Ecological Archives E092-089-A3

Richard J. Vogt, James A. Rusak, Alain Patoine, and Peter R. Leavitt. 2011. Differential effects of energy and mass influx on the landscape synchrony of lake ecosystems. Ecology 92:1104–1114.

Appendix C. Calculation of ecosystem synchrony (S).

Time series of climatic, limnological, and biological parameters were individually Z-transformed by subtracting the mean of each raw time series from the respective time series observation, then dividing each observation by the standard deviation (SD) of the raw time series (Rusak et al. 1999). As such, each Z-transformed variable was centered on 0.0 and varied from 3.0 to -3.0. As seen in Fig. C1, time series of some parameters (e.g., air temperature) were more visibly synchronous among climate stations than were other environmental time series (e.g., annual precipitation). To quantify this visual impression, synchrony (S) of each parameter was estimated as the average Pearson correlation coefficient (r) for all pairs of Z-transformed time series (Patoine and Leavitt 2006) (Fig. C2). Parameters with elevated S values, such as air temperature (S = 0.90) (closed histograms, solid mean line), exhibited more uniformly elevated pair-wise correlations among sites than did less synchronous parameters, such as mean annual precipitation (S = 0.55) (open histograms, dashed mean line). In general, ecosystem time series vary from S = 1.0 for perfectly synchronous parameters, to 0.0 for asynchronous time series, while slightly negative values (ca. S = -0.10) can arise when parameters vary out of phase. Statistical significance of each S value was determined using a permutation test whereby the observed S was compared to a distribution of r values derived from 999 randomizations of the original time series (Rusak et al. 1999).

FIG. C1.



FIG. C2.

LITERATURE CITED

Patoine, A., and P. R. Leavitt. 2006. Century-long synchrony of algal fossil pigments in a chain of Canadian prairie lakes. Ecology 87:1710–1721.

Rusak, J. A., N. D. Yan, K. M. Somers, and D. J. McQueen. 1999. The temporal coherence of zooplankton population abundances in neighboring North-temperate lakes. American Naturalist 153:46–58.


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