CANCELLED - A simplified perspective on quantifying spatial patterning in ecology

Background/Question/Methods

Ecological processes are spatially explicit. Changes in these processes associated with climate shifts requires apt comparative methodology. In two recent Landscape Ecology articles, DeWitt et al. identified qualities logically and functionally desirable for metrics of spatial autocorrelation. The traditional measure, Moran’s I, demonstrated two of 14 identified qualities. I has a long history in landscape ecology and ideals it is thought to represent are valuable capital if the metric can be improved. A method to fit traditional I to the theoretical distribution of regular correlations was developed and tested. The method calculates a crossproduct between spatially explicit measurements and a proximity matrix corresponding to inverse distances between sample locations. This crossproduct is then calculated for k data randomizations. The proportion of crossproducts from randomizations less than the observed value is used to calculate a t statistic which is used to calculate a correlation-equivalent metric, Ir, as t/√(n – 2 + t²).

Results/Conclusions

The new metric, now a statistic, realized all 14 desirable traits, fit existing intuition for correlations, and enabled comparison across disparate contexts. For 29 empirical case studies, I enabled rough comparison among variables within studies but in 7 instances was incorrectly signed. Average I and Ir among studies were poorly related (R²= .09). I was thus a poor metric of spatial pattern. Metrics of spatial pattern are currently important in ecology but will become especially so due to re-regionalization of patterns accompanying climate change. Thus rigorous metrics of pattern, such as Ir as opposed to I, that allow comparisons among studies and timepoints are needed.