Summary: The delay differential equation
was used by W. S. C. Gurney, S. P. Blythe and R. M. Nisbet [Nature 287, 17-21 (1980)] in describing the dynamics of Nicholson’s blowflies. We show that for , every nonnegative solution of tends to zero as . On the other hand, for , is uniformly persistent. Moreover, if in addition, , then every positive solution of tends to as .