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

Abstract

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 .

Spatial and Temporal Taylor's Law in 1-Dim Chaotic Maps

“…In our case, each trajectory was independent of each other, and the relationship between STL and TTL only depends on the temporal correlation in each trajectory. So, our results were complementary to past research [11,12], which considered the case of dependent trajectories and argued how the dependence between the trajectories, such as the environmental synchrony and density-dependent dispersal, affected the exponent, although the possibility that the temporal correlation might affect the exponent of TTL was pointed out in [12].…”

“…In this letter, we investigate both STL and TTL in the chaotic regime of 1-D maps, discussing a possible mechanism of both STL and TTL. There are only a few studies that have investigated the relationship of STL and TTL [10,11,12]. They use empirical data with a probabilistic model, but no theoretical explanation was provided.…”

A Dynamic Taylor's Law

“…Empirical studies will also be conducted to investigate the respective domain of validity of those two different Taylor's law. We suspect that the new dynamic Taylor's law may be more relevant for some specific cases as those discussed in [8,27]. Ecological considerations will be highlighted in such data studies.…”

“…By doing so, we do not affect the behaviour of partial sums when k n → ∞. Indeed, if the condition a > 1 is fulfilled in (27), see Appendix A.2, we can show that Var…”

“…Such models include dependence over the time and should rather be used in order to describe dynamical evolution of a population [7]. It is, in fact, relevant in populations dynamics and in particular for ecological application, see also [8,27] and the reference therein.…”