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Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression

Authors

  • L. Mauricio Bini,

  • J. Alexandre F. Diniz-Filho,

  • Thiago F. L. V. B. Rangel,

  • Thomas S. B. Akre,

  • Rafael G. Albaladejo,

  • Fabio S. Albuquerque,

  • Abelardo Aparicio,

  • Miguel B. Araújo,

  • Andrés Baselga,

  • Jan Beck,

  • M. Isabel Bellocq,

  • Katrin Böhning-Gaese,

  • Paulo A. V. Borges,

  • Isabel Castro-Parga,

  • Vun Khen Chey,

  • Steven L. Chown,

  • Paulo De Marco, Jr,

  • David S. Dobkin,

  • Dolores Ferrer-Castán,

  • Richard Field,

  • Julieta Filloy,

  • Erica Fleishman,

  • Jose F. Gómez,

  • Joaquín Hortal,

  • John B. Iverson,

  • Jeremy T. Kerr,

  • W. Daniel Kissling,

  • Ian J. Kitching,

  • Jorge L. León-Cortés,

  • Jorge M. Lobo,

  • Daniel Montoya,

  • Ignacio Morales-Castilla,

  • Juan C. Moreno,

  • Thierry Oberdorff,

  • Miguel Á. Olalla-Tárraga,

  • Juli G. Pausas,

  • Hong Qian,

  • Carsten Rahbek,

  • Miguel Á. Rodríguez,

  • Marta Rueda,

  • Adriana Ruggiero,

  • Paula Sackmann,

  • Nathan J. Sanders,

  • Levi Carina Terribile,

  • Ole R. Vetaas,

  • Bradford A. Hawkins


L. M. Bini, J. A. F. Diniz-Filho, P. de Marco, Jr and L. C. Terribile, Depto de Biologia Geral, ICB, Univ. Federal de Goiás, CP 131, 74.001–970 Goiânia, GO, Brazil. – T. F. L. V. B. Rangel, Dept of Ecology and Evolutionary Biology, Univ. of Connecticut, Storrs, CT 06269, USA. – T. S. B. Akre, Dept of Biological and Environmental Sciences, Longwood Univ., Farmville, VA 23909, USA. – R. G. Albaladejo and A. Aparicio, Depto de Biología Vegetal y Ecología, Univ. de Sevilla, c/Prof. García Gonzalez no 2, ES-41012 Sevilla, Spain. – F. S. Albuquerque, D. Montoya, I. Morales-Castilla, M. Á. Olalla-Tarraga, M. Á. Rodríguez and M. Rueda, Depto de Ecología, Univ. de Alcalá, ES-28871 Alcalá de Henares, Madrid, Spain. – M. B. Araújo, A. Baselga, J. F. Gómez and J. M. Lobo, Depto de Biodiversidad y Biología Evolutiva, Museo Nacional de Ciencias Naturales (CSIC), ES-28006 Madrid, Spain. – J. Beck, Dept of Environmental Sciences, Inst. of Biogeography, Univ. of Basel, St.Johanns-Vorstadt 10, CH-4056 Basel, Switzerland. – M. I. Bellocq and J. Filloy, Depto de Ecología, Genética y Evolución, Facultad de Ciencias Exactas y Naturales, Univ. de Buenos Aires, and CONICET, Ciudad Universitaria Pab. 2 (1428) Buenos Aires, Argentina. – K. Böhning-Gaese and W. D. Kissling, Inst. für Zoologie, Johannes Gutenberg-Univ. Mainz, Becherweg 13, DE-55099 Mainz, Germany. – P. A. V. Borges, Depto de Ciências Agrárias, Univ. dos Açores, CITA A (Azorean Biodiversity Group), Terra Chã, PT-9700–851 Angra do Heroísmo, Terceira, Açores, Portugal. – I. Castro-Parga, Depto de Ecología, C/Darwin 2, Univ. Autónoma de Madrid, ES-28049 Madrid, Spain. – V. K. Chey, Entomology Section, Forest Research Centre of Sabah, Sepilok, P.O. Box 1407, 90715 Sandakan, Malaysia. – S. L. Chown, DST-NRF Centre of Excellence for Invasion Biology, Stellenbosch Univ., Private Bag XI, Matieland 7602, South Africa. – D. S. Dobkin, High Desert Ecological Research Inst., 15 S.W. Colorado Ave., Suite 300, Bend, OR 97702, USA. – D. Ferrer-Castán, Área de Ecología, Facultad de Biología, Univ. de Salamanca, ES-37007 Salamanca, Spain. – R. Field, School of Geography, Univ. of Nottingham, Nottingham NG7 2RD, UK. – E. Fleishman, National Center for Ecological Analysis and Synthesis, 735 State St, Suite 300, Santa Barbara, CA 93101, USA. – J. Hortal, NERC Centre for Population Biology, Imperial College at Silwood Park, Ascot SL5 7PY, UK. – J. B. Iverson, Dept of Biology, Earlham College, Richmond, IN 