Journal of Animal Ecology

2003

72

, 343–355

© 2003 British Ecological Society

Blackwell Science, Ltd

Rodents, cowpox virus and islands: densities, numbers and thresholds

MICHAEL BEGON*, SARAH M. HAZEL*†, SANDRA TELFER*†, KEVIN BOWN*†, DAVID CARSLAKE*†, RACHEL CAVANAGH*†, JULIAN CHANTREY*†, TREVOR JONES† and MALCOLM BENNETT†

Centre for Comparative Infectious Diseases and

*

Population and Evolutionary Biology Research Group, School of Biological Sciences, University of Liverpool, Liverpool, UK; and

†

Department of Veterinary Pathology, University of Liverpool, Leahurst, South Wirral, UK

Summary

1.

The population dynamics of bank voles and wood mice, and of cowpox virus infectionin these two species, was studied over a 2-year period in a mainland population and in14 nearby island populations of varying sizes.

2.

For both species, there was no intrinsic variation in the pattern of host dynamics withisland size: small island populations behaved as though they were small subsamples ofa larger population, displaying no more than the expected random variation from thegeneral pattern.

3.

None the less, the relative numbers of bank voles to wood mice increased markedlywith decreasing island size; and bank vole densities tended to be higher on smallerislands.

4.

Only 22 animals were discovered to have moved either between islands or betweenthe mainland and the islands, out of 1883 captured in all. None the less, it was apparentthat males were more likely to move than females.

5.

Overall patterns of cowpox virus dynamics were similar in all cases. However, on allislands there were extended periods when cowpox virus infection was apparentlyabsent, and on the small islands the numbers of infected individuals were mostly verylow and in many cases infection was never found.

6.

For both host species, there was no evidence for a threshold population size for cowpoxvirus (critical community size) in terms of density, but clear evidence for one in terms ofthe numerical size of populations. This suggests little support for density-dependenttransmission, despite this having been the usual default assumption for non-sexuallytransmitted infections.

7.

There was also evidence for a separate invasion threshold (between ecological andepidemiological invasion) and persistence threshold (between epidemiological invasionand persistence). This is contrary to the output of the most-quoted (deterministic)models – persistence and invasion threshold one and the same – highlighting the factthat little attention has been paid in the past to the practical meaning of the theoreticalconcept of a threshold.

8.

In the case of the wood mice, a superficial similarity to the bank vole thresholds waspotentially misleading. Wood mouse thresholds were influenced at least as much by thebank vole thresholds as they were by the dynamics within the wood mouse populationsthemselves.

Key-words

: bank vole, cowpox virus, pathogen dynamics, threshold population size,wood mouse.

Journal of Animal Ecology

(2003)

72

, 343–355

Correspondence: Mike Begon, School of Biological Sciences, The University of Liverpool, Liverpool L69 7ZB, U.K. Tel. 44(0)151 7954525. Fax: 44 (0)151 7954408. E-mail: mbegon@liv.ac.uk.

344

M. Begon

et al.

© 2003 British Ecological Society,

Journal of Animal Ecology

,

72

,343–355

Introduction

As part of the recent upsurge of interest in host–pathogendynamics, especially in natural populations (e.g. Hudson

et al

. 2002), one of the core concepts has been that ofa ‘critical community size’ or ‘threshold populationsize’, embodying the idea that ‘there must be somethreshold host density or population size below whichinfection cannot persist’ (Swinton

et al

. 2002). Somehave 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, ‘dictatedby the problem at hand’. Conventional deterministicepidemiological theory (Begon

et al

. 2002) indicatesthat the threshold for a pathogen to invade a host popu-lation is a density in the case of density-dependenttransmission (contact rate between hosts increaseswith density), and that there is no threshold populationsize in the case of frequency-dependent transmission(contact rate constant). In these models, the invasionthreshold is also a threshold for persistence of infection.On the other hand, more realistic (but far less tractable)stochastic models have separate thresholds for invasionand persistence, and they emphasize the importance ofstochastic fade-out (i.e. non-persistence) of infection,the chances of which clearly increase in smaller popula-tions. Again, though, this ‘size’ has variously been seenas 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, examplesin which a particular pathogen is repeatedly observedin host populations above a certain size but is absentfrom those below. The most quoted example is thatof measles in human populations: around 250 000–300 000 people (e.g. Black 1966). Sustained brucellosis(

Brucella abortus

infection) appears to require herds ofbison (

Bison bison

L.) of at least 200 animals (Dobson& Hudson 1995).

Beyond the presence or absence of pathogens inpopulations of different sizes, theory predicts, at leastfor typically assumed density-dependent transmission,that the prevalence of infection should increase inpopulations of increasingly higher density above thecritical threshold (e.g. Anderson 1982). Evidence forthis, though, appears to be lacking for wildlife popula-tions. Furthermore, while the importance of spatialdynamics and population structure in host–pathogenpopulations interactions is increasingly acknowledged(Hess

et al

. 2002), and a metapopulation approach tohost–pathogen dynamics, especially, has been advocated(Grenfell & Harwood 1997), data on host–pathogendynamics in aggregates of small wildlife populationshave also been absent.

Here, then, data are presented on the dynamics of apathogen, cowpox virus, and two of its hosts, the bankvole

Clethrionomys glareolus

Schreber and the woodmouse

Apodemus sylvaticus

L., over a period of 2 yearsin 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 beenstudied. To establish a context for the host–pathogendynamics, the dynamics of the hosts themselves overthe islands and mainland are first described, followingwhich patterns of pathogen presence and absence, anddynamics generally, are examined.

