experimental design: control/intervention
The timing of experimental interventions (reduction in possum population density) and observations (lethal crosssectional surveys of ferrets) at the study sites are given in Table 1. The predominant methods used to reduce possum population density included leghold trapping, poisoning using treemounted bait stations (compound 1080, encapsulated cyanide, broadifacoum), and aerially delivered cereal and/or carrot baits containing 1080. Further details are given below, including possible effects of possum control on ferret populations. These data may be analysed in many ways. Two approaches are used here. The first and simplest is a CI (control, intervention) design that compares estimates of λ from sites with no history of possum population reduction (experimental control treatment) with those from sites following a sustained reduction in possum population density (experimental intervention treatment). The Castlepoint, Cape Palliser, Awatere Valley, Scargill Valley and Lake Ohau sites made up the experimental control treatment, whilst Hohotaka, Rangitikei, Tiromoana/Mt Cass and Waipawa sites made up the experimental intervention treatment. The Castlepoint and Scargill Valley sites included in the experimental control treatment (Table 1) were subsequently subjected to the experimental intervention treatment, and so also form part of the BACI design (see below). For analysis of the CI design, only survey data collected from these two sites before the experimental intervention were included in the analysis.
Table 1. Summary of the application of experimental interventions (X) and observations (O) of M. bovis infection in feral ferrets (following the notation of Manly 1992). The experimental intervention is the sustained reduction of possum density by lethal control (‘press’ cf. ‘pulse’). Observations are crosssectional surveys of the ferret population. Numbers in parentheses are sample sizes Year  Site* 

AWA  CP  CPR  HH  LO  RA  SCAR  TIRO  WAIP 


Pre94     X     X  X 
1994   O (15)        
1995   O (2)   O (22)    O (78)†  O (19)†  
1996        †  † 
1997      O (72)  X  O (50)†  O (50)†  O (28) 
1998   O (31) X  O (19)  O (55)    O (33)† X  O (39)†  
1999   O (27)  O (14)     O (58)   O (4) 
2000  O (47)  O (14)  O (7)   O (40)  O (30)  O (62)   
2001  O (42)  O (8)  O (1)     O (85)   
2002  O (32)         
experimental design: before/after control/intervention
The second approach follows a BACI (before vs. after, control vs. intervention) design (Green 1979), which inferentially is considerably stronger than a simple CI design. Four sites were used in the BACI design, these being Castlepoint (experimental intervention), Cape Palliser (experimental control), Scargill Valley (experimental intervention) and Awatere Valley (experimental control) (Table 1). These sites were originally chosen to be matched as practicably as possible for possum density (in the absence of experimental intervention), ferret density, and the force of M. bovis in fection.
Possum control over a 6400ha area encompassing the Scargill Valley survey area started in winter/spring of 1998 using leghold traps, cyanide paste and encapsulated cyanide (Feratox®). Maintenance control to maintain the possum population at the lowered postcontrol population density was undertaken using encapsulated cyanide in 1999 and 2000. Possum control over a 6510ha area encompassing the Castlepoint survey area started during the summer/autumn of 1998 using leghold traps and encapsulated cyanide, with further maintenance control in 1999. Mycobacterium bovisinfected possums had been found at the Awatere Valley, Cape Palliser, Scargill Valley and Castlepoint sites, and reducing the population density of possums at the latter two sites can reasonably be assumed to reduce the density of M. bovis infected possums (Caley et al. 1999), and hence density of M. bovisinfected possum carcasses. Indeed, possums macroscopically infected with M. bovis were removed during trapping at Castlepoint during 1998.
estimating possum population density
Two indices of possum population density were obtained. The first was based on the number of possums caught incidentally in traps targeted at catching ferrets, using a modified version of Leslie's Removal Method (Seber 1982) modified to account for unequal sampling effort. The measure of abundance was the estimated number of possums per trap (rather than density). This was done as homeranges of possums are in general small compared with the distance between traps. These data were collected from all sites, and provide a standardized index of possum population density enabling comparisons between surveys at all sites.
