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).
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.