Population dynamics of brushtail possums subject to fertility control

Authors


Dave Ramsey, Landcare Research, Private Bag 11052, Palmerston North, New Zealand (fax + 64 6355 9230; e-mail ramseyd@landcareresearch.co.nz).

Summary

  • 1Reducing the fertility of pest species using immunocontraceptive vaccines holds promise for the humane and effective control of vertebrate pest populations. However, despite much research into the development of contraceptive vaccines, there are few data illustrating the effectiveness of fertility control for managing wild populations of vertebrate pests.
  • 2In New Zealand, introduced brushtail possums Trichosurus vulpecula have been the focus for the development of contraceptive vaccines to provide a possible alternative to lethal control techniques.
  • 3The effect of fertility control on the population dynamics of brushtail possums was investigated experimentally using surgical sterilization to suppress breeding on six 12-ha study sites between January 1996 and October 2000. Sterilization treatments, consisting of 0%, 50% and 80% of resident females sterilized, were applied at a particular site, with adjustments made annually on recruits to maintain levels of sterility. Mark–recapture trapping was used to estimate age-specific demographic rates and their relative contribution to age-specific population growth rates (λ).
  • 4Sterility treatments resulted in reductions to per capita rates of local recruitment (surviving young per adult female) of 60% and 74% on average for 50% and 80% levels of sterility, respectively. However, immigration by yearling-aged possums compensated for reductions in local recruitment because of sterility treatments, leading to the stable (λ = 1) population trajectories on sterility treatment sites.
  • 5There was some evidence that sterilized females had higher annual survival rates than fertile females, but otherwise there was no evidence of any other compensatory responses to imposed sterility. However, additional studies are needed to clarify possible density-dependent responses that could compensate for the effects of fertility control.
  • 6Synthesis and applications. Demographic compensation by pest populations can negate the effects of fertility control. Results from this study suggest that immigration can easily compensate for fertility control in pest species where adult survival is high and fecundity is low. This suggests that fertility control will need to be applied at large spatial scales to reduce this effect. Where adult survival makes a relatively high contribution to the population growth rate, the benefits of fertility control would be enhanced if integrated with conventional control to provide rapid initial population reduction.

Introduction

Australian brushtail possums Trichosurus vulpecula Kerr, introduced into New Zealand in the 1850s to establish a fur trade, are now a serious pest (Clout & Sarre 1997; Clout & Erickson 2000) and the main wildlife vector for bovine tuberculosis (Tb), which they transmit to livestock (Caley et al. 1999). Current methods of managing possums in the wild usually involve the use of poison bait, spread over large areas. While this method is effective, it is often costly and needs continual maintenance to give long-lasting results. There are increasing concerns about possible effects on non-target populations and public health, as well as ethical considerations (Morgan & Hickling 2000). For these reasons, research is currently aimed at developing fertility control using contraceptive vaccines for possums, to provide a possible alternative long-term, cost-effective solution. Current research is mainly directed at reducing fertility by developing immunological blocks to fertilization or embryonic development (Cowan 1996; Cowan 2000), or manipulating hormonal regulation and gonadal development (Eckery et al. 1998).

While fertility control is seen as a possible solution to public concerns and animal welfare issues surrounding conventional lethal control, there are few data illustrating its effectiveness as a management tool. Models of fertility control in mammals suggest it will be relatively more effective on species with high fecundity and shorter lifespan (Hone 1992), and hence is predicted to be less effective on marsupials compared with eutherians, as marsupials generally have lower birth rates and higher survivorship than eutherians (Sinclair 1997). Models of fertility control for brushtail possums suggest the expected level of population suppression for a given sterilization rate is dependent on assumptions about the strength of density-dependent compensation, with fertility control being less effective if density-dependent compensatory responses operate through recruitment rather than adult survival (Barlow 1994; Barlow, Kean & Briggs 1997).

