Population Viability Analysis
309
i.e., the total variance is the sum of the environmental variance plus the
expected sampling variance. This total variance can be estimated as
va r(S
–
) = ᎏ
10(10 – 1)
ᎏ
We can estimate the expected sampling variance as the mean of the sampling variances
E [var(S ԽS)] = ᎏ
10
ᎏ
so that the estimate of the environmental variance is obtained by solving for
σ 2
σ 2 = ᎏ
(10 – 1)
ᎏ – ᎏ
10
ᎏ
However, sampling variances are usually not all equal, so we have to weight
them to obtain an unbiased estimate of σ 2 . The general theory says to use a
weight, w i ,
w i = ᎏ
σ 2 + var
1
΂S
i ԽS i ΃
ᎏ
so that by replacing var(S ˆ
i ԽS i ) with its estimator vâr(S ˆ
i ԽS i ), the estimator of the
weighted mean is
⌺
10
i=1
΂S i – S
–
΃
2
⌺
10
i=1
va r΂S
i ԽS i ΃
⌺
10
i=1
΂S i – S
–
΃
2
⌺
10
i=1
va r΂S
i ԽS i ΃