Appendix 1—table 1. Mathematical definition of the models included in our model space.

Model	Cost function		Softmax function
Linear model 1		${\displaystyle SV=\left(R\right)-\left({\mathit{\beta }}_{\mathit{E}}\cdot E\right)}$	$p\left(accept\right)=\frac{1}{1+e^{-(\alpha +SV)}}$
Linear model 2		${\displaystyle SV=\left({\mathit{\beta }}_{\mathit{R}}\cdot R\right)-\left({\mathit{\beta }}_{\mathit{E}}\cdot E\right)}$	$p\left(accept\right)=\frac{1}{1+e^{-SV}}$
Linear model 3		${\displaystyle SV=\left({\mathit{\beta }}_{\mathit{R}}\cdot R\right)-\left({\mathit{\beta }}_{\mathit{E}}\cdot E\right)}$	$p\left(accept\right)=\frac{1}{1+e^{-(\alpha +SV)}}$
Parabolic model 1		${\displaystyle SV=\left(R\right)-\left({\mathit{\beta }}_{\mathit{E}}\cdot E^2\right)}$	$p\left(accept\right)=\frac{1}{1+e^{-(\alpha +SV)}}$
Parabolic model 2		${\displaystyle SV=\left({\mathit{\beta }}_{\mathit{R}}\cdot R\right)-\left({\mathit{\beta }}_{\mathit{E}}\cdot E^2\right)}$	$p\left(accept\right)=\frac{1}{1+e^{-SV}}$
Parabolic model 3		${\displaystyle SV=\left({\mathit{\beta }}_R\cdot R\right)-\left({\mathit{\beta }}_E\cdot E^2\right)}$	$p\left(accept\right)=\frac{1}{1+e^{-(\alpha +SV)}}$
Exponential model 1		${\displaystyle SV=\left(R\right)\cdot e^{\left(\mathbf{-}{\mathit{\beta }}_{\mathit{E}}\cdot E\right)}}$	$p\left(accept\right)=\frac{1}{1+e^{-5\bullet (\alpha +SV)}}$
Exponential model 2		${\displaystyle SV=\left({\mathit{\beta }}_{\mathit{R}}\cdot R\right)\cdot e^{\left(\mathbf{-}{\mathit{\beta }}_{\mathit{E}}\cdot E\right)}}$	$p\left(accept\right)=\frac{1}{1+e^{-5\bullet (-0.5+SV)}}$
Exponential model 3		${\displaystyle SV=\left({\mathit{\beta }}_{\mathit{R}}\cdot R\right)\cdot e^{\left(\mathbf{-}{\mathit{\beta }}_{\mathit{E}}\cdot E\right)}}$	$p\left(accept\right)=\frac{1}{1+e^{-5\bullet (\alpha +SV)}}$