Accounting for female reproductive cycles in a superpopulation capture-recapture framework

Superpopulation capture-recapture models are useful for estimating the abundance of long-lived, migratory species because they are able to account for the fluid nature of annual residency at migratory destinations. Here we extend the superpopulation POPAN model to explicitly account for heterogeneity in capture probability linked to reproductive cycles (POPAN-tau). This extension has potential application to a range of species that have temporally variable life stages (e.g., non-annual breeders such as albatrosses and baleen whales) and results in a significant reduction in bias over the standard POPAN model. We demonstrate the utility of this model in simultaneously estimating abundance and annual population growth rate (lamda) in the New Zealand (NZ) southern right whale (Eubalaena australis) from 1995 to 2009. DNA profiles were constructed for the individual identification of more than 700 whales, sampled during two sets of winter expeditions in 1995-1998 and 2006-2009. Due to differences in recapture rates between sexes, only sex-specific models were considered. The POPAN-tau models, which explicitly account for a decrease in capture probability in non-calving years, fit the female data set significantly better than do standard superpopulation models (deltaAIC > 25). The best POPAN-tau model (AIC) gave a super-population estimate of 1162 females for 1995-2009 (95% CL 921, 1467) and an estimated annual increase of 5% (95% CL--2%, 13%). The best model (AIC) gave a superpopulation estimate of 1007 males (95% CL 794, 1276) and an estimated annual increase of 7% (95% CL 5%, 9%) for 1995-2009. Combined, the total superpopulation estimate for 1995-2009 was 2169 whales (95% CL 1836, 2563). Simulations suggest that failure to account for the effect of reproductive status on the capture probability would result in a substantial positive bias (+19%) in female abundance estimates.