Nonlinear canonical correspondence analysis and its application.

The canonical correspondence analysis (CCA) is a multivariate direct gradient analysis method performing well in many fields, however, when it comes to approximating the unimodal response of species to an environmental gradient, which still assumes that the relationship between the environment and the weighted species score is linear. In this work, we propose a nonlinear canonical correspondence analysis method (NCCA), which first determines the most appropriate nonlinear explanatory factor through two screenings by correlation and LASSO regression, and successively uses the linear regression method and the improved heuristic optimal quadratic approximation method to fit the chi-square transformation values of the response variables. Thus, our method effectively reflects the nonlinear relationship between the species and the environment factors, and a biplot is employed to visualize the effects of the later on the distribution of species. The results from applying this method over a real dataset show that the NCCA method not only maintains the advantages of the polynomial canonical correspondence analysis (PCCA) proposed by Makarenkov (2002), but also outperforms Makarenkov's method in explaining the variance of response variables.