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Study areaWe conducted our study in two suburbs in Wellington, New Zealand (Fig. 1). The 4.7-hectare site in the suburb of Kelburn (-41.285°S, 174.770°E) was situated on the grounds of student accommodation for Victoria University of Wellington. The site comprised bungalow houses, two accommodation halls, and access roads and paths. About half of the vegetation at the Kelburn site was a mix of tended grass lawns and gardens containing a variety of native New Zealand plant species, e.g., flax (Phormium spp.), longwood tussock (Carex comans), and cabbage tree (Cordyline australis). The other half was a mix of dense ground cover dominated by invasive weed species and native and exotic trees and shrubs, e.g., pōhutukawa (Metrosideros excelsa), common oak (Quercus robur), kawakawa (Piper excelsum), and taupata (Coprosma repens). The second suburb was Roseneath (−41.292°S, 174.801°E) on a small peninsula on the north-eastern side of Mount Victoria. The site was 8.5 hectares comprising 76 residential properties, public thoroughfares, and footpaths. We conducted fieldwork in the gardens of 25 of these properties. The vegetation varied considerably between gardens, comprising native and introduced garden plants and invasive weeds, especially blackberry (Rubus fruticosus).Figure 1(A) The study was conducted in the suburbs of Kelburn (left yellow dot) and Roseneath (right yellow dot) in the city of Wellington, New Zealand. The black polygon represents the 1475 ha area that will be targeted for ship rat (Rattus rattus) eradication in Wellington city, New Zealand. In each suburb, we radio-collared ship rats and deployed three types of devices (bait stations, chew cards, and WaxTags) to estimate home range and detection parameters. (B) In Kelburn, we radio-collared 14 rats and deployed eight devices. (C) In Roseneath, we radio-collared 16 rats and deployed 30 devices. The yellow circles indicate home range centers of individual rats, the red triangles indicate the location of bait stations and detection devices, and the small black dots indicate the telemetry locations of rats.Full size imageRat capture, radio-collaring, and field methodologyWe set 100 live-capture cage traps (custom-made, spring-loaded traps) in Kelburn from 12 July to 15 August 2020, and another 100 in Roseneath from 20 August to 20 October 2020. We baited cage traps with apple coated in chocolate spread and checked them at least once every 24 h. We set cage traps in areas with complex vegetative groundcover and understorey to maximize capture rates of ship rats (see35), and to provide shelter from inclement weather. We provided additional shelter by inserting bedding inside a tin can placed in the cage traps, along with a plastic cover over the traps to limit exposure to wind and rain. Cage traps were active for 5 days per week on average. We released all non-target species (house mice Mus musculus, European hedgehogs Erinaceus europaeus, and Eurasian blackbirds Turdus merula).We transferred any trap containing a captured rat into a sealed plastic container. Depending on the estimated size of the captured rat, we placed between one and three cotton balls soaked in isoflurane (99.9%, Attane, Piramal Critical Care Inc., Bethlehem, Pennsylvania, USA) inside the plastic container. A rat was anesthetized when it lost balance and was unable to regain balance when we gently rotated the container. We then removed the rat from the cage trap and placed it next to a heat pad with its head close to the cotton balls soaked in isoflurane to maintain anaesthesia while handling them. We fitted all rats weighing  > 110 g with a V1C 118B VHF radio-collar (Lotek, Havelock North, New Zealand). We marked each collared rat with a unique pelage code using a permanent blonde hair dye60. We also recorded biometrics, including sex, weight, and length. When processing was finished, we placed the rat into another container to recover. This container had a heating pad for warmth and an apple for food to avoid a drop in body temperature and hypoglycemia, which are common problems with anaesthesia62. When the rat appeared mobile, energetic, and behaving normally, we released it at the point of capture.We monitored radio-collared rats using a Yagi antenna (Lotek, Havelock North, New Zealand) and a Telonics R-1000 receiver (Telonics Inc., Mesa, Arizona, USA). We conducted radio-telemetry work during August–November 2020, with fixes taken during the day and night. We recorded a total of three