11. Variability and Measurement Error in Extinction Risk Analysis
171
Model Structure
To simplify the bookkeeping, we follow standard practice and consider only
females in the model. This simplification assumes that males are in sufficient
abundance that they do not limit the dynamics of the population. Following
Forsman and colleagues (1993), we recognize female owls in three categories:
• Juveniles, which includes all individuals between 0 and 1 year old (i.e., between
hatching and 1 year after hatching)
• Subadults, which includes all individuals between 1 and 2 years old
• Adults which includes all individuals older than 2 years
Although the analysis by Burnham and co-workers (1994) of demographic data
from all populations of the Northern Spotted Owl distinguished first-year adults
into a second subadult stage, subadult2, the rates for this stage are statistically
indistinguishable from those of the rest of the adult stage in the data from the
Olympic Peninsula population (Forsman et al. 1993). Because we are primarily
interested in the Olympic Peninsula population, we used only three stages.
Our model is a modification of a simple matrix model of the form
juveniles t+1
subadults t+1
adults t+1
=
0
S juveniles
0
F subadults
0
S subadults
F adults
0
S adults
juveniles t
subadults t
adults t
where F represents fecundity and S represents survival rate over a yearly time step
indexed by t. Our modification to this matrix model includes the effects of a
limited number of territories, which imposes a ceiling on the number of pairs of
owls that may breed in a given year. Given the total number of territories, we first
fill as many of them as possible with adult owls and then fill any remaining ones
with subadults. This procedure reflects the idea that the greater experience of
older owls may give them a competitive advantage in establishing themselves in
territories that have fallen vacant. Because of this ceiling, the number of breeding
birds never exceeds the number of territories, although the number of floaters
(nonbreeding adults without territories) theoretically can increase indefinitely if
reproduction is high enough.
Demographic Parameters
The demographic rates for juvenile, subadult, and adult survival and fecundity
that were used to parameterize the model are shown in Table 11.1. The values are
based on those estimated for the Olympic Peninsula population as reported in the
work of Forsman and co-workers (1993). The mean juvenile survival rate that
they reported is probably an underestimate because it does not account for emigration by juvenile owls. Using data from two populations of the Northern Spotted
Owl (Olympic Peninsula and Roseburg), Burnham and associates (1994)
171
Model Structure
To simplify the bookkeeping, we follow standard practice and consider only
females in the model. This simplification assumes that males are in sufficient
abundance that they do not limit the dynamics of the population. Following
Forsman and colleagues (1993), we recognize female owls in three categories:
• Juveniles, which includes all individuals between 0 and 1 year old (i.e., between
hatching and 1 year after hatching)
• Subadults, which includes all individuals between 1 and 2 years old
• Adults which includes all individuals older than 2 years
Although the analysis by Burnham and co-workers (1994) of demographic data
from all populations of the Northern Spotted Owl distinguished first-year adults
into a second subadult stage, subadult2, the rates for this stage are statistically
indistinguishable from those of the rest of the adult stage in the data from the
Olympic Peninsula population (Forsman et al. 1993). Because we are primarily
interested in the Olympic Peninsula population, we used only three stages.
Our model is a modification of a simple matrix model of the form
juveniles t+1
subadults t+1
adults t+1
=
0
S juveniles
0
F subadults
0
S subadults
F adults
0
S adults
juveniles t
subadults t
adults t
where F represents fecundity and S represents survival rate over a yearly time step
indexed by t. Our modification to this matrix model includes the effects of a
limited number of territories, which imposes a ceiling on the number of pairs of
owls that may breed in a given year. Given the total number of territories, we first
fill as many of them as possible with adult owls and then fill any remaining ones
with subadults. This procedure reflects the idea that the greater experience of
older owls may give them a competitive advantage in establishing themselves in
territories that have fallen vacant. Because of this ceiling, the number of breeding
birds never exceeds the number of territories, although the number of floaters
(nonbreeding adults without territories) theoretically can increase indefinitely if
reproduction is high enough.
Demographic Parameters
The demographic rates for juvenile, subadult, and adult survival and fecundity
that were used to parameterize the model are shown in Table 11.1. The values are
based on those estimated for the Olympic Peninsula population as reported in the
work of Forsman and co-workers (1993). The mean juvenile survival rate that
they reported is probably an underestimate because it does not account for emigration by juvenile owls. Using data from two populations of the Northern Spotted
Owl (Olympic Peninsula and Roseburg), Burnham and associates (1994)