The mating system and social structure of the population may also influence the effectiveness of fertility control if they affect the birth and/or death rates (Caughley, Pech & Grice 1992; Barlow 2000). Ji, Clout & Sarre (2000) examined the responses of male possums in populations where 50% of the adult females were surgically sterilized. They found that surgically sterilized females continued to have oestrous cycles outside the normal breeding season. This resulted in an increase in the local density of males, which, it was hypothesized, were being attracted to the area because of the prolonged breeding activity. However, the potential effects of these behavioural and other compensatory responses to fertility control on the population dynamics of possums remain unknown. As compensatory increases in either adult or juvenile survival or immigration rates may compromise the efficacy of fertility control (Sinclair 1997), empirical evidence is needed on the magnitude of these responses (if any) before fertility control can be considered a viable management technique for brushtail possums.

To investigate the efficacy of artificially inhibiting the birth rate as an alternative control technique for brushtail possums, a field experiment was undertaken over 5 years to determine the effect of various levels of infertility (sterilized females) on population dynamics. Specifically, age-specific local recruitment, immigration and survival were estimated together with their relative contribution to the population growth rate (λ) for populations where either 50% or 80% of adult females had been made permanently infertile by surgical sterilization. Comparisons were made between these parameters and those on control sites where no sterility treatments were applied.

Materials and methods

study areas

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).

population monitoring

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).

sterilization treatments

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:

image(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:

image(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 ii+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:

image(eqn 3 )

where inline image and inline image are the population abundance of adults in year i and i + 1, respectively. The population growth rate of the yearling component is given by:

image(eqn 4 )

where inline image and inline image are the population abundance of yearlings in year i and i + 1, respectively. The inline image (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 inline image and inline image 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 (inline image) was estimated as eb, where b was the slope of the regression line (Caughley 1977).

The decomposition of inline image is given by the following expression (Nichols et al. 2000):

image(eqn 5 )

where inline image is the population growth of adult possums during the ith year; inline image is the probability that an adult possum alive at time i + 1 was in the adult population at time i; inline image is the probability that an adult possum alive at time i + 1 was in the yearling population at time i; and inline image 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:

image(eqn 6 )

where inline image is the annual population growth rate of yearling-aged possums during the ith year; inline image is the probability that a yearling possum alive at time i + 1 was a dependent pouch young at time i; and inline image is the probability that a yearling possum alive at time i + 1 immigrated between time i and i + 1. These inline image[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:

image

Where:

image(eqn 7 )

and inline image are the members of the inline image that were caught as members of the inline image 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 inline image in equation 7 is specific to reverse-time analysis and is calculated as:

image( eqn 8 )

where inline image is the capture probability for age class s at period i using conventional forward time modelling, and inline image 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 inline image 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 inline image as the yearling possums that were removed could not be seen again as adults. When there are no losses on capture inline image the forward-time and reverse-time estimates of capture probability are equal (Nichols & Hines 2002).

Estimation of inline image and inline image was relatively straightforward, with the forward-time capture probability for adults inline image and yearlings inline image 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 inline image were obtained, inline image was estimated using data on losses-on-capture (see Appendix 2) to estimate inline image.

In order to estimate inline image, it is necessary to have information on capture probability of pouch young inline image 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:

image(eqn 9 )

where inline image is the number of pouch young tagged with their mother, and inline image is an estimate of the total size of the pouch young cohort. This was obtained using:

image(eqn 10 )

where inline image and inline image are the total number of yearling and adult female possums caught at time i, respectively; inline image and inline image are the breeding rates of yearling and adult female possums, respectively; and inline image and inline image 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 inline image was obtained by a bootstrapping procedure. Conditioning on each of the inline image releases at time i, capture histories were simulated in reverse time using the point estimates of the inline image and age-specific capture probabilities. For each individual in each inline image, a random uniform number between 0 and 1 was drawn and compared with the appropriate inline image. 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 inline image. 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 inline image. The inline image and simulated inline image were used to calculate the inline image and, hence, an estimate of the inline image using equation 7. This bootstrapping process was repeated 1000 times for each inline image, with the standard error estimated as the standard deviation of the 1000 bootstrap estimates.

