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Keywords:

  • bank vole;
  • cowpox virus;
  • pathogen dynamics;
  • threshold population size;
  • wood mouse

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    The population dynamics of bank voles and wood mice, and of cowpox virus infection in these two species, was studied over a 2-year period in a mainland population and in 14 nearby island populations of varying sizes.
  • 2
    For both species, there was no intrinsic variation in the pattern of host dynamics with island size: small island populations behaved as though they were small subsamples of a larger population, displaying no more than the expected random variation from the general pattern.
  • 3
    None the less, the relative numbers of bank voles to wood mice increased markedly with decreasing island size; and bank vole densities tended to be higher on smaller islands.
  • 4
    Only 22 animals were discovered to have moved either between islands or between the mainland and the islands, out of 1883 captured in all. None the less, it was apparent that males were more likely to move than females.
  • 5
    Overall patterns of cowpox virus dynamics were similar in all cases. However, on all islands there were extended periods when cowpox virus infection was apparently absent, and on the small islands the numbers of infected individuals were mostly very low and in many cases infection was never found.
  • 6
    For both host species, there was no evidence for a threshold population size for cowpox virus (critical community size) in terms of density, but clear evidence for one in terms of the numerical size of populations. This suggests little support for density-dependent transmission, despite this having been the usual default assumption for non-sexually transmitted infections.
  • 7
    There was also evidence for a separate invasion threshold (between ecological and epidemiological invasion) and persistence threshold (between epidemiological invasion and persistence). This is contrary to the output of the most-quoted (deterministic) models – persistence and invasion threshold one and the same – highlighting the fact that little attention has been paid in the past to the practical meaning of the theoretical concept of a threshold.
  • 8
    In the case of the wood mice, a superficial similarity to the bank vole thresholds was potentially misleading. Wood mouse thresholds were influenced at least as much by the bank vole thresholds as they were by the dynamics within the wood mouse populations themselves.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

As part of the recent upsurge of interest in host–pathogen dynamics, especially in natural populations (e.g. Hudson et al. 2002), one of the core concepts has been that of a ‘critical community size’ or ‘threshold population size’, embodying the idea that ‘there must be some threshold host density or population size below which infection cannot persist’ (Swinton et al. 2002). Some have stated that the threshold is a population density, others that it is the numbers in a population, and others (e.g. Swinton et al. 2002) that it can be either, ‘dictated by the problem at hand’. Conventional deterministic epidemiological theory (Begon et al. 2002) indicates that the threshold for a pathogen to invade a host population is a density in the case of density-dependent transmission (contact rate between hosts increases with density), and that there is no threshold population size in the case of frequency-dependent transmission (contact rate constant). In these models, the invasion threshold is also a threshold for persistence of infection. On the other hand, more realistic (but far less tractable) stochastic models have separate thresholds for invasion and persistence, and they emphasize the importance of stochastic fade-out (i.e. non-persistence) of infection, the chances of which clearly increase in smaller populations. Again, though, this ‘size’ has variously been seen as a density or the numbers in a population (Swinton et al. 2002).

Whatever these uncertainties, empirical evidence for thresholds of any sort has been rare – that is, examples in which a particular pathogen is repeatedly observed in host populations above a certain size but is absent from those below. The most quoted example is that of measles in human populations: around 250 000–300 000 people (e.g. Black 1966). Sustained brucellosis (Brucella abortus infection) appears to require herds of bison (Bison bison L.) of at least 200 animals (Dobson & Hudson 1995).

Beyond the presence or absence of pathogens in populations of different sizes, theory predicts, at least for typically assumed density-dependent transmission, that the prevalence of infection should increase in populations of increasingly higher density above the critical threshold (e.g. Anderson 1982). Evidence for this, though, appears to be lacking for wildlife populations. Furthermore, while the importance of spatial dynamics and population structure in host–pathogen populations interactions is increasingly acknowledged (Hess et al. 2002), and a metapopulation approach to host–pathogen dynamics, especially, has been advocated (Grenfell & Harwood 1997), data on host–pathogen dynamics in aggregates of small wildlife populations have also been absent.