Cowpox virus is a member of the genus

Orthopoxvirus

in the family Poxviridae (Baxby & Bennett 1999) foundthroughout much of Europe and western Asia. Despiteits name, it rarely infects cattle, and disease is mostoften diagnosed in domestic cats. It is also a zoonosisalthough human cases are rare (Baxby, Bennett &Getty 1994). Wild rodents are generally accepted to bethe reservoir hosts in which cowpox virus circulatesnaturally (Chantrey

et al

. 1999). In Great Britain, anti-body has been found in the occasional house mouse,

Mus domesticus

L., but the highest seroprevalence is inbank 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 twospecies exhibited broadly parallel patterns, with peaksof susceptible and infectious individuals coinciding,each year, with the peak period of breeding from late-summer to early winter. The numbers infected overallwere similar in the two species (they were of similarimportance as reservoirs), but the prevalence of infectionwas typically much higher in bank voles (Hazel

et al

.2000). Overall, a global frequency-dependent trans-mission term appeared to be better than a density-dependent term in accounting for the dynamics in bothspecies (Begon

et al

. 1998; 1999), and for both, estimatedbetween-species transmission rates were extremely lowcompared 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 ourexperimental studies have demonstrated that it candelay significantly the onset of reproduction in bothbank voles and wood mice (Feore

et al

. 1997); and thatin both species in the field, cowpox virus infection leadsto increased survival in the summer, possibly as a resultof the suppression of (costly) reproductive activity, butreduced survival over the winter in the absence ofbreeding (Telfer

et al

. 2002).

Methods

Study sites comprised a mainland and 14 islands in anarea of mixed woodland habitat on the Wirral Peninsulain north-west England (Fig. 1). The mainland, ManorWood (Grid ref. 294 816), was approximately 8 ha inextent, within which a 1-ha trapping grid was estab-lished, bounded on one side by a pondage area (inwhich the islands were located) and on the other threesides by woodland. A 10

×

10 grid was marked out with

345

Rodents, cowpox and islands

© 2003 British Ecological Society,

Journal of Animal Ecology

,

72

,343–355

100 trap stations, permanently situated at 10-m intervals(notional grid area 10

4

m

2

). Two Longworth traps (PenlonLtd, Oxfordshire, UK) were placed at each trap station.The traps were baited with whole wheat grain and filledwith autoclaved hay for bedding. Trapping sessionswere at four weekly intervals, and in each session, trapswere set over 3 days. Traps were checked at least daily.All bedding material and obvious waste was removedfrom traps containing animals and they were cleanedwith 70% ethanol prior to being reset. Traps weresterilized in an autoclave between trapping sessions.

Trapping procedures on the islands, which varied insize from 0·02

×

10

4

m

2

to 1·14

×

10

4

m

2

, were similar,except that they were trapped over their whole areausing grids of trap-pairs placed in lines at 10-m intervalsbut with an irregular shape overall, matching those ofthe islands. Also, within 1 week in every 4 weeks, eachisland was trapped on two consecutive nights. The datapresented here are for the period April 1998–March2000. Although the variation in island size is more orless continuous, for clarity of presentation a distinctionis sometimes made between the three ‘large’ islands(0·31

×

10

4

m

2

or greater) and the 11 ‘small’ islands(0·15

×

10

4

m

2

or smaller).Captured animals were identified using subcutane-

ous microchip transponders injected into the scruff ofthe neck on first capture, which could be detected usinga 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

µ

L blood sample taken from thetail-tip. Each animal was then released at the exact siteof capture.

To monitor rodent dynamics, minimum number aliveestimates of bank voles and wood mice were made foreach site by taking the total number of individualscaught in a given trapping session and adding to itthose not caught in that session but caught both pre-viously and subsequently (Krebs 1966).

To monitor cowpox virus dynamics, sera wereseparated from the blood samples and stored at

−

20

°

C.The presence of cowpox virus antibody was thendetermined by immunofluorescence (IF) assay (Bennett

et al

. 1997). Hence, the raw data for cowpox virusinfection comprise animals being either seropositive orseronegative (that is, showing evidence of having beeninfected in the past). A total of 13 samples had a singleequivocal seropositive (a weak signal) both precededand succeeded by seronegatives. These were re-checkedand classified according to the second test (six wereconfirmed positive). To identify simple, overall differencesin infection prevalence between islands or betweenspecies, it is necessary only to calculate the proportionof animals caught that were seropositive at some stagein their life (referred to as ‘overall prevalence’). How-ever, in order to deduce patterns of current infection, itis necessary to analyse these data further to estimatethe number of infectious individuals at each time point.

This analysis is described in Telfer

et al

. (2002), butbriefly: it is necessary to estimate the number of individualsthat 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, andare likely to remain infectious (having a detectableviraemia) for about 4 weeks after initial infection(Chantrey 1999). Suppose, first, that the record for anindividual host is complete (caught in every one of asuccession of samples), and that successive samplesdetect a seroconversion – say between samples 3 and 4.We assume that seroconversion had an equal chance ofoccurring on any of the 28 days between the twosamples. There is thus a 50% chance that the individualwas 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

atthe time of sample 4, but also a 50% chance that it wasin class

R

. Hence, this individual would be entered as

S

at sample 2, 0·5

S

−

0·5

I

at sample 3, 0·5

I

−

0·5

R

at sample4,

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 fromsample 3, seropositive at sample 4. We assume thatseroconversion had an equal chance of occurring onany of the 56 days between samples 2 and 4 and,

Fig. 1. The study sites: the ‘mainland’, Manor Wood(wooded area shaded) and 14 wooded islands: three large and11small (designated ‘S’ or just by number, for clarity).

