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

Godeau, Ugoline; Bouget, Christophe; Piffady, Jérémy; Pozzi, Tiffani; Gosselin, Frédéric

doi:10.1002/ece3.7016

Cited by 3 publications

(3 citation statements)

References 66 publications

(101 reference statements)

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“…Godeau et al . 30 identify twelve mathematical formulae that generate a sigmoid curve. Each is based on a different biological relationship between the variables on the x and y axes (respectively the explanatory and explained variables).…”

Section: Discussionmentioning

confidence: 99%

“…More generally, a sigmoid response function can be generated by many different mathematical forms, including the logistic. Godeau et al 30 identify twelve mathematical formulae that generate a sigmoid curve. Each is based on a different biological relationship between the variables on the x and y axes (respectively the explanatory and explained variables).…”

Section: Discussionmentioning

confidence: 99%

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Generating the sigmoid form in neuroscience: A threshold-crossing model

Auty

2023

Preprint

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The conventional interpretation1of a logistic curve in biology is that it indicates the presence of an infection-like mechanism bounded by a saturation limit e.g. saturation occurs when the whole population has been infected. However, a logistic form may be generated by the fluctuating approach of biological systems to, and then exceeding, an effect threshold.The commonly observed trends in frequency and degree of cognitive loss in neurodegenerative disease (NDD) are consistent with a threshold-crossing model. Whereas direct evidence of real life NDD being driven by an infection-like mechanism remains elusive2,3.Variation in susceptibility to NDD may be explained by variation in the rate of biological ageing (e.g. neurodegeneration rate, or, metabolic interference), height of threshold and initial reserve. Each is potentially modifiable and clinically informative.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Generating the sigmoid form in neuroscience: A threshold-crossing model

Auty

2023

Preprint

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“…For example, the hyperbolic functions were introduced in the 1760s by Vincenzo Riccati and Johann Heinrich Lambert (Bradley et al., 2007); the inverse trigonometric function for tangent was proposed in 1736 by Euler; the Gudermannian function was introduced by the German mathematician Christoph Gudermann (1798–1852) (Beyer, 2018); the logistic function was introduced between 1838 and 1847 by Pierre François Verhulst (Miner, 1933). These functions are widely used in many fields, such as machine learning (Menon et al., 1996) and ecology (Godeau et al., 2020), but have never been used to characterize soil water retention data, to the best of our knowledge.…”

Section: Methodsmentioning

confidence: 99%

A Family of Soil Water Retention Models Based on Sigmoid Functions

Zuo

Zhang

2023

Water Resources Research

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The soil water retention curve is the fundamental soil hydraulic property to characterize soil water movement and solute transport. Many efforts have been devoted in the past decades to developing models to describe soil water retention curves. However, most of them are empirical equations or assume that soil pore size distributions conform to a lognormal distribution. Yet, few effects have been undertaken to systematically propose and compare a series of possible alternative probability density functions to describe the sigmoid retention curves with parameters physically explainable. Here, we proposed a family of five soil water retention models based on sigmoid functions with parameters of clear physical implications coinciding with the statistical measures of soil pore size distribution. Compared with the widely used models (i.e., Brooks & Corey, 1964; Kosugi, 1996; van Genuchten, 1980), the proposed models have somewhat improved performances to characterize water retention data for a wide range of soil textures without introducing additional model parameters. Two of the proposed models are capable of characterizing the observed two local extrema in the moisture capacity curves. The associated unsaturated hydraulic conductivity models of the proposed soil water retention models are also derived, which show superior performance in characterizing the observed hydraulic conductivities compared with competing models, especially in macropore regimes. Additionally, we analyzed the parameter‐equivalent conversion between the proposed and the existing models, and a simple linear regression equation can be used to derive the parameters of the proposed models from the existing and other alternative different proposed models.

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Species range size shapes distance‐decay in community similarity

Martín‐Devasa

Martínez‐Santalla

Gómez‐Rodríguez

et al. 2022

Diversity and Distributions

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Aim: (i) To assess the dependence between the form of the decrease in biological similarity with distance (distance-decay) and species range size and (ii) to introduce the use of a sigmoidal model, the Gompertz function, as a flexible alternative able to fit distance-decay models under a wide variety of species range sizes.Location: Applicable worldwide. Methods:We computed distance-decay curves from simulated communities to assess how the species range sizes shape the functional form of distance-decay patterns (i.e. negative exponential, power-law or sigmoidal [Gompertz] relationships). Simulations were performed using different sample sizes and species detection probabilities. We also used distribution data of South American mammals to explore the relationship between species range size and the distance-decay form in an empirical dataset.Results: Our simulations showed that the power-law is the best supported model when range sizes tend to be small. An increase in range sizes leads to a negative exponential relationship, taking the shape of a sigmoidal (Gompertz) relationship with the largest range size values. Similar results have been found in the distance-decay pattern of South American mammals. Remarkably, the Gompertz function fits the data reasonably well in all scenarios. Main conclusions:The functional form of distance-decay patterns depends on a key biogeographical attribute: species range size. This dependence makes it an interesting tool to detect biodiversity threats associated with species range expansion, such as the biotic homogenization of faunas. The Gompertz function is the mathematical model that best accommodates different frequency distributions of species range size and, thus, allows cross-taxa comparison of this biogeographical and ecological pattern.

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

Abstract: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Cited by 3 publications

References 66 publications

Generating the sigmoid form in neuroscience: A threshold-crossing model

Generating the sigmoid form in neuroscience: A threshold-crossing model

A Family of Soil Water Retention Models Based on Sigmoid Functions

Species range size shapes distance‐decay in community similarity

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