Here, then, data are presented on the dynamics of a pathogen, cowpox virus, and two of its hosts, the bank vole Clethrionomys glareolus Schreber and the wood mouse Apodemus sylvaticus L., over a period of 2 years in a series of 14 woodland islands of varying size, within a lake adjacent to a mainland population, Manor Wood, the dynamics of which have also been studied. To establish a context for the host–pathogen dynamics, the dynamics of the hosts themselves over the islands and mainland are first described, following which patterns of pathogen presence and absence, and dynamics generally, are examined.

Cowpox virus is a member of the genus Orthopoxvirus in the family Poxviridae (Baxby & Bennett 1999) found throughout much of Europe and western Asia. Despite its name, it rarely infects cattle, and disease is most often diagnosed in domestic cats. It is also a zoonosis although human cases are rare (Baxby, Bennett & Getty 1994). Wild rodents are generally accepted to be the reservoir hosts in which cowpox virus circulates naturally (Chantrey et al. 1999). In Great Britain, antibody has been found in the occasional house mouse, Mus domesticus L., but the highest seroprevalence is in bank voles, wood mice and field voles, Microtus agrestis L., and they are believed to be the reservoir hosts (Crouch et al. 1995; Chantrey et al. 1999).

In previous work on the dynamics of cowpox virus in populations of bank voles and wood mice, the two species exhibited broadly parallel patterns, with peaks of susceptible and infectious individuals coinciding, each year, with the peak period of breeding from late-summer to early winter. The numbers infected overall were similar in the two species (they were of similar importance as reservoirs), but the prevalence of infection was typically much higher in bank voles (Hazel et al. 2000). Overall, a global frequency-dependent transmission term appeared to be better than a density-dependent term in accounting for the dynamics in both species (Begon et al. 1998; 1999), and for both, estimated between-species transmission rates were extremely low compared to those within species (Begon et al. 1999).

Cowpox virus does not cause obvious signs of clinical disease in rodents in the field or the laboratory, but our experimental studies have demonstrated that it can delay significantly the onset of reproduction in both bank voles and wood mice (Feore et al. 1997); and that in both species in the field, cowpox virus infection leads to increased survival in the summer, possibly as a result of the suppression of (costly) reproductive activity, but reduced survival over the winter in the absence of breeding (Telfer et al. 2002).

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

study sites and trapping procedures

Study sites comprised a mainland and 14 islands in an area of mixed woodland habitat on the Wirral Peninsula in north-west England (Fig. 1). The mainland, Manor Wood (Grid ref. 294 816), was approximately 8 ha in extent, within which a 1-ha trapping grid was established, bounded on one side by a pondage area (in which the islands were located) and on the other three sides by woodland. A 10 × 10 grid was marked out with 100 trap stations, permanently situated at 10-m intervals (notional grid area 104 m2). Two Longworth traps (Penlon Ltd, Oxfordshire, UK) were placed at each trap station. The traps were baited with whole wheat grain and filled with autoclaved hay for bedding. Trapping sessions were at four weekly intervals, and in each session, traps were set over 3 days. Traps were checked at least daily. All bedding material and obvious waste was removed from traps containing animals and they were cleaned with 70% ethanol prior to being reset. Traps were sterilized in an autoclave between trapping sessions.

image

Figure 1. The study sites: the ‘mainland’, Manor Wood (wooded area shaded) and 14 wooded islands: three large and 11small (designated ‘S’ or just by number, for clarity).

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Trapping procedures on the islands, which varied in size from 0·02 × 104 m2 to 1·14 × 104 m2, were similar, except that they were trapped over their whole area using grids of trap-pairs placed in lines at 10-m intervals but with an irregular shape overall, matching those of the islands. Also, within 1 week in every 4 weeks, each island was trapped on two consecutive nights. The data presented here are for the period April 1998–March 2000. Although the variation in island size is more or less continuous, for clarity of presentation a distinction is sometimes made between the three ‘large’ islands (0·31 × 104 m2 or greater) and the 11 ‘small’ islands (0·15 × 104 m2 or smaller).

Captured animals were identified using subcutaneous microchip transponders injected into the scruff of the neck on first capture, which could be detected using a handheld reader (Labtrac by AVID plc, East Sussex, UK). On first capture within a session, the species, sex, mass and reproductive condition of each animal was recorded, and a 20–40 µL blood sample taken from the tail-tip. Each animal was then released at the exact site of capture.

data analysis

To monitor rodent dynamics, minimum number alive estimates of bank voles and wood mice were made for each site by taking the total number of individuals caught in a given trapping session and adding to it those not caught in that session but caught both previously and subsequently (Krebs 1966).

