<p>In this work, a hybrid ODE-PDE model is proposed to study the spatial dynamics of species with annually short breeding season. By transforming the model to a discrete dynamical system, we investigate the invasion dynamics in terms of the spreading speed and traveling waves of the system in an unbounded spatial domain. The results show that the spreading speed is coincident with the minimal wave speed of traveling waves for both monotone and nonmonotone birth functions. Moreover, we determine the existence of the critical domain size for the system in a bounded domain with hostile boundary conditions. The result demonstrates that the persistence of species can be predicted by the critical domain size. The formulas for computing the spreading speed and critical domain size are provided. Numerical simulations are conducted to illustrate theoretical results, and the impact of the length of breeding season on the evolution of species is further explored. It is suggested that the uniform distribution of adults to give birth in breeding season is a favorable reproduction strategy.</p>