346

M. Begon

et al.

© 2003 British Ecological Society,

Journal of Animal Ecology

,

72

,343–355

arguing as before, such an individual would be enteredas

S

at sample 1, 0·75

S

−

0·25

I

at sample 2, 0·25

S

−

0·5

I

−

0·25

R

at sample 3, 0·25

I

−

0·75

R

at sample 4,

R

at sample5, and so on. Out of 113 individuals that seroconvertedoverall, 19 had one missing sample at the time ofseroconversion and were treated as just described, and19 had more than one missing sample and were treatedin an appropriate manner following the same line ofargument.

A further question arises with individuals that wereseropositive at first capture. Those of juvenile weight(Telfer

et al

. 2002) were assumed to be less than 6 weeksold. They were therefore assumed to have been aliveand seronegative at the time of only one previous sample(and not alive prior to that) and were entered as 0·5

I

−

0·5

R

at the sample of first capture, but also as 0·5

S

−

0·5

I

at the previous sample. Those of subadult weight (Telfer

et al

. 2002) were assumed to be greater than 6 but lessthan 10 weeks old. They were therefore assumed tohave been missing at the sample prior to their firstcapture and seronegative at the sample prior to that.They were entered as 0·25

I

−

0·75

R

at the sample of firstcapture, but also as 0·25

S

−

0·5

I

−

0·25

R

at the previoussample and 0·75

S

−

0·25

I

at the sample prior to that.However, most animals seropositive at first capture

(118 of 131) had already achieved adult weight. Thosecaught in the first two samples at a given site (30 intotal) were ignored, since they could have been sero-positive long before sampling began: their period ofinfection could not be ascribed with any confidence.But rather than eliminating the remaining 88 altogether,they were treated as a separate class. The biologicallyreasonable assumption was made that, typically, theyhad been present but not caught for both of the twoprevious samples, and they were treated accordingly asdescribed above. Their dynamics were then examinedalongside those of the known seroconverters.

Results

The dynamics of bank voles and wood mice over the2-year period are shown in Fig. 2. In Fig. 2a, thesedynamics are shown separately for bank voles on eachof the 14 islands and Manor Wood. It is apparent thatthe patterns of dynamics on each of the three largeislands are similar to one another and to those forManor Wood, but that no clear pattern is discernibleamongst the lower numbers on the 11 small islands.However, when the numbers of bank voles are combinedfor the large islands as a whole and the small islands asa whole and compared to the pattern for Manor Wood(Fig. 2b), it is apparent that the patterns of dynamicsfor all three are essentially indistinguishable. The sameconclusion 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 hostdynamics with island size, and that the small island

populations behave as though they were small subsamplesof a larger population, displaying no more than theexpected random variation from the general pattern.This is further supported by the strengths of correla-tions between the numbers (log MNA) in each trappingsession for the three groups (Manor Wood, MW, largeislands, L, and small islands, S): bank voles, MW andL:

r

= 0·68; MW and S:

r

= 0·50; L and S:

r

= 0·75; woodmice, MW and L:

r

= 0·68; MW and S:

r

= 0·80; L andS:

r

= 0·64 (

P

< 0·01 in all cases). The patterns themselvesshow in all cases the expected annual cycle (Hazel

et al

.2000).

In spite of the similarities in overall pattern amongstthe islands and the mainland, the relative numbers ofbank voles and wood mice varied markedly with islandsize. Thus, 48% of animals caught in Manor Wood werewood mice (379 wood mice, 413 bank voles) comparedto 27% on the large islands (234 wood mice, 623 bankvoles) and only 13% on the small islands (28 woodmice, 190 bank voles). In fact, on three small islands nowood mice were caught, and the maximum numbercaught on any small island was seven (small island 7),of which no more than three were caught at the sametime.

The density of bank voles (mean MNA per unit area)was also significantly greater on small islands than onlarge (means per 10

4

m

2

±

95%CI: large 32·9

±

8·6,small 61·7

±

22·6;

t

= 2·4,

P

< 0·05). An estimate for ManorWood 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 of10

4

m2) suggests that large island densities differ littlefrom the mainland.

Over the 2 years, a total of 21 animals were discoveredto have moved either between islands or between themainland and the islands, one of which (a wood mouse)moved twice (i.e. 22 movements). This compares with1883 captured in all (with animals that moved countedtwice, since they could also have moved from their secondlocation). Not one of these animals was infectious whenit moved, and only one (a bank vole male) became infectedafter it moved (from small island 7 to large island 2).

Unsurprisingly, the percentage (both species combined)was significantly higher for those first caught on anisland (20 out of 1091 = 1·8%) than for those firstcaught in Manor Wood (2 out of 792 = 0·03%; χ2 = 8·8,P < 0·01); but the rates of discernible movement wereclearly low in all cases. For the island animals, thepercentage moving was significantly higher for woodmice (11 out of 273 = 4·0%) than for bank voles (9 outof 818 = 1·1%; χ2 = 9·4, P < 0·01); and males appearedmore likely to move than females: for the bank voles, all9 that moved were male (compared to 345 out of 730island bank voles with sex definitely assigned overall;χ2 = 8·9, P < 0·01), though for wood mice the difference

347Rodents, cowpox and islands

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

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

348M. Begon et al.