To monitor cowpox virus dynamics, sera were separated from the blood samples and stored at −20 °C. The presence of cowpox virus antibody was then determined by immunofluorescence (IF) assay (Bennett et al. 1997). Hence, the raw data for cowpox virus infection comprise animals being either seropositive or seronegative (that is, showing evidence of having been infected in the past). A total of 13 samples had a single equivocal seropositive (a weak signal) both preceded and succeeded by seronegatives. These were re-checked and classified according to the second test (six were confirmed positive). To identify simple, overall differences in infection prevalence between islands or between species, it is necessary only to calculate the proportion of animals caught that were seropositive at some stage in their life (referred to as ‘overall prevalence’). However, in order to deduce patterns of current infection, it is necessary to analyse these data further to estimate the number of infectious individuals at each time point.

This analysis is described in Telfer et al. (2002), but briefly: it is necessary to estimate the number of individuals that were susceptible (uninfected), denoted S, infectious, I, and recovered, R, in each sample. Hosts typically ‘seroconvert’ (pass from seronegative to seropositive) around 2 weeks after first becoming infected, and are likely to remain infectious (having a detectable viraemia) for about 4 weeks after initial infection (Chantrey 1999). Suppose, first, that the record for an individual host is complete (caught in every one of a succession of samples), and that successive samples detect a seroconversion – say between samples 3 and 4. We assume that seroconversion had an equal chance of occurring on any of the 28 days between the two samples. There is thus a 50% chance that the individual was in class S at the time of sample 3, but also a 50% chance that it was already in class I at that time. Similarly, there is a 50% chance that it was in class I at the time of sample 4, but also a 50% chance that it was in class R. Hence, this individual would be entered as S at sample 2, 0·5S–0·5I at sample 3, 0·5I–0·5R at sample 4, R at sample 5, and so on.

Suppose, however, that a record is incomplete, and that a seroconversion occurs during a missing period; for example, seronegative in sample 2, missing from sample 3, seropositive at sample 4. We assume that seroconversion had an equal chance of occurring on any of the 56 days between samples 2 and 4 and, arguing as before, such an individual would be entered as S at sample 1, 0·75S–0·25I at sample 2, 0·25S–0·5I–0·25R at sample 3, 0·25I–0·75R at sample 4, R at sample 5, and so on. Out of 113 individuals that seroconverted overall, 19 had one missing sample at the time of seroconversion and were treated as just described, and 19 had more than one missing sample and were treated in an appropriate manner following the same line of argument.

A further question arises with individuals that were seropositive at first capture. Those of juvenile weight (Telfer et al. 2002) were assumed to be less than 6 weeks old. They were therefore assumed to have been alive and seronegative at the time of only one previous sample (and not alive prior to that) and were entered as 0·5I–0·5R at the sample of first capture, but also as 0·5S–0·5I at the previous sample. Those of subadult weight (Telfer et al. 2002) were assumed to be greater than 6 but less than 10 weeks old. They were therefore assumed to have been missing at the sample prior to their first capture and seronegative at the sample prior to that. They were entered as 0·25I–0·75R at the sample of first capture, but also as 0·25S–0·5I–0·25R at the previous sample and 0·75S–0·25I at the sample prior to that.

However, most animals seropositive at first capture (118 of 131) had already achieved adult weight. Those caught in the first two samples at a given site (30 in total) were ignored, since they could have been seropositive long before sampling began: their period of infection could not be ascribed with any confidence. But rather than eliminating the remaining 88 altogether, they were treated as a separate class. The biologically reasonable assumption was made that, typically, they had been present but not caught for both of the two previous samples, and they were treated accordingly as described above. Their dynamics were then examined alongside those of the known seroconverters.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

