바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

Residual spatial autocorrelation in macroecological and biogeographical modeling: a review

Journal of Ecology and Environment / Journal of Ecology and Environment, (P)2287-8327; (E)2288-1220
2019, v.43 no.2, pp.191-201
https://doi.org/10.1186/s41610-019-0118-3
Guetchine Gaspard (University of Kentucky)

(University of Texas at Dallas)
  • Downloaded
  • Viewed

Abstract

Macroecologists and biogeographers continue to predict the distribution of species across space based on the relationship between biotic processes and environmental variables. This approach uses data related to, for example, species abundance or presence/absence, climate, geomorphology, and soils. Researchers have acknowledged in their statistical analyses the importance of accounting for the effects of spatial autocorrelation (SAC), which indicates a degree of dependence between pairs of nearby observations. It has been agreed that residual spatial autocorrelation (rSAC) can have a substantial impact on modeling processes and inferences. However, more attention should be paid to the sources of rSAC and the degree to which rSAC becomes problematic. Here, we review previous studies to identify diverse factors that potentially induce the presence of rSAC in macroecological and biogeographical models. Furthermore, an emphasis is put on the quantification of rSAC by seeking to unveil the magnitude to which the presence of SAC in model residuals becomes detrimental to the modeling process. It turned out that five categories of factors can drive the presence of SAC in model residuals: ecological data and processes, scale and distance, missing variables, sampling design, and assumptions and methodological approaches. Additionally, we noted that more explicit and elaborated discussion of rSAC should be presented in species distribution modeling. Future investigations involving the quantification of rSAC are recommended in order to understand when rSAC can have an adverse effect on the modeling process.

keywords
Spatial autocorrelation, Residual spatial autocorrelation, Non-stationarity, Missing variables, Sampling design, Scale, Species distribution models

Reference

1.

Ali GA, Roy AG, Legendre P. Spatial relationships between soil moisture patterns and topographic variables at multiple scales in a humid temperate forested catchment. Water Resour Res. 2010;46:10.

2.

Anselin L. Under the hood: issues in the specification and interpretation of spatial regression models. Agric Econ. 2002;27:247–67.

3.

Anselin L, Bera AK. Spatial dependence in linear regression models with an introduction to spatial econometrics. In: Ullah A, Giles DEA, editors. Handbook of applied economic statistics. New York: Marcel Dekker;1998. p. 237–89.

4.

Anselin L, Syabri I, Kho Y. GeoDa: an introduction to spatial data. Geogr Anal. 2006;38:5–22.

5.

Augustin NH, Cummins RP, French DD. Exploring spatial vegetation dynamics using logistic regression and a multinomial logit model. J Appl Ecol. 2001;38:991–1006.

6.

Austin MP. Spatial prediction of species distribution: an interface between ecological theory and statistical modelling. Ecol Model. 2002;157:101–18.

7.

Bahn V, O’Connor RJ, Krohn WB. Importance of spatial autocorrelation in modeling bird distributions at a continental scale. Ecography. 2006;29:835–44.

8.

Betts MG, Diamond AW, Forbes GJ, Villard M-A, Gunn JS. The importance of spatial autocorrelation, extent and resolution in predicting forest bird occurrence. Ecol Model. 2006;191:197–224.

9.

Bini L, Alexandre J, Diniz-Filho F, TFLVB R, TSB A, Albaladejo RG, Albuquerque FS, Aparicio A, Araújo MB, Baselga A, Beck J, Bellocq MI, Böhning-Gaese K, PAV B, Castro-Parga I, Chey VK, Chown SL, de Marco P Jr, Dobkin DS, Ferrer-Castán D, Field R, Filloy J, Fleishman E, Gómez JF, Hortal J, Iverson JB, Kerr JT, Kissling WD, Kitching IJ, León-Cortés JL, Lobo JM, Montoya D, Morales-Castilla I, Moreno JC, Oberdorff T, Olalla-Tárraga MÁ, Pausas JG, Qian H, Rahbek C, Rodríguez MÁ, Rueda M, Ruggiero A, Sackmann P, Sanders NJ, Terribile LC, Vetaas OR, Hawkins BA. Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression. Ecography. 2009;32:193–204.

