In this paper, we briefly review the progress in the way of temporal and spatial variability in mammalian population system, and Moran's theorem and Moran's effect to the synchronization of population fluctuations. One of the most universal phenomena of all natural populations is their variability in numbers in space and time. However, there are distinguishable differences among populations in the way the population size fluctuates. One of the major challenges in population and community ecology is to expla...