host abundance and dynamics

The dynamics of bank voles and wood mice over the 2-year period are shown in Fig. 2. In Fig. 2a, these dynamics are shown separately for bank voles on each of the 14 islands and Manor Wood. It is apparent that the patterns of dynamics on each of the three large islands are similar to one another and to those for Manor Wood, but that no clear pattern is discernible amongst the lower numbers on the 11 small islands. However, when the numbers of bank voles are combined for the large islands as a whole and the small islands as a whole and compared to the pattern for Manor Wood (Fig. 2b), it is apparent that the patterns of dynamics for all three are essentially indistinguishable. The same conclusion applies to the dynamics of wood mice (Fig. 2c). This suggests strongly that for both species, there is no intrinsic variation in the pattern of host dynamics with island size, and that the small island populations behave as though they were small subsamples of a larger population, displaying no more than the expected random variation from the general pattern. This is further supported by the strengths of correlations between the numbers (log MNA) in each trapping session for the three groups (Manor Wood, MW, large islands, L, and small islands, S): bank voles, MW and L: r= 0·68; MW and S: r= 0·50; L and S: r= 0·75; wood mice, MW and L: r= 0·68; MW and S: r= 0·80; L and S: r= 0·64 (P < 0·01 in all cases). The patterns themselves show in all cases the expected annual cycle (Hazel et al. 2000).

image

Figure 2. Rodent dynamics, April 1998–March 2000. (a) Bank vole numbers (log (minimum number alive + 1)), for Manor Wood and each of the 14 islands. (b) Bank vole numbers for Manor Wood, large islands combined and small islands combined. (c) Wood mouse numbers for Manor Wood, large islands combined and small islands combined.

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In spite of the similarities in overall pattern amongst the islands and the mainland, the relative numbers of bank voles and wood mice varied markedly with island size. Thus, 48% of animals caught in Manor Wood were wood mice (379 wood mice, 413 bank voles) compared to 27% on the large islands (234 wood mice, 623 bank voles) and only 13% on the small islands (28 wood mice, 190 bank voles). In fact, on three small islands no wood mice were caught, and the maximum number caught on any small island was seven (small island 7), of which no more than three were caught at the same time.

The density of bank voles (mean MNA per unit area) was also significantly greater on small islands than on large (means per 104 m2 ± 95%CI: large 32·9 ± 8·6, small 61·7 ± 22·6; t= 2·4, P < 0·05). An estimate for Manor Wood is not strictly comparable because the ‘open’ nature of the grid will tend to generate an overestimate, but the value, 44·0 (based on the notional area of 104 m2) suggests that large island densities differ little from the mainland.

movement between islands and the mainland

Over the 2 years, a total of 21 animals were discovered to have moved either between islands or between the mainland and the islands, one of which (a wood mouse) moved twice (i.e. 22 movements). This compares with 1883 captured in all (with animals that moved counted twice, since they could also have moved from their second location). Not one of these animals was infectious when it moved, and only one (a bank vole male) became infected after it moved (from small island 7 to large island 2).

Unsurprisingly, the percentage (both species combined) was significantly higher for those first caught on an island (20 out of 1091 = 1·8%) than for those first caught in Manor Wood (2 out of 792 = 0·03%; χ2 = 8·8, P < 0·01); but the rates of discernible movement were clearly low in all cases. For the island animals, the percentage moving was significantly higher for wood mice (11 out of 273 = 4·0%) than for bank voles (9 out of 818 = 1·1%; χ2 = 9·4, P < 0·01); and males appeared more likely to move than females: for the bank voles, all 9 that moved were male (compared to 345 out of 730 island bank voles with sex definitely assigned overall; χ2 = 8·9, P < 0·01), though for wood mice the difference was not significant: 7 out of 11 were male, compared to 133 out of 265 overall (χ2 = 0·84). Numbers were too small to detect any seasonal patterns in the movements or any age effects. There was no tendency for the 22 movements to redistribute animals between islands of different sizes (or the mainland). For departures, the break-down was Manor Wood 2, large islands 13, small islands 7; for arrivals it was Manor Wood 3, large islands 14, small islands 5. Again unsurprisingly, a large island was therefore more likely than a small island on average to receive an immigrant.

cowpox virus dynamics

Cowpox virus time series

In all time series (Fig. 3), the inclusion of the additional information from those animals already seropositive on first capture served simply to reinforce patterns apparent amongst the seroconverters, where the period of actual infection could be ascribed with more confidence. In Manor Wood (Fig. 3a), cowpox virus infection was more prevalent amongst bank voles than wood mice (the two host species were roughly equally abundant –Fig. 2). Both species showed a peak of infection in late 1999, but infection was apparently absent in wood mice throughout 1998 and early 1999, while in bank voles, numbers infected (and indeed the prevalence of infection) declined through 1998. Indeed, the peak of infection in early 1998 may have been underestimated as first-time positives in the first two trapping sessions were ignored. Nonetheless, infected individuals of at least one species were present on the trapping grid essentially throughout the study period, albeit sometimes in very low numbers.

