Geoscience Reference
In-Depth Information
• Demographic variation must be incorporated in this basic model. Other-
wise, estimates of persistence will be too high because the effect of demo-
graphic variation for small populations is not included in the model.
• Temporal variation must be included for the parameters of the model,
including some probability of a natural catastrophe. Examples of catastrophes
(for some species) are fires (e.g., Yellowstone National Park, USA, 1988), hur-
ricanes, typhoons, earthquakes, and extreme drought or rainfall resulting in
flooding. Catastrophes must be rare, or else the variation would be considered
part of the normal temporal variation. However, the covariance of the param-
eters is also important. Good years for survival are probably also good years for
reproduction. Likewise, bad years for reproduction may also lead to increased
mortality. The impact of this correlation of reproduction and survival can
drastically affect results. For example, the model of Stacey and Taper (1992) of
acorn woodpecker population dynamics performs very differently depending
on whether adult survival, juvenile survival, and reproduction are boot-
strapped as a triplet or given as individual rates across the 10-year period. If the
positive correlation of the survival rates and reproduction is included in the
model, estimated persistence is improved.
• Spatial variation in the parameters of the model must be incorporated if the
population is spatially segregated. If spatial attributes are to be modeled, then
immigration and emigration parameters must be estimated, as well as dispersal
distances. The difficulty of estimating spatial variation is that the covariance of
the parameters must be estimated as a function of distance; that is, what is the
covariance of adult survival of two subpopulations as a function of distance?
• Individual heterogeneity must be included in the model or the estimates of
persistence will be too low. Individual heterogeneity requires that the basic
model be extended to an individual-based model (DeAngelis and Gross 1992).
As the variance of individual parameters increases in the basic model, the per-
sistence time increases. Thus, instead of just knowing estimates of the param-
eters of our basic model, we also need to know the statistical distributions of
these parameters across individuals. This source of variation is not mentioned
in discussions of population viability analysis such as Boyce (1992), Remmert
(1994), Hunter (1996), Meffe and Carroll (1994), or Shaffer (1981, 1987).
• For short-term projects, the sources of variation just mentioned may be
adequate. However, if time periods of more than a few generations are pro-