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

was not significant: 7 out of 11 were male, compared to133 out of 265 overall (χ2 = 0·84). Numbers were toosmall to detect any seasonal patterns in the movementsor any age effects. There was no tendency for the 22movements to redistribute animals between islands ofdifferent sizes (or the mainland). For departures, thebreak-down was Manor Wood 2, large islands 13,small islands 7; for arrivals it was Manor Wood 3, largeislands 14, small islands 5. Again unsurprisingly, alarge island was therefore more likely than a smallisland on average to receive an immigrant.

Cowpox virus time series

In all time series (Fig. 3), the inclusion of the additionalinformation from those animals already seropositive

on first capture served simply to reinforce patternsapparent amongst the seroconverters, where theperiod of actual infection could be ascribed withmore confidence. In Manor Wood (Fig. 3a), cowpoxvirus infection was more prevalent amongst bankvoles than wood mice (the two host species wereroughly equally abundant – Fig. 2). Both species showeda peak of infection in late 1999, but infection wasapparently absent in wood mice throughout 1998 andearly 1999, while in bank voles, numbers infected(and indeed the prevalence of infection) declinedthrough 1998. Indeed, the peak of infection in early1998 may have been underestimated as first-timepositives in the first two trapping sessions were ignored.Nonetheless, infected individuals of at least one specieswere present on the trapping grid essentially through-out the study period, albeit sometimes in very lownumbers.

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

349Rodents, cowpox and islands

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

On the large islands (Fig. 3b,c), patterns were similarto this in several respects: numbers infected and pre-valences of infection were generally higher in bank volesthan in wood mice, a late-1999 peak of infection wasapparent in both species, and levels of infection tendedto decline through 1998. However, on all of the islands therewere extended periods between late 1998 and mid 1999when cowpox virus infection was apparently absent.

On the small islands (Fig. 3d), the numbers ofinfected individuals were mostly very low (and in manycases infection was never found). None the less, theperiods of occurrence in time were broadly similarto those seen in the larger populations, though in allcases there were extended periods (lasting from 3 to6 months) where no cowpox virus infection was apparent.Note, moreover, that on small islands 2, 6 and 9, only asingle seroconverter was caught (though their prob-abilities of infection are distributed over more than one

session). It was only on the two largest of the smallislands – numbers 8 (0·09 × 104 m2) and 11 (0·15 × 104 m2)– that infection persisted in more than one individual, andonly one island had infected individuals in both years.

Occurrence of cowpox in different populations

The overall prevalences of infection over the 2-yearstudy period are shown for bank voles and wood mice,respectively, plotted against density (mean MNA per104 m2; Fig. 4a,d), against abundance (mean MNA;Fig. 4b,e), and against island area (Fig. 4c,f). Area andabundance are both indices of the numbers in the hostpopulations: the latter is the more direct measure forthe study period itself, but island area provides, perhaps,a better longer-term perspective, uninfluenced bystochastic variation, given that the habitat was verysimilar in all cases.

Fig. 3. Continued

350M. Begon et al.

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

Fig. 4. Overall prevalences of infection, April 1998–March 2000, on the 14 islands and in Manor Wood (notional (grid) area104 m2), plotted against density (mean minimum number alive per sample per 104 m2), numbers (log (mean MNA) + (1), andarea (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 ) Woodmice, area.

351Rodents, cowpox and islands

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

Fig. 4. Continued

For bank voles, there is no evidence of a densitythreshold (Fig. 4a) but a clear suggestion that cowpoxwas found in populations above a particular numericalsize and absent below that threshold. This is clearest,

visually, for area (Fig. 4c). Indeed, the positive pre-valences on the three smallest islands represent singleindividuals only: that is, they invaded in the ecologicalbut not in the epidemiological sense (no evidence of

352M. Begon et al.

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

subsequent transmission). Hence, a threshold area ofaround 0·09 × 104 m2 is suggested. For wood mice, thepicture is superficially similar, with no obvious densitythreshold (Fig. 4d) but evidence of a threshold popu-lation size (Fig. 4e,f). Also, the two high overall pre-valences on small islands represent only one in four andone in five animals trapped (Fig. 3c), and hence notinvasion in the epidemiological sense. The thresholdarea is similar to that observed in bank voles. In woodmice, however, below the ‘threshold’, the host popula-tions themselves are, as previously noted, extremelysmall and mostly transitory (with frequent extinctionson the small islands).

Logistic regression was used to investigate furtherwhat factors best explained the occurrence of cowpoxvirus in bank vole and wood mouse populations. Thedependent variable was whether or not cowpox wasever recorded on an island. The three islands that werenever inhabited by wood mice were excluded from thewood mouse analysis. Akaike’s Information Criterion(AIC) was used for model selection; models with AICvalues that differ by less than 2 are similar in their abilityto describe the data (Burnham & Anderson 1992). Inboth species, the probability of cowpox being recordedon an island is related to average population size butnot average population density (Table 1). Island area isstrongly correlated with bank vole and wood mousepopulation size (average MNA; bank voles: r = 0·97,P < 0·001; wood mice: r = 0·94, P < 0·001), and con-sequently, average bank vole and wood mouse MNA arealso strongly correlated (r = 0·85, P < 0·001). Unsur-prisingly, therefore, island area and average populationsize of the sympatric species can also be used to predictthe occurrence of cowpox in an island population.Indeed, average MNA, island area, and average MNAof 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 bankvoles; and in wood mice, the superiority of bank voleMNA over wood mouse MNA is close to significance(difference in AIC = 1·85).

