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).