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.