Once estimated, the values of inline image, inline image and inline image 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 inline image releases for each time period used as weights for each value of inline image. The rate of increase inline image was included in the analysis as a covariate, to determine whether year-to-year variation in inline image 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 inline image 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:

image(eqn 11 )

where inline image is the per capita rate of local recruitment, inline image is the jack-knife estimate of abundance of yearling possums in year i + 1, and inline image is the jack-knife estimate of abundance of adult female possums in year i. The sampling variance of i was calculated using the delta method (Seber 1982) as:

image( eqn 12 )

Where:

image

This assumes that each of the random variables is independent.

other analyses

The effect of the sterilization procedure on individual females was examined by comparing the annual survival of sterilized adult females with fertile adult females by fitting CJS models in the program mark. Sterile and fertile individuals were categorized by site, which was included as a fixed effect in the analysis. The goodness-of-fit of the ‘global’ model was assessed using the pooled chi-squared goodness-of-fit tests from tests 2 and 3 using program release (Burnham et al. 1987). Models for capture probability were fitted first, and included the interactive effects of site, sterility and time. The ‘best’ model of capture probability was then used to model survival and included the same effects. Models were ranked as previously using AICc and Akaike weights (Burnham & Anderson 1998; Burnham & Anderson 2001).

The breeding rate of fertile females was compared between sterility treatments using logistic regression (Collett 1991). Area (Orongorongo/Turitea) was fitted as a fixed effect in the model. The median birth date for pouch young born to resident females was similarly compared using anova. All analyses were performed using Splus 6·1 ( Insightful Corporation 2001).

Results

breeding statistics

Low breeding rates occurred on all sites during 1996, with only 24% and 45% of adult females breeding on control sites in the Orongorongo Valley and Turitea, respectively (Fig. 1a). However, in subsequent years treatment levels of sterility successfully suppressed breeding, with median levels of 69%, 30% and 14% of adult females breeding on control, 50% and 80% sterility sites, respectively (Fig. 1a). Accounting for the fixed effect of area (Orongorongo or Turitea), the rate of breeding in fertile females was similar among sterility treatments (logistic regression inline image = 0·79, P = 0·67; Fig. 1b) and, similarly, there were no significant differences in the median dates of birth (anovaF2,25 = 0·03, P = 0·97). The rate of spring breeding also did not appear to increase among fertile females at sites with imposed sterility (inline image = 1·7, P = 0·43). Thus, sterility treatments did not significantly influence either the rate or the timing of breeding in unsterilized females.

Figure 1.

Breeding parameter estimates for sterility treatment sites in the Orongorongo Valley and Turitea from 1996 to 2000. (a) The percentage of all adult females with dependent young in September–October of each year; (b) the percentage of adult fertile females with dependent young in September–October of each year.

population trajectories

Between 1996 and 2000, population abundance exhibited no strong upward or downward trend on any site, with the exception of the Turitea control (0% sterility) site, which averaged a 20% annual increase (Fig. 2a,b and Table 1). Overall, average population growth rates (inline image) were close to unity for all sterility treatment sites (Table 1).

Figure 2.

Jack-knife estimates of population abundance (N) in September–October of each year between 1996 and 2000 for (a) sterility treatment sites in the Orongorongo Valley, and (b) sterility treatment sites at Turitea. Open circles are the yearling subpopulation size and closed circles are the adult subpopulation size. Error bars are the 95% confidence limits.

Table 1.  The average population growth rate (inline image) between September and October each year from 1996 to 2000 for each sterility treatment site in each of the Orongorongo Valley and Turitea
 TuriteaOrongorongo
inline image(95% CI)inline image(95% CI)
Control1·21(0·977–1·49)1·01(0·851–1·20)
50%1·04(0·709–1·54)1·01(0·900–1·14)
80%1·01(0·794–1·30)1·06(0·847–1·318)

decomposition of the annual population growth rate

Forward-time CJS models fitted to mark–recapture data from the September–October trapping sessions each year to estimate annual age-specific capture probabilities indicated that models with capture probability constant across time and age classes, but differing for each site, were the most preferred based on ΔQAICc and Akaike weights.

