11. Variability and Measurement Error in Extinction Risk Analysis
177
Generation Time
The Mace and Lande (1991) criteria for classifying species uses multiples of the
generation time as the horizon for estimating the risk of extinction, so it is
necessary to calculate the generation time before applying the criterion. We calculate the generation time of the Northern Spotted Owl by using the standard
definitions (Mertz 1970) and the demographic rates of Table 11.1. The resulting
value is 8.88 years. Generation time represents a weighted mean of the product of
fecundity and the number of survivors at each age, so an individual owl may live
considerably longer than this span. Applying the Mace and Lande (1991) criteria
to the Spotted Owl thus requires estimating their probabilities of extinction after
10 years, 89 years, and 100 years.
Population Trends
A traditional analysis of population change focuses on the long-term behavior of
the deterministic component of population dynamics. From the mean values for
fecundity and survival given in Table 11.1, we estimated the value of λ, the
asymptotic annual rate of population increase (Caswell 1989; Ferson 1990), as the
eigenvalue of the matrix
0
0.358
0
0.206
0
0.862
0.380
0
0.862
The resulting value of λ was 0.9911, which suggests a slowly declining population under the assumption that the demographic rates do not change. This value is
close to 1.0, which corresponds to a stationary population; estimates of its standard error depend on assumptions about covariances among the parameters. By
raising 0.9911 to the hundredth power, we can compute a forecast based on λ that
suggests a population decline of about 60% after 100 years.
There is, of course, little chance that the demographic rates of a real biological
population will remain exactly unchanged for an extended period of time. Indeed,
they are known to fluctuate with each new year. In our initial study of stochastic
population trends, we simulated the effect of fluctuations in demographic rates
from environmental variability as measured by interannual standard deviations
listed in Table 11.1. We began each simulation with the population at stable stage
distribution and consisting (somewhat arbitrarily) of twice as many adult and
subadult owls as would fill the territories exactly. These extra adult and subadult
owls constituted the initial pool of floaters. Although about a dozen time steps
would have been sufficient, we estimated the stable stage structure by beginning
the simulation with an even distribution and running it for 200 time steps to erase
any transient behavior. We replicated each run 1,000 times, looking at the number
177
Generation Time
The Mace and Lande (1991) criteria for classifying species uses multiples of the
generation time as the horizon for estimating the risk of extinction, so it is
necessary to calculate the generation time before applying the criterion. We calculate the generation time of the Northern Spotted Owl by using the standard
definitions (Mertz 1970) and the demographic rates of Table 11.1. The resulting
value is 8.88 years. Generation time represents a weighted mean of the product of
fecundity and the number of survivors at each age, so an individual owl may live
considerably longer than this span. Applying the Mace and Lande (1991) criteria
to the Spotted Owl thus requires estimating their probabilities of extinction after
10 years, 89 years, and 100 years.
Population Trends
A traditional analysis of population change focuses on the long-term behavior of
the deterministic component of population dynamics. From the mean values for
fecundity and survival given in Table 11.1, we estimated the value of λ, the
asymptotic annual rate of population increase (Caswell 1989; Ferson 1990), as the
eigenvalue of the matrix
0
0.358
0
0.206
0
0.862
0.380
0
0.862
The resulting value of λ was 0.9911, which suggests a slowly declining population under the assumption that the demographic rates do not change. This value is
close to 1.0, which corresponds to a stationary population; estimates of its standard error depend on assumptions about covariances among the parameters. By
raising 0.9911 to the hundredth power, we can compute a forecast based on λ that
suggests a population decline of about 60% after 100 years.
There is, of course, little chance that the demographic rates of a real biological
population will remain exactly unchanged for an extended period of time. Indeed,
they are known to fluctuate with each new year. In our initial study of stochastic
population trends, we simulated the effect of fluctuations in demographic rates
from environmental variability as measured by interannual standard deviations
listed in Table 11.1. We began each simulation with the population at stable stage
distribution and consisting (somewhat arbitrarily) of twice as many adult and
subadult owls as would fill the territories exactly. These extra adult and subadult
owls constituted the initial pool of floaters. Although about a dozen time steps
would have been sufficient, we estimated the stable stage structure by beginning
the simulation with an even distribution and running it for 200 time steps to erase
any transient behavior. We replicated each run 1,000 times, looking at the number