image

Figure 3. Cowpox virus dynamics, April 1998–March 2000. Inf = estimated number of infected individuals on the basis of seroconversion; Firsts = estimated number from those seropositive on first capture (see text for details). (a) Bank voles and wood mice in Manor Wood. (b) Bank voles on the large islands. (c) Wood mice on the large islands. (d) Bank voles and wood mice on the small islands (where on S6 only animals seropositive on first capture were caught, and on other islands no such animals were caught).

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On the large islands (Fig. 3b,c), patterns were similar to this in several respects: numbers infected and prevalences of infection were generally higher in bank voles than in wood mice, a late-1999 peak of infection was apparent in both species, and levels of infection tended to decline through 1998. However, on all of the islands there were extended periods between late 1998 and mid 1999 when cowpox virus infection was apparently absent.

On the small islands (Fig. 3d), the numbers of infected individuals were mostly very low (and in many cases infection was never found). None the less, the periods of occurrence in time were broadly similar to those seen in the larger populations, though in all cases there were extended periods (lasting from 3 to 6 months) where no cowpox virus infection was apparent. Note, moreover, that on small islands 2, 6 and 9, only a single seroconverter was caught (though their probabilities of infection are distributed over more than one session). It was only on the two largest of the small islands – numbers 8 (0·09 × 104 m2) and 11 (0·15 × 104 m2) – that infection persisted in more than one individual, and only one island had infected individuals in both years.

Occurrence of cowpox in different populations

The overall prevalences of infection over the 2-year study period are shown for bank voles and wood mice, respectively, plotted against density (mean MNA per 104 m2; Fig. 4a,d), against abundance (mean MNA; Fig. 4b,e), and against island area (Fig. 4c,f). Area and abundance are both indices of the numbers in the host populations: the latter is the more direct measure for the study period itself, but island area provides, perhaps, a better longer-term perspective, uninfluenced by stochastic variation, given that the habitat was very similar in all cases.

image

Figure 4. Overall prevalences of infection, April 1998–March 2000, on the 14 islands and in Manor Wood (notional (grid) area 104 m2), plotted against density (mean minimum number alive per sample per 104 m2), numbers (log (mean MNA) + (1), and area (log area (in units of104 m2) + (2). Large islands and Manor Wood are indicated by squares; small islands by triangles. (a) Bank voles, density. (b) Bank voles, numbers. (c) Bank voles, area. (d) Wood mice, density. (e) Wood mice, numbers. (f) Wood mice, area.

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For bank voles, there is no evidence of a density threshold (Fig. 4a) but a clear suggestion that cowpox was found in populations above a particular numerical size and absent below that threshold. This is clearest, visually, for area (Fig. 4c). Indeed, the positive prevalences on the three smallest islands represent single individuals only: that is, they invaded in the ecological but not in the epidemiological sense (no evidence of subsequent transmission). Hence, a threshold area of around 0·09 × 104 m2 is suggested. For wood mice, the picture is superficially similar, with no obvious density threshold (Fig. 4d) but evidence of a threshold population size (Fig. 4e,f). Also, the two high overall prevalences on small islands represent only one in four and one in five animals trapped (Fig. 3c), and hence not invasion in the epidemiological sense. The threshold area is similar to that observed in bank voles. In wood mice, however, below the ‘threshold’, the host populations themselves are, as previously noted, extremely small and mostly transitory (with frequent extinctions on the small islands).

Logistic regression was used to investigate further what factors best explained the occurrence of cowpox virus in bank vole and wood mouse populations. The dependent variable was whether or not cowpox was ever recorded on an island. The three islands that were never inhabited by wood mice were excluded from the wood mouse analysis. Akaike's Information Criterion (AIC) was used for model selection; models with AIC values that differ by less than 2 are similar in their ability to describe the data (Burnham & Anderson 1992). In both species, the probability of cowpox being recorded on an island is related to average population size but not average population density (Table 1). Island area is strongly correlated with bank vole and wood mouse population size (average MNA; bank voles: r= 0·97, P < 0·001; wood mice: r= 0·94, P < 0·001), and consequently, average bank vole and wood mouse MNA are also strongly correlated (r = 0·85, P < 0·001). Unsurprisingly, therefore, island area and average population size of the sympatric species can also be used to predict the occurrence of cowpox in an island population. Indeed, average MNA, island area, and average MNA of the sympatric species are all fairly similar in their ability to describe the data. However, for both species, the best predictor of cowpox is average MNA of bank voles; and in wood mice, the superiority of bank vole MNA over wood mouse MNA is close to significance (difference in AIC = 1·85).

