Detrended variability
As populations decline, the influence of stochasticity is expected to increase and contribute to their extinction. This should manifest itself in greater annual variability in population change at closer proximity to extinction. To investigate this, we extract the residuals from models of the structure λ ~ years to extinction and square them to remove the trend. We then natural log-transform these squared residuals for normality. Therefore, these values represent the logged, detrended annual variability [ln(residuals)2 ] in population growth rate. We fit LMMs with the structure[ln(residuals2)] ~ years to extinction + log10(BM) + years to extinction:log10(BM). Support for the hypothesis that variability in annual population growth rate increases as extinction draws nearer in time would be found by a negative relationship with years to extinction in these models.
For each analysis, we present a ranking of the best fitting models in Table 2. We present a full summary of the best fitting models in the Supporting Information (see Table S1 in Supporting Information).