How few whales were there after whaling? Inference from contemporary mtDNA diversity

Reconstructing the history of exploited populations of whales requires fitting a trajectory through at least three points in time: (i) prior to exploitation, when abundance is assumed to be at the maximum allowed by environmental carrying capacity; (ii) the point of minimum abundance or 'bottleneck', usually near the time of protection or the abandonment of the hunt; and (iii) near the present, when protected populations are assumed to have undergone some recovery. As historical abundance is usually unknown, this trajectory must be extrapolated according to a population dynamic model using catch records, an assumed rate of increase and an estimate of current abundance, all of which have received considerable attention by the International Whaling Commission (IWC). Relatively little attention has been given to estimating minimum abundance (N(min)), although it is clear that genetic and demographic forces at this point are critical to the potential for recovery or extinction of a local population. We present a general analytical framework to improve estimates of N(min) using the number of mtDNA haplotypes (maternal lineages) surviving in a contemporary population of whales or other exploited species. We demonstrate the informative potential of this parameter as an a posteriori constraint on Bayesian logistic population dynamic models based on the IWC Comprehensive Assessment of the intensively exploited southern right whales (Eubalaena australis) and published surveys of mtDNA diversity for this species. Estimated historical trajectories from all demographic scenarios suggested a substantial loss of mtDNA haplotype richness as a result of 19th century commercial whaling and 20th century illegal whaling by the Soviet Union. However, the relatively high rates of population increase used by the IWC assessment predicted a bottleneck that was implausibly narrow (median, 67 mature females), given our corrected estimates of N(min). Further, high levels of remnant sequence diversity (theta) suggested that pre-exploitation abundance was larger than predicted by the logistic model given the catch record, which is known to be incomplete. Our results point to a need to better integrate evolutionary processes into population dynamic models to account for uncertainty in catch records, the influence of maternal fidelity on metapopulation dynamics, and the potential for inverse density dependence (an 'Allee effect') in severely depleted populations.