The main goal of species distribution modeling is to identify important underlying factors related to broad-scale ecological patterns in order to make meaningful explanations or accurate predictions. When standard statistical methods such as regression are used to formulate these models, assumptions about the spatial structure of the data and the model parameters are often violated. Autocorrelation and non-stationarity are characteristics of spatial data and models, respectively, and if present and unaccounted for in model development, they can result in poorly specified models as well as inappropriate spatial inference and prediction. While these spatial issues are addressed here in an ecological context using species distribution models, they are broadly relevant to any statistical modeling applications using spatial data.
AraújoMWhittakerRLadleRErhardM (2005) Reducing uncertainty in projections of extinction risk from climate change. Global Ecology and Biogeography14(6): 529–538.
2.
AtkinsonPM (1997) Geographical information science. Progress in Physical Geography21(4): 573–582.
3.
AtkinsonPM (2001) Geographical information science: Geocomputation and nonstationarity. Progress in Physical Geography25(1): 111–122.
4.
AustinM (2007) Species distribution models and ecological theory: A critical assessment and some possible new approaches. Ecological Modelling200
(1–2): 1–19.
5.
AustinMPVan NielKP (2011) Improving species distribution models for climate change studies: Variable selection and scale. Journal of Biogeography38(1): 1–8.
6.
BahnVO’ConnorRKrohnW (2006) Importance of spatial autocorrelation in modeling bird distributions at a continental scale. Ecography29: 835–844.
7.
BealeCLennonJElstonDBrewerMYearsleyJ (2007) Red herrings remain in geographical ecology: A reply to Hawkins et al. (2007). Ecography30: 845–847.
8.
BealeCMLennonJJYearsleyJM. (2010) Regression analysis of spatial data. Ecology Letters13(2): 246–264.
9.
BickfordSLaffanS (2006) Multi-extent analysis of the relationship between pteridophyte species richness and climate. Global Ecology and Biogeography15: 588–601.
10.
BiniLMDiniz-FilhoJAFRangelTFLVB. (2009) Coefficient shifts in geographical ecology: An empirical evaluation of spatial and non-spatial regression. Ecography32(2): 193–204.
11.
CassemiroFASBarretoBRangelTDiniz-FilhoJ (2007) Non-stationarity, diversity gradients and the metabolic theory of energy. Global Ecology and Biogeography16(6): 820–822.
12.
CliffADOrdJK (2009) What were we thinking?Geographical Analysis41(4): 351–363.
13.
De KnegtHJVan LangeveldeFCoughenourMB. (2010) Spatial autocorrelation and the scaling of species-environment relationships. Ecology91(8): 2455–2465.
14.
Diniz–FilhoJAFBiniLM (2005) Modelling geographical patterns in species richness using eigenvector–based spatial filters. Global Ecology and Biogeography14(2): 177–185.
15.
Diniz-FilhoJAFBiniLHawkinsB (2003) Spatial autocorrelation and red herrings in geographical ecology. Global Ecology and Biogeography12: 53–64.
16.
Diniz–FilhoJAFRangelTFLVBBiniLM (2008) Model selection and information theory in geographical ecology. Global Ecology and Biogeography17(4): 479–488.
17.
DormannC (2007a) Effects of incorporating spatial autocorrelation into the analysis of species distribution data. Global Ecology and Biogeography16: 129–138.
18.
DormannC (2007b) Assessing the validity of autologistic regression. Ecological Modelling207(2–4): 234–242.
19.
DormannCMcPhersonJAraújoMB. (2007) Methods to account for spatial autocorrelation in the analysis of species distributional data: A review. Ecography30: 609–628.
20.
DuncanRPCasseyPBlackburnTM (2009) Do climate envelope models transfer? A manipulative test using dung beetle introductions. Proceedings of the Royal Society B: Biological Sciences276(1661): 1449.
21.
EiserhardtWLBjorholmSSvenningJ-C. (2011) Testing the water-energy theory on American palms (Arecaceae) using geographically weighted regression. PLoS ONE6(11): e27027.
22.
ElithJLeathwickJ (2009) Species distribution models: Ecological explanation and prediction across space and time. Annual Review of Ecology, Evolution, and Systematics40: 677–697.
23.
ElithJGrahamCAndersonRGroupNW (2006) Novel methods improve prediction of species’ distributions from occurrence data. Ecography29(2): 129–151.
24.
FeeleyKJSilmanMR (2011) Keep collecting: Accurate species distribution modelling requires more collections than previously thought. Diversity and Distributions17(6): 1132–1140.
25.
Ferrer–CastánDVetaasOR (2005) Pteridophyte richness, climate and topography in the Iberian Peninsula: Comparing spatial and nonspatial models of richness patterns. Global Ecology and Biogeography14(2): 155–165.
26.
FerrierSGuisanA (2006) Spatial modelling of biodiversity at the community level. Journal of Applied Ecology43(3): 393–404.