The relative contributions to the adult population growth rate of adult survivors (inline image), yearling recruits (inline image) and immigrants (inline image) and their bootstrap standard errors in each year are given in Appendix 1. Logistic regression analysis of inline image revealed no significant differences between sterility treatments. However, there were significant differences between areas and a significant effect because of inline image (Table 2). Similar analysis for inline image revealed no significant differences as a result of sterility treatment, area or inline image (Table 3). Survival of adults from the previous year (inline image) made the dominant contribution to the adult population growth rate, contributing around 65% to the adult population growth rate when inline image was high (1·3 year−1) and around 79% when inline image was low (0·9 year−1) (Fig. 3). Recruitment of resident yearling-aged animals (inline image) made a minor contribution to the growth rate of adults, especially on sites in the Orongorongo Valley (Fig. 4).

Table 2.  Results from logistic regression analysis of the effects of area [Orongorongo Valley (OV) and Turitea (TU)], adult population growth rate (inline image) and sterility treatment on the proportional contribution of adult survivors to the adult population growth rate (inline image)
TermD.f.DevianceResidual d.f.Residual devianceP
Null  23163·5 
Area (OV or TU)1 8·622154·9< 0·01
inline image172·721 82·2< 0·01
Sterility treatment2 3·419 78·8   0·19
Table 3.  Results from logistic regression analysis of the effects of Area [Orongorongo Valley (OV) or Turitea (TU)], adult population growth rate (inline image) and sterility treatment on the proportional contribution of yearling recruits to the adult population growth rate (inline image)
TermD.f.DevianceResidual d.f.Residual devianceP
Null  2314·7 
Area (OV or TU)13·12211·70·08
inline image10·42111·30·53
Sterility treatment22·319 8·90·31
Figure 3.

Predicted values from a logistic regression model of the effects of area (Orongorongo and Turitea), adult population growth rate (inline image) and sterility treatment on the proportional contribution of adult survivors to the adult population growth rate (inline image). Predicted values are for each level for each categorical variable (area, sterility treatment) and for the upper and lower quartile of the observed values for inline image. Error bars are the standard error.

Figure 4.

Predicted values from a logistic regression model of the effects of area (Orongorongo and Turitea), adult population growth rate (inline image) and sterility treatment on the proportional contribution of local yearling recruits to the adult population growth rate (inline image). Predicted values are for each level for each categorical variable (area, sterility treatment) and for the upper and lower quartile of the observed values for inline image. Error bars are the standard error.

The relative contributions to the yearling population growth rate of recruitment of locally born young (inline image) and yearling immigrants (1 − inline image) and their bootstrap standard errors in each year are given in Appendix 1. Logistic regression analysis of the contribution of local recruits to the yearling population growth rate revealed that inline image differed significantly because of the additive effects of area, inline image and sterility treatments (Table 4). Local recruitment made the dominant contribution to the yearling growth rate on control sites, predicted to contribute 51% to the growth rate of yearlings when inline image was low (0·5 year−1) and 41% when inline image was high (2·5 year−1) (Fig. 5). In comparison, local recruitment on 50% and 80% sterility sites was predicted to contribute only 21% and 19%, respectively, when inline image was low, and 14% and 13%, respectively, when inline image was high (Fig. 5).

Table 4.  Results from logistic regression analysis of the effects of area [Orongorongo Valley (OV) or Turitea (TU)], yearling population growth rate (inline image) and sterility treatment on the proportional contribution of locally born young to the yearling population growth rate (inline image)
TermD.f.DevianceResidual d.f.Residual devianceP
Null  2391·7 
Area (OV or TU)122·22269·5< 0·01
inline image1 6·82162·7< 0·01
Sterility treatment229·81932·8< 0·01
Figure 5.

Predicted values from a logistic regression model of the effects of area (Orongorongo or Turitea), yearling population growth rate (inline image) and sterility treatment on the proportional contribution of local recruitment to the yearling population growth rate (inline image). Predicted values are for each level for each categorical variable (area, sterility treatment) and for the upper and lower quartile of the observed values for inline image. Error bars are the standard error.