10.

Bonada N, Dolédec S, Statzner B. Spatial autocorrelation patterns of stream invertebrates: exogenous and endogenous factors. J Biogeogr. 2012;39:56–68.

11.

Borcard D, Legendre P, Drapeau P. Partialling out the spatial component of ecological variation. Ecology. 1992;73:1045–55.

12.

Büchi L, Christin PA, Hirzel AH. The influence of environmental structure on the life-history traits and diversity of species in a metacommunity. Ecol Model. 2009;220:2857–64.

13.

Carl G, Kühn I. Analyzing spatial autocorrelation in species distributions using Gaussian and logit models. Ecol Model. 2007;207:159–70.

14.

Chang J, Chen D, Ye X, Li S, Liang W, Zhang Z, Li M. Coupling genetic and species distribution models to examine the response of the Hainan partridge (Arborophila ardens) to late Quaternary climate. PLoS One. 2012. https://doi.org/10.1371/journal.pone.0050286.

15.

Chun Y, Griffith DA. Modeling network autocorrelation in space–time migration flow data: an eigenvector spatial filtering approach. Ann Assoc Am Geogr. 2011;101:523–36.

16.

Ciccarelli D, Bacaro G. Quantifying plant species diversity in coastal dunes:a piece of help from spatially constrained rarefaction. Folia Geobot. 2016;51:129–41.

17.

Cliff N. An improved internal consistency reliability estimate. J Educ Behav Stat. 1984;9:151–61.

18.

Crase B, Liedloff A, Vesk PA, Fukuda Y, Wintle BA. Incorporating spatial autocorrelation into species distribution models alters forecasts of climatemediated range shifts. Glob Change Biol. 2014;20:2566–79.

19.

Crase B, Liedloff A, Wintle BA. A new method for dealing with residual spatial autocorrelation in species distribution models. Ecography. 2012;35:879–88.

20.

Davis AJS, Singh KK, Thill J, Meentemeyer RK. Accounting for residential propagule pressure improves prediction of urban plant invasion. Ecosphere. 2016. https://doi.org/10.1002/ecs2.1232.

21.

de Oliveira G, Araújo MB, Rangel TF, Alagador D, Diniz-Filho JAF. Conserving the Brazilian semiarid (Caattinga) biome under climate change. Biodivers Conserv. 2012;21:2913–26.

22.

de Oliveira G, Rangel TF, Lima-Ribeiro MS, Terribile LC, JAF D-F. Evaluating, partitioning, and mapping the spatial autocorrelation component in ecological niche modeling: a new approach based on environmentally equidistant records. Ecography. 2014;37:637–47.

23.

Diniz-Filho JAF, Bini LM. Modelling geographical patterns in species richness using eigenvector-based spatial filters. Glob Ecol Biogeogr. 2005;14:177–85.

24.

Diniz-Filho JAF, Bini LM, Hawkins BA. Spatial autocorrelation and red herrings in geographical ecology. Glob Ecol Biogeogr. 2003;12:53–64.

25.

Diniz-Filho JAF, Rangel TFLVB, Bini LM. Model selection and information theory in geographical ecology. Glob Ecol Biogeogr. 2008;17:479–88.

26.

Dirnböck T, Dullinger S. Habitat distribution models, spatial autocorrelation, functional traits and dispersal capacity of alpine plant species. J Veg Sci. 2004;15:77–84.

27.

Dorken ME, Freckleton RP, Pannell JR. Small-scale and regional spatial dynamics of an annual plant with contrasting sexual systems. J Ecol. 2017;105:1044–57.

28.

Dormann C. Effects of incorporating spatial autocorrelation into the analysis of species distribution data. Glob Ecol Biogeogr. 2007a;16:129–38.