Finally, amongst the populations in which cowpoxhad been present at all, the overall prevalence of infectionand the density of bank voles were not positivelycorrelated, as predicted by theory, but negativelycorrelated (Fig. 4a; r = −0·76, P ≈ 0·02). There is a hintof a similar relationship for wood mice (Fig. 4d; r = −0·58),although this is not significant and is largely the con-sequence of the low overall prevalence in Manor Wood.

Discussion

In spite of a clear tendency for wood mice to move morefrequently between islands than bank voles, and formales to move more frequently than females (signi-ficant only for bank voles) – both of which are consistentwith previous studies on mobility in woodland rodents(Corbet & Harris 1996) – overall measurable rates ofmovement were low, even at relatively peak times of theyear for movement. These measured rates, however, areinevitably underestimates of the true rates, since theycannot take account of animals that moved islands priorto their first capture. Analysis of the genotypes on differentislands, by contrast, reflect such movements; and ananalysis of microsatellite loci in bank voles fromManor Wood and the two largest islands (wheresample sizes were therefore large enough for analysis)indicates a low but significant level of differentiationbetween populations (but none within), with the greatestdifferentiation occurring between Manor Wood andthe island furthest from it (large island 2; Barker 2002).These data therefore further support the view thatthe dynamics (including the host–pathogen dynamics)of most island populations most of the time aredominated by demographic processes occurring withinthe population, but movement rates appear to besufficiently high to ensure that no island remainsisolated for long from animals (including potentiallyinfectious animals) from other islands or the mainland.Thus, the network of islands appears to function as ametapopulation.

In view of the degree of isolation of the islands, thesimilarities in the patterns of host dynamics on themare striking. Even the smaller islands, where absolutenumbers were such as to ensure that stochastic effectsplayed a major part in determining the patternsobserved, showed the same seasonal patterns of hostdynamics as in other, larger populations once theirnumbers were combined. As far as the patterns them-selves are concerned, the seasonal cycle was entirely tobe expected from previous studies (Hazel et al. 2000).The decline in the relative abundance of wood mice onislands of decreasing size, in the absence of significant

Table 1. Logistic regression analysis of the presence andabsence of cowpox virus infection in bank vole and woodmouse populations of different sizes. The abilities of differentmodels to account for observed patterns can be judged fromthe significance values in column 4. Models are similar in theirability to account for the patterns if their AIC values (column5) 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 likelihood

No. parameters

Significance if removed AIC

Bank volesConstant 19·12 1 – 21·12Bv MNA 14·85 2 0·039 18·85Bv density 18·31 2 0·368 22·31Area 15·07 2 0·044 19·07Wm MNA 15·62 2 0·061 19·62

Wood miceConstant 15·16 1 – 17·16Wm MNA 7·19 2 0·005 11·19Wm density 14·53 2 0·43 18·53Area 8·59 2 0·010 12·59Bv MNA 5·34 2 0·002 9·34

353Rodents, cowpox and islands

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

changes in the nature of the habitat, has not apparentlybeen observed previously but is not unexpected in viewof the greater mobility and territory size of wood mice(Corbet & Harris 1996). Higher densities on smallerislands have been observed in many island systems: apattern often ascribed to the relative absence of pred-ators 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 animplausible argument in the case of avian predators,while mustelids have only very rarely been observed onthe study site. On the other hand, broadening thedefinition of predators to include the many pathogensand parasites that affect bank voles and wood mice, ofwhich cowpox virus is only one (e.g. Birtles et al. 2001;Cavanagh et al. 2002; Noyes et al. 2002), some at leastmay be below their critical threshold population sizeon the smaller islands, with a consequent increase intypical host density (see also below). Alternatively, animalsin the small populations on small islands are morelikely to be closely related, and close relatives in rodentpopulations are known to be more tolerant of living inclose proximity, while island populations in generalmay live at higher densities and be less territorial(Nevison et al. 2000).

In comparing the patterns of cowpox virus infection inManor Wood and on the various islands, it is impor-tant to remember that absence of infection in ManorWood means absence of infection on the trapping grid,but not necessarily absence from the larger populationof which it is part. Absence of infection on an island,however, suggests far more strongly that infection wastruly absent, since trapping grids covered the whole ofeach island. Naturally, trapping cannot be 100% efficient.However, a comparison of MNA estimates and capture–recapture estimates of population size for moreextensive data sets obtained using the same protocols,in Manor Wood and another mainland site (Chantrey1999), indicated that more than 90% of the animals inour populations are trapped.

