Seasonal density dependence, timing of mortality, and sustainable harvesting

Birth-pulse populations are often characterized with discrete-time models, that use a single function to relate the post-breeding population size to the post-breeding size of the previous year. Recently, models of seasonal density dependence have been constructed that emphasize interactions during shorter time periods also. Here, we study two very simple forms of density-dependent mortality, that lead to Ricker and Beverton-Holt type population dynamics when viewed over the whole year. We explore the consequences of harvest timing to equilibrium population sizes under such density dependence. Whether or not individual mortality compensates for the harvested quota, the timing of harvesting has a strong impact on the sustainability of a harvesting quota. Further, we show that careless discretization of a continuous mortality scheme may seriously underestimate the reduction in population size caused by hunting and overestimate the sustainable yield. We also introduce the concept of the demographic value of an individual, which reflects the expected contribution to population size over time in the presence of density dependence. Finally, we discuss the possibility of calculating demographic values as means of optimizing harvest strategies. Here, a Pareto optimal harvest strategy will minimize the loss of demographic value from the population for a given yield.