Because of the significant reductions in inline image as a result of sterility treatments, estimates of per capita local recruitment i were also reduced by sterility treatments. The number of offspring surviving until yearling age per adult female averaged 0·13 and 0·17 on control (0% sterility) sites in the Orongorongo Valley and Turitea, respectively, but only 0·03 and 0·05, respectively, on 80% sterility sites (Fig. 6). Estimates of i and their standard errors in each year are given in Appendix 1.

Figure 6.

Mean per capita local recruitment rates () for each sterility treatment site in the Orongorongo Valley and Turitea. Error bars are the standard error of the mean (n = 4).

Model selection results for CJS models fitted to estimate survival rates of sterilized and fertile females revealed that models of capture probability that included the interactive effects of site, sterility treatment and time (year) received the most support, as judged by ΔAICc values. Using this best model of capture probability, four survival rate models that included either the additive or interactive effects of site and sterility, and an additive effect of time, received the most support as judged by ΔAICc values (Table 5). Although average survival rates of sterile females were higher than fertile females at the same site (Fig. 7), the 95% confidence intervals (CI) for the sterility term in the model with the most support (S + St) overlapped 0 (inline image = 0·65; 95% CI = −0·03, 1·32 on a logit scale). A likelihood ratio test between this model and the more restricted model without the sterility term indicated a marginal level of significance (P = 0·09).

Table 5.  Model selection results for CJS models fitted to estimate apparent annual survival (φ) for adult fertile and sterile female possums. S, site effect; St, sterility effect; t, time (year) effect. Models are ranked according to differences between the model AICc and the model with the lowest AICc (ΔAICc). wi indicates the relative support (Akaike weights) for each model. The capture probability component of all models includes the interactive effects of all factors (e.g. S × St × t)
ModelDevianceKAICcΔAICcwi
φ(S + St)215·4381303·8 00·33
φ(S × St)213·9391304·5 0·700·23
φ(S)218·3371304·6 0·740·23
φ(S + St + t)212·3401305·2 1·350·17
φ(.)225·5361309·5 5·690·02
φ(S × t)199·5481310·5 6·640·01
φ(S + t)216·1411311·3 7·430·01
φ(St)225·5371311·7 7·880
φ(S × St + t)211·1441313·0 9·200
φ(St × t)218·4411313·5 9·710
φ(t)223·8391314·510·630
φ(St + t)223·6401316·512·710
φ(S × St × t)189·5551316·712·880
Figure 7.

Estimates of the mean annual apparent survival rates of intact (fertile) adult females (open circles) and sterile adult females (closed circles) for each sterility treatment site in the Orongorongo Valley and Turitea. Estimates are from model including the additive effects of site and sterility [φ(S + St)p(S × St × t)] (see text for details).

Discussion

The methods presented here for decomposing contributions to λ from different age classes differ slightly from the robust design approach given in Nichols et al. (2000). They advocate calculating age-specific capture probabilities using the ratio of the number caught to an estimate of population size using a closed capture estimator, for example:

image

where inline image, inline image and inline image are the capture probability estimate, total number caught and population size estimate, respectively, for age class a in primary capture session i. Unfortunately, this estimator did not prove to be very efficient when applied to the possum capture data, with imprecision in estimates of inline image leading to many estimates of γ greater than 1 (and estimates of 1 −γ less than 0). Applying conventional age-structured CJS models in forward time for the estimation of the inline image greatly ameliorated this problem, as model selection procedures could be employed. This analysis suggested that capture probabilities for yearling- and adult-aged possums could be adequately modelled using estimates of inline image that were constant across time and age classes. An alternative approach using joint likelihoods and multistate models under the robust design also allows the construction of reduced parameter models (Nichols et al. 2000). However, because of the complications of estimating capture probability and population size of pouch young (which was dependent on the capture probability, population size and breeding rate of their mothers), this was not attempted for the possum data set.

Permanent sterilization of a proportion of females successfully suppressed breeding rates, regardless of whether the population was a notionally spring breeding population or not. In both the Orongorongo Valley (no spring breeding) and Turitea (spring breeding), fertile females on sterility sites did not breed earlier and did not have an increased breeding rate compared with females on control sites. Levels of spring breeding were also similar between sterility treatments. Hence, there was no evidence that fertile females on sterility sites attempted to compensate for reduced productivity caused by sterilization treatments.

