In this paper, a parasitic-mutualistic model of mistletoes and birds defined in a heterogneous and periodically evolving domain is comprehensively investigated to reveal some new dynamical phenomena caused by the domain evolution. By establishing the core spatial-temporal risk index R0B and R0M for birds population and mistletoes-birds population, respectively, the fundamental extinction, persistence and coexistence behaviors are studied, and distinguished by such indexes. Moreover, the impact of domain evolution on the viability of mistletoes is examined as well, and it is concluded that the average expansion of the domain can enhance mistletoes' transmission capability, therefore, pro-mote the viability of mistletoes, and vice versa. Finally, numerical simulations are also exhibited for some specific cases to verify the theoretical conclusions.

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