29.

Dormann C. Assessing the validity of autologistic regression. Ecol Model. 2007b;207:234–42.

30.

Dowd M, Grant J, Lu L. Predictive modeling of marine benthic macrofauna and its use to inform spatial monitoring design. Ecol Appl. 2014;24:862–76.

31.

Dronova I, Beissinger SR, Burnham JW, Gong P. Landscape-level associations of wintering waterbird diversity and abundance from remotely sensed wetland characteristics of Poyang lake. Remote Sens-Basel. 2016. https://doi.org/10.3390/rs8060462.

32.

Ennen JR, Agha M, Matamoros WA, Hazzard SC, Lovich JE. Using climate, energy, and spatial-based hypotheses to interpret macroecological patterns of North America chelonians. Can J Zool. 2016;94:453–61.

33.

Epperson BK. Spatial and space–time correlations in ecological models. Ecol Model. 2000;132:63–76.

34.

Estrada A, Delgado MP, Arroyo B, Traba J, Morales MB. Forecasting large-scale habitat suitability of European bustards under climate change: the role of environmental and geographic variables. PLoS One. 2016. https://doi.org/10.1371/journal.pone.0149810.

35.

Estrada CG, Rodriguez-Estrella R. In the search of good biodiversity surrogates:are raptors poor indicators in the Baja California Peninsula desert? Anim Conserv. 2016;19:360–8.

36.

Ficetola GF, Manenti R, De Bernard F, Padoa-Schioppa E. Can patterns of spatial autocorrelation reveal population processes? An analysis with the fire salamander. Ecography. 2012;35:693–703.

37.

Getis A. A history of the concept of spatial autocorrelation: a geographer’s perspective. Geogr Anal. 2008;40:297–309.

38.

Griffith DA. A linear regression solution to the spatial autocorrelation problem. J Geogr Syst. 2000;2:141–56.

39.

Griffith DA, Peres-Neto PR. Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses. Ecology. 2006;87:2603–13.

40.

Guénard G, Lanthier G, Harvey-Lavoie S, Macnaughton CJ, Senay C, Lapointe M, Legendre P, Boisclair D. A spatially- explicit assessment of the fish population response to flow management in a heterogeneous landscape Guillaume. Ecosphere. 2016. https://doi.org/10.1002/ecs2.1252.

41.

Güler B, Jentsch A, Apostolova I, Bartha S, Bloor JMG, Campetella G, Canullo R, Házi J, Kreyling J, Pottier J, Szabó G, Terziyska T, Uğurlu E, Wellstein C, Zimmermann Z, Dengler J. How plot shape and spatial arrangement affect plant species richness counts: implications for sampling design and rarefaction analyses. J Veg Sci. 2016;27:692–703.

42.

Gwenzi D, Lefsky MA. Spatial modeling of Lidar-derived woody biomass estimates collected along transects in a heterogeneous savanna landscape. IEEE J Sel Top Appl. 2017;10:372–84.

43.

Hawkins BA, Diniz-Filho JAF, Bini LM, De Marco P, Blackburn TM. Red herrings revisited: spatial autocorrelation and parameter estimation in geographical ecology. Ecography. 2007;30:375–84.

44.

Hefley TJ, Broms KM, Brost BM. The basis function approach for modeling autocorrelation in ecological data. Ecology. 2017a;98:632–46.

45.

Hefley TJ, Hooten MB, Russell RE, Walsh DP, Powell JA. When mechanism matters: Bayesian forecasting using models of ecological diffusion. Ecol Lett. 2017b;20:640–50.

46.

Hindrikson M, Remm J, Pilot M, Godinho R, Stronen AV, Baltrūnaité L, Czarnomska SD, Leonard JA, Randi E, Nowak C, Åkesson M, López-Bao JV, Álvares F, Llaneza L, Echegaray J, Vilà C, Ozolins J, Rungis D, Aspi J, Paule L, Skrbinšek T, Saarma U. Wolf population genetics in Europe: a systematic review, meta-analysis and suggestions for conservation and management. Biol Rev. 2017;92:1601–29.

