Indexing variability: A case study with climate change impacts on ecosystems

We developed a methodology to index statistical changes in the variance of ecological measures over time. While ecological indicators are used to assess ecosystem health, vulnerability, risk and damage to ecosystems, their primary focus has been on changes to the mean of the ecological state or process. Little work has been done on incorporating variability into ecological indices. The methodology developed here is based on the Modified Levene's test of variance and a moving block where an initial time period (block) of ecosystem behavior is compared to the moving block. This allows for the detection of not only shifts in variance but also the magnitude of the shift on a continuous basis. Our results compared well with the benchmarked results from the Centered Cumulative Sum of Squares Algorithm (CUSUM) for detection of variance changes in fixed time series. The output from this methodology is a continuous stream of parameters (significant variance shift, magnitude of the shift, and the direction of the variance shift) suitable for indexing variance or integrating into an index measuring ecosystem change. Results suggest that the block interval widths should be at least 50 and that a smoothing factor of five be used to avoid false positives. We used modeled vegetation carbon output to analyze the utility of the methodology, illustrating that different model assumptions and CO2 regimes affect the variability of the ecological response. The degree of risk resource managers may want to explore can be altered by choices in the block length, the length of the string used to smooth variance shifts, the assumption that the initial period has constant variance and the alpha levels used to determine statistical significance.