Spatial synchrony in population fluctuations: extending the Moran theorem to cope with spatially heterogeneous dynamics

The recent interest in the spatial structure and dynamics of populations motivated numerous theoretical and empirical studies of spatial synchrony, the tendency of populations to fluctuate in unison over regional areas. The first comprehensive framework applied to spatial synchrony was probably the one elaborated by P. A. P. Moran back in 1953. He suggested that if two populations have the same linear density-dependent structure, the correlation between them will be equal to that between the local density-independent conditions. Surprisingly, the consequences of violating the assumption that the dynamics of the populations are identical has received little attention. In this paper, making the assumption that population dynamics can be described by linear and stationary autoregressive processes, I show that the observed spatial synchrony between two populations can be decomposed into two multiplicative components: the demographic component depending on the values of the autoregressive coefficients, and the correlation of the environmental noise. The Moran theorem corresponds to the special case where the demographic component equals unity. Using published data, I show that the spatial variability in population dynamics may substantially contribute to the spatial variability of population synchrony, and thus should not be neglected in future studies.