Spatial heterogeneity

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Land cover surrounding Madison, WI. Fields are colored yellow and brown, water is colored blue, and urban surfaces are colored red.

Spatial heterogeneity is a property generally ascribed to a landscape or to a population. It refers to the uneven distribution of various concentrations of each species within an area. 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. A population showing spatial heterogeneity is one where various concentrations of individuals of this species are unevenly distributed across an area; nearly synonymous with "patchily distributed."


Environments with a wide variety of habitats such as different topographies, soil types, and climates are able to accommodate a greater amount of species. The leading scientific explanation for this is that when organisms can finely subdivide a landscape into unique suitable habitats, more species can coexist in a landscape without competition, a phenomenon termed "niche partitioning." Spatial heterogeneity is a concept parallel to ecosystem productivity, the species richness of animals is directly related to the species richness of plants in a certain habitat. Vegetation serves as food sources, habitats, and so on. Therefore, if vegetation is scarce, the animal populations will be as well. The more plant species there are in an ecosystem, the greater variety of microhabitats there are. Plant species richness directly reflects spatial heterogeneity in an ecosystem.


Spatial heterogeneity could be either local or stratified, the former is called spatial local heterogeneity, referring to the phenomena that the value of an attribute at one site is different from its surrounding, such as hotspot or cold spot; the latter is called spatial stratified heterogeneity, referring to the phenomena that the within strata variance is less than the between strata variance, such as ecological zones and landuse classes.


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:[1]

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. The value of q is within [0, 1], 0 indicates no spatial stratified heterogeneity, 1 indicates perfect spatial stratified heterogeneity. The value of q indicates the percent of the variance of an attribute explained by the stratification. The q follows a noncentral F probability density function.

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.


Spatial stratified heterogeneity[edit]

Optimal parameters-based geographical detector[edit]

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.[2][3]

Interactive detector for spatial associations[edit]

Interactive Detector for Spatial Associations (IDSA) estimates power of interactive determinants (PID) on the basis of spatial stratified heterogeneity, spatial autocorrelation, and spatial fuzzy overlay of explanatory variables.[4]

Geographically optimal zones-based heterogeneity[edit]

Geographically Optimal Zones-based Heterogeneity (GOZH) explores individual and interactive determinants of geographical attributes (e.g., global soil moisture) across a large study area based on the identification of explainable geographically optimal zones.[5]

Robust geographical detector[edit]

Robust Geographical Detector (RGD) overcomes the limitation of the sensitivity in spatial data discretization and estimates robust power of determinants of explanatory variables.[6]


Spatial heterogeneity can be re-phrased as scaling hierarchy of far more small things than large ones. It has been formulated as a scaling law. [7]

Spatial heterogeneity or scaling hierarchy can be measured or quantified by ht-index - a head/tail breaks induced number. [8] [9]

See also[edit]


  1. ^ Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 67: 250-256.
  2. ^ Song, Yongze; Wang, Jinfeng; Ge, Yong; Xu, Chengdong (2020-07-03). "An optimal parameters-based geographical detector model enhances geographic characteristics of explanatory variables for spatial heterogeneity analysis: cases with different types of spatial data". GIScience & Remote Sensing. 57 (5): 593–610. doi:10.1080/15481603.2020.1760434. ISSN 1548-1603.
  3. ^ Song, Yongze (2021-04-27). "Optimal Parameters-based Geographical Detectors (OPGD) Model for Spatial Heterogeneity Analysis and Factor Exploration".
  4. ^ Song, Yongze; Wu, Peng (2021-08-03). "An interactive detector for spatial associations". International Journal of Geographical Information Science. 35 (8): 1676–1701. doi:10.1080/13658816.2021.1882680. ISSN 1365-8816.
  5. ^ Luo, Peng; Song, Yongze; Huang, Xin; Ma, Hongliang; Liu, Jin; Yao, Yao; Meng, Liqiu (March 2022). "Identifying determinants of spatio-temporal disparities in soil moisture of the Northern Hemisphere using a geographically optimal zones-based heterogeneity model". ISPRS Journal of Photogrammetry and Remote Sensing. 185: 111–128. doi:10.1016/j.isprsjprs.2022.01.009.
  6. ^ Zhang, Zehua; Song, Yongze; Wu, Peng (May 2022). "Robust geographical detector". International Journal of Applied Earth Observation and Geoinformation. 109: 102782. doi:10.1016/j.jag.2022.102782.
  7. ^ Jiang B. 2015. Geospatial analysis requires a different way of thinking: The problem of spatial heterogeneity. GeoJournal 80(1), 1-13.
  8. ^ Jiang B. and Yin J. 2014. Ht-index for quantifying the fractal or scaling structure of geographic features, Annals of the Association of American Geographers, 104(3), 530–541.
  9. ^ Jiang B. 2013. Head/tail breaks: A new classification scheme for data with a heavy-tailed distribution, The Professional Geographer, 65 (3), 482 – 494.