Bearing this in mind, the time series data suggest thatthere was cowpox virus infection in the Manor Woodpopulation throughout the 2-year study period, but forall of the islands, including the largest, there wereperiods when no cowpox virus infected hosts werepresent. Nonetheless, the patterns over time in all caseswere remarkably similar. Previous work, too, foundthat prevalence was higher in bank voles than woodmice (Hazel et al. 2000), and also that the numbers ofinfected hosts increased markedly coincident withthe rise in host abundance in late autumn, as observedhere in 1999. On the other hand, a decline in thenumbers infected between the middle and end of theyear is not normally observed (Hazel et al. 2000), butwas seen here in essentially all populations in 1998, inthe absence of anything similarly atypical in the pattern

of host dynamics. Thus, host–cowpox dynamicsappeared to be synchronized in the different popula-tions. There are (at least) two possible explanations.First, even a small amount of host movement may besufficient to effectively unite and even synchronizehost–cowpox virus dynamics. However, given the lowrates of movement and short infectious period ofcowpox, the probability of an infectious host moving isrelatively small.

An alternative would be that cowpox virus persisted,during its apparent absence, in some environmentalreservoir, and, moreover, that transmission from thisreservoir to the host varied in parallel in the differentpopulations. As with most wildlife diseases, the naturalroutes of cowpox virus transmission have not yet beenconfirmed experimentally. Nonetheless, a variety ofevidence from this and related orthopoxvirusesindicates direct transmission between infectious andsusceptible hosts is the main route of infection (Robinson& Kerr 1999). This is further supported by the highexplanatory power of models incorporating directtransmission fitted to time series of rodent–cowpox virusdynamics (Begon et al. 1998, 1999), and by analyseswhich indicate that susceptible rodents are significantlymore likely to become infected with cowpox virus whenthey are closely juxtaposed, in both space and time, toinfectious hosts (David Carslake, unpublished data).On the other hand, like many poxviruses cowpox virusis known to be able to survive for extended periods outsideits host (Baxby & Bennett 1999), the closely relatedectromelia virus is transmissible amongst laboratoryanimals on bedding (Fenner 1999), and around one-quarterof human cases of cowpox cannot be traced to contactwith a cat or rodent (Baxby et al. 1994). Some role for anenvironmental reservoir for cowpox virus in bridgingthe gaps in time series cannot therefore be ruled out.

Threshold population sizes (critical communitysizes) are commonplace in theoretical expositions, butthey have only very rarely been documented in wildlifepopulations (Dobson & Hudson 1995). Perhaps forthis reason, there is no conventional expectation ofwhat to expect by way of a match between observedthresholds and the predictions of theory. For thebenchmark types of pathogen transmission (Begonet al. 2002), deterministic models predict a single densitythreshold with density-dependent transmission (validfor both pathogen invasion and persistence) but nothreshold in either numbers or density with frequency-dependent transmission. In this latter case, though, themodels do predict a threshold contact rate betweenhosts that is independent of density (Swinton et al.2002), which can presumably be achieved only if thereare sufficient numbers of individuals available to makecontact with. Stochastic models (Bartlett 1960; Nåsell1999) generate separate thresholds for invasion andpersistence (the latter being higher), and by their naturedeal more naturally with numbers of individuals. Moregenerally, stochastic models draw attention to theimportance of stochastic fade-out (failure to persist),

354M. Begon et al.

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

which occurs when the chain of infection in a popula-tion is broken. The chances of this depend on thebehaviour of individual hosts (Swinton et al. 2002) andagain are likely to increase with decreasing densitywhere contact rates are density-dependent but withdecreasing 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 dynamicswithin that period (Fig. 3). It has been possible there-fore to determine whether any type of threshold is detec-table, whether the nature of that threshold supports thecontention of an underlying density-dependent orfrequency-dependent process, and whether the thresholdapplies to persistence (i.e. is a threshold above which theinfection is always present) or combines persistence andinvasion.

For bank voles, when the 2-year period is consideredas a whole, a threshold population size is apparent, butin terms of the numbers in populations rather thandensities. 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 appar-ently disappeared from every one of the island populations.Rather, as population (island) size increases, there is aprogression from ‘no cowpox’ to ‘ecological invasion’(the occasional infected host but no apparent trans-mission), to ‘epidemiological invasion’ (a succession ofinfected animals but disappearance of cowpox withinthe 2-year period), to ‘persistence’ (Manor Wood only).An argument can therefore be made for both an inva-sion threshold (between ecological and epidemiolo-gical invasion) and a persistence threshold (betweeninvasion and persistence), though both will be fuzzyrather than sharp: the probability of pathogen invasionon small islands is finite even when it is small, and theprobability of pathogen extinction is finite even inManor Wood. Such patterns are likely to be found in allreal populations, as opposed to those imagined bydeterministic models. Moreover, such arguments applynot only if invasion is literal (migration of an infectedhost), but also if the invasion of the pathogen is from anenvironmental reservoir.

The fact that this appears to be a numbers ratherthan a density threshold reinforces previous analysesof cowpox–rodent infection dynamics (Begon et al.1998, 1999) in suggesting little support for density-dependent transmission, despite this having been theusual default assumption for non-sexually transmittedinfections. Furthermore, the present results provide littlesupport for the contention that density thresholds arelikely to be appropriate ‘for wildlife populations thatextend continuously over habitat ranges’ (Swintonet al. 2002), as is the case here. Finally, given the lack ofsupport for density-dependent transmission, the absenceof the positive correlation predicted by theory betweenprevalence and density is unsurprising (and would, inany case, be found above an invasion-and-persistencethreshold).