Table 1.  Logistic regression analysis of the presence and absence of cowpox virus infection in bank vole and wood mouse populations of different sizes. The abilities of different models to account for observed patterns can be judged from the significance values in column 4. Models are similar in their ability to account for the patterns if their AIC values (column 5) differ by less than 2 (AIC = (– 2 log likelihood) + 2*(no. parameters)). The AIC value for the best model is in bold type
Model–2 Log likelihoodNo. parametersSignificance if removedAIC
Bank voles
Constant19·12121·12
Bv MNA14·8520·03918·85
Bv density18·3120·36822·31
Area15·0720·04419·07
Wm MNA15·6220·06119·62
Wood mice
Constant15·16117·16
Wm MNA 7·1920·00511·19
Wm density14·5320·4318·53
Area 8·5920·01012·59
Bv MNA 5·3420·0029·34

Finally, amongst the populations in which cowpox had been present at all, the overall prevalence of infection and the density of bank voles were not positively correlated, as predicted by theory, but negatively correlated (Fig. 4a; r=−0·76, P≈ 0·02). There is a hint of a similar relationship for wood mice (Fig. 4d; r=−0·58), although this is not significant and is largely the consequence of the low overall prevalence in Manor Wood.

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

host dynamics

In spite of a clear tendency for wood mice to move more frequently between islands than bank voles, and for males to move more frequently than females (significant only for bank voles) – both of which are consistent with previous studies on mobility in woodland rodents (Corbet & Harris 1996) – overall measurable rates of movement were low, even at relatively peak times of the year for movement. These measured rates, however, are inevitably underestimates of the true rates, since they cannot take account of animals that moved islands prior to their first capture. Analysis of the genotypes on different islands, by contrast, reflect such movements; and an analysis of microsatellite loci in bank voles from Manor Wood and the two largest islands (where sample sizes were therefore large enough for analysis) indicates a low but significant level of differentiation between populations (but none within), with the greatest differentiation occurring between Manor Wood and the island furthest from it (large island 2; Barker 2002). These data therefore further support the view that the dynamics (including the host–pathogen dynamics) of most island populations most of the time are dominated by demographic processes occurring within the population, but movement rates appear to be sufficiently high to ensure that no island remains isolated for long from animals (including potentially infectious animals) from other islands or the mainland. Thus, the network of islands appears to function as a metapopulation.

In view of the degree of isolation of the islands, the similarities in the patterns of host dynamics on them are striking. Even the smaller islands, where absolute numbers were such as to ensure that stochastic effects played a major part in determining the patterns observed, showed the same seasonal patterns of host dynamics as in other, larger populations once their numbers were combined. As far as the patterns themselves are concerned, the seasonal cycle was entirely to be expected from previous studies (Hazel et al. 2000). The decline in the relative abundance of wood mice on islands of decreasing size, in the absence of significant changes in the nature of the habitat, has not apparently been observed previously but is not unexpected in view of the greater mobility and territory size of wood mice (Corbet & Harris 1996). Higher densities on smaller islands have been observed in many island systems: a pattern often ascribed to the relative absence of predators on smaller islands that cannot support them (Brown & Gibson 1983). This may be the case here, though the relative lack of spatial isolation makes it an implausible argument in the case of avian predators, while mustelids have only very rarely been observed on the study site. On the other hand, broadening the definition of predators to include the many pathogens and parasites that affect bank voles and wood mice, of which cowpox virus is only one (e.g. Birtles et al. 2001; Cavanagh et al. 2002; Noyes et al. 2002), some at least may be below their critical threshold population size on the smaller islands, with a consequent increase in typical host density (see also below). Alternatively, animals in the small populations on small islands are more likely to be closely related, and close relatives in rodent populations are known to be more tolerant of living in close proximity, while island populations in general may live at higher densities and be less territorial (Nevison et al. 2000).

cowpox dynamics

In comparing the patterns of cowpox virus infection in Manor Wood and on the various islands, it is important to remember that absence of infection in Manor Wood means absence of infection on the trapping grid, but not necessarily absence from the larger population of which it is part. Absence of infection on an island, however, suggests far more strongly that infection was truly absent, since trapping grids covered the whole of each island. Naturally, trapping cannot be 100% efficient. However, a comparison of MNA estimates and capture–recapture estimates of population size for more extensive data sets obtained using the same protocols, in Manor Wood and another mainland site (Chantrey 1999), indicated that more than 90% of the animals in our populations are trapped.

