Rejecting the mean:: Estimating the response of fen plant species to environmental factors by non-linear quantile regression

Question: Is quantile regression an appropriate statistical approach to estimate the response of fen species to single environmental factors? Background: Data sets in vegetation field studies are often characterized by a large number of zeros and they are generally incomplete in respect to the factors which possibly influence plant species distribution. Thus, it is problematic to relate plant species abundance to single environmental factors by the ordinary least squares regression technique of the conditional mean. Location: Riparian herbaceous fen in central Jutland (Denmark). Methods: Semi-parametric quantile regression was used to estimate the response of 18 plant species to six environmental factors, 95% regression quantiles were chosen to reduce the impact of multiple unmeasured factors on the regression analyses. Results of 95% quantile regression and ordinary least squares regression were compared. Results: The standard regression of the conditional mean underestimated the rates of change of species cover due to the selected factor in comparison to 95% regression quantiles. The fitted response curves indicated a general broad tolerance of the studied fen species to different flooding durations but a narrower range concerning groundwater amplitude. The cover of all species was related to soil exchangeable phosphate and base-richness. A relationship between soil exchangeable potassium and species cover was only found for 11 species. Conclusion: Considering the characteristics of data sets in vegetation science, non-linear quantile regression is a useful method for gradient analyses.