Geoscience Reference
In-Depth Information
mates used in the model. Uncertainty about the model is not included in this
confidence interval because the model is assumed to be known. However, a
better confidence interval will probably be achieved by sorting the 1,000 val-
ues into ascending order and using the 25th and 975th values as a 95 percent
confidence interval. This procedure accounts for the likely asymmetric distri-
bution of the estimates of persistence.
Discussion
j
The real problem with PVA is not the model, but obtaining the data to drive
the model (Ruggiero et al. 1994). Much of the published work on PVA ignores
this essential point (Thomas 1990). For example, Mangel and Tier (1994:
608-611) simplify the process to the point that they miss major issues con-
cerning data reliability and quality of the product (estimates of persistence).
Their four “facts” are as follows:
• “A population can grow, on average, exponentially and without bound and
still not persist.” This is because of catastrophes that will bring even a thriving
population to zero.
• “There is a simple and direct method for the computation of persistence
times that virtually all biologists can use.” They suggest a simple model with
one age class and a population ceiling that the population cannot exceed, but
the ceiling does not cause density dependence effects of growth parameters. As
a result, their approach to estimating persistence is likely to underestimate per-
sistence if the ceiling is set too low because the population can never grow away
from the absorbing state of extinction.
• “The shoulder of the MacArthur-Wilson model occurs with other models
as well, but disappears when catastrophes are included.” They suggest a slow,
steady rise in persistence times as the population ceiling is increased.
• “Extinction times are approximately exponentially distributed and this
means that extinctions are likely.” Thus, they conclude the most likely value of
a population is zero, or the mode of an exponential distribution. I believe this
result is obtained because of the simplistic assumptions they have used. Realis-
tic models that incorporate the sources of variation described in this chapter
do not result in such simplistic results.
