Effects of environmental synchrony and density‐dependent dispersal on temporal and spatial slopes of Taylor's law

Taylor's law (TL) is an empirical rule that describes an approximate relationship between the variance and mean of population density: log 10 (variance) ≈ log 10 ( a ) +  b  × log 10 (mean). Population synchrony is another prevailing feature observed in empirical populations. This study investigated the effects of environmental synchrony and density‐dependent dispersal on the temporal ( b T ) and spatial ( b S ) slopes of TL, using an empirical dataset of gray‐sided vole populations and simulation analyses based on the second‐order autoregressive (AR) model. Eighty‐five empirical populations satisfied the temporal and spatial TLs with b T = 1.943 (± SE 0.143) and b S = 1.579 (± SE 0.136). The pairwise synchrony of population was 0.377 ± 0.199 (mean ±  SD ). Most simulated populations that obeyed the AR model satisfied the form of the temporal and spatial TLs without being affected by the environmental synchrony and density‐dependent dispersal; however, those simulated slopes were too steep. The incorporation of environmental synchrony resulted in reduced simulated slopes, but those slopes, too, were still unrealistically steep. By incorporating density‐dependent dispersal, simulated slopes decreased and fell within a realistic range. However, the simulated populations without environmental synchrony did not exhibit an adequate degree of density synchrony. In simulations that included both environmental synchrony and density‐dependent dispersal, 92.7% of the simulated datasets provided realistic values for b T , b S and population synchrony. Because the two slopes were more sensitive to the variation of density‐dependent dispersal than that of environmental synchrony, density‐dependent dispersal may be the key to the determination of b T and b S .