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discrete time spatially extended models play important role ecology modelling population dynamics species ranging microorganisms birds important question bottom individualbased models approximated top models dynamics study class spatially explicit individualbased models contest competition species compete space local cells disperse nearby cells start describing simulations model exhibit largescale discrete oscillations characterize oscillations measuring spatial correlations develop two new approximate descriptions resulting spatial population dynamics first based local interactions individuals allows us give difference equation approximation system small dispersal distances second approximates longrange interactions individualbased model approximations capture demographic stochasticity individualbased model show dispersal stabilizes population dynamics calculate extinction probability individualbased model show convergence local approximation nonspatial global approximation individualbased model dispersal distance population size simultaneously tend infinity results provide new approximate analytical descriptions complex bottomup model deepen understanding spatial population dynamics