The experiment was undertaken on six 12-ha live trapping grids at two different locations. Three sites were established in the Orongorongo Valley, east of Wellington (174°58′E, 41°21′S), and three in the Turitea catchment, east of Palmerston North (175°41′E, 40°26′S), New Zealand. Sites were established in October–November 1995 in native podocarp/hardwood forest. Vegetation in the Orongorongo Valley was dominated by emergent species Metrosideros robusta A. Cunn., Dacrydium cupressinum Lamb., Prumnopitys ferruginea D. Don. and Prumnopitys taxifolia D. Don. (Fitzgerald 1976; Campbell 1990; Ramsey et al. 2002). The forest canopy was between 6 and 20 m and comprised mainly Elaeocarpus dentatus J. R. Forst. & G. Forst., Laurelia novae-zelandiae A. Cunn., Melicytus ramiflorus J. R. Forst. & G. Forst., Hedycarya arborea J. R. Forst & G. Forst., Knightia excelsa R. Br., Weinmannia racemosa L. f., Schefflera digitata J. R. Forst. & G. Forst., Pseudowintera axillaris J. R. Forst. & G. Forst. and five species of tree fern. The area also included stands of kanuka Kunzea ericoides A. Rich. and hard beech Nothofagus truncata Col. Ckn. The Turitea catchment site was situated in the Tararua ranges near Palmerston North and had vegetation comprising remnant podocarp/kamahi forest now dominated by a canopy of Beilschmiedia tawa A. Cunn. with associated Melicytus ramiflorus, Hedycarya arborea, Knightia excelsa and scattered Dacrydium cupressinum and Prumnopitys ferruginea (Esler 1969). At each site, between 132 and 150 cage traps were placed on a marked grid at 30 m spacing. Populations in the Orongorongo Valley typically have one birth pulse per year in autumn (March–July), while populations in the Turitea catchment have been observed to have an occasional second, smaller pulse of breeding in spring (September–December) (D. Ramsey, unpublished data).
Trapping followed the robust design (Pollock 1982; Nichols & Pollock 1990), with each population trapped for a minimum of three primary sessions a year with each primary session consisting of secondary sessions of four or five consecutive nights trapping. Trapping started on all sites during October–November 1995 and continued until October 2000. The exception was the control site in the Orongorongo Valley, which has been continuously trapped since 1966 (Crawley 1973; Efford 1998). Newly caught possums were anaesthetized with ether (1995–99) or 50–100 mg ketamine hydrochloride (2000) (Parnell Laboratories New Zealand Ltd, Auckland, New Zealand) by intramuscular injection and given a unique tattoo and ear tag. Before the animal was released at the point of capture, measurements were taken that included head, body and total lengths; testis length and width for males; weight and tooth wear. For females, an estimate of breeding success was made in late June by examining the pouch for young. Head lengths of pouch young were measured to estimate date of birth (Efford 1998) by assuming a head length at birth of 7 mm and a linear growth rate of 0·27 mm day−1 (Orongorongo Valley) or 0·35 mm day−1 (Turitea) (D. Ramsey, unpublished data). Pouch young caught with their mothers in September–October were usually large enough to tag. Recaptured animals were identified and weighed before being released. Animals not first caught with their mother were assigned a minimum age using a logistic regression algorithm discriminating on body-size measurements. Separate regressions were constructed for Orongorongo Valley and Turitea using possums whose birth cohorts were known. Independent possums were classified as either yearlings (= 20 months old) or adults (> 20 months old) (Efford 1998).
Fertility control was imposed by surgically sterilizing females by ligating the oviducts. This method ensured ovarian function remained intact and mimicked the action of the most likely candidate fertility control vaccines. Three levels of sterilization treatment were applied, with 0%, 50% or 80% of adult females at a particular site sterilized. As the effect of surgery on survival of animals was unknown, sham operations (no sterilization) were undertaken to balance the level of surgical manipulation across treatments. However, no sham operations were undertaken on the Orongorongo Valley control (0% sterility) site, so that consistency could be maintained with the previous long-term monitoring data collected at this site. Two replicates of each treatment were undertaken, with one complete replicate at sites in the Orongorongo Valley and one replicate in the Turitea catchment. Treatments were assigned to sites within each area at random, with the exception of the control site in the Orongorongo Valley. Sterilization treatments were applied during January–April 1996, with adjustments to maintain sterility levels made annually on recruits. All trapping and surgical procedures were approved by the Landcare Research Animal Ethics Committee, Lincoln, New Zealand.