The second index of possum population density was based on the nationally recognized residual trapcatch (RTC) methodology (NPCA 2001). At the time of the study, the RTC method for monitoring changes in possum population density involved catching possums on lines of 20 softcatch leghold traps, with the starting point of each line randomly selected within available possum habitat (stratified random sampling). For repeated yearly surveys, a new random sample of starting points was selected each year. The 20 traps in each line were spaced at 20m intervals along transects which ran in a north–south direction. Traps were lured with a mix of flour (5 parts) and icing sugar (1 part), and set for 3 fine nights. The trapcatch statistic for each line was calculated as the average number of possums caught per trap per night. The RTC method was used to monitor changes in the population density of possums at Scargill Valley and Castlepoint resulting from possum control and to monitor natural fluctuations in the population density of possums at Cape Palliser and Awatere Valley. Possums captured at Scargill Valley and Castlepoint point during RTC monitoring were killed, whereas those captured at Cape Palliser and Awatere Valley were released. Possums captured during ferret trapping (see below) were treated similarly (humanely killed at experimental intervention sites and released at experimental control sites).
sampling ferret populations
Ferrets were captured in Victor SoftCatch® leghold traps (size 1.5) baited with fresh rabbit Oryctolagus cuniculus L., hare Lepus europaeus occidentalis de Winton or domestic chicken meat. Traps were set at approximately 200m intervals, usually over 5–10 nights. Suffering of animals was minimized by using rubber jawed (cf. steel jawed) traps, and checking traps as soon as practically possible each morning following setting. The use of leghold traps increases the efficiency of trapping, and enables traps to be set down burrows out of the way of livestock. Alternative methods of obtaining large samples, such as shooting, were not feasible logistically. Any nontarget animals captured were released, and ferret and possums [if the experimental treatment so required] were humanely killed at the trap site where they were captured. All fieldwork procedures were approved by the Landcare Research Animal Ethics Committee (Approval Project no. 98/10/4), conforming to the legal requirements of New Zealand. Methods used to diagnose M. bovis infection and estimate ferret age are presented in Caley & Hone (2002). All ferret and possum carcasses were either incinerated or disposed of in covered offal pits.
Lethal crosssectional sampling of ferret populations is essentially a form of population control. There has been no examination of the effect of ferret control on the force of M. bovis infection in feral ferrets. Lethal sampling of ferret populations infected with M. bovis should decrease the force of M. bovis infection in ferret populations by reducing the density of M. bovisinfected carcasses available to be scavenged by ferrets – assuming this is a significant mechanism of transmission. Ferret population density was estimated in each trapping session at each site using Leslie's Removal Method (Seber 1982), modified to account for unequal sampling effort. Possible changes in the population density of ferrets caused by sampling were assessed by regressing the natural logarithm of population density on time, and testing using a ttest (Sokal & Rohlf 1995) whether the instantaneous rate of increase (r) estimated as the slope of this regression (Caughley & Sinclair 1994) was significantly less than zero. The test is onetailed, as we expected a priori that lethal ferret sampling should decrease ferret population density. This approach to hypothesis testing is in line with one of the recommendations of Krebs (2000), who argued there should be much more use of onetailed tests in ecology, especially in the case of planned experiments.
analysis of control/intervention design
For the experimental control sites, λ was estimated from agespecific prevalence data assuming a stepexponential model (Lee 1992), with λ modelled as being zero up until the age of weaning (at 1·75 months), and a constant thereafter (though allowed to differ between sites). The rate of diseaseinduced mortality (α), and the effect of gender were estimated during the model fitting procedure (α = 1·4 year^{−1}; 2·2 increased hazard for males), assuming these effects to be constant across all sites. This particular model was chosen during the model selection exercise of Caley & Hone (2002). For the experimental intervention sites, estimates of λ were made using the same model, although with the effect of sex and diseaseinduced mortality fixed at estimates from the experimental control sites. To avoid any effect of ferret sampling, only data collected during the first survey from each site was used for estimating λ used in this analysis. Differences in the means of λ (denoted ) and possum density between the treatments were compared using a ttest (Sokal & Rohlf 1995). Again the ttests were onetailed, as we hypothesized a priori that the possum control intervention treatment would reduce both possum population density and λ.
An important assumption of the analysis is that the experiment was not confounded (e.g. ferret population density reduced) by the method used to control possums. Two studies have reported on the effect of possum control on the population density of ferrets. Groundlaid, 1080poisoned jam baits (note this is not a currently approved control method) resulted in significant mortality of resident ferrets (Moller, Showers & Wright 1996). In contrast, Caley et al. (1999) recorded no change in the yeartoyear population density of ferrets at a site subjected to possum control using a variety of means, including 1080jam baits (above ground), cyanide baits (above ground), aerially sown 1080cereal baits, 1080cereal baits in bait stations, broadifacoum cereal bait in aboveground bait stations, and leghold trapping. High ferret mortality was recorded following a rabbit poisoning operation using brodifacoum to target rabbits (Alterio 1996). Hence, ferrets appear highly susceptible to secondary poisoning from a chronic anticoagulant like brodifacoum. Five of the sites reported on here had been subject to possum control before being surveyed (Hohotaka, Scargill Valley, Waipawa, Rangitikei, Tiromoana/Mt Cass). Other than Hohotaka (for which no change in ferret population density was observed, see Caley et al. 1999), none of these sites used anticoagulants as the method for either initial or maintenance control of possums, before our ferret surveys. Hence, we assumed that possum control had not greatly influenced ferret population density at these sites, and tested this by comparing the population density of ferrets between the treatments using a ttest (twotailed this time).
