24:
50:
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
108:. 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
431:. The literature cites this paper and states this law as "geographic variables exhibit uncontrolled variance." Often referred to as the second law of geography, or Michael Goodchild's second law of geography, it is one of many concepts competing for that term, including
406:
The model-agnostic
Spatial Transformation And modeRation (meta-STAR) is a framework for integrating the spatial heterogeneity into spatial statistical models (e.g. spatial ensemble methods, spatial neural networks), so to improve their accuracy. It involves the use of
389:
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.
371:
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.
380:
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.
270:
514:
Alona Levy-Jurgenson and others, Assessing heterogeneity in spatial data using the HTA index with applications to spatial transcriptomics and imaging, Bioinformatics, Volume 37, Issue 21, November 2021, Pages 3796–3804,
530:"An optimal parameters-based geographical detector model enhances geographic characteristics of explanatory variables for spatial heterogeneity analysis: cases with different types of spatial data"
148:
similar within a directly local neighbourhood, but which significantly differ in the nearby surrounding-areas beyond this directly local neighbourhood (e.g. hot spots, cold spots). The
481:
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.
398:
Robust
Geographical Detector (RGD) overcomes the limitation of the sensitivity in spatial data discretization and estimates robust power of determinants of explanatory variables.
349:
307:
649:"Identifying determinants of spatio-temporal disparities in soil moisture of the Northern Hemisphere using a geographically optimal zones-based heterogeneity model"
168:
Spatial local heterogeneity can be tested by LISA, Gi and SatScan, while spatial stratified heterogeneity of an attribute can be measured by geographical detector
128:, 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
490:
Jiang B. 2013. Head/tail breaks: A new classification scheme for data with a heavy-tailed distribution, The
Professional Geographer, 65 (3), 482–494.
178:
46:
within an area. A landscape with spatial heterogeneity has a mix of concentrations of multiple species of plants or animals (biological), or of
472:
Jiang B. 2015. Geospatial analysis requires a different way of thinking: The problem of spatial heterogeneity. GeoJournal 80(1), 1–13.
156:
variance of its attributes' values is significantly lower than its between-strata variance, such as collections of ecological zones or
27:
Land cover surrounding
Madison, WI. Fields are colored yellow and brown, water is colored blue, and urban surfaces are colored red.
291:
is within , 0 indicates no spatial stratified heterogeneity, 1 indicates perfect spatial stratified heterogeneity. The value of
318:-statistic; * denotes statistical significant at level 0.05, ** for 0.001, *** for smaller than 10;(D) subscripts 1, 2, 3 of
326:
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
432:
587:"Optimal Parameters-based Geographical Detectors (OPGD) Model for Spatial Heterogeneity Analysis and Factor Exploration"
428:
423:
In a 2004 publication titled "The
Validity and Usefulness of Laws in Geographic Information Science and Geography,"
799:
Goodchild, Michael (2004). "The
Validity and Usefulness of Laws in Geographic Information Science and Geography".
502:
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 67: 250-256.
917:
436:
338:
Spatial heterogeneity for multivariate data and 3D data can also be statistically assessed using the
973:
601:
529:
85:
145:
648:
424:
586:
415:, plus handles the geo-spatial datasets representing geographic phenomena at multiple scales.
647:
Luo, Peng; Song, Yongze; Huang, Xin; Ma, Hongliang; Liu, Jin; Yao, Yao; Meng, Liqiu (2022).
287:
stands for the size of the population, σ stands for variance of the attribute. The value of
660:
295:
indicates the percent of the variance of an attribute explained by the stratification. The
132:
there are. Plant species richness directly reflects spatial heterogeneity in an ecosystem.
8:
968:
153:
17:
933:
812:
664:
937:
901:
874:
816:
773:
746:
727:
676:
629:
567:
427:
proposed Spatial heterogeneity could be a candidate for a law of geography similar to
873:
Zhang, Yu; Sheng, Wu; Zhao, Zhiyuan; Yang, Xiping; Fang, Zhixiang (30 January 2023).
778:
731:
680:
633:
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571:
559:
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820:
672:
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808:
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66:
of far more small things than large ones. It has been formulated as a scaling law.
617:
545:
839:"Mining Type-β Co-Location Patterns on Closeness Centrality in Spatial Data Sets"
516:
448:
265:{\displaystyle q=1-{\frac {1}{N\sigma ^{2}}}\sum _{h=1}^{L}N_{h}\sigma _{h}^{2}}
891:
763:
722:
712:
695:
554:
962:
625:
563:
69:
Spatial heterogeneity or scaling hierarchy can be measured or quantified by
782:
747:"Harnessing heterogeneity in space with statistically guided meta-learning"
745:
Xie Y, Chen W, He E, Jia X, Bao H, Zhou X, Ghosh R, Ravirathinam P (2023).