47374, USA. – J. T. Kerr, Dept of Biology, Univ. of Ottawa, Ottawa, ON, Canada KIN 6N5. – I. J. Kitching, Dept of Entomology, The Natural History Museum, Cromwell Road, London SW7 5BD, UK. – J. L. León-Cortés, Depto de Ecología y Sistemática Terrestre, El Colegio de la Frontera Sur, Carr. Panamericana y Av. Periférico Sur s/n, San Cristóbal de las Casas, Chiapas 29290, México. – J. C. Moreno, Depto de Biología, C/ Darwin 2, Univ. Autonoma de Madrid, ES-28049 Madrid, Spain. – T. Oberdorff, IRD, DMPA, Museum National d'Histoire Naturelle, 43 Rue Cuvier, FR-75005 Paris, France. – J. G. Pausas, Centro de Investigación sobre Desertificación (CIDE, CSIC), Apartado Oficial, ES-46470 Albal, Valencia, Spain. – H. Qian, Research and Collections Center, Illinois State Museum, 1011 East Ash Street, Springfield, IL 62703, USA. – C. Rahbek, Center for Macroecology, Dept of Biology, Univ. of Copenhagen, DK-2100 Copenhagen, Denmark. – A. Ruggiero and P. Sackmann, Laboratorio Ecotono, Centro Regional Universitario Bariloche, Univ. Nacional del Comahue – INIBIOMA-CONICET, Quintral 1250 (8400) Bariloche, Rio Negro, Argentina. – N. J. Sanders, Dept of Ecology and Evolutionary Biology, Univ. of Tennessee, Knoxville, TN 37996, USA. – O. R. Vetaas, UNIFOB Global, Univ. of Bergen, NO-5015 Bergen, Norway. – B. A. Hawkins (bhawkins@uci.edu), Dept of Ecology and Evolutionary Biology, Univ. of California, Irvine, CA 92697, USA.

Abstract

A major focus of geographical ecology and macroecology is to understand the causes of spatially structured ecological patterns. However, achieving this understanding can be complicated when using multiple regression, because the relative importance of explanatory variables, as measured by regression coefficients, can shift depending on whether spatially explicit or non-spatial modeling is used. However, the extent to which coefficients may shift and why shifts occur are unclear. Here, we analyze the relationship between environmental predictors and the geographical distribution of species richness, body size, range size and abundance in 97 multi-factorial data sets. Our goal was to compare standardized partial regression coefficients of non-spatial ordinary least squares regressions (i.e. models fitted using ordinary least squares without taking autocorrelation into account; “OLS models” hereafter) and eight spatial methods to evaluate the frequency of coefficient shifts and identify characteristics of data that might predict when shifts are likely. We generated three metrics of coefficient shifts and eight characteristics of the data sets as predictors of shifts. Typical of ecological data, spatial autocorrelation in the residuals of OLS models was found in most data sets. The spatial models varied in the extent to which they minimized residual spatial autocorrelation. Patterns of coefficient shifts also varied among methods and datasets, although the magnitudes of shifts tended to be small in all cases. We were unable to identify strong predictors of shifts, including the levels of autocorrelation in either explanatory variables or model residuals. Thus, changes in coefficients between spatial and non-spatial methods depend on the method used and are largely idiosyncratic, making it difficult to predict when or why shifts occur. We conclude that the ecological importance of regression coefficients cannot be evaluated with confidence irrespective of whether spatially explicit modelling is used or not. Researchers may have little choice but to be more explicit about the uncertainty of models and more cautious in their interpretation.

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