Constrained ordination methods aims at finding an environmental gradient along which the species abundances are maximally separated. The species response functions, which describe the expected abundance as a function of the environmental score, are according to the ecological fundamental niche theory only meaningful if they are bell-shaped. Many classical model-based ordination methods, however, use quadratic regression models without imposing the bell-shape and thus allowing for meaningless U-shaped response functions. The analysis output (e.g. a biplot) may therefore be potentially misleading and the conclusions are prone to errors. In this paper we presenta log-likelihood ratio criterion with a penalisation term to enforce more bell-shaped response shapes. We report the results of a simulation study and apply our method to metagenomics data from microbial ecology.
Zhang, Y. & Thas, O. (2016). Constrained ordination analysis with enrichment of bell-shaped response functions. PLoS One, 11 (4), 1-21.