47.

Hongoh V, Berrang-Ford L, Scott ME, Lindsay LR. Expanding geographical distribution of the mosquito, Culex pipiens, in Canada under climate change. Appl Geogr. 2012;33:53–62.

48.

Ingberman B, Fusco-Costa R, de Araujo Monteiro-Filho EL. A current perspective on the historical geographic distribution of the endangered Muriquis (Brachyteles spp.): Implications for conservation. PLOS ONE. 2016. https://doi.org/10.1371/journal.pone.0150906.

49.

Ishihama F, Takeda T, Oguma H, Takenaka A. Comparison of effects of spatial autocorelation on distribution predictions of four rare plant species in the Watarase wetland. Ecol Res. 2010;25:1057–69.

50.

Jackson MM, Gergel SE, Martin K. Citizen science and field survey observations provide comparable results for mapping Vancouver Island white-tailed ptarmigan (Lagopus Leucura saxatillis) distributions. Biol Conserv. 2015;181:162–72.

51.

Kim D. Incorporation of multi-scale spatial autocorrelation in soil moisture–landscape modeling. Phys Geogr. 2013;34:441–55.

52.

Kim D. Modeling spatial and temporal dynamics of plant species richness across tidal creeks in a temperate salt marsh. Ecol Indic. 2018;93:188–95.

53.

Kim D, Hirmas DR, McEwan RW, Mueller TG, Park SJ, Šamonil P, Thompson JA, Wendroth O. Predicting the influence of multi-scale spatial autocorrelation on soil–landform modeling. Soil Sci Soc Am J. 2016;80:409–19.

54.

Kim D, Shin Y. Spatial autocorrelation potentially indicates the degree of changes in the predictive power of environmental factors for plant diversity. Ecol Indic. 2016;60:1130–41.

55.

Kissling WD, Carl G. Spatial autocorrelation and the selection of simultaneous autoregressive models. Glob Ecol Biogeogr. 2008;17:59–71.

56.

Kleisner KM, Walter JF III, Diamond SL, Die DJ. Modeling the spatial autocorrelation of pelagic fish abundance. Mar Ecol Prog Ser. 2010;411:203–13.

57.

Komac B, Esteban P, Trapero L, Caritg R. Modelization of the current and future habitat suitability of Rhododendron ferrugineum using potential snow accumulation. PLoS One. 2016. https://doi.org/10.1371/journal.pone.0147324.

58.

Kühn I. Incorporating spatial autocorrelation may invert observed patterns. Divers Distrib. 2007;13:66–9.

59.

Le Rest K, Pinaud D, Monestiez P, Chadoeuf J, Bretagnolle V. Spatial leave-oneout cross-validation for variable selection in the presence of spatial autocorrelation. Glob Ecol Biogeogr. 2014;23:811–20.

60.

Legendre P. Spatial autocorrelation: trouble or new paradigm? Ecology. 1993;74:1659–73.

61.

Lennon JJ. Red-shifts and red herrings in geographical ecology. Ecography. 2000;23:101–13.

62.

Lichstein JW, Simons TR, Shriner SA, Franzreb KE. Spatial autocorrelation and autoregressive models in ecology. Ecol Monogr. 2002;72:445–63.

63.

Lloyd NJ, Nally RM, Lake PS. Spatial autocorrelation of assemblages of benthic invertebrates and its relationship to environmental factors in two upland rivers in southeastern Australia. Divers Distrib. 2005;11:375–86.

64.

Marmion M, Luoto M, Heikkinen RK, Thuiller W. The performance of state-of-theart modelling techniques depends on geographical distribution of species. Ecol Model. 2009;220:3512–20.

65.