Bearing this in mind, the time series data suggest that there was cowpox virus infection in the Manor Wood population throughout the 2-year study period, but for all of the islands, including the largest, there were periods when no cowpox virus infected hosts were present. Nonetheless, the patterns over time in all cases were remarkably similar. Previous work, too, found that prevalence was higher in bank voles than wood mice (Hazel et al. 2000), and also that the numbers of infected hosts increased markedly coincident with the rise in host abundance in late autumn, as observed here in 1999. On the other hand, a decline in the numbers infected between the middle and end of the year is not normally observed (Hazel et al. 2000), but was seen here in essentially all populations in 1998, in the absence of anything similarly atypical in the pattern of host dynamics. Thus, host–cowpox dynamics appeared to be synchronized in the different populations. There are (at least) two possible explanations. First, even a small amount of host movement may be sufficient to effectively unite and even synchronize host–cowpox virus dynamics. However, given the low rates of movement and short infectious period of cowpox, the probability of an infectious host moving is relatively small.

An alternative would be that cowpox virus persisted, during its apparent absence, in some environmental reservoir, and, moreover, that transmission from this reservoir to the host varied in parallel in the different populations. As with most wildlife diseases, the natural routes of cowpox virus transmission have not yet been confirmed experimentally. Nonetheless, a variety of evidence from this and related orthopoxviruses indicates direct transmission between infectious and susceptible hosts is the main route of infection (Robinson & Kerr 1999). This is further supported by the high explanatory power of models incorporating direct transmission fitted to time series of rodent–cowpox virus dynamics (Begon et al. 1998, 1999), and by analyses which indicate that susceptible rodents are significantly more likely to become infected with cowpox virus when they are closely juxtaposed, in both space and time, to infectious hosts (David Carslake, unpublished data). On the other hand, like many poxviruses cowpox virus is known to be able to survive for extended periods outside its host (Baxby & Bennett 1999), the closely related ectromelia virus is transmissible amongst laboratory animals on bedding (Fenner 1999), and around one-quarter of human cases of cowpox cannot be traced to contact with a cat or rodent (Baxby et al. 1994). Some role for an environmental reservoir for cowpox virus in bridging the gaps in time series cannot therefore be ruled out.

Threshold population sizes (critical community sizes) are commonplace in theoretical expositions, but they have only very rarely been documented in wildlife populations (Dobson & Hudson 1995). Perhaps for this reason, there is no conventional expectation of what to expect by way of a match between observed thresholds and the predictions of theory. For the benchmark types of pathogen transmission (Begon et al. 2002), deterministic models predict a single density threshold with density-dependent transmission (valid for both pathogen invasion and persistence) but no threshold in either numbers or density with frequency-dependent transmission. In this latter case, though, the models do predict a threshold contact rate between hosts that is independent of density (Swinton et al. 2002), which can presumably be achieved only if there are sufficient numbers of individuals available to make contact with. Stochastic models (Bartlett 1960; Nåsell 1999) generate separate thresholds for invasion and persistence (the latter being higher), and by their nature deal more naturally with numbers of individuals. More generally, stochastic models draw attention to the importance of stochastic fade-out (failure to persist), which occurs when the chain of infection in a population is broken. The chances of this depend on the behaviour of individual hosts (Swinton et al. 2002) and again are likely to increase with decreasing density where contact rates are density-dependent but with decreasing numbers where contact rates are constant (frequency-dependent transmission).

The present results combine a 2-year overview (Fig. 4, Table 1) with a description of infection dynamics within that period (Fig. 3). It has been possible therefore to determine whether any type of threshold is detectable, whether the nature of that threshold supports the contention of an underlying density-dependent or frequency-dependent process, and whether the threshold applies to persistence (i.e. is a threshold above which the infection is always present) or combines persistence and invasion.

