The species-area relation III. A third model for a delimited community

Lack of definition of mathematical terms in ecology: The case of the sigmoid class of functions in macro-ecology

Defining mathematical terms and objects is a constant issue in ecology; often definitions are absent, erroneous, or imprecise. Through a bibliographic prospection, we show that this problem appears in macro-ecology (biogeography and community ecology) where the lack of definition for the sigmoid class of functions results in difficulties of interpretation and communication. In order to solve this problem and to help harmonize papers that use sigmoid functions in ecology, herein we propose a comprehensive definition of these mathematical objects. In addition, to facilitate their use, we classified the functions often used in the ecological literature, specifying the constraints on the parameters for the function to be defined and the curve shape to be sigmoidal. Finally, we interpreted the different properties of the functions induced by the definition through ecological hypotheses in order to support and explain the interest of such functions in ecology and more precisely in biogeography.