Geoscience Reference
In-Depth Information
Then, there is an estimated number of
ˆ
1
= 1318.2 − 597.9 = 720.3 adults,
and
N
ˆ
2
= 1318.2 − 308 = 1010.2 deer.
Assume that the sample sizes used to estimate
ˆ
1
and
ˆ
2
were
n
1
=
n
2
=
400. Then, Equation (5.12) gives estimated variances of
·
p
Var(
ˆ
1
= {0.4536(1 − 0.4536)/400}(1 − 400/1318.2) = 0.0004316
and
·
p
Var(
ˆ
2
= {0.3464(1 − 0.3464)/400}(1 − 400/1010.2) = 0.0003419.
Also, from Equation (5.10),
·
ˆ
) 1318.2
2
2
2
Var(
N
=
×
0.0004316 1010.2
+
×
0.0003419)/(0.4536 0.3464)
−
1
=
95602.9
giving
·
ˆ
1
. An approximate 95% confidence inter-
val for the population size before the severe loss is then 1318.2 ± 1.96 × 309.2
or 712 to 1924. These limits are rather wide even assuming large samples
for estimating the population proportion of fawns.
Using the fact that the variance of (
N
ˆ
1
) is the same as that of (
N
ˆ
2
) and
the variance of (
ˆ
1
) is the same as that of (
ˆ
2
), approximate confidence
intervals can be obtained for the initial number of fawns, the final num-
ber of fawns, and the final population size. Treating adults as type
X
animals also allows variance, standard error, and confidence limits to
be obtained for the initial number of adults. However, these calculations
are not carried further here.
SE(
N
)
=
95602.9
=
309.2
5.4 Relationship between Change-in-Ratio
and Mark-Recapture Methods
Assume we capture, mark, and release
n
1
animals at time 1 in a closed popu-
lation of size
N
1
. At time 2, assume
n
2
animals are captured, of which
m
are
marked. The Lincoln-Petersen estimate of the size of the population pre-
sented in Chapter 7 is then
N
ˆ
1
=
n
1
n
2
/
m
. Viewed as a change-in-ratio study,