decomposition of the annual population growth rate
A retrospective analysis (Caswell 2000) was undertaken to determine the relative contribution of demographic parameters (survival, recruitment) to the annual population growth rate (λ). Trapping undertaken in September–October was chosen as the annual census date because pouch young were marked with their mothers during this period. Capture data for the intervening periods were not used. Here λ is the realized annual growth rate rather than the asymptotic growth rate derived from population projection matrices (Caswell 2001), and is defined as:
(eqn 1 )
where λi is the population growth rate during year i, and Ni and Ni+1 are the population abundance estimates in year i and i + 1, respectively. Following Nichols et al. (2000), λ can be decomposed into contributions from survivors and new recruits as:
(eqn 2 )
where γi+1 is the probability that a member of the population at time i + 1 (Ni+1) was a member of the population at time i (Ni) (e.g. survivors from time i), and hence (1 − γi+1) is the probability that a member of the Ni+1 was recruited between time i and i + 1. Thus, the γi+1 can be regarded as a measure of the relative contribution of survivors and recruits to population growth between years i and i + 1 (Nichols et al. 2000; Nichols & Hines 2002).
Recruitment into a population can potentially come either from reproduction from resident females (local recruitment) or from animals arriving from outside the study population (immigration). In order to decompose λ into contributions from local recruitment, immigration and survival, it is necessary to condition on age structure, as recruitment into the next age class that cannot be explained by survival from the previous age class must be a result of immigration (Stokes 1984; Nichols & Pollock 1990). Three age classes were considered in the analysis: pouch young, dependent young first caught with their mothers and tagged at approximately 8 months old; yearlings, possums first caught in the year following their birth at approximately 20 months old; and adults, all possums approximately ≥ 32 months old.
The relative contribution (γ) of demographic parameters (survival, fecundity/local recruitment and immigration) of each age class to the annual population growth rate λ was estimated using methods detailed in Nichols et al. (2000). This retrospective analysis uses reverse-time capture–recapture analysis to estimate γ. By reversing the time order of capture history data, inference can be made on the recruitment process, which is statistically equivalent to inference on the survival process using forward time (Pollock, Solomon & Robson 1974; Pradel 1996). However, the analysis of the contribution of different demographic components to λ for age-structured data is not straightforward (Nichols et al. 2000). For example, using reverse-time capture–recapture, it was desirable to condition on animals caught as yearlings at time i + 1 and estimate the probabilities that those animals were either pouch young of resident females at time i (γi+1) or new immigrants arriving between time i and i + 1 (1 − γi+1). As there were three age classes, the population growth rate given in equation 1 can be partitioned into two components. The population growth rate of adults is given as:
(eqn 3 )
where and are the population abundance of adults in year i and i + 1, respectively. The population growth rate of the yearling component is given by:
(eqn 4 )
where and are the population abundance of yearlings in year i and i + 1, respectively. The (a = 2, 1) was estimated using the jack-knife closed population estimator (Burnham & Overton 1978), which is robust to individual heterogeneity in capture probabilities. Estimates of and and their sampling variance in each year were obtained using a bootstrap procedure. For each age class within each primary trapping session, a random sample of the capture histories over the secondary capture periods was selected (with replacement), conditional on the total number of individuals captured. The ratio of 50 bootstrap jack-knife estimates of abundance in year i + 1 and year i was used to generate 2500 estimates of the population growth rate. The mean and standard error of the population growth rate was estimated as the mean and standard deviation of these 2500 bootstrap estimates. An estimate of the overall average population growth rate over the study period was made by fitting a linear regression to the natural log of the jack-knife abundance estimates of the total population in September–October each year. The average growth rate () was estimated as eb, where b was the slope of the regression line (Caughley 1977).
The decomposition of is given by the following expression (Nichols et al. 2000):
(eqn 5 )
where is the population growth of adult possums during the ith year; is the probability that an adult possum alive at time i + 1 was in the adult population at time i; is the probability that an adult possum alive at time i + 1 was in the yearling population at time i; and is the probability that an adult possum alive at time i + 1 immigrated between time i and i + 1. Similarly, the decomposition of the population growth rate of the yearling subpopulation can be expressed as:
(eqn 6 )
where is the annual population growth rate of yearling-aged possums during the ith year; is the probability that a yearling possum alive at time i + 1 was a dependent pouch young at time i; and is the probability that a yearling possum alive at time i + 1 immigrated between time i and i + 1. These [rs = 22, 21 or 10, referring to either age classes 2 (adults), 1 (yearlings) or 0 (pouch young)] were estimated using the closed-form maximum likelihood estimators (MLE) detailed in Nichols et al. (2000), for example:
(eqn 7 )
and are the members of the that were caught as members of the where n is the total number of animals caught in periods i or i−1 for either age class r or s. The capture probability parameter in equation 7 is specific to reverse-time analysis and is calculated as:
( eqn 8 )
where is the capture probability for age class s at period i using conventional forward time modelling, and is the probability that an animal of age class s captured at period i survives trapping and handling and is released (Nichols & Hines 2002). Equations 7 and 8 were used to produce unbiased estimates of in the presence of losses on capture. During 1998 and 1999 an attempt was made to limit the influx of immigrant yearling possums on sterility grids by removing a proportion of unmarked yearlings during the October trapping session. This attempt was largely unsuccessful. However, not accounting for losses on capture could produce biased estimates of as the yearling possums that were removed could not be seen again as adults. When there are no losses on capture the forward-time and reverse-time estimates of capture probability are equal (Nichols & Hines 2002).
