Geoscience Reference
In-Depth Information
standard deviation 4.2. To simulate individual heterogeneity in overwinter
fawn survival, values can be drawn from this normal distribution to generate
survival estimates.
This model can be expanded to incorporate temporal variation (year ef-
fects), sex effects, and area effects, as described for mule deer fawns by Bartmann
et al. (1992). An example of modeling temporal variation in greater flamingos
(
Phoenicopterus ruber roseus
) as a function of winter severity is provided by
Cézilly et al. (1996). The approach suggested here of modeling winter severity
as a random variable and estimating survival as a function of this random vari-
able is an alternative to the variance estimation procedures of the previous sec-
tion. Both provide a mechanism for injecting variation into a population via-
bility model. The main advantage of using weather data to drive the temporal
variation of the model is that considerably more weather data are available than
are biological data on survival or reproductive rates.
The major drawback of the indirect estimation approach proposed in this
section is that sampling variation of the functional relationship is ignored in
the simulation procedure. That is, the logistic regression model includes sam-
pling variation because its parameters are estimated from observed data. The
parameter estimates of the logistic regression model include some unknown
estimation error. Their direct use results in potentially biased estimates of per-
sistence, depending on how much sampling error is present. Therefore, a
“good” model relating the covariate to the biological process is needed.
Bootstrap Approach
j
Stacey and Taper (1992) used a bootstrap procedure to incorporate temporal
variation into a model of acorn woodpecker (
Melanerpes formicivorus
) popula-
tion viability. They used estimates of adult and juvenile survival and reproduc-
tive rates resulting from a 10-year field study to estimate population persis-
tence. To incorporate the temporal variation from the 10 years of estimates,
they randomly selected with replacement one estimate from the observed val-
ues to provide an estimate in the model for a year.
This procedure is known in the statistical literature as a bootstrap sampling
procedure. The technique is appealing because of its simplicity. However, for
estimating population viability, a considerable problem is inherent in the pro-
cedure. That is, the estimates used for bootstrapping contain sampling varia-
tion and demographic variation, as well as the environmental variation that
the modeler is attempting to incorporate. To illustrate how demographic vari-