For bank voles, when the 2-year period is considered as a whole, a threshold population size is apparent, but in terms of the numbers in populations rather than densities. It is clear from the time series data, however, that this is not a simple invasion-and-persistence threshold, since even within this 2-year period, infection apparently disappeared from every one of the island populations. Rather, as population (island) size increases, there is a progression from ‘no cowpox’ to ‘ecological invasion’ (the occasional infected host but no apparent transmission), to ‘epidemiological invasion’ (a succession of infected animals but disappearance of cowpox within the 2-year period), to ‘persistence’ (Manor Wood only). An argument can therefore be made for both an invasion threshold (between ecological and epidemiological invasion) and a persistence threshold (between invasion and persistence), though both will be fuzzy rather than sharp: the probability of pathogen invasion on small islands is finite even when it is small, and the probability of pathogen extinction is finite even in Manor Wood. Such patterns are likely to be found in all real populations, as opposed to those imagined by deterministic models. Moreover, such arguments apply not only if invasion is literal (migration of an infected host), but also if the invasion of the pathogen is from an environmental reservoir.

The fact that this appears to be a numbers rather than a density threshold reinforces previous analyses of cowpox–rodent infection dynamics (Begon et al. 1998, 1999) in suggesting little support for density-dependent transmission, despite this having been the usual default assumption for non-sexually transmitted infections. Furthermore, the present results provide little support for the contention that density thresholds are likely to be appropriate ‘for wildlife populations that extend continuously over habitat ranges’ (Swinton et al. 2002), as is the case here. Finally, given the lack of support for density-dependent transmission, the absence of the positive correlation predicted by theory between prevalence and density is unsurprising (and would, in any case, be found above an invasion-and-persistence threshold).

In the case of the wood mice, a superficial similarity to the bank voles is potentially misleading. Below the apparent threshold, it is less a case of cowpox being (mostly) absent from the host population than of the host population itself being mostly absent. On the other hand, it is strictly incorrect to talk about a threshold for either of the host species: theory suggests that they combine to provide a resource for cowpox virus and thus to generate a joint threshold (Bowers & Turner 1997). The extent to which they do so, however, depends on the degree of interspecies transmission, and this has been estimated to be very low in the present case (Begon et al. 1999), suggesting that there are effectively separate thresholds for each species. This, though, is another conclusion derived from deterministic models where invasion and persistence thresholds are one and the same. In (stochastic) practice, re-invasion by cowpox virus of an island population of either species may often be of crucial significance to both of them, in spite of the relatively low level of transmission between them. This will be especially true if environmental contamination plays any part in transmission. In the present case, as it is inconceivable that an acute infection such as cowpox could circulate independently in the very small wood mouse populations (lack of susceptibles), wood mouse thresholds must be influenced at least as much by the bank vole thresholds as they are by the dynamics within the wood mouse populations themselves (borne out by the logistic regression). This would explain the apparently similar thresholds in bank voles and wood mice. Indeed, there is some evidence that an ecological invasion of cowpox in wood mice (only one infected individual) only occurs when cowpox has successfully invaded (more than one infected individual) a sympatric bank vole population (two of the large islands in 1998; one of the small islands in 1999). Successful invasion in wood mice is more infrequent and tends to occur when wood mice numbers are relatively high (such as in 1999 and on large island 1). This suggests that it may often be difficult to observe thresholds in the field, as the risk experienced by a population depends on factors other than its own size/density.

Thus, the present results confirm that thresholds can be observed in wildlife populations and suggest that numbers thresholds may be more common than has sometimes been imagined. They certainly caution against any general expectation of a density threshold, even though this is the prediction from the most commonly quoted theoretical treatments, and even when the host–pathogen system extends continuously over available habitat. They also emphasize that empirical assessments of thresholds are likely to reflect patterns of both invasion and persistence (separable only in stochastic models), and also interspecific transmission, even if this is only rare. Finally, and perhaps most generally, these results highlight the fact that little attention has been paid to the practical meaning of the theoretical concept of a threshold, probably because there have been few empirical studies with which to confront it.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

We are most grateful to Leverhulme Estates for access to the study site, to NERC for financial support, to Chris McCracken for logistical support, and to Faye Barker and Moira Gilliver for help with trapping.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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