Population abundance exhibited no significant upward or downward trend over the duration of the study, with the exception of the control site at Turitea, which exhibited an average 20% annual increase. Thus, reductions in the birth rate because of sterility treatments did not result in population declines over the course of the study. Examining the contribution of population vital rates (births, survival and immigration) to annual population growth at each site revealed the contribution of underlying demographic processes driving annual population change.

Overall, sterility treatments suppressed per capita rates of local recruitment. In this context, local recruitment refers to both male and female young born in situ that survived until the late yearling stage (i.e. 20 months old) per adult female. Averaged over areas, the reduction in the per capita rate of local recruitment was 60% and 74% on 50% and 80% sterility treatments, respectively. The contribution of local recruitment to the population growth rate of yearlings was similarly reduced, but was dependent on the magnitude of the yearling population growth rate and differed among areas. The population growth rate of yearlings in year i (inline image) that would have occurred through local recruitment only can be calculated as inline image. These calculations show that local recruitment only would be inadequate to replace the disappearance of yearling-aged possums through death, emigration or recruitment to the adult age class on any site (Table 6). However, average population growth rates revealed that the yearling subpopulation was increasing, on average, over the course of the study on all sites (Table 6). On sterility treatment sites, immigration made the dominant contribution to the population growth rate of yearlings, compared with that made by local recruitment. On control sites, local recruitment made the dominant contribution to the population growth rate of yearlings on one site only (Orongorongo Valley). At Turitea, the contribution to the yearling population growth rate was dominated by immigration on all sites. However, the contribution by local recruitment to the yearling population growth rate on sterility treatment sites was reduced compared with that on the control site, because of the reduction in per capita rates of local recruitment by sterility treatments.

Table 6.  The average population growth rate of yearlings on control and sterility treatment sites predicted from local recruitment only (inline image) compared with the average population growth rate because of both local recruitment and immigration (inline image)
 OrongorongoTuritea
Local recruitment onlyIncluding immigrationLocal recruitment onlyIncluding immigration
Control0·941·510·251·60
50% sterility0·391·630·133·11
80% sterility0·091·960·121·20

This suppression of local recruitment indicates that the apparent survival rate of pouch young did not compensate for reductions in the birth rate because of sterility treatments. Hence, it is expected that the percentage suppression of local recruitment would be approximately linear with the percentage suppression of the birth rate as a result of sterility. The greater than expected suppression on 50% sterility sites, and the Turitea 50% sterility site in particular, was mainly because of the sterility rate on this site being higher than the nominal 50% over most of the study period (Fig. 1a). In addition, there were no compensatory increases in either the yearling recruitment to the adult population or the annual apparent survival rates of adults in terms of their contribution to the adult population growth rate. Hence, the only demographic response to artificial reductions in fertility has been compensatory increases in the immigration rate of yearling-aged possums, resulting in stable population trajectories (λ = 1). These results are in contrast to the studies of Twigg & Williams (1999) and Twigg et al. (2000) on the effect of sterility on wild rabbit populations in Australia, who found that local recruitment rates compensated for reductions in the birth rate as a result of sterility. One caveat to our conclusion, however, is that densities of possums on most sites have been relatively constant, because of the stabilizing effect of immigration. Hence, density-dependent compensation in local recruitment or adult apparent survival was unlikely to be observed.

The compensatory yearling immigration observed in this study suggests that yearling dispersers may be tuned to the local density of resident yearlings. Hence, a decision to ‘settle’ in a particular area may be partially based on an assessment of the number of resident yearlings, as an indication of the number of potential ‘vacancies’. This makes sense for a species with high adult survival, where existing resident yearlings could rapidly fill any vacancies caused by turnover in the adult subpopulation. However, the rules governing settlement decisions by dispersing possums remain speculative (Efford 1996; Efford 1998). However, if true, this mechanism governing settlement by dispersing yearlings could have direct implications for the operational success of fertility control, as spatial variation in fecundity (i.e. spatial variation in the proportion sterilized) is likely to be inversely related to the settlement patterns of dispersing yearling possums that will limit the overall effectiveness of fertility control. Spatial variation in the proportion sterilized is likely where vectored immunocontraception is used (Barlow 1994) and there is spatial aggregation of the vector. Likewise, fertility control applied at too small a spatial scale would be nullified by immigration.

