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.