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We consider mathematical population dynamics models in deterministic and stochastic environments. For deterministic environments, we study three models: an intraguild model with the effects of spatial heterogeneous environment and fast migration of individuals; a fishery model with Marine Protected Area where fishing is prohibited and an area where the fish population is harvested; a predator-prey model which has one prey and two predators with Beddington-DeAngelis functional responses. For stochastic environments, we study SIRS epidemic model and predator-prey models under telegraph noise. We try to present the dynamical behavior of these models and show out the existence or vanishing of species in the models.