Estimation of and was relatively straightforward, with the forward-time capture probability for adults and yearlings estimated by fitting Cormack–Jolly Seber (CJS) models, conditioning on age at first capture using the program mark (White & Burnham 1999). Models were fitted that allowed for both time-dependent and time-independent age-specific capture probability, noting that the capture probability of pouch young cannot be estimated (e.g. a possum released as a pouch young that survived over the next year interval is caught as a yearling). Only models with time-dependent age-specific survival rates were considered as part of the candidate set of models. The set of models was ranked using methods detailed in Burnham & Anderson (1998) using Akaike's information criterion adjusted for sample size (AICc). The most general model considered (time-varying age-specific survival and capture probability) was tested for goodness-of-fit using the parametric bootstrap test in program mark. The overdispersion parameter c was estimated by dividing the observed deviance of the general model by the mean of 100 bootstrap samples. Models were corrected for overdispersion using this estimate of c, and the fit of all the models considered was compared using Akaike's information criterion corrected for overdispersion (QAICc) by taking the difference between all models and the model with the lowest QAICc (Burnham & Anderson 1998; White & Burnham 1999). The relative support for each of the candidate models was assessed by calculating normalized Akaike weights (wi) (Burnham & Anderson 1998). Once estimates of were obtained, was estimated using data on losses-on-capture (see Appendix 2) to estimate .
In order to estimate , it is necessary to have information on capture probability of pouch young that is not directly available from standard age-structured models. Capture probability of dependent pouch young can be estimated from an approximation of the total size of the pouch young cohort:
(eqn 9 )
where is the number of pouch young tagged with their mother, and is an estimate of the total size of the pouch young cohort. This was obtained using:
(eqn 10 )
where and are the total number of yearling and adult female possums caught at time i, respectively; and are the breeding rates of yearling and adult female possums, respectively; and and are the capture probabilities of female yearling and adult possums, respectively, obtained from the conventional age-structured CJS analysis applied to capture histories for female possums.
An estimate of sampling variance for each of the MLE of the was obtained by a bootstrapping procedure. Conditioning on each of the releases at time i, capture histories were simulated in reverse time using the point estimates of the and age-specific capture probabilities. For each individual in each , a random uniform number between 0 and 1 was drawn and compared with the appropriate . If the random number was less than the estimate the animal was deemed to have been present at time (i – 1), if otherwise it was not. If the animal was present at time interval (i – 1) another random number was drawn and compared with the appropriate capture probability estimates from the forward-time age-structured model . If the random number was less than the estimated capture probability, the animal was assumed to have been caught at time interval i−1 and thus was entered as a member of the . The and simulated were used to calculate the and, hence, an estimate of the using equation 7. This bootstrapping process was repeated 1000 times for each , with the standard error estimated as the standard deviation of the 1000 bootstrap estimates.
Once estimated, the values of , and were compared between sterility treatments using generalized linear models. A binomial error structure was assumed by using a logit link function, with the number of releases for each time period used as weights for each value of . The rate of increase was included in the analysis as a covariate, to determine whether year-to-year variation in was dependent on the age-specific rate of increase. Area (Orongorongo or Turitea) was also included as a fixed effect in the analysis.
Finally, estimates of were used to make an estimate of per capita local recruitment, defined as the number of pouch young born in year i surviving to the yearling age class in year i + 1 per adult female in year i, thus:
(eqn 11 )
where is the per capita rate of local recruitment, is the jack-knife estimate of abundance of yearling possums in year i + 1, and is the jack-knife estimate of abundance of adult female possums in year i. The sampling variance of B̂i was calculated using the delta method (Seber 1982) as:
( eqn 12 )
This assumes that each of the random variables is independent.