Geoscience Reference
In-Depth Information
S
&
1981
(1
-
S
&
1981
)
}
var(
S
&
1981
) =
}
46
which equals 0.0047773. A spreadsheet program (VARCOMP.WB1) com-
putes the estimate of temporal process variation for 1981-87,
s
ˆ
2
, as 0.0170632
ˆ
= 0.1306262), with a 95 percent confidence interval of (0.0064669,
0.0869938) for
s
(
s
s
. These confidence
intervals represent the uncertainty of the estimate of temporal variation, that is,
the sampling variation of the estimate of temporal variation.
The procedure demonstrated here is applicable to estimation of other
sources of variation (e.g., spatial variation) and to variables other than survival
rates, such as per capita reproduction. The method is more general than the
usual analysis of variance procedures because each observation is not assumed
to have the same variance, in contrast to analysis of variance, in which each cell
is assumed to have the same within-cell variance.
2
, and (0.0804167, 0.2949472) for
Indirect Estimation of Variance Components
j
Individual heterogeneity occurs in both reproduction and survival. Estimation
of individual variation in reproduction is an easier problem than estimation of
individual variation in survival because some animals reproduce more than
once, whereas they only die once. Bartmann et al. (1992) demonstrated that
overwinter survival of mule deer fawns is related to their mass at the start of the
winter. Thus one approach to modeling individual heterogeneity is to find a
correlate of survival that can be measured and develop statistical models of the
distribution of this correlate. Then, the distribution of the correlate can be sam-
pled to obtain an estimate of survival for the individual. Lomnicki (1988) also
suggests mass as an easily measured variable that relates to an animal's fitness.
To demonstrate this method, I use a simplification of the logistic regression
model of Bartmann et al. (1992):
1
1 -
}
2
log
=
b
0
+
b
1
mass
where survival (
S
) is predicted as a function of weight. Weight of fawns at the
start of winter was approximately normally distributed, with mean 32 kg and
