are 1, and thus produces growth rates that are not realizable, even in the best of
conditions. To account for these additional factors, Robinson and Redford (1991)
recommended multiplying (C1) by 0.6, 0.4, or 0.2, depending on whether
the maximum longevity of the species was 5 year, between 5 and 10 year, or 10
year. Slade et al. (1998) acknowledge these other life-history parameters more
explicitly, by solving:
(13.12)for, where pis the adult survival rate and lis the survival rate from birth to age
at first reproduction. This growth rate can be interpreted directly as max, without
any further adjustment. If estimates of pandlare not available, Slade et al.
(1998) offer some alternatives for how to make reasonable guesses. In determin-
ing values for the life-history parameters (, ,p, and l), it is important to
consider what these values might be in the absence of harvest and at low density.
Where data are unavailable to estimate rmaxor the life-history parameters for
the species in question, biologists can look to better-known closely related
species with similar life histories. In establishing guidelines for the application of
PBR to stocks of marine mammals, Wade (1998) recommended using default
values for rmaxof 0.04 for cetaceans and 0.12 for pinnipeds. To our knowledge,
no such taxonomic generalizations of rmaxfor birds have been completed.
Instead, biologists familiar with the species in question should consider the avail-
able knowledge for conspecific or congeneric birds.
If direct estimates of growth rates (i.e. from mark-recapture models, see Chapter
5 and Williams et al. 2002) were available for several populations at varying densi-
ties, one might consider estimating the maximum growth rate from the relation-
ship between growth rate and density by finding the limit as density approached
zero. However, this would require assuming that the populations were in equiva-
lent habitat (i.e. that there were not source and sink areas) and that all populations
had the same density at carrying capacity, and the same maximum growth rate.
13.6.2Other aspects of density dependence
In the logistic growth model (equation 13.1), the ratio of population size, N,
to carrying capacity, K, determines the reduction in growth rate due to density-
dependence. Two approaches can be taken to estimate carrying capacity:
(1) identifying the limiting resource, determining how much of it is there, then
calculating the maximum population size it could sustain; or (2) observing an
unexploited population at equilibrium, or calculating Kfrom the relationship
between growth and density at a number of replicates sites. Both of these
approaches can pose significant challenges and are subject to considerable uncer-
tainty. While determining the maximum sustained yield does require knowing
1 p^1 lblbp(^ 1)(^ 1)318 |Exploitation