Several ecological and evolutionary hypotheses have been proposed to explain the latitudinal diversity gradient (LDG), but a general model for this conspicuous pattern remains elusive. Mid-domain effect (MDE) models generate gradients of species diversity by randomly placing the geographic ranges of species in one- or two-dimensional spaces, thus excluding both evolutionary processes and the effect of contemporary climate. Traditional MDE models are statistical and static because they determine the size of ranges either randomly or based on empirical frequency distributions. Here we present a simple dynamic null model for the LDG that simulates stochastic processes of range shifts, extinction and speciation. The model predicts higher species diversity and higher extinction and speciation rates in the tropics, and a strong influence of range movements in shaping the LDG. These null expectations should be taken into consideration in studies aimed at understanding the many factors that generate latitudinal diversity gradients.