fixes per rat per night, taken at two-hour intervals between the hours of sunset (2200 h) and sunrise (0500 h). We mostly attempted one day-time fix (1200 h); however, if a tracked rat was active (determined by a VHF signal that was moving or changing amplitude), we attempted a second fix in the afternoon. To minimize location error, we used the close approach radio-tracking method described by63. Once a successful fix was made, we used a handheld GPS unit to record the location, date, and time. Telemetry fixes were collected for each radio-collared rat for 18–97 days.After approximately one week of radiotracking an animal, we obtained an initial crude estimate of the center of each rat’s home range as the mean of all eastings and northings (based on a minimum of 15 telemetry points per rat). A bait station baited with non-toxic pellets (Protecta Sidekick bait stations, Bell Laboratories Inc., Windsor, Wisconsin, USA), a WaxTag with a peanut butter odor incorporated into the wax (PCR WaxTags, Traps.co.nz, Rolleston, New Zealand), and a chew card (a corflute card baited with peanut butter) were deployed at varying distances (max. 50 m) and cardinal directions from the estimated home range center of each individual rat. This layout maximized the likelihood of encounters with devices, compared with a regular grid-type deployment where some of the devices could fall outside a collared rat’s home range and thus never be encountered. Note that the crude estimate of the location of the home range center for each rat was only used to guide device placement, i.e., it was not used in any statistical analyses, or to describe rat home range sizes. Further, to avoid a choice-type experiment (i.e., all three devices set immediately next to each other), we randomly assigned a distance and cardinal direction to each device type within each rat’s home range but ensured all devices were deployed  > 15 m apart. The three device types were chosen because they are used by Predator Free Wellington to conduct their eradication operations.Every deployed device had a trail camera (Browning Strike Force HD Pro Micro Series, Morgan, Utah, USA) taking video of rats encountering and interacting with the device. We set cameras to take 20 s of video footage when triggered, followed by a 1 s re-trigger interval. We fixed trail cameras to trees at a height of 50 cm above ground level and placed the devices 1.5 m in front of the camera (after64). This strategy allowed accurate identification of pelage codes on marked rats. We cleared vegetation in front of and immediately behind the trail cameras to avoid accidental triggers. We used pegs to mark a 30-cm-radius circle around each device and considered a rat–device encounter when a rat entered that circle. We serviced trail camera–device pairs at least once every three days. This included adding more non-lethal bait to bait stations and peanut butter to monitoring devices, installing new WaxTags or chew cards if they had been destroyed, and replacing batteries and SD cards in trail cameras. We set up 54 trail camera–device pairs. However, due to trail camera malfunctions, we were able to retrieve footage from only 38 cameras, 8 in Kelburn and 30 in Roseneath. Trail camera–device pairs were active for 20–70 days, but we retained data from only the first 20 days for the analyses.Video processingAll video footage was viewed and interpreted by the same individual (HRM) for consistency. We extracted the following information: date and time of rat sightings, rat ID (according to the pelage code, or designated as ‘R’ for unmarked rats), the duration of the visit to a device, whether or not an encounter occurred (as defined above), and whether or not an interaction occurred. We defined an interaction as a rat either gnawing on a chew card or WaxTag or entering a bait station.Data analysisWe combined all ship rat telemetry data with the device encounter and interaction data, and developed a hierarchical Bayesian model to infer factors influencing the key parameters σ, ε0, and θ. The analytical approach builds on that described in65. For the purpose of estimating ε0 and θ, multiple encounters or interactions by the same individual with the same device on the same night were counted as a single encounter or interaction.The VHF telemetry data Zij were composed of xij (eastings) and yij (northings) locations for each individual rat i at site j (either Kelburn or Roseneath). To simplify the notation, we drop the j subscript from all subsequent equations. We modelled the probability of observing Zi as a symmetric bivariate normal variable$$P({Z}_{i})= prod_{i=1}^{{L}_{i}}Normal(Delta {x}_{i}|0,{sigma }_{i}^{2})Normal(Delta {y}_{i}|0,{sigma }_{i}^{2})$$
