Modeling the impact of sex-selective harvesting and climate change on the polar bear mating system: A mechanistic approach to the Allee effect

Polar bears are susceptible to an Allee effect. Low population densities and an unpredictable sea ice habitat make mate finding an essential component of their reproductive dynamics. Climatic warming is predicted to shorten the mating season and to reduce the ability of males to track females through an increasingly fragmented sea ice habitat, thus reducing the probability of female fertilization. Using a two-sex dynamical systems approach, we develop new models to predict the pairing dynamics of polar bears throughout the mating season, and give the proportion of successfully mated females, given a certain population size, operational sex ratio, and mating season duration. The models are parameterized and validated using data from five populations in Nunavut, Canada, and describe the mating dynamics well. In agreement with observations, the models suggest that there is currently no Allee effect. However, we show that male tracking is the critical component of the mating system. We quantitatively describe how increased sea ice fragmentation influences fertilization rates through both decreased mating season duration and reduced male tracking ability. Current Canadian harvesting policies encourage hunters to select for males, although prolonged sex-selective harvesting has resulted in strongly female-biased sex ratios. If this policy continues, sex-selective harvesting and climatic warming could interact to induce an Allee effect. The operational sex ratio, below which an Allee effect is expected, is shown to be strongly dependent on overall population size and habitat area. However, below such a threshold, a decline in fertilization rates will be strongly nonlinear, implying rapid extinction.