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The effectiveness and validity of applying variation partitioning methods incommunity ecology has been questioned. Here, using mathematical deduction andnumerical simulation, we made an attempt to uncover the underlying mechanismsdetermining the effectiveness of variation partitioning techniques. Thecovariance among independent variables determines the under-fitting andover-fitting problem with the variation partitioning process. Ideally, it isassumed that the covariance among independent variables will be zero (nocorrelation at all), however, typically there will be some colinearities.Therefore, we analyzed the role of slight covariance on influencing speciesvariation partitioning. We concluded that when the covariance between spatialand environmental predictors is positive, all the three components-pureenvironmental, spatial variations and mixed covariation were over-fitted, withthe sign of the true covariation being negative. In contrast, when thecovariance is negative, all the three components were under-fitted with thesign of true covariation being positive. Other factors, including extra noiselevels, the strengths of variable coefficients and the patterns of landscapegradients, could reduce the fitting problems caused by the covariance ofvariables. The conventional calculation of mixed covariation is incorrect andmisleading, as the true and estimated covariations are always sign-opposite. Inconclusion, I challenge the conventional three-step procedure of variationpartitioning, suggesting that a full regression model with all variablestogether is robust enough to correctly partition variations.

Covariance among independent variables determines the overfitting and  underfitting problems in variation partitioning methods: with a special focus  on the mixed co-variation