Figure S1 Comparison of the years immediately following restocking events to years without restocking, given a greater range of growth models. In the main text, we only presented the results of the normalized deviates from the highest ranked model, and only of the two treatments within populations that received additions (see Methods). Here we include the results from each of the three growth models, and then the highest ranked model. Additionally, we show the deviates from the populations that were never restocked. In all model scenarios, small populations have a greater per capita growth rate following restocking events.

Figure S2 Scatter plot of boost in per capita rate of increase at low population numbers. Populations at low number show a per capita growth increase following the addition of new individuals. Scatter plots of normalized deviates from the best fitting growth models for post-supplement and years without population additions.

Table S1 Twenty four South African protected areas in the population relocation database. World Database of Protected Areas (WPDA) category by management purpose: II, ecosystem conservation and recreation; IV, conservation through management intervention; and V, landscape conservation and recreation. The number of populations represents the data usable in our analyses, though there are more. None of the reserves contained any species of top predators roaming freely in the same areas with grazing mammals. Messina Proefplas is an experimental farm and while it is a fenced, protected area like the other sites, it is not considered a ''nature reserve'' by the WDPA. Karoo Nature Reserve was redesignated Camdeboo National Park in 2005. Asterisk (*) indicates protected areas had populations with discontinuous records or insufficient data, but appear in the analyses of geographic range (Figure 1).

Table S2 (see attached text file) Further details of each population examined in this article, including the number of observations (x, y) pairs (''Obs.''), and the results of the population growth model statistics. The parameters and AICc values for the three models fitted to each of the 125 populations that we examined. The error term is assumed to be Gaussian, given the log-transformation of the raw population counts. See Methods for details of the population growth model and the DD parameters.

Table S3 Model structure and correlates used to examine growth rate r(20). D is the RMS deviation of the model from the data. N is the number of points in the analysis. The error term is assumed to be Gaussian. The highest ranking model of covariates is model of population growth without any ecological covariates. This material is available as part of the online article from:

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