Abstract
Constant immigration can stabilize population size fluctuations but its effects on extinction remain unexplored. We show that constant immigration significantly reduced extinction in fruitfly populations with relatively stable or unstable dynamics. In unstable populations with oscillations of amplitude around 1.5 times the mean population size, persistence and constancy were unrelated. Low immigration enhanced persistence without affecting constancy whereas high immigration increased constancy without enhancing persistence. In relatively stable populations with erratic fluctuations of amplitude close to the mean population size, both low and high immigration enhanced persistence. In these populations, the amplitude of fluctuations relative to mean population size went down due to immigration, and their dynamics were altered to low-period cycles. The effects of immigration on the population size distribution and intrinsic dynamics of stable versus unstable populations differed considerably, suggesting that the mechanisms by which immigration reduced extinction risk depended on underlying dynamics in complex ways.