11. Variability and Measurement Error in Extinction Risk Analysis
179
Table 11.3. Observed probabilities (as percentages) of quasi-extinction (falling below
15 breeding pairs) within 100 years, under various assumptions about habitat concerning
the initial number of territories, the occurrence of windstorms, and the effect of
maturation of young forests. a
Initial territories
No windstorms
Windstorms
No regrowth
200
19.2
20.0
300
9.4
11.7
With regrowth
200
20.0
19.2
300
10.3
10.8
a The meanings of the labels are given in the legend for Table 11.2. These probabilities were estimated
from simulations with 1,000 replications, so the tabled value ±2.8% forms 95% confidence intervals.
Review of Assumptions
We deliberately created the model with a number of conservatisms that are appropriate considering the status of the Northern Spotted Owl and the prevailing
balance between scientific knowledge and ignorance about its life history and
ecological fate. For instance, we assumed that no immigrants supplement the
population on the Olympic Peninsula. Our use of quasi-extinction to account for
possible influence of Allee effects was also conservative. We considered any
population to be as good as extinct if it reached the quasi-extinction level of 15
breeding pairs. This will be conservative if Allee effects are not so severe, and
there may be reason to suspect that this is the case. For instance, if Allee effects do
not act as a strict threshold but instead become gradually stronger over a range of
population densities, they would cause only an increased chance of actual extinction at such low levels rather than surety of an extinction vortex. Similarly, the
model’s strict ceiling on reproduction is conservative if the form of density dependence in the life history of owls is less exacting and more gradual in effect.
The strongest conservatism arises from the linear structure of the population
model. Because the matrix model was parameterized with vital rates whose overall effect leads to a declining population, the model thereby guarantees that
predicted population trajectories exhibit no trend for positive population growth
from any level of abundance. Any increases in population size are the result of
random fluctuations. As a consequence, the eventual fate of any population is a
decline to extinction. However, if the observed vital rates are depressed only
because recent habitat loss left the current population above its now lower carrying capacity, then the present decline in population may not continue in the future.
Once the population declines to a level near its new carrying capacity, the vital
rates may stabilize and the population may be capable of sustaining itself under
these less crowded conditions. Our model does not assume that this will be the
case and, indeed, assumes that the present gloomy life history characteristics will
persist in the future. This assumption is surely very conservative because, if vital
rates depend at all on habitat, then they should improve as the population comes
into balance with a stable or even growing area of suitable habitat.
179
Table 11.3. Observed probabilities (as percentages) of quasi-extinction (falling below
15 breeding pairs) within 100 years, under various assumptions about habitat concerning
the initial number of territories, the occurrence of windstorms, and the effect of
maturation of young forests. a
Initial territories
No windstorms
Windstorms
No regrowth
200
19.2
20.0
300
9.4
11.7
With regrowth
200
20.0
19.2
300
10.3
10.8
a The meanings of the labels are given in the legend for Table 11.2. These probabilities were estimated
from simulations with 1,000 replications, so the tabled value ±2.8% forms 95% confidence intervals.
Review of Assumptions
We deliberately created the model with a number of conservatisms that are appropriate considering the status of the Northern Spotted Owl and the prevailing
balance between scientific knowledge and ignorance about its life history and
ecological fate. For instance, we assumed that no immigrants supplement the
population on the Olympic Peninsula. Our use of quasi-extinction to account for
possible influence of Allee effects was also conservative. We considered any
population to be as good as extinct if it reached the quasi-extinction level of 15
breeding pairs. This will be conservative if Allee effects are not so severe, and
there may be reason to suspect that this is the case. For instance, if Allee effects do
not act as a strict threshold but instead become gradually stronger over a range of
population densities, they would cause only an increased chance of actual extinction at such low levels rather than surety of an extinction vortex. Similarly, the
model’s strict ceiling on reproduction is conservative if the form of density dependence in the life history of owls is less exacting and more gradual in effect.
The strongest conservatism arises from the linear structure of the population
model. Because the matrix model was parameterized with vital rates whose overall effect leads to a declining population, the model thereby guarantees that
predicted population trajectories exhibit no trend for positive population growth
from any level of abundance. Any increases in population size are the result of
random fluctuations. As a consequence, the eventual fate of any population is a
decline to extinction. However, if the observed vital rates are depressed only
because recent habitat loss left the current population above its now lower carrying capacity, then the present decline in population may not continue in the future.
Once the population declines to a level near its new carrying capacity, the vital
rates may stabilize and the population may be capable of sustaining itself under
these less crowded conditions. Our model does not assume that this will be the
case and, indeed, assumes that the present gloomy life history characteristics will
persist in the future. This assumption is surely very conservative because, if vital
rates depend at all on habitat, then they should improve as the population comes
into balance with a stable or even growing area of suitable habitat.