Spatial cross-correlation of undisturbed, natural shortleaf pine stands in northern Georgia

Abstract

In this study a cross-correlation statistic is used to analyse the spatial relationship among stand characteristics of natural, undisturbed shortleafpine stands sampled during 1961-72 and 1972-82 in northern Georgia. Stand characteristics included stand age, site index, tree density, hardwood competition, and mortality. In each time period, the spatial cross-correlation statistic was used to construct cross-correlograms and cumulative crosscorrelograms for all significant pairwise combination of stand characteristics. Both the cross-correlograms and cumulative cross-correlograms identified small-scale clustering and weak directional gradients for different stand characteristics in each time period. The cumulative cross-correlograms, which are based on inverse distance weighting were more sensitive in detecting small-scale clustering than the cross-correlograms based on a 0-1 weighting. Further analysis suggested that the significant cross-correlation observed among basal area growth and other stand characteristics were due, in a large part, on a subset of sample plots located in the northern part of the state, rather than regional or broad-scale variation as first thought. The ability to analyse the spatial relationship between two or more response surfaces should provide valuable insight in the development of ecosystem level models and assist decision makers in formulating pertinent policy on intelligent multiresource management.

Spatial correlations of Diceroprocta apache and its host plants: evidence for a negative impact from Tamarix invasion

“…The spatial relationships between two variables were assessed by estimation of the cross-correlation between a given variable (y i ) and value of a second variable at a distant spatial location (z j ). A modified, bivariate form of Moran's coefficient, I YZ , serves this purpose (Wartenberg, 1985;Reich et al, 1994). Interpretation of I YZ is similar to a Pearson correlation coefficient, with typical values ranging from À1 to 1.…”

“…A generalised test for cross-correlation (Reich et al, 1994;Bonham et al, 1995), i.e. that cross-correlation is greatest among near neighbours and decreases with distance, was performed using spatial proximity weights equal to the inverse of the distance between quadrats (w ij 1=d ij ).…”

“…that cross-correlation is greatest among near neighbours and decreases with distance, was performed using spatial proximity weights equal to the inverse of the distance between quadrats (w ij 1=d ij ). The significance of departure of the observed cross-correlation statistic from the expected value under the null hypothesis of random spatial association (Reich et al, 1994) was assessed, and 95% confidence intervals were constructed, using a random permutation test as explained above.…”

“…Spatial relationships at different scales were explored by calculating Moran's I with different sets of spatial proximity weights (Cliff & Ord, 1981;Jumars et al, 1988). A generalised test for spatial autocorrelation (Reich et al, 1994) was formulated as Moran's I computed with spatial weights equal to the inverse of distance between pairs of quadrats (w ij 1=d ij ). Autocorrelation at discrete distances, as utilised in the correlograms below, was measured using binary spatial proximity weights where w ij 1 if quadrats i and j are separated by the given distance and w ij 0 otherwise.…”

“…The manner in which spatial crosscorrelation varies with distance is indicative of the scales of association between variables. Following Reich et al (1994), cross-correlograms were created using the same binary spatial proximity weights used for the univariate correlograms. The significance of each cross-correlogram was assessed in exactly the same manner as the univariate correlograms.…”