Effects of strength and timing of harvest on seasonal population models: stability switches and catastrophic shifts

Population abundance of many species is controlled by a combination of density-dependent processes during different periods of the annual cycle. In the context of population exploitation or conservation programs, sequential density dependence has the potential to dramatically change population responses to harvesting. Looking for a better understanding of the potential effects of harvesting on the dynamics of seasonal populations, we carry out a theoretical analysis of a discrete model for a semelparous population with an annual cycle involving three discrete density-dependent events: breeding, natural mortality, and harvesting. Our study reveals how the interplay between the model parameters determines the importance of harvest timing on stability and population abundance, especially when two nontrivial stable equilibria coexist. We address the possibility for compensatory mortality and report different forms of the hydra effect, including non-smooth ones due to catastrophic shifts. These drastic switches may include hysteresis, which has important implications for conservation goals. Regarding variability, we show that increasing the harvesting effort may either stabilize or destabilize the population, and these effects strongly depend on harvest timing and natural mortality rates. Our results also emphasize the importance of sampling populations after every discrete event occurs during one cycle. Indeed, though the dynamics are not affected by census timing, the model shows that changes in population abundance in response to changes in harvesting pressure are substantially different depending on when population is sampled. Thus, a manager would receive different (and sometimes contradictory) messages depending on census time, which could lead to managing mistakes.