Geometric growth rate
According to the extinction vortex, as a consequence of declining
individual fitness due to genetic deterioration and Allee effects, the
year-to-year rate of population change (geometric growth rate) is
expected to become increasingly negative as population size diminishes.
We calculate geometric growth rate (λ) as: λ = ln (Nt /
Nt+1), where Nt is the population
abundance in a given year and Nt+1 is the population
size one year further away from extinction. To permit finite estimates
of a populations’ final growth rate before extirpation, we add a
constant [1] to each population abundance measurement. We were not
able to calculate geometric growth rate in years where there were gaps
of more than one year until the next abundance count. We fit LMMs with
the structure λ ~ log10(population size) +
log10(BM) + log10(population
size):log10(BM) . A positive coefficient for population
size in these models would support the hypothesis that per capita growth
rate decreases with population size.