In the case of the wood mice, a superficial similarityto the bank voles is potentially misleading. Below theapparent threshold, it is less a case of cowpox being(mostly) absent from the host population than of thehost population itself being mostly absent. On the otherhand, it is strictly incorrect to talk about a threshold foreither of the host species: theory suggests that theycombine to provide a resource for cowpox virus andthus to generate a joint threshold (Bowers & Turner1997). 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 presentcase (Begon et al. 1999), suggesting that there are effect-ively separate thresholds for each species. This, though,is another conclusion derived from deterministicmodels where invasion and persistence thresholds areone and the same. In (stochastic) practice, re-invasionby cowpox virus of an island population of either speciesmay often be of crucial significance to both of them, inspite of the relatively low level of transmission betweenthem. This will be especially true if environmental con-tamination plays any part in transmission. In thepresent case, as it is inconceivable that an acute infec-tion such as cowpox could circulate independently inthe very small wood mouse populations (lack of sus-ceptibles), wood mouse thresholds must be influencedat least as much by the bank vole thresholds as they areby the dynamics within the wood mouse populationsthemselves (borne out by the logistic regression). Thiswould explain the apparently similar thresholds in bankvoles and wood mice. Indeed, there is some evidencethat an ecological invasion of cowpox in wood mice(only one infected individual) only occurs when cowpoxhas successfully invaded (more than one infected indi-vidual) a sympatric bank vole population (two of thelarge islands in 1998; one of the small islands in 1999).Successful invasion in wood mice is more infrequentand tends to occur when wood mice numbers are rela-tively high (such as in 1999 and on large island 1). Thissuggests that it may often be difficult to observe thresh-olds in the field, as the risk experienced by a populationdepends on factors other than its own size/density.

Thus, the present results confirm that thresholds canbe observed in wildlife populations and suggest thatnumbers thresholds may be more common than hassometimes been imagined. They certainly cautionagainst any general expectation of a density threshold,even though this is the prediction from the most com-monly quoted theoretical treatments, and even when thehost–pathogen system extends continuously over avail-able habitat. They also emphasize that empirical assess-ments of thresholds are likely to reflect patterns of bothinvasion and persistence (separable only in stochasticmodels), and also interspecific transmission, even ifthis is only rare. Finally, and perhaps most generally,these results highlight the fact that little attention hasbeen paid to the practical meaning of the theoreticalconcept of a threshold, probably because there havebeen few empirical studies with which to confront it.

355Rodents, cowpox and islands

© 2003 British Ecological Society, Journal of Animal Ecology, 72,343–355

Acknowledgements

We are most grateful to Leverhulme Estates for accessto the study site, to NERC for financial support, toChris McCracken for logistical support, and to FayeBarker and Moira Gilliver for help with trapping.

References

Anderson, R.M. (1982) Epidemiology. Modern Parasitology(ed. F.E.G.Cox), pp. 204–251. Blackwell Scientific Pub-lications, Oxford.

Barker, F.S. (2002) Determination of kinship and the localpopulation structure of the endemic hosts of the cowpox virus,the bank vole, Clethrionomys glareolus and the wood mouse,Apodemus sylvaticus. Unpublished PhD Thesis. Universityof Liverpool.

Bartlett, M.S. (1960) Stochastic Population Models in Ecologyand Epidemiology. Methuen, London.

Baxby, D. & Bennett, M. (1999) Cowpox virus (Poxviridae).Encyclopedia of Virology, 2nd edn (eds R.G. Webster &A. Granoff), pp. 298–304. Academic Press, London.

Baxby, D., Bennett, M. & Getty, B. (1994) Human cowpox;a review based on 54 cases, 1969–93. British Journal ofDermatology, 131, 598–607.

Begon, M., Hazel, S.M., Baxby, D., Bown, K., Cavanagh, R.,Chantrey, J., Jones, T. & Bennett, M. (1999) Transmissiondynamics of a zoonotic pathogen within and betweenwildlife host species. Proceedings of the Royal Society ofLondon Series B, 266, 1939–1945.

Begon, M., Bennett, M., Bowers, R.G., French, N.P., Hazel,S.M. & Turner, J. (2002) A clarification of transmissionterms in host–microparasite models: numbers, densitiesand areas. Epidemiology and Infection, 129, 147–153.

Begon, M., Feore, S., Bown, K., Chantrey, J., Jones, T. & Bennett,M. (1998) The population dynamics of cowpox virus infectionin bank voles: testing fundamental assumptions. EcologyLetters, 1, 82–86.

Bennett, M., Crouch, A.J., Begon, M., Duffy, B., Feore, S.,Gaskell, R.M., Kelly, D.F., McCracken, C.M., Vicary, L. &Baxby, D. (1997) Cowpox in British voles and mice. Journalof Comparative Pathology, 116, 35–44.

Birtles, R.J., Hazel, S., Bown, K., Begon, M., Raoult, D. &Bennett, M. (2001) Longitudinal monitoring of bartonellosisin British wood mice and bank voles. Epidemiology andInfection, 126, 323–329.

Black, F.L. (1966) Measles endemicity in insular populations:critical community size and its evolutionary implication.Journal of Theoretical Biology, 11, 207–211.

Bowers, R.G. & Turner, J. (1997) Community structure andthe interplay between interspecific infection and competi-tion. Journal of Theoretical Biology, 187, 95–109.

Brown, J.H. & Gibson, A.C. (1983) Biogeography. C.V.Mosby, St. Louis.