(1)
where σi is the standard deviation of a normal distribution with zero mean, Li is the number of location fixes for individual i, and Δxi and Δyi are the straight-line distances from the home range center of individual i to xi and yi, respectively.Home range centers can be estimated using various methods, all of which have underlying assumptions (e.g.,66,67). We calculated the home range center for each individual as the mean of all xi and yi, i.e., the centroid of all locations that we recorded for each individual ( > 30 VHF fixes in all instances). Under this formulation, the home range center is assumed to be perfectly observed, an assumption that is supported by the sample size of telemetry locations that we obtained for each individual (see Supplementary Table 266).We modelled σi as a log-normal variable with mean ln(μi), which was a function of the sex of the individual:$$lnleft({sigma }_{i}right)sim Normal(mathit{ln}left({mu }_{i}right), V)$$
(2)
$$lnleft({mu }_{i}right)= {beta }_{0}+ {beta }_{1}{sex}_{i}$$
(3)
where V is the variance of ln(σi), and ln(μi) is a linear function of a categorical variable indicating whether rat i is a male (0) or a female (1). The priors on the β coefficients and V were Normal(0, 10) and InverseGamma(0.01, 0.01), respectively.The encounter data (Eimt) across all devices m and nights t was modelled as a Bernoulli process:$${E}_{imt}sim Bernoulli({gamma }_{imt})$$
(4)
$$logitleft({gamma }_{imt}right)sim MultivariateNormal(logitleft({P}_{imt}right), varSigma )$$
(5)
where γimt is a latent variable representing the degree to which the nightly probability of rat i encountering a given device is not independent of the encounter outcomes of nearby devices, i.e., we assumed there is spatial autocorrelation in the nightly probability of encountering a device. To account for the spatial autocorrelation not explained by the covariates explicitly modelled (i.e., σ and device type, see below), we included an exponential spatial covariance error structure (Σ) as follows:$$varSigma = {nu }^{2}{e}^{-varphi r}$$
(6)
where ν2 is the variance, φ is a correlation distance parameter, and r is the distance (in m) between pairs of devices68,69. Further, because not all devices were available on all nights, Σ was calculated iteratively for each night considering only those devices that were available. We used moderately informative log-normal priors for the covariance parameters to obtain proper posteriors69: ν2 ~ logN(3,1) and φ ~ logN(1,1).The nightly probability of encounter of device m by individual i on night t (Pimt) was calculated using a half-normal detection function70:$${P}_{imt}= {{left({varepsilon }_{0, im}{e}^{left(-frac{{d}_{im}^{2}}{2{sigma }_{i}^{2}}right)}right)}^{{tau E}_{it}^{*}}}times {{left({varepsilon }_{0,im}{e}^{left(-frac{{d}_{im}^{2}}{2{sigma }_{i}^{2}}right)}right)}^{1-{E}_{it}^{*}}}$$
(7)
where ε0,im is the maximum nightly probability of encounter for device m, or the probability if device m was placed at the center of the home range of rat i. The variable σi is the standard deviation from Eq. (1) (i.e., σi is estimated jointly from the telemetry and encounter data) and dim is the distance (in m) between the home range center of rat i and device m; only devices within a distance of 3.72σi from the home range center were considered in the calculation in Eq. (7)70. Finally, τ is a strictly positive parameter (i.e., τ  > 0), measuring the degree of device-shyness, which is multiplied by an indicator variable (left({E}_{it}^{*}right)) which takes a value of 0 when individual i has not encountered a device (of any type) on nights prior to night t, or a value of 1 if it had previously encountered one, regardless of the type of device it encountered. If τ  1 then rats are ‘device-shy’ and thus more likely to avoid devices on nights following an initial encounter. ({E}_{it}^{*}) was reset to 0 after 20 days of no encounters with a device. Following65 we set the prior on τ as Gamma(0.933, 8.33) (shape and rate parameters, respectively).Values of ε0,im were predicted as a function of σi, device type, and individual effects using the following equation:$$logitleft({varepsilon }_{0, im}right)={alpha }_{0}+ {alpha }_{1}mathrm{ln}left({sigma }_{i}right)+ {alpha }_{2}{chewcard}_{m}+{alpha }_{3}{waxtag}_{m}+{delta }_{i}$$
(8)
