Threshold dynamics of a predator–prey model with maturation delay in an almost periodic environment

In this paper, we propose and study an almost periodic predator–prey model that incorporates a maturation delay and general seasonal variations. The basic reproduction number $R_{0}$ for this model is introduced, and a threshold-type result in terms of $R_{0}$ is established by comparison arguments, skew-product semiflows, and persistence theory. It is shown that the predator population tends to die out and the predator-free almost periodic state is globally attractive if $R_{0}<1$ , while the predators and prey coexist if $R_{0}>1$ . Moreover, we study a Daphnia–algae model by numerical simulations, and investigate the effects of maturation delay and predation rate on $R_{0}$ . Numerical simulations indicate that shortening the length of maturation delay of Daphnia is beneficial for the persistence of Daphnia.