that this will lead to a profusion of detailed simulation models, perhaps several for each disease system, each producing contrasting predictions in a rather opaque way. Rather than just pointing this out and extolling the contrasting merits of simplicity, however, the modelling community should lead the way in standardising some of the general model approaches and frameworks that could usefully guide the practical control of wildlife disease. Methods for comparing different models with each other and with patchy and imperfect field data should also be developed to the point where they can be applied by non-specialists. For their part, field veterinarians and biologists should realise that models are a simplified representation of reality, and that predictions will never be as accurate as they would like. In most cases, there is a lack of good quality, basic data over a sufficient period of time with which to validate models, so that there is always a risk that model predictions will be quantitatively and even qualitatively wrong. This should not discourage field workers from embracing modelling as a tool in their armoury against wildlife disease, but it should discourage them from using models uncritically, and then B I O L O G I C A L C O N S E RVAT I O N complaining when control strategies based on them fail. Modellers can help in this regard by expressing their predictions as relative risk of various events or control strategies, rather than making concrete forecasts of disease incidence. A major challenge for both modellers and field biologists is to match model output with the sorts of data that can be practically collected in the field. Validation of wildlife disease models relies on much shorter data series than are available for many diseases of humans and domestic livestock. 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