Statistical analysis
We used the minimum number known alive (MNKA) method to estimate the population numbers. Because the offspring were brought back to the laboratory, the population number per trapping session was estimated by the sum of the number of founders and offspring that were first captured per trapping session in each enclosure. The recruitment rate was calculated as the proportion of recruits captured at t trapping session to adult females captured at t + 2 trapping session in each enclosure. The proportion of the reproductive condition of each sex was calculated as the proportion of reproductive active voles captured at t trapping session to adults captured at the t trapping session in each sex each enclosure.
Founder population densities (Poisson distribution), proportion of reproductive individuals, and recruitment rates (linear model), were analysed using generalized linear mixed models (GLMMs) in SPSS v.19 (IBM, Armonk, NY, USA) with Log/Logit link functions. Because the population number, recruitment, and proportion of reproductive condition were sampled per trapping session during our experiment, these data were analysed using the repeated measures method in GLMMs. Post hoc comparisons for significant treatment effects were followed the sequential Bonferroni post hoc procedure. Comparisons of the means were considered significant at P< 0.05. All data are expressed as mean ± standard error.
The relationship between the numbers of female or male founder and corresponding recruitment, and the proportion of reproductive condition were analysed with general least-square regression, using the mean number of female or male founders per enclosure in 2012 or 2015 as independent variable and the corresponding mean value of recruitment, and proportion of reproduction per enclosure as dependent variable.
The recursive model in SEM (IBM, Armonk, NY, USA) was used to explore the pathways of how density, through FCM level of founder voles, affected reproductive traits (recruitment and proportion of reproductive conditions). We first considered a full model that included all possible pathways, and, then, sequentially eliminated non-significant pathways until we attained the final model. We reported path coefficients as standardised effect sizes. This analysis was performed with a longitudinal data set, which included cumulative time of trapping session, founder number, recruitment, proportion of reproductive condition and mean FCM level per trapping session in 2012 and 2015, respectively. Founder number was sqrt-transformed and the proportion was arcsine transformed. We used the χ 2 test (ifp > 0.05, then no paths were missing, and the model was a good fit) and root mean square error of approximation (RMSEA) (ifp < 0.05, then no paths were missing, and the model was a very good fit) to evaluate the fit of the model.