Geoscience Reference
In-Depth Information
promoted by Ludwig (1996a) and Dennis et al. (1991). Schneider and Yodzis
(1994) used the term
quasi-extinction
to mean a population drop such that only
20 females remain.
The usual approach for estimating persistence is to develop a probability
distribution for the number of years before the model “goes extinct,” or falls
below a specified threshold. The percentage of the area under this distribution
in which the population persists beyond a specified time period is taken as an
estimate of the probability of persistence. To obtain MVP, probabilities of
extinction are needed for various initial population sizes. The expected time to
extinction is a misleading indicator of population viability (Ludwig 1996b)
because for small populations, the probability of extinction in the immediate
future is high, even though the expected time until extinction may be quite
large. The skewness of the distribution of time until extinction thus makes the
probability of extinction for a specified time interval a more realistic measure
of population viability.
Simple stochastic models have yielded qualitative insights into population
viability questions (Dennis et al. 1991). But because population growth is gen-
erally considered to be nonlinear, with nonlinear dynamics making most sto-
chastic models intractable for analysis (Ludwig 1996b), and because catastro-
phes and their distribution pose even more difficult statistical problems
(Ludwig 1996b), analytical methods are generally inadequate to compute
these probabilities. Therefore, computer simulation is commonly used to pro-
duce numerical estimates for persistence or MVP. Analytical models lead to
greater insights given the simplifying assumptions used to develop the model.
However, the simplicity of analytical models precludes their use in real analy-
ses because of the omission of important processes governing population
change such as age structure and periodic breeding. Lack of data suggests the
use of simple models, but lack of data really means lack of information. Lack
of information suggests that no valid estimates of population persistence are
possible because there is no reason to believe that unstudied populations are
inherently simpler (and thus justify simple analytical models) than well-stud-
ied populations for which the inadequacy of simple analytical models is obvi-
ous. The focus of this chapter is on computer simulation models to estimate
population viability via numerical techniques, where the population model
includes the essential features of population change relevant to the species of
interest.
The most thorough recent review of the PVA literature was provided by
Boyce (1992). Shaffer (1981, 1987), Soulé (1987), Nunney and Campbell
