(e.g. Williams et al. 2002). There are two basic approaches to coping with this
uncertainty. Decision-theoretic approaches such as adaptive management
(see 13.7.3) incorporate uncertainty in a formal manner. In the case of partial
observability, estimates of population size and their associated sampling vari-
ances are incorporated directly in the process of making decisions. As noted
above, another ad hocapproach to dealing with uncertainty is to base harvest
decisions on “minimum population sizes” that are typically smaller than true
abundances. These minimum sizes might be obtained as the lower end of a 95%
confidence interval for population size. This approach is intended to be conser-
vative, in the sense that the usual error in determining allowable harvest will be
to restrict take to a smaller harvest than could likely be sustained.
13.6 Assessing population dynamics
The assumption that underlies the justification of sustainable harvesting is that
negative density-dependence creates surplus production at density levels below
saturation. The certainty with which exploitation can be justified, and the preci-
sion with which it can be managed, depend on understanding the population
dynamics of the species in question, especially with regard to density-dependence
and the effects of harvest. The PBR formula requires minimal information because
it makes many assumptions about the dynamics. Errors due to these assumptions
are guarded against by taking a conservative approach. As more information is
known about the specific population dynamics of a species, the management
recommendations can be less restrictive.
13.6.1Maximum growth rate (rmax)
The maximum growth rate used in the PBR formula (equation (13.4)) is calcu-
lated by subtracting one from the discrete growth rate (max) that would be experi-
enced by the population in the absence of harvest, when the density was very low,
and in the absence of Allee effects (see below, Section 13.6.2). It is important to
note that this may notcorrespond to any observed growth rate for that population,
since most populations will not be at such a low density. On the other hand, rmax
should not be taken as a rate of population growth under unrealistic assumptions.
Robinson and Redford (1991) provide a formula for calculating maxfrom mini-
mal life-history information. They begin by solving Cole’s (1954) formula:
(13.11)forC, where is the age at first reproduction, is the age at last reproduction, and
bis the number of female offspring per reproductive female per time period. This
formula assumes that both adult survival and survival to age at first reproduction
1 C^1 bCbC(^ 1)Assessing population dynamics| 317