Spatial heterogeneity

A landscape with spatial heterogeneity has a mix of concentrations of multiple species of plants or animals (biological), or of terrain formations (geological), or environmental characteristics (e.g. rainfall, temperature, wind) filling its area.

[1] Spatial heterogeneity or scaling hierarchy can be measured or quantified by ht-index: a head/tail breaks induced number.

[2][3] Environments with a wide variety of habitats such as different topographies, soil types, and climates are able to accommodate a greater amount of species.

[4] Spatial local heterogeneity can be tested by LISA, Gi and SatScan, while spatial stratified heterogeneity of an attribute can be measured by geographical detector q-statistic:[4] where a population is partitioned into h = 1, ..., L strata; N stands for the size of the population, σ2 stands for variance of the attribute.

:[5] Optimal Parameters-based Geographical Detector (OPGD) characterizes spatial heterogeneity with the optimized parameters of spatial data discretization for identifying geographical factors and interactive impacts of factors, and estimating risks.

[12] The literature cites this paper and states this law as "geographic variables exhibit uncontrolled variance.

Land cover surrounding Madison, WI. Fields are colored yellow and brown, water is colored blue, and urban surfaces are colored red.
A hand map with different spatial patterns. Note: p is the probability of q -statistic; * denotes statistical significant at level 0.05, ** for 0.001, *** for smaller than 10 −3 ;(D) subscripts 1, 2, 3 of q and p denotes the strata Z1+Z2 with Z3,Z1 with Z2+Z3, and Z1 and Z2 and Z3 individually, respectively; (E) subscripts 1 and 2 of q and p denotes the strata Z1+Z2 with Z3+Z4,and Z1+Z3 with Z2+Z4, respectively.
HTA [ 5 ] p-values for different distributions.