  In this paper, we consider the diffusive Nicholson's blowflies model in
spatially heterogeneous environment when the diffusion rate is large. We show
that the ratio of the average of the maximum per capita egg production rate to
that of the death rate affects the dynamics of the model. The unique positive
steady state is locally asymptotically stable if the ratio is less than a
critical value. However, when the ratio is greater than the critical value,
large time delay can make the unique positive steady state unstable through
Hopf bifurcation. Especially, the first Hopf bifurcation value tends to that of
the ''average'' DDE model when the diffusion rate tends to infinity. Moreover,
we show that the direction of the Hopf bifurcation is forward, and the
bifurcating periodic solution from the first Hopf bifurcation value is
orbitally asymptotically stable, which improves the earlier result by Wei and
Li (Nonlinear. Anal., 60: 1351-1367, 2005).