where α2 and α3 quantify the increase or decrease in the maximal probability of encountering a chew card or a WaxTag relative to a bait station (which is the reference category). The δi parameters account for individual differences in ε0. Finally, we allowed ε0 to be a function of ln(σi) because we assumed encounter probability at home range center will decrease with increasing home range size (as suggested by71 and shown by65). The priors on the α coefficients and δ were Normal(0, 10) and Normal(0, 1), respectively.The interaction data (Iimn) across all devices m and nights n when encounters occurred was modelled as a Bernoulli process with probability θ, which was a function of device type and individual effects:$${mathrm{I}}_{imn}sim Bernoullileft({theta }_{imn}right)$$
(9)
$$logitleft({theta }_{imn}right)={lambda }_{0}+ {lambda }_{1}{chewcard}_{m}+{lambda }_{2}{waxtag}_{m}+{lambda }_{3}{I}_{in}^{*}+{rho }_{i}$$
(10)
where θimn is the probability of rat i interacting with device m given that it has encountered it on night n, and λ1 and λ2 quantify the increase or decrease in the conditional probability of interaction for a chew card or a WaxTag relative to a bait station. The λ3 parameter is analogous to τ in Eq. (7) but for the process of interaction given encounter with a device. However, by incorporating λ3 directly into a linear equation, this parameter can take negative values and thus should be interpreted differently to τ: if λ3  0 indicates that individuals become ‘device-happy’ after an initial interaction. This parameter is multiplied by an indicator variable ({(I}_{in}^{*})) which takes a value of 0 when individual i has not interacted with a device (of any type) on nights prior to night n, or a value of 1 when it has interacted with one previously, regardless of the type of device it interacted with. If a rat had not interacted with a device for 20 days, ({I}_{in}^{*}) was reset to 0. Finally, the ρi parameters account for individual differences in θ. The priors on the λ coefficients and ρ were Normal(0, 10) and Normal(0, 1), respectively. Although we explicitly modelled spatial autocorrelation in the probability of encountering a device, we did not do so for the probability of interaction given an encounter. In this instance we assumed that whether an animal chose to interact with an encountered device would depend on its previous experience (as quantified by λ3) rather than the spatial location of nearby devices.We used Markov Chain Monte Carlo (MCMC) simulation to estimate model parameters using Python programming language. The variance parameter V was sampled from the full conditional posteriors, but all other parameters were estimated using the Metropolis algorithm69. Posterior summaries were taken from four chains containing 3000 samples each (with a burn-in of 2000 and a thinning rate of 30). Convergence on posteriors was assessed by visual inspection and a scale reduction factor  More

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Departamento de Ecología, Universidad Autónoma de Madrid, Madrid, SpainManuel B. Morales & Juan TrabaCentro de Investigación en Biodiversidad y Cambio Global, Universidad Autónoma de Madrid, Madrid, SpainManuel B. Morales, Juan Traba & Elena D. ConcepciónMuseo Nacional de Ciencias Naturales, CSIC, Madrid, SpainMario Díaz & Elena D. ConcepciónConservation Biology Group, Landscape Dynamics and Biodiversity Program, Conservation Biology Group (GBiC), Forest Science and Technology Centre of Catalonia (CTFC), Solsona, SpainDavid Giralt, Francesc Sardà-Palomera & Gerard BotaInstituto de Investigación en Recursos Cinegéticos (CSIC-UCLM-JCCM), Ciudad Real, SpainFrançois Mougeot & Beatriz ArroyoEstación Biológica de Doñana, CSIC, Sevilla, SpainDavid SerranoDepartament de Biologia Evolutiva, Ecologia i Ciències Ambientals, Facultat de Biologia, Universitat de Barcelona, Barcelona, SpainSanti MañosaInstitut de Recerca de la Biodiversitat (IRBio), Universitat de Barcelona, Barcelona, SpainSanti MañosaUSC 1339 Centre d’Etudes Biologiques de Chizé, INRAE, CNRS & Université de La Rochelle, F-79360, Villiers-en-Bois, FranceSabrina GabaUMR 7372 Centre d’Etudes Biologiques de Chizé, CNRS & Université de La Rochelle, F-79360, Villiers-en-Bois, FranceSabrina GabaCIBIO/InBio–University of Porto and Institute of Agronomy–University of Lisbon, Lisbon, PortugalFrancisco MoreiraSwedish University of Agricultural Sciences, Uppsala, SwedenTomas PärtSustainable Forest Management Research Institute (iuFOR), Universidad de Valladolid & INIA, Valladolid, SpainRocío Tarjuelo More