Spatial Autocorrelation in Geographical Ecology

Spatial autocorrelation (SAC) is a frequent phenomenon in ecogeographic data because observations from nearby locations are often more similar than would be expected on a random basis. In many cases, the presence of SAC is seen as a ‘problem’ for data analysis because confidence intervals of classical statistical tests (anova, correlation and regression) are wrongly estimated when observations are not independent, and hence the significance levels of correlation or regression coefficients are biased (“type I error inflation”). It is less clear to what extent parameter estimates (i.e. beta coefficients) of statistical models are influenced by the presence of SAC. In this project we tested the potential of different statistical methods to deal with spatial autocorrelation in modelling species distributions and species richness at broad spatial scales. We were particularly interested in understanding how the inclusion of residual SAC in statistical models affects inference in geographical ecology. This is not simply a statistical problem but has profound implications for biogeography, macroecology and global change research because biased estimates and incorrect model specifications will influence the testing of hypotheses and the prediction of species distributions.

Keywords: Autoregressive model, parameter estimation, spatial autocorrelation, type I error inflation.

Publications:

• Dormann, C.F., McPherson, J.M., Araújo, M.B., Bivand, R., Bolliger, J., Carl, G., Davies, R.G., Hirzel, A., Jetz, W., Kissling, W.D., Kühn, I., Ohlemüller, R., Peres-Neto, P.R., Reineking, B., Schröder, B., Schurr, F.M. & Wilson, R. (2007): Methods to account for spatial autocorrelation in the analysis of species distributional data: a review. Ecography 30: 609–628. [Abstract]
• Kissling, W.D. & Carl, G. (2008): Spatial autocorrelation and the selection of simultaneous autoregressive models. Global Ecology and Biogeography 17: 59–71. [Abstract]
• Bini, L.M., Diniz-Filho, J.A.F., Rangel, T.F.L.V.B., Akre, T.S.B., Albaladejo, R.G., Albuquerque, F.S., Aparicio, A., Araújo, M.B., Baselga, A., Beck, J., Bellocq, M.I., Böhning-Gaese, K., Borges, P.A.V., Castro-Parga, I., Chey, V.K., Chown, S.L., de Marco, P., Dobkin, D.S., Ferrer-Castán, D., Field, R., Filloy, J., Fleishman, E., Gómez, J.F., Hortal, J., Iverson, J.B., Kerr, J.T., Kissling, W.D., Kitching, I.J., León-Cortés, J.L., Lobo, J.M., Montoya, D., Morales-Castilla, I., Moreno, J.C., Oberdorff, T., Olalla-Tárraga, M.A., Pausas, J.G., Qian, H., Rahbek, C., Rodríguez, M.A., Rueda, M., Ruggiero, A., Sackmann, P., Sanders, N.J., Terribile, L.C., Vetaas, O.R. & Hawkins, B.A. (2009): Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression. Ecography 32: 193–204. [Abstract]

 

Figure: Spatial autocorrelation patterns in environmental variables, species distributions and residuals of statistical models (from Dormann et al. 2007). Spatial autocorrelation is a frequent phenomenon in ecological data and can affect estimates of model coefficients and inference from statistical models.

 

W. Daniel Kissling