YouHua Chen Department of Renewable Resources, University of Alberta, Edmonton, T6G 2H1, Canada Computational Ecology and Software ISSN 2220-721X http://www.iaees.org/publications/journals/ces/online-version.asp 2014 4 3 147 162 International Academy of Ecology and Environmental Sciences Hong Kong 30 April 2014 5 June 2014 1 September 2014 variation partitioning covariance correlation environmental filtering spatial autocorrealtion The effectiveness and validity of applying variation partitioning methods in community ecology has been questioned. Here, using mathematical deduction and numerical simulation, we made an attempt to uncover the underlying mechanisms determining the effectiveness of variation partitioning techniques. The covariance among independent variables determines the under-fitting and over-fitting problem with the variation partitioning process. Ideally, it is assumed that the covariance among independent variables will be zero (no correlation at all), however, typically there will be some colinearities. Therefore, we analyzed the role of slight covariance on influencing species variation partitioning. We concluded that when the covariance between spatial and environmental predictors is positive, all the three components-pure environmental, spatial variations and mixed covariation were over-fitted, with the sign of the true covariation being negative. In contrast, when the covariance is negative, all the three components were under-fitted with the sign of true covariation being positive. Other factors, including extra noise levels, the strengths of variable coefficients and the patterns of landscape gradients, could reduce the fitting problems caused by the covariance of variables. The conventional calculation of mixed covariation is incorrect and misleading, as the true and estimated covariations are always sign-opposite. In conclusion, I challenge the conventional three-step procedure of variation partitioning, suggesting that a full regression model with all variables together is robust enough to correctly partition variations. DOI 10.0000/issn-2220-721x-compuecol-2014-v4-0013 http://www.iaees.org/publications/journals/ces/articles/2014-4(3)/covariance-among-independent-variables-determines-the-overfitting.pdf