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Table 1 The twenty SAR models compared in the model selection, including the number of parameters, general model shape, whether or not the model contains an asymptote, and the overall rank obtained based on the best fitting model, model generality and efficiency (see “Methods” section)

From: A global consistent positive effect of urban green area size on bird richness

Model No. parameters Model code Model shape Asymptotic nature Overall rank
Linear 2 linear Linear No 1
Kobayashi 2 koba Convex No 2
Power 2 power Convex No 3
Exponential 2 expo Convex No 4
Extended Power 1 3 epm1 Convex/Sigmoida No 5
Asymptotic 3 asymp Convex Yes 6
Monod 2 monod Convex Yes 7
Rational 3 ratio Convex Yes 8
Beta-P 4 betap Sigmoid Yes 9
Weibull-3 3 weibull3 Sigmoid Yes 10
Morgan–Mercer–Flodin 3 mmf Sigmoid Yes 11
Logistic 3 heleg Sigmoid Yes 12
Weibull-4 4 weibull4 Sigmoid Yes 13
Persistence Function 1 3 P1 Convex No 14
Persistence Function 2 3 P2 Sigmoid No 15
Extended Power 2 3 epm2 Sigmoid No 16
Gompertz 3 gompertz Sigmoid Yes 17
Chapman–Richards 3 chapman Sigmoid Yes 18
Power Rosenzweig 3 power_R Convex No 19
Negative Exponential 2 negexpo Convex Yes 20
  1. aThe epm1 model can be either convex or sigmoidal in shape depending on the parameter values