Figure 1.
The spatial-temporal variability link.
(A) We derived an analytical relationship linking regional temporal variance of a process (Var(Y)) to summed spatial variances at time k (∑var(Xk)). Inter-patch synchrony (∑cov(Xi,Xj)) and persistence (∑cov(Xk,Xl)) modify this link and lead temporal and spatial variance to scale as a function of number of patches (ni) and time points (nk) when these terms are zero. (B) We evaluate the usefulness, for prediction and description, of the corresponding (relative) relationship that uses dimensionless coefficients: Regional temporal CV (CVY), mean spatial CV (), and indices of synchrony (φT) and persistence (φS). While an exact solution exists (Eq. S28, File S1), we use a more useful approximation,
, that gives an expected temporal CV for a given spatial CV when synchrony and persistence are negligible (Eq. S31,File S1).
Figure 2.
Spatial imprinting of ecosystem processes.
Theorized mechanism by which temporal fluctuations of patches create spatial variability in the landscape, which may in turn be a proxy for temporal variability. Spatiotemporal patterns (inter-patch synchrony and persistence) modify the correspondence of spatial and temporal variability (Fig. 1), so it is unknown whether the link is strong enough for predictive (e.g., space-for-time substitution) applications and whether modifying terms have diagnostic/descriptive value.
Figure 3.
Anatomy of a plot between spatial and regional temporal variability.
A stochastic null model of a three patch mosaic illustrated several features of a plot between log mean spatial CV and log regional temporal CV. (A) Three regions exist in which a variable (point) can fall - an “independent dynamics region” when values are independent between patches i and j and time points k and l, a “synchrony region” when inter-patch synchrony boosts temporal CV, and a “persistence region” when spatial gradients are retained over time; (B) Weak linear relationship when variables share similar spatiotemporal variability, leading to scatter from small variations in synchrony or persistence; (C) Strong linear relationships when variables differ in spatiotemporal variabililty and occupy the “independent dynamics region” (black circles), but also when all variables are equally dispaced by synchrony (blue circles) or by persistence (red circles); (D) Deviation of regression slope from ∼1 (black circles) when variables change in synchrony or persistence as a function of variability. Here, a gradient exists from variables with low variability and synchrony to variables with high variability and persistence. Spatial CV values are means of spatial CV measured at time point k. Each point represents a variable and is a mean of ten replicates.
Figure 4.
Empirical CV plots illustrating an underlying spatial-temporal link (Fig. 1B).
The regional temporal CV of an ecosystem variable (data point) was predictable from its spatial CV in microcosm (n = 7) (A, D), rock pool (n = 33) (B, E), and lake systems (n = 60) (C, F). The predictive value of spatial variability was consistent in that linear associations emerged whether spatial variability was estimated as the mean of spatial CV’s at time k (A–C), or whether a spatial CV from an initial time point (k) was used to predict temporal CV of the remaining (k+1…n) time series (D–F). Dashed lines denote the relationship expected for stochastic processes i.e., when values are independent across space and time. These were obtained by simulating random numbers with the same data structure as empirical data sets. Abiotic variables (blue circles) were consistently more stable and less spatially patchy than biotic variables (red circles).
Figure 5.
The modifying role of inter-patch synchrony.
Relationship between spatial CV and regional temporal CV as modified by the degree of inter-patch synchrony in (A) microcosm, (B) rock pools and (C) lakes. Synchrony increased regional temporal CV relatively little over that explained by spatial CV. Black points = empirical variables, blue points = simulated, randomly-generated variables (n = 20; see File S1) to represent “independent dynamics region.”
Figure 6.
Patterns of spatiotemporal variation underlying the temporal variability of ecosystem variables.
The interplay of the three components of temporal variance - spatial variation, synchrony and persistence - was captured by plotting the normalized values of each term in Fig. 1A against each other. Values of each term were standardized to the sum of all three terms such that the resulting proportions summed to one. Variables were assigned to a priori groupings based on their likely genesis and mode of regulation, where blue points = species populations, green = atmospheric, red = non-population biotic, black = watershed. n = 136, and includes an additional 36 rare rock pool species that were excluded from earlier analyses due to sparseness of data. Points scatter across theorized modes of dynamics described in Table 1: A = destabilized by synchrony, B = stabilized by persistence, destabilized by synchrony, C = stabilized by persistence, D = stabilized by compensatory dynamics, Intersection of A-D = stabilized by asynchrony. Gray histograms show frequency distributions for each component of temporal variance.
Table 1.
Theorized modes of dynamics in landscape variables, their effect on regional temporal variation, and ecological examples.
Table 2.
Conditions under which the spatial variability of an ecological process is a precise or accurate substitute for its regional temporal variability.