27.
FinleyAO (2011) Comparing spatially–varying coefficients models for analysis of ecological data with non–stationary and anisotropic residual dependence. Methods in Ecology and Evolution2(2): 143–154.
28.
FoodyGM (2004) Spatial nonstationarity and scale-dependency in the relationship between species richness and environmental determinants for the sub-Saharan endemic avifauna. Global Ecology and Biogeography13: 315–320.
29.
FoodyGM (2008) GIS: Biodiversity applications. Progress in Physical Geography32(2): 223–235.
30.
FortinMJDaleM (2005) Spatial Analysis: A Guide for Ecologists. Cambridge: Cambridge University Press.
31.
FortinMJDaleMR (2009) Spatial autocorrelation in ecological studies: A legacy of solutions and myths. Geographical Analysis41(4): 392–397.
32.
FotheringhamAS (2009) ‘The problem of spatial autocorrelation’ and local spatial statistics. Geographical Analysis41(4): 398–403.
33.
FotheringhamASBrunsdonCCharltonM (2002) Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Chichester: Wiley.
34.
FranklinJ (1995) Predictive vegetation mapping: Geographic modeling of biospatial patterns in relation to environmental gradients. Progress in Physical Geography19: 474–499.
35.
FranklinJ (2009) Mapping Species Distributions: Spatial Inference and Prediction. Cambridge: Cambridge University Press.
36.
FranklinJMillerJ (2009) Statistical methods – Modern regression. In: FranklinJ (ed.) Mapping Species Distribution: Spatial Inference and Prediction. Cambridge: Cambridge University Press, 113–153.
37.
GaoJLiS (2011) Detecting spatially non-stationary and scale-dependent relationships between urban landscape fragmentation and related factors using geographically weighted regression. Applied Geography31(1): 292–302.
38.
GetisA (2008) A history of the concept of spatial autocorrelation: A geographer’s perspective. Geographical Analysis40(3): 297–309.
39.
GriffithDA (2008) Spatial-filtering-based contributions to a critique of geographically weighted regression (GWR). Environment and Planning A40: 2751–2769.
40.
GuisanAZimmermannN (2000) Predictive habitat distribution models in ecology. Ecological Modelling135: 147–186.
41.
HanspachJKühnISchweigerO. (2011) Geographical patterns in prediction errors of species distribution models. Global Ecology and Biogeography20(5): 779–788.
42.
HarrisPFotheringhamASCrespoRCharltonM (2010) The use of geographically weighted regression for spatial prediction: An evaluation of models using simulated data sets. Mathematical Geosciences42(6): 657–680.
43.
HawkinsBDiniz-FilhoJBiniL. (2007) Red herrings revisited: Spatial autocorrelation and parameter estimation in geographical ecology. Ecography30: 375–384.
44.
HeikkinenRLuotoMAraújoM. (2006) Methods and uncertainties in bioclimatic envelope modelling under climate change. Progress in Physical Geography30(6): 751–777.
45.
HendenJAImsRAYoccozNG (2009) Nonstationary spatio-temporal small rodent dynamics: Evidence from long-term Norwegian fox bounty data. Journal of Animal Ecology78(3): 636–645.
46.
HirzelALe LayG (2008) Habitat suitability modeling and niche theory. Journal of Applied Ecology45: 1372–1381.
47.
HothornTMüllerJSchröderB. (2011) Decomposing environmental, spatial, and spatiotemporal components of species distributions. Ecological Monographs81(2): 329–347.
48.
JetzWRahbekCLichsteinJW (2005) Local and global approaches to spatial data analysis in ecology. Global Ecology and Biogeography14: 97–98.
49.
KentM (2007) Biogeography and macroecology: Now a significant component of physical geography. Progress in Physical Geography31(6): 643–657.
50.
KisslingWDCarlG (2008) Spatial autocorrelation and the selection of simultaneous autoregressive models. Global Ecology and Biogeography17: 59–71.
51.
KühnI (2007) Incorporating spatial autocorrelation may invert observed patterns. Diversity and Distributions13: 66–69.
52.
KupferJFarrisC (2007) Incorporating spatial non-stationarity of regression coefficients into predictive vegetation models. Landscape Ecology22: 837–852.
53.
LegendreP (1993) Spatial autocorrelation: Trouble or new paradigm?Ecology74(6): 1659.
54.
LennonJJ (2000) Red–shifts and red herrings in geographical ecology. Ecography23(1): 101–113.
55.
LoboJMJiménez-ValverdeAHortalJ (2010) The uncertain nature of absences and their importance in species distribution modeling. Ecography33(1): 103–114.
56.
LozierJDAnielloPHickersonMJ (2009) Predicting the distribution of Sasquatch in western North America: Anything goes with ecological niche modelling. Journal of Biogeography36(9): 1623–1627.
57.
McAlpineCRhodesRBowenM. (2008) Can multiscale models of species’ distribution be generalized from region to region? A case study of the koala. Journal of Applied Ecology45: 558–567.
