Statistical analysis
During trapping sessions we identified individual melomys that were captured at each site by their unique microchips. Because melomys on Indian Island have very small home ranges (tending to be caught in the same or adjacent traps throughout the trapping period: Jolly et al. unpub. data) and since we never observed captures of melomys marked at other sites (Jolly et al. unpub. data), we treated each site as independent with regard to demographics and behaviour (Fig. 1; Table S1).
To estimate between-session survival, we analysed the mark-recapture data to estimate recapture and survival rates using Cormack-Jolly-Seber models in program MARK (see Supporting Information for details).
To test whether the presence of quolls impacted melomys population size, we used a hierarchical model in which population size was made a function of quoll presence/absence, capture session, and the interaction between these factors. Population size at each site during each session is estimated in this process, and we fitted this model in a Bayesian framework (see Supporting Information for details).
To assess whether the introduction of quolls affected the behaviour of melomys populations, we divided the responses of melomys in open field tests into two independent response variables: whether individuals emerged or not during the 0-10 min period (binomial: 0 or 1); and whether individuals emerged and interacted with the novel object or not during the 10-20 min period (binomial: 0 or 1). We used generalised linear mixed-effects models with binomial errors and a logit link to test the effect of quoll presence (two levels: quolls present and quolls absent) and trapping session (continuous), with site included as a random effect, on the behavioural response variables. P -values were obtained by likelihood ratio tests of the full model with the effect in question against the model without the effect. This analysis was performed using R with the lme4 software package (Bateset al. 2007).
To assess whether the numerical impact of quolls on melomys affected the seed harvesting rate of invaded melomys populations, we first examined the relationship between melomys population size (estimated above) and the total number of control (unscented) seeds harvested from each site. Here we used a simple linear model with number of seeds harvested as a linear function of population size, quoll presence/absence and the interaction between these effects. To test whether there was an additional effect of quoll presence, beyond their effect on population size, we defined a new variable, Δks, as the difference in seed take between scented and unscented treatments within each site.session. Here any effect of melomys density is cancelled out (because density is common to both treatments within each site.session). Thus, we fitted a model in which Δks is a function of quoll presence/absence, session and the interaction between these effects. All analyses were performed using R version 3.3.2 (R Core Team 2019).