Mattsson BJ, Zipkin EF, Gardner B, Blank PJ, Sauer JR, Royle JA. Explaining localscale species distributions: relative contributions of spatial autocorrelation and landscape heterogeneity for an avian assemblage. PLoS One. 2013. https://doi.org/10.1371/journal.pone.0055097.

66.

Merckx B, Goethals P, Steyaert M, Vanreusel A, Vincx M, Vanaverbeke J. Predictability of marine nematode biodiversity. Ecol Model. 2009;220:1449–58.

67.

Mets KD, Armenteras D, Dávalos LM. Spatial autocorrelation reduces model precision and predictive power in deforestation analyses. Ecosphere. 2017. https://doi.org/10.1002/ecs2.1824.

68.

Miller J, Franklin J, Aspinall R. Incorporating spatial dependence in predictive vegetation models. Ecol Model. 2007;202:225–42.

69.

Miller JA. Species distribution models: spatial autocorrelation and non-stationarity. Prog Phys Geogr. 2012;36:681–92.

70.

Miralha L, Kim D. Accounting for and predicting the influence of spatial autocorrelation in water quality modeling. ISPRS Int J Geo-Inf. 2018. https://doi.org/10.3390/ijgi7020064.

71.

Naimi B, Skidmore AK, Groen TA, Hamm NAS. Spatial autocorrelation in predictors reduces the impact of positional uncertainty in occurrence data on species distribution modelling. J Biogeogr. 2011;38:1497–509.

72.

Nicolaus M, Brommer JE, Ubels R, Tinbergen M, Dingemanse NJ. Exploring patterns of variation in clutch size–density reaction norms in a wild passerine bird. J Evolution Biol. 2013;26:2031–43.

73.

Ortiz-Yusty CE, Páez V, Zapata FA. Temperature and precipitation as predictors of species richness in northern Andean amphibian from Colombia. Caldasia. 2013;35:65–80.

74.

Piazzini S, Caruso T, Favilli L, Favilli L, Manganelli G. Role of predators, habitat attributes, and spatial autocorrelation on the distribution of eggs in the northern spectacled salamander (Salamandrina perspicillata). J Herpetol. 2011;45:389–94.

75.

Pickup G, Chewings VH. Random field modeling of spatial variations in erosion and deposition in flat alluvial landscapes in arid Central Australia. Ecol Model. 1986;33:269–96.

76.

Platts PJ, McClean CJ, Lovett JC, Marchant R. Predicting three distributions in an east African biodiversity hotspot: model selection, data bias and envelope uncertainty. Ecol Model. 2008;218:121–34.

77.

Poley LG, Pond BA, Schaefer JA, Brown GS, Ray JC, Johnson DS. Occupancy patterns of large mammals in the far north of Ontario under imperfect detection and spatial autocorrelation. J Biogeogr. 2014;41:122–32.

78.

Record S, Charney ND, Zakaria RM, Ellison AM. Projecting global mangrove species and community distributions under climate change. Ecosphere. 2013b. https://doi.org/10.1890/ES12-00296.1.

79.

Record S, Fitzpatrick MC, Finley AO, Veloz S, Ellison AM. Should species distribution models account for spatial autocorrelation? A test of model projections across eight millennia of climate change. Glob Ecol Biogeogr. 2013a;22:760–71.

80.

Revermann R, Schmid H, Zbinden N, Spaar R, Schröder B. Habitat at the mountain tops: how long can rock Ptarmigan (Lagopus muta helvetica)survive rapid climate change in the Swiss Alps? A multi-scale approach. J Ornithol. 2012;153:891–905.

81.

Rodriguez A, Gómez JF, Nieves-Aldrey JL. Modeling the potential distribution and conservation status of three species of oak gall wasps (Hymenoptera:Cynipidae) in the Iberian range. J Insect Conserv. 2015;19:921–34.

82.

Roth T, Bühler C, Amrhein V. Estimating effects of species interactions on populations of endangered species. Am Nat. 2016;187:457–67.

83.

