Synchrony of spatial populations: heterogeneous population dynamics and reddened environmental noise

Many species exhibit widespread spatial synchrony in population fluctuations. This pattern is of great ecological interest and can be a source of concern when a species is rare or endangered. Moran's theorem suggests that if two (or more) populations sharing a common linear density-dependence in the renewal process are disturbed with correlated noise, they will become synchronized with correlation matching the noise correlation. In this report, correlation of nonidentical populations that are described by linear and stationary autoregressive processes is analyzed. We show that the expected spatial synchrony between two populations can be decomposed into two multiplicative components. One is the demographic component related to the values of the autoregressive coefficients and the noise color. The other is the spatial correlation of the environmental colored noise. The main results are consistent with the predictions of previous experiments and simulations, and the importance of this report is to provide theoretical support.