Concerning demographic limitations on the population growth rate of West Australian (Breeding Stock D) humpback whales

Abstract

The upper bound of 0.126 on the maximum demographically possible annual growth rate for humpback whales that has standardly been imposed
on recent applications of age-aggregated assessment models for this species in the IWC Scientific Committee, is based on an analysis that assumes
steady age structure. It is conceivable that transient age-structure effects could admit greater population growth rates for short periods than suggested
by such a bound. This possibility is addressed by developing an age-structured population model in which possible density dependent changes in
pregnancy rate, age at first parturition and natural mortality are modelled explicitly, and allowance is made for the possibility of natural mortality
increasing at older ages. The model is applied to the case of the west Australian humpback whale population (Breeding Stock D), for which breeding
ground surveys over the 1982–1994 period provide a point estimate of 0.10 for the annual population growth rate. Results based upon the breeding
population survey estimate of abundance of 10,032 in 1999 suggest that 0.12 is the maximum demographically feasible annual rate of increase for
this stock over 1982–1994 if it is a closed population. This result is based on essentially the same parameter choices as led to the earlier r = 0.126
bound, i.e. that in the limit of low population size the age at first parturition approaches five years from above, the annual pregnancy rate 0.5 from
below, and the annual natural mortality rate 0.01 from above. Transient effects do not appear able to reconcile the observed rate of increase with
less extreme values of demographic parameters than led to the previously imposed upper bound of 0.126 on the maximum possible annual growth
rate. Although use of extreme values reported for demographic parameters for Northern Hemisphere humpback whale populations, rather than those
considered here, would reduce this suggested maximum rate of 0.12, the conclusion that transient effects have a very limited impact on observed
population growth rates would be unlikely to change.