Santos SM, Mira AP, Mathias ML. Factors influencing large-scale distribution of two sister species of pine voles (Microtus lusitanicus and Microtus duodecimcostatus): the importance of spatial autocorrelation. Can J Zool. 2009;87:1227–40.

84.

Seymour L. Spatial data analysis: theory and practice. J Am Stat Assoc. 2005;100:353.

85.

Sheehan KL, Esswein ST, Dorr BS, Yarrow GK, Johnson RJ. Using species distribution models to define nesting habitat of the eastern metapopulation of double-crested cormorants. Ecol Evol. 2017;7:409–18.

86.

Siderov K. Spatial data analysis: theory and practice. Austral Ecol. 2005;30:237–41.

87.

Siesa ME, Manenti R, Padoa-Schioppa E, de Bernardi F, Ficetola GF. Spatial autocorrelation and the analysis of invasion processes from distribution data:a study with the crayfish Procambarus clarkia. Biol Invasions. 2011;13:2147–60.

88.

Tallowin O, Allison A, Algar AC, Kraus F, Meiri S. Papua New Guinea terrestrialvertebrate richness: elevation matters most for all except reptiles. J Biogeogr. 2017;44:1734–44.

89.

Tarkhnishvili D, Gavashelishvili A, Mumladze L. Palaeoclimatic models help to understand current distribution of Caucasian forest species. Biol J Linn Soc. 2012;105:231–48.

90.

Václavík T, Kupfer JA, Meentemeyer RK. Accounting for multi-scale spatial autocorrelation improves performance of invasive species distribution modelling (iSDM). J Biogeogr. 2012;39:42–55.

91.

Václavík T, Meentemeyer RK. Invasive species distribution modeling (iSDM): are absence data and dispersal constraints needed to predict actual distributions? Ecol Model. 2009;220:3248–58.

92.

Veloz SD. Spatially autocorrelated sampling falsely inflates measures of accuracy for presence-only niche models. J Biogeogr. 2009;36:2290–9.

93.

Warren DL, Cardillo M, Rosauer DF, Bolnick DI. Mistaking geography for biology: inferring processing from species distributions. Trends Ecol Evol. 2014;29:572–80.

94.

Weeks AM, de Jager NR, Haro RJ, Sandland GJ. Spatial and temporal relationships between the invasive snail Bithynia tentaculata and submersed aquatic vegetation in Pool 8 of the upper Mississippi River. River Res Appl. 2017;33:729–39.

95.

Wieczorek K, Bugaj-Nawrocka A. Invasive aphids of the tribe Siphini: a model of potentially suitable ecological niches. Agr Forest Entomol. 2014;16:434–43.

96.

Wiegand T, Moloney KA. Rings, circles, and null-models for point pattern analysis in ecology. Oikos. 2004;104:209–29.

97.

Wu D, Liu J, Zhang G, Ding W, Wang W, Wang R. Incorporating spatial autocorrelation in cellular automata model: an application to the dynamics of Chinese tamarisk (Tamarisk chinensis Lour.). Ecol Model. 2009;220:3490–8.

98.

Wu W, Zhang L. Comparison of spatial and non-spatial logistic regression models for modeling the occurrence of cloud cover in north-eastern Puerto Rico. Appl Geogr. 2013;37:52–62.

99.

Wulder MA, White JC, Coops NC, Nelson T, Boots B. Using spatial autocorrelation to compare outputs from a forest growth model. Ecol Model. 2007;209:264–76.

100.

Yu MH. Modeling tree growth and seedling recruitment in a selectively logged temperature forest. The City University of New York: PhD Dissertation; 2012.

101.

Zhang L, Ma Z, Guo L. An evaluation of spatial autocorrelation and heterogeneity in the residuals of six regression models. For Sci. 2009;55:533–48.

102.

Zhu W, Jia S, Lü A, Yan T. Analyzing and modeling the coverage of vegetation in the Qaidam basin of China: the role of spatial autocorrelation. J Geogr Sci. 2012;22:346–58.

Journal of Ecology and Environment