A. Status of the Spectacled Eider - U.S. Fish and Wildlife Service

where x = age. The fertility rate is therefore:
f= p m~ 1 (2)
where p represents the survival rate. The proportion surviving (survivorship) to each age (li)
is:
X CC.)
x=O
The intrinsic rate of growth of the population (r) is then calculated iteratively from Lotka’s
equation:
Before introducing uncertainty in the estimation of birth and survival rates, it is instructive to
use a simple example to examine the magnitude of differences expected in demographic
statistics. The example is based on Coulson’s (1984) Common Eider data. No estimate is
given for juvenile survival rate. Juvenile survival rate is, therefore, initially solved for by
assuming r = 0 and solving equation 4. If a population were to grow at the same rate for a
long period of time, eventually the proportion ofanimals in each age would remain the same
from year to year. This is called stable age distribution. The proportion of first-time nesters
(recruits) to the total number of nesters can also be calculated. The proportion first-time
nesters can be estimated from banding data (Coulson 1984). This proportion can potentially
serve as a diagnostic to tell whether the nesting population is primarily old birds (a sign of low
recruitment) or young birds (a sign of lowered adult survival). If we assume that a population
decline can be attributed to change in a single parameter, we can calculate the stable age
distribution and the proportion ofrecruits. The results of assuming a 15%/year decline (the
estimate from the YKD ground plot data; Stehn et al. 1993), are presented in Figure Ill-la.
Most of the population is 0-year-olds (eggs) which makes detecting differences in older
categories difficult to see.
A more informative depiction of age structure includes only ages older than two (Figure
llI-lb). If we assume that the current rate of decline is the point estimate from the ground plot
survey (r = -0.15), we can ask what proportion of nesting females would be first-time nesters
if the decline was solely because of decreases in various parameters. If the decline was due
entirely to reduced juvenile (first-year) survival rate, the proportion of first-time nesters is
much less (6.3%) than if the decline was due to a reduction in adult survival rates (21 %).
Two factors suggest that the age structure may have changed towards a higher proportion
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