58.
McPhersonJJetzW (2007) Type and spatial structure of distribution data and the perceived determinants of geographical gradients in ecology: The species richness of African birds. Global Ecology and Biogeography16: 657–667.
59.
Martín–QuellerEGil–TenaASauraS (2011) Species richness of woody plants in the landscapes of Central Spain: The role of management disturbances, environment and non–stationarity. Journal of Vegetation Science22(2): 238–250.
60.
MillerJ (2010) Species distribution modeling. Geography Compass4(6): 490–509.
61.
MillerJHanhamRQ (2011) Spatial nonstationarity and the scale of species–environment relationships in the Mojave Desert, California, USA. International Journal of Geographical Information Science25(3): 423–438.
OsbornePSuárez-SeoaneS (2002) Should data be partitioned spatially before building large scale distribution models?Ecological Modelling157: 249–259.
64.
OsbornePFoodyGSuárez-SeoaneS (2007) Non-stationarity and local approaches to modelling the distribution of wildlife. Diversity and Distributions13: 313–323.
65.
PeelMCBlöschlG (2011) Hydrological modeling in a changing world. Progress in Physical Geography35(2): 249.
66.
PetersonAT (2006) Ecological niche modeling and spatial patterns of disease transmission. Emerging Infectious Diseases12(12): 1822–1826.
67.
PioreckyMDPrescottDRC (2006) Multiple spatial scale logistic and autologistic habitat selection models for northern pygmy owls, along the eastern slopes of Alberta’s Rocky Mountains. Biological Conservation129(3): 360–371.
68.
PowneyGDGrenyerROrmeCDL. (2010) Hot, dry and different: Australian lizard richness is unlike that of mammals, amphibians and birds. Global Ecology and Biogeography19(3): 386–396.
69.
PykeGHEhrlichPR (2010) Biological collections and ecological/environmental research: A review, some observations and a look to the future. Biological Reviews85(2): 247–266.
70.
RahbekCGravesG (2001) Multiscale assessment of patterns of avian species richness. Proceedings of the National Academy of Sciences98(8): 4534–4539.
71.
RangelTFDiniz-FilhoJAFBiniLM (2010) SAM: A comprehensive application for spatial analysis in macroecology. Ecography33(1): 46–50.
72.
RichardsonDThuillerW (2007) Home away from home – objective mapping of high-risk source areas for plant introductions. Diversity and Distributions13: 299–312.
73.
SáACLPereiraJMCCharltonME (2010) The pyrogeography of sub-Saharan Africa: A study of the spatial non-stationarity of fire–environment relationships using GWR. Journal of Geographical Systems13(3): 227–248.
74.
SandelBSmithAB (2009) Scale as a lurking factor: Incorporating scale-dependence in experimental ecology. Oikos118(9): 1284–1291.
75.
SeguradoPAraújoMKuninW (2006) Consequences of spatial autocorrelation for niche-based models. Journal of Applied Ecology43: 433–444.
76.
SimpsonE (1951) The interpretation of interaction in contingency tables. Journal of the Royal Statistical SocietyB13: 238–241.
77.
SmuldersMNelsonTAJelinskiDE. (2010) A spatially explicit method for evaluating accuracy of species distribution models. Diversity and Distributions16(6): 996–1008.
78.
StockwellD (2006) Niche Modeling: Predictions from Statistical Distributions. Boca Raton, FL: Chapman and Hall/CRC.
79.
SuSXiaoRZhangY (2012) Multi-scale analysis of spatially varying relationships between agricultural landscape patterns and urbanization using geographically weighted regression. Applied Geography32(2): 360–375.
80.
SyphardADRadeloffVCKeulerNS. (2008) Predicting spatial patterns of fire on a southern California landscape. International Journal of Wildland Fire17(5): 602–613.
81.
ToblerWR (1970) A computer movie simulating urban growth in the Detroit region. Economic Geography46: 234–240.
82.
TognelliMFKeltDA (2004) Analysis of determinants of mammalian species richness in South America using spatial autoregressive models. Ecography27(4): 427–436.
83.
WheelerDC (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A39(10): 2464–2481.
84.
WheelerDCCalderCA (2007) An assessment of coefficient accuracy in linear regression models with spatially varying coefficients. Journal of Geographical Systems9(2): 145–166.
85.
WillisKWhittakerR (2002) Species diversity – scale matters. Science295: 1245–1248.
86.
ZaniniFPelletJSchmidtBR (2009) The transferability of distribution models across regions: An amphibian case study. Diversity and Distributions15(3): 469–480.
87.
ZhangLGoveJHHeathLS (2005) Spatial residual analysis of six modeling techniques. Ecological Modelling186(2): 154–177.
88.
ZimmermannNEEdwardsTCGrahamCH. (2010) New trends in species distribution modelling. Ecography33(6): 985–989.