analysis of before/after control/intervention design
The first problem encountered when analysing this type of observationinterventionobservation data is that some animals spend time in both treatments. During the first sampling session, all animals captured have been subject to one treatment only, making estimation of λ up to this point relatively easy (Caley & Hone 2002). However, in subsequent sampling sessions, some individuals have been subject to either both treatments, or only the second treatment (estimation of λ is again straightforward for these animals), as shown schematically in Fig. 2. Dealing with animals that have spent time in more than one treatment is problematical. One way around this problem is to exclude these individuals from the analysis. This approach is undesirable as it wastes information.
Alternatively, if the time period an animal has spent before capture is divided into two treatment periods, no ferret sampling (Treatment 1), and after the start of ferret sampling (Treatment 2), the prevalence of infection can be expressed as a function of the respective forces of infection in each treatment and the time spent by each individual in each treatment. More specifically, if the times spent in Treatment 1 and Treatment 2 are t_{1} and t_{2}, respectively, then the probability (Pr) of being infected at capture can be expressed as:
 Pr(infected at capture) = 1 − Pr(not infected during t_{1})Pr(not infected during t_{2}).
An exponential model ignoring diseaseinduced mortality (setting α = 0) is adequate for modelling the force of M. bovis infection in feral ferrets, and is much more tractable than the exponential model including diseaseinduced mortality (Caley & Hone 2002). This is the approach taken here. To avoid confusion, from now on we denote the force of infection estimated assuming no diseaseinduced mortality as λ′. Assuming a constant force of infection during each treatment period ( during t_{1}, during t_{2}), the prevalence of infection at capture for ferrets that spend time in both treatment periods can be modelled as:
 (eqn 1)
Combining these results gives a model of the prevalence of infection in a system where the force of infection takes on two timedependent values (Model 1).
 ( (Model 1))
Expressions for agespecific prevalence in Model 1 are all nested within eqn 1, which makes calculations simple. Rearranging eqn 1 gives the prevalence of M. bovis infection as a function of the λs in the different treatments, and the time spent in each treatment (eqn 2).
 (eqn 2)
 (eqn 3)
The model used previously for two treatments (Model 1) can be extended to three treatments, to estimate the additional effect of possum control on the force of infection:
 (eqn 4)
where is the force of infection during the period t_{3} that the animal is subjected to treatment 3 (here, a reduction in possum population density in combination with lethal ferret sampling). Let Δ be the reduction in λ′ over and above that observed after the start of ferret sampling, hence:
 (eqn 5)
Substituting for and into eqn 4 and rearranging yields:
 (eqn 6)
Here, a denotes the age of ferrets and eqn 6 can be used to estimate , τ and (τ + Δ) using a GLM (again subtracting g from either a, t_{2} or t_{3} as appropriate). Where τ is estimated to be significantly different from zero, estimates of Δ and its standard error (assuming Δ and τ are independent) are then calculated as:
 (eqn 7)
 (eqn 8 )
Otherwise, estimates of Δ and its standard error were obtained by refitting eqn 6 without the t_{2} term.
For each site, testing whether or differed from zero was undertaken using a onetailed ttest. Initial analyses of this data set (Caley 2001) ignored any sex effects on λ′, however, subsequent analyses revealed that the sex ratio was unlikely to be independent of the time spent in different treatments, with the proportion of males in crosssectional survey samples decreasing over time (χ^{2} = 4·3, d.f. = 2, P = 0·12). We accommodated for this by increasing the time spent by males in all treatments by a factor of 2·2, in line with the results of Caley & Hone (2002). Hence, the results here differ slightly to those presented by Caley (2001). A metaanalysis approach was used to combine the results from the different sites within the North Island (Castlepoint and Cape Palliser) and South Island (Awatere Valley and Scargill Valley). The probabilities arising from the ttests (examining whether the treatments ‘ferret sampling’ or ‘possum control’ influenced λ′) from the different sites were combined using the formulae presented by Fisher (1935) (cited by Underwood (1997)):
 (eqn 9)
Here, P_{i} is the probability associated with the i^{th} site, and k is the number of sites. C is distributed as χ^{2} with 2 k degrees of freedom. Analyses were undertaken using the software R (Ihaka & Gentleman 1996) and GLIM4 (Francis, Green & Payne 1993).