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

The final risk factor is the effect of genetic changes, such as loss of heterozygosity and
inbreeding depression, upon population fitness (translated as population growth rates). Mating
among closely related individuals can expose lethal recessive alleles, which can compromise
either survival or fecundity of the individual. Loss of heterozygosity has been linked to
reduced fitness and can lead to a reduced ability of the species to adapt to new circumstances.
As with demographic stochasticity, inbreeding depression is important only for small
population sizes.
Not only must these factors be integrated into a single model, but the model must be stochastic
in nature. Deterministic models, such as the Leslie model for demographic projections, are
inadequate for two reasons. First, deterministic models usually cannot incorporate changes in
demographic parameters that are caused by low population size, such as demographic
stochasticity and density decompensatory mechanisms (mechanisms that reduce birth and
survival rates at low density such as reduced ability to defend against predators, difficulty in
finding a mate, etc.). Second, deterministic models have difficulty incorporating variations in
birth and survival rates and synergistic effects between risk factors. Synergistic effects are
expected in small populations and are referred to as extinction vortices (Gilpin & Soul~ 1986).
An example would be a decreased population size that is initially caused by environmental
variation that then leads to loss of genetic variability, which further leads to a reduction in
population growth rate and a further population decline.
Although there are benefits to using more detailed models to model extinction, these stochastic
models require the estimation of many parameters and, hence, require many data. For this
reason, analytical models that allow the calculation of extinction statistics from data on the
population’s mean growth rate and the variance in that rate have been developed. One group
of models allows the calculation of expected (mean) extinction time (Leigh 1981; Richter-Dyn
and Goel 1972; Goodman 1987). These models solve for the mean extinction time and are
analytical models. Unfortunately, because population growth is a multiplicative process,
extinction distributions tend to be log-normally distributed. A log-normal distribution of
extinction probabilities peaks on the left side and has a long tail on the right. This results in
the median probabilities of extinction (the time with a 50% chance ofgoing extinct) that is
much less than the mean extinction time. The probability of extinction which corresponds to
the mean extinction time (the statistic given by the aforementioned analytical models) is
unknown. The mean actually corresponds to the balance point in the lop-sided log-normal
distribution: a point of questionable relevance to managers. Managers are usually interested
in low probabilities of extinction, such as a 5% or 20% chance of going extinct.
Another analytical model that avoids the need for detailed demographic data and yet gives an
analytical means of calculating an entire extinction distribution from a time series of
abundances was developed by Dennis et al. (1991). The accuracy of this technique depends on
two critical assumptions: (1) abundance estimates are for the entire population; and (2)
abundance estimates are very accurate, so that interannual variance reflects actual population
fluctuations and not imprecision of abundance estimates. Unfortunately, as populations
Appendix I - Page 2