129:
23:
855:
838:
42:. It refers to the uneven distribution of various concentrations of each
334:
denotes the strata Z1+Z2 with Z3+Z4,and Z1+Z3 with Z2+Z4, respectively.
121:
93:
39:
144:
categorises the geographic phenomena whose its attributes' values are
700:
International Journal of Applied Earth Observation and Geoinformation
109:
97:
35:
384:
157:
875:"An urban crowd flow model integrating geographic characteristics"
837:
Zou, Muquan; Wang, Lizhen; Wu, Ping; Tran, Vanha (23 July 2022).
366:
125:
105:
101:
89:
47:
43:
375:
340:
113:
510:
508:
348:
528:
Song, Yongze; Wang, Jinfeng; Ge, Yong; Xu, Chengdong (2020).
117:
505:
606:
International Journal of Geographical Information Science
306:
140:
There exist two main types of spatial heterogeneity. The
152:
categorises the geographic phenomena whose the within-
181:
498:
496:
361:
872:
653:ISPRS Journal of Photogrammetry and Remote Sensing
602:"An interactive detector for spatial associations"
310:A hand map with different spatial patterns. Note:
264:
922:Annals of the Association of American Geographers
801:Annals of the Association of American Geographers
738:
493:
960:
794:
792:
385:Geographically optimal zones-based heterogeneity
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160:classes within a given geographic area depict.
116:is directly related to the species richness of
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517:https://doi.org/10.1093/bioinformatics/btab569
367:Optimal parameters-based geographical detector
836:
789:
694:Zhang, Zehua; Song, Yongze; Wu, Peng (2022).
376:Interactive detector for spatial associations
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866:
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104:are able to accommodate a greater amount of
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909:
832:
830:
900:
890:
863:
854:
798:
772:
762:
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711:
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352:HTA p-values for different distributions.
341:"HTA index (HeTerogeneity Average index)"
918:"On the First Law of Geography: A Reply"
347:
305:
22:
827:
275:where a population is partitioned into
961:
915:
599:
112:productivity, the species richness of
34:is a property generally ascribed to a
584:
934:10.1111/j.1467-8306.2004.09402009.x
813:10.1111/j.1467-8306.2004.09402008.x
418:
13:
14:
985:
751:Knowledge and Information Systems
433:Tobler's second law of geography
409:spatial networks/transformations
362:Spatial stratified heterogeneity
150:spatial stratified heterogeneity
687:
673:10.1016/j.isprsjprs.2022.01.009
600:Song, Yongze; Wu, Peng (2021).
429:Tobler's first law of geography
696:"Robust geographical detector"
640:
593:
578:
534:GIScience & Remote Sensing
521:
484:
475:
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303:probability density function.
54:
1:
618:10.1080/13658816.2021.1882680
546:10.1080/15481603.2020.1760434
459:
401:
394:Robust geographical detector
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142:spatial local heterogeneity
80:
10:
990:
892:10.1038/s41598-023-29000-5
764:10.1007/s10115-023-01847-0
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15:
713:10.1016/j.jag.2022.102782
356:
437:Arbia's law of geography
135:
124:serves as food sources,
16:Not to be confused with
425:Michael Frank Goodchild
88:with a wide variety of
916:Tobler, Waldo (2004).
353:
335:
314:is the probability of
266:
236:
120:in a certain habitat.
28:
843:ISPRS Int. J. Geo-Inf
585:Song, Yongze (2021).
351:
309:
299:follows a noncentral
267:
216:
62:can be re-phrased as
60:Spatial heterogeneity
32:Spatial heterogeneity
26:
856:10.3390/ijgi11080418
179:
665:2022JPRS..185..111L
454:Spatial association
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18:Spatial variability
879:Scientific Reports
723:20.500.11937/88650
555:20.500.11937/79549
413:spatial moderators
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92:such as different
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64:scaling hierarchy
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974:Spatial analysis
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612:(8): 1676–1701.
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540:(5): 593–610.
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86:Environments
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659:: 111–128.
55:Terminology
969:Ecosystems
963:Categories
849:(8): 418.
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460:References
279:= 1, ...,
122:Vegetation
98:soil types
40:population
732:248470509
681:246496936
634:234812819
626:1365-8816
572:219418482
564:1548-1603
402:meta-STAR
249:σ
218:∑
205:σ
192:−
110:ecosystem
36:landscape
947:10 March
942:33201684
821:17912938
783:37035130
443:See also
283:strata;
158:land-use
126:habitats
102:climates
90:habitats
81:Examples
71:ht-index
38:or to a
902:9886992
774:9994417
661:Bibcode
164:Testing
114:animals
106:species
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357:Models
154:strata
118:plants
100:, and
938:S2CID
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728:S2CID
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568:S2CID
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622:ISSN
560:ISSN
411:and
330:and
322:and
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