Table S1. Population-level models with density-dependent functions describing births (fN) and deaths (μN) in the bruchid metapopulations (taken from Bellows (1981) were fitted to data from an independent study (Bonsall et al. 2005; Bull et al. 2006; Bull et al. 2007; Bull & Bonsall 2008) in order to estimate parameter values describing population dynamics in these systems (growth rate r, death rate d, density dependence a (the function from Hassell et al (1976) has a second parameter for density dependence b) and likelihood variance v). Models were fit to replicates separately so that the models which best described the systems could be identified. Models estimated different parameter values depending on the nature of density-dependence acting on births or deaths. The estimated parameter values for each model fitted to each replicate are listed. The fit of the models were measured using AIC values calculated from the model likelihood values. The two best fitting models (MacFadyen birth and death) were then fitted to all of the replicates combined to estimate the parameter values which best describe the population dynamics across all the time series. The AIC value and parameter estimates with 95% confidence limits (Morgan 2000) for the model which best describes the dynamics are listed in bold print.

Appendix S1. Model Fitting.

Appendix S2. Stochastic models.

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