impact of incidental take on populations of marine mammals, species whose status
and dynamics are often poorly known. The approach that has emerged as a default
assessment in the face of uncertainty is referred to as “Potential Biological
Removal” (PBR, Wade 1998). The formula for PBR is:
(13.4)where rmaxis the theoretical maximum growth rate at low population density (as
above), Nminis the minimum population estimate, and FRis a recovery factor
between 0.1 and 1.0. The formula specifies the maximum harvest that can poten-
tially be removed from the population while allowing the population to achieve or
maintain its optimum sustainable population size (Wade 1998). Note that if
recovery is not a concern, and FRis set to 1.0, the formula can be rearranged,
(13.5)showing that this method can be used to seek the maximum sustained yield by
controlling harvest rate, an approach that produces a stable equilibrium. It is
conservative because a minimum estimate of the population size is used, ensur-
ing that the actual harvest rate is not greater than optimal harvest rate (h*). The
recovery factor, FR, is used to seek further conservatism, particularly when the
status and dynamics are very poorly known, and when there is a desire to allow a
depleted population to quickly recover to an optimal level. The recovery factor is
typically set to 0.1 for endangered species, and 0.5 for threatened species (Taylor
et al. 2000). These levels have been shown to guard against the typical levels of
uncertainty and potential bias associated with dynamics of marine mammals
(Wade 1998; Taylor et al. 2000), but similar work has not been done with birds.
To apply the PBR formula, an estimate of population size, Nmin, and an
estimate of potential growth rate, rmax, are needed. The population size estimate
should reflect confidence that the actual population size is greater than the estim-
ate used. Where methods are available to obtain an unbiased estimate of N, the
lower bound of the 95% confidence interval can be used (Taylor 1993). Where
such data are not available, the minimum number known alive, or some similar
measure, could be used. This value should be updated, and PBR recalculated,
whenever new data are available. The maximum potential growth rate, rmax, is
technicallymax1, where maxis the maximum discrete rate of population
growth. If data are available about survival and reproductive rates for a species,
there are methods for calculating max(see Slade et al. 1998; Caswell 2001).
Otherwise, biologists can rely on comparisons to related species for which such
hPBRN
min^12 rmax,PBR^12 rmaxNminFR308 |Exploitation