11. Variability and Measurement Error in Extinction Risk Analysis
183
Table 11.4. Probability (as a percentage) of quasi-extinction to 15 breeding pairs over
three time horizons and two hypotheses about territory availability.
a
Habitat
Time horizon
Low estimate
Point estimate
High estimate
200 territories
18 years
0
0
0
89 years
0
13.7
99
100 years
0
20.0
100
300 territories
18 years
0
0
0
89 years
0
6.7
98
100 years
0
9.4
99
a High and low estimates are given describing bounds on a point estimate that assumes measurement
error has no effect. All estimates are based on 1,000 replicate simulations assuming windstorms and
regrowth.
Table 11.4 presents the results of this investigation. The high estimates for risk
were generated by decrementing the mean vital rates listed in Table 11.1 by their
respective standard errors. The low estimates were derived by incrementing the
vital rates by the same amounts. The risk estimates resulting from using the mean
vital rates as listed in Table 11.1 are here labeled point estimates. We emphasize
that these point estimates ignore the effect of measurement errors. Note that,
despite the fact that plus or minus one standard error is a fairly modest range, the
potential effect of ignorance due to measurement error is considerably larger than
the risk consequences of the habitat assumption. For instance, if we make our
simulations based on the best estimate of temporal variability, we compute a
13.7% quasi-extinction risk over 89 years for 200 territories. But this result is
swamped by the uncertainty associated with measurement error: the true risk
could be as large as 99% or as little as 0%. Given this range, it would be
remarkable indeed if the best estimates happened to actually be, by chance, also
accurate. Most prudent scientists or managers would be hesitant to rely on determinations having so little precision.
Discussion
It is clear from our analysis that the choice of time scale can strongly affect both
the outcome and the reliability of a population viability analysis. Shorter time
scales suffer less from measurement error but proportionally more from environmental variability. At very short time scales, divergent trajectories may still differ
only negligibly. At very long time scales, measurement error may make it impossible to distinguish between even widely divergent trajectories. Although it is
clear that some intermediate time scale can strike a balance between these
different sources of uncertainty, there are probably no general rules that one can
use to determine the ideal choice. The appropriate scale depends on characteristics
of an organism’s life history as well as on the particular model that one uses to
study it and, possibly, on the question that one wishes to answer.
183
Table 11.4. Probability (as a percentage) of quasi-extinction to 15 breeding pairs over
three time horizons and two hypotheses about territory availability.
a
Habitat
Time horizon
Low estimate
Point estimate
High estimate
200 territories
18 years
0
0
0
89 years
0
13.7
99
100 years
0
20.0
100
300 territories
18 years
0
0
0
89 years
0
6.7
98
100 years
0
9.4
99
a High and low estimates are given describing bounds on a point estimate that assumes measurement
error has no effect. All estimates are based on 1,000 replicate simulations assuming windstorms and
regrowth.
Table 11.4 presents the results of this investigation. The high estimates for risk
were generated by decrementing the mean vital rates listed in Table 11.1 by their
respective standard errors. The low estimates were derived by incrementing the
vital rates by the same amounts. The risk estimates resulting from using the mean
vital rates as listed in Table 11.1 are here labeled point estimates. We emphasize
that these point estimates ignore the effect of measurement errors. Note that,
despite the fact that plus or minus one standard error is a fairly modest range, the
potential effect of ignorance due to measurement error is considerably larger than
the risk consequences of the habitat assumption. For instance, if we make our
simulations based on the best estimate of temporal variability, we compute a
13.7% quasi-extinction risk over 89 years for 200 territories. But this result is
swamped by the uncertainty associated with measurement error: the true risk
could be as large as 99% or as little as 0%. Given this range, it would be
remarkable indeed if the best estimates happened to actually be, by chance, also
accurate. Most prudent scientists or managers would be hesitant to rely on determinations having so little precision.
Discussion
It is clear from our analysis that the choice of time scale can strongly affect both
the outcome and the reliability of a population viability analysis. Shorter time
scales suffer less from measurement error but proportionally more from environmental variability. At very short time scales, divergent trajectories may still differ
only negligibly. At very long time scales, measurement error may make it impossible to distinguish between even widely divergent trajectories. Although it is
clear that some intermediate time scale can strike a balance between these
different sources of uncertainty, there are probably no general rules that one can
use to determine the ideal choice. The appropriate scale depends on characteristics
of an organism’s life history as well as on the particular model that one uses to
study it and, possibly, on the question that one wishes to answer.