Burnham, K.P. & Anderson, D.R. (1992) Data-based selectionof an appropriate biological model: The key to modern dataanalysis. Wildlife 2001: Populations (eds D. R. McCullough& R. H. Barrett), pp. 16–30. Elsevier. Science Publishers,London.

Cavanagh, R., Begon, M., Bennett, M., Ergon, T., Graham,I.M., de Haas, P.E.W., Hart, C.A., Koedam, M., Kremer,K., Lambin, X., Roholl, P. & van Soolingen, D. (2002)Mycobacterium microti infection (vole tuberculosis) in wildrodent populations: a potential reservoir for pulmonarytuberculosis in humans. Journal of Clinical Microbiology,40, 3281–3285.

Chantrey, J. (1999) Studies on the epidemiology of cowpoxvirus in its rodent reservoir hosts. Unpublished PhD Thesis.University of Liverpool.

Chantrey, J., Meyer, H., Baxby, D., Begon, M., Bown, K.,

Feore, S., Jones, T., Montgomery, W.I. & Bennett, M.(1999) Cowpox: reservoir hosts and geographic range.Epidemiology and Infection, 122, 455–460.

Corbet, G.B. & Harris, S., eds. (1996) The Handbook of BritishMammals, 3rd edn. Blackwell Science, Oxford.

Crouch, A.C., Baxby, D., McCracken, C.M., Gaskell, R.M. &Bennett, M. (1995) Serological evidence for the reservoirhosts of cowpox virus in British wildlife. Epidemiology andInfection, 115, 185–191.

Dobson, A.P. & Hudson, P.J. (1995) Microparasites: observedpatterns in wild animal populations. Ecology of InfectiousDiseases in Natural Populations (eds B.T. Grenfell & A.P.Dobson), pp. 52–89. Cambridge University Press, Cambridge.

Fenner, F. (1999) Mousepox and rabbitpox viruses. Ency-clopedia of Virology, 2nd edn (eds R.G. Webster & A.Granoff), pp. 861–867. Academic Press, London.

Feore, S.M., Bennett, M., Chantrey, J., Jones, T., Baxby, D. &Begon, M. (1997) The effect of cowpox virus infection onfecundity in bank voles and wood mice. Proceedings of theRoyal Society of London Series B, 264, 1457–1461.

Grenfell, B.T. & Harwood, J. (1997) (Meta) populationdynamics of infectious diseases. Trends in Ecology andEvolution, 12, 395–399.

Hazel, S.M., Baxby, D., Bennett, M., Bown, K., Cavanagh, R.,Chantrey, J., Jones, T.R. & Begon, M. (2000) A longitudinalstudy of endemic disease in its wildlife reservoir: cowpoxand wild rodents. Epidemiology and Infection, 124, 551–562.

Hess, G.R., Randolph, S.E., Arneberg, P., Chemini, C.,Furlanello, C., Harwood, J., Roberts, M.G. & Swinton, J.(2002) Spatial aspects of disease dynamics. The Ecology ofWildlife Diseases (eds P.J. Hudson, A. Rizzoli, B.T. Grenfell,H. Heesterbeek & A.P. Dobson), pp. 102–118. OxfordUniversity Press, Oxford.

Hudson, P.J., Rizzoli, A., Grenfell, B.T., Heesterbeek, H. &Dobson, A.P. (eds) (2002) The Ecology of Wildlife Diseases.Oxford University Press, Oxford.

Krebs, C. (1966) Demographic changes in fluctuating popu-lations of Microtus californicus. Ecological Monographs,36, 239–273.

Nåsell, I. (1999) On the time to extinction in recurrent epi-demics. Journal of the Royal Statistical Society Series B, 61,309–330.

Nevison, C.M. Barnard, C.J. Beynon, R.J. & Hurst, J.L.(2000) The consequences of inbreeding for recognizingcompetitors. Proceedings of the Royal Society of LondonSeries B, 267, 687–694.

Noyes, H.A., Ambrose, P., Barker, F., Begon, M., Bennett,M., Bown, K.J. & Kemp, S.J. (2002) Host specificity ofTrypanosoma (Herpetosoma) species: evidence that bankvoles (Clethrionomys glareolus) carry only one T. (H.)evotomys 18S rRNA genotype but wood mice (Apodemussylvaticus) carry a least two polyphyletic parasites. Parasito-logy, 124, 185–190.

Robinson, A.J. & Kerr, P.J. (1999) Poxvirus infections in wildmammals. Infectious Diseases of Wild Mammals, 3rd edn(eds E. Williams, I. Barker & T. Thorne), pp. 179–201. IowaState University Press, Ames.

Swinton, J., Woolhouse, M.E.J., Begon, M.E., Dobson, A.P.,Ferroglio, E., Grenfell, B.T., Guberti, V., Hails, R.S.,Heesterbeek, J.A.P., Lavazza, A., Roberts, M.G., White,P.J. & Wilson, K. (2002) Microparasite transmission andpersistence. The Ecology of Wildlife Diseases (eds P.J. Hudson,A. Rizzoli, B.T. Grenfell, H. Heesterbeek & A.P. Dobson),pp. 83–101. Oxford University Press, Oxford.

Telfer, S., Bennett, M., Bown, K.J., Cavanagh, R., Crespin,L., Hazel, S., Jones, T. & Begon, M. (2002) The effects ofcowpox virus on survival in natural rodent populations:increases and decreases. Journal of Animal Ecology, 71,558–568.

Received 11 June 2002; accepted 27 November 2002