There is a plethora of non-linear models to describe bivariate relationships related to ecological, biological and environmental problems, and this makes difficult to have a general aspect about the suitable models for a new-born dataset. Additionally, there is a special interest for bivariate non-linear models which can describe the relative variation of the dependent variable (NLR models) (i.e. these models provide a restricted range of values between 0 and 1) because they can easily be adjusted to fit different datasets which describe the same relationship. The aim of this study is to provide a review and synthesis of NLR models which can be used to describe bivariate relationships which follow bell-shaped, simple-double sigmoid, bilinear and periodical patterns. This attempt aims to save time and effort for the selection of a NLR model based on five steps (a) preparation of data, (b) visual identification of the suitable model based on pre-constructed graphs, (c) a starting point using the simpler form (base function) of the selected models which are given in complex general forms, (d) directions to increase the number of coefficients in order to improve fitting and (e) techniques to modify the given NLR models in order to derive new ones with inverted patterns.
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