Comparisons of the survival rates of fertile and sterile females suggested that sterile females had higher survival rates. Such a finding is expected if there are significant costs to reproduction, and is similar to the results observed for the effect of sterility on female rabbit survival (Twigg et al. 2000). Theoretical studies of fertility control have explored the potential for changes in a population's vital rates to compensate for reductions in the birth rate (Bomford 1990; Caughley, Pech & Grice 1992; Barlow, Kean & Briggs 1997; Sinclair 1997; Hobbs, Bowden & Baker 2000; Hood, Chesson & Pech 2000; Davis & Pech 2002). Generic stage-structured modelling undertaken by Davis & Pech (2002) suggested the overall response of populations to fertility control was critically dependent on the role of sterilized females in density-dependent processes. If sterile females are not involved in any density-dependent process then they accumulate in the population without (negatively) influencing the population growth rate. Such a scenario can lead to fertility control, resulting in higher populations than uncontrolled populations (Davis & Pech 2002). However, such a scenario is unlikely for brushtail possums as the existing evidence suggests possums are regulated primarily by extrinsic rather than intrinsic mechanisms (i.e. competition for food resources) (Thomas et al. 1993; Ramsey et al. 2002). Thus, sterile females are expected to play a role in any exploitative competition for food and therefore should contribute to any density-dependent response.

Presently, there are no data on the probable magnitude of compensatory responses to fertility control in brushtail possums at reduced population density. As the most likely scenario for practical application of fertility control is following an initial population reduction using conventional control (Cowan 1996; Bayliss & Choquenot 1999), additional studies will need to be undertaken to determine the operational nature and magnitude of any density-dependent compensatory responses. This will be necessary so that the potential of fertility control for inhibiting population recovery can be predicted. Future studies will need to reduce population density experimentally on sites with imposed sterility to determine the effect of reduced density on both recruitment and mortality, and attempt to determine the strength and nature of any compensatory responses.

In summary, the results to date suggest sterility rates of 50% or greater can result in at least a 50% reduction in per capita recruitment when populations are close to carrying capacity (K). However, moderate levels of immigration can ameliorate this reduction. It is not known to what extent density-dependent compensation in recruitment rates will impair the effectiveness of fertility control. The high contribution of adult survival to the annual population growth rate of adults, and the higher survivorship of sterile females compared with fertile females, suggests the benefits of fertility control would be enhanced if integrated with conventional control to provide rapid initial population reduction. However, population models will need data on the nature and strength of compensatory responses at reduced density to improve predictions on the rate of recovery of possum populations following application of integrated conventional and fertility control strategies.

Acknowledgements

This study could not have been undertaken without the co-operation of many people. In particular, thanks are due to Warwick Baldwin, Scott Akin-Sellars, Kathryn Knightbridge, Amelia Pascoe, Dave Hurst, Grant Smith, Ruth Fleeson and Aaron Miller for help with the implementation and running of the possum mark–recapture fieldwork. Thanks also to Terry Fletcher for assistance with possum sterilizations and to Greg Arnold for statistical advice. Many thanks to Murray Efford for access to the long-term possum population data used for the Orongorongo control site and for much helpful advice on mark–recapture analysis. Many thanks also to Phil Cowan who provided thoughtful advice, suggestions and support at various times. Peter Caley and Tony Arthur made helpful suggestions and comments on a draft manuscript, which was edited by Anne Austin. This work was funded by the New Zealand Government through the Ministry of Agriculture and Forestry, Policy division.

Supplementary material

The following material is available from http://www.blackwellpublishing.com/products/journals/suppmat/JPE/JPE1006/JPE1006sm.htm.

Appendix 1. The proportional contribution to the annual population growth rate by age and treatment, and the per capita local recruitment rates

Appendix 2. Summary statistics used in the mark–recapture analysis

Ancillary