Years to extinction
Firstly, we assess how proximity to extinction changed as a function of population size and the body size of the species. To make each time series compatible in the same analyses, we convert time to count backwards from extinction to produce a new variable (‘years to extinction’) with a consistent meaning across all populations. For an extinction vortex to be present, time to extinction is expected to change as a function of the logarithm of population size. To test this, and simultaneously the influence of body mass (BM), we fit GLMMs with the structures years to extinction ~ population size + log10(BM) + population size:log10(BM) and years to extinction ~ log10(population size) + log10(BM) + log10(population size):log10(BM) , including a first-order autoregressive error structure to account for time series autocorrelation. Following Fagan and Holmes (2006), we exclude the final abundance count from each time series. We attempted to fit these models with a negative binomial error distribution, however none of the models would converge. We therefore fit a Poisson error distribution and test the models for overdispersion using the ‘DHARMa’ (Hartig 2020) package.