11. Variability and Measurement Error in Extinction Risk Analysis
175
variate is used as the number of survivors. To simulate the number of offspring,
we generated a random variate from Poisson distribution with the product of the
tabled fecundity and the number of potential mothers as its mean. The resulting
Poisson variate is the total number of offspring. As a result of incorporating
demographic stochasticity into the model, all the abundances in each of the stages
are integer numbers.
Density Dependence
Density dependence in the Northern Spotted Owl is probably most strongly controlled by the existence of large and nonoverlapping territories held by breeding
pairs. Because there is only a finite number of such territories available and
because owls never reproduce unless they hold a territory, reproduction within the
population is limited. We implemented this form of density dependence as a
ceiling on the number of breeding pairs equal to the number of available territories. Above this number, any additional owls cannot produce offspring, even
though they may be reproductively mature. However, if there are more territories
than adults, then subadults may also form breeding pairs and reproduce at their
own rate.
Allee effects (Allee 1931) may also influence the population dynamics of these
owls; these effects are a kind of density dependence because they consist of
changes in per capita rates with population size. These effects result in reductions
in fecundity or survival rates at low (rather than high) population densities and can
be due to inability to locate mates, insufficient group protection against competitors, inbreeding depression, and a variety of other ecological and genetic mechanisms. Such effects potentially lead to what has been called an extinction vortex
(Gilpin and Soul´ e 1986) in which an already sparse population declines still
further.
We acknowledge that Allee effects may be important in this system, but without
specific empirical information on the topic, one cannot model them realistically
and therefore cannot directly quantify their impact. Because we do not know the
details of any Allee effects, we use a conservative method to explore the possible
magnitude of their consequences. Instead of using zero or one as the population
size at which we say a population is extinct, we raise this threshold to a higher
number and suggest that if the population ever gets as low as the new threshold it
should be considered extinct because of the possible influence of Allee effects.
McKelvey and co-workers (1993) suggest that there may be a minimum size for a
self-sustaining cluster of Spotted Owls. They suggest that this minimum size is as
high as about 20 breeding pairs, although there is considerable uncertainty on this
issue. Following a discussion of clustering by the Forest Service (Criterion 7,
USFS 1992), we adopt the threshold of 15 breeding pairs as the “quasi-extinction”
level (Ginzburg et al. 1982). If the population declines to this level, we will
consider it as good as extinct because it may then no longer be large enough to
maintain itself. A way to study different hypotheses about the strength of Allee
175
variate is used as the number of survivors. To simulate the number of offspring,
we generated a random variate from Poisson distribution with the product of the
tabled fecundity and the number of potential mothers as its mean. The resulting
Poisson variate is the total number of offspring. As a result of incorporating
demographic stochasticity into the model, all the abundances in each of the stages
are integer numbers.
Density Dependence
Density dependence in the Northern Spotted Owl is probably most strongly controlled by the existence of large and nonoverlapping territories held by breeding
pairs. Because there is only a finite number of such territories available and
because owls never reproduce unless they hold a territory, reproduction within the
population is limited. We implemented this form of density dependence as a
ceiling on the number of breeding pairs equal to the number of available territories. Above this number, any additional owls cannot produce offspring, even
though they may be reproductively mature. However, if there are more territories
than adults, then subadults may also form breeding pairs and reproduce at their
own rate.
Allee effects (Allee 1931) may also influence the population dynamics of these
owls; these effects are a kind of density dependence because they consist of
changes in per capita rates with population size. These effects result in reductions
in fecundity or survival rates at low (rather than high) population densities and can
be due to inability to locate mates, insufficient group protection against competitors, inbreeding depression, and a variety of other ecological and genetic mechanisms. Such effects potentially lead to what has been called an extinction vortex
(Gilpin and Soul´ e 1986) in which an already sparse population declines still
further.
We acknowledge that Allee effects may be important in this system, but without
specific empirical information on the topic, one cannot model them realistically
and therefore cannot directly quantify their impact. Because we do not know the
details of any Allee effects, we use a conservative method to explore the possible
magnitude of their consequences. Instead of using zero or one as the population
size at which we say a population is extinct, we raise this threshold to a higher
number and suggest that if the population ever gets as low as the new threshold it
should be considered extinct because of the possible influence of Allee effects.
McKelvey and co-workers (1993) suggest that there may be a minimum size for a
self-sustaining cluster of Spotted Owls. They suggest that this minimum size is as
high as about 20 breeding pairs, although there is considerable uncertainty on this
issue. Following a discussion of clustering by the Forest Service (Criterion 7,
USFS 1992), we adopt the threshold of 15 breeding pairs as the “quasi-extinction”
level (Ginzburg et al. 1982). If the population declines to this level, we will
consider it as good as extinct because it may then no longer be large enough to
maintain itself. A way to study different hypotheses about the strength of Allee