## 2 Materials and Methods
### Fitting of the Hearing Prostheses  
The CI and the hearing aid parameters were fit to individual hearing loss profiles by minimizing the normalized root mean square difference reflecting the 'loss of action potentials', i.e.,  
\[\mathrm{LAP}(\Omega)=\frac{\sqrt{\left(\mathrm{AN}_{\mathrm{nh}}-\mathrm{AN}_ {\Omega}\right)^{2}}}{\sqrt{\mathrm{AN}_{\mathrm{nh}}^{2}}}+\lambda_{\Omega}, \tag{1}\]  
where \(\mathrm{AN}_{\Omega}(\mathrm{n},\mathrm{t})\) are AN firing rates predicted for prosthesis option \(\Omega\in\{\mathrm{ua},\mathrm{ac},\mathrm{el},\mathrm{co}\}\), i.e., unaided hearing, acoustic amplification, electrical stimulation, and electrical stimulation combined with acoustic amplification. \(\lambda_{\Omega}\) is a parameter to adjust LAP for the 'costs' of acoustical amplification and cochlear implantation. The cost parameter for unaided hearing \(\lambda_{\Omega=\mathrm{ua}}=0\), for sole acoustical amplification \(0\leq\lambda_{\Omega=\mathrm{ac}}\leq 0.1\), for sole electrical stimulation \(0\leq\lambda_{\Omega=\mathrm{el}}\leq 0.25\), and for electrical stimulation combined with acoustical amplification \(\lambda_{\Omega=\mathrm{co}}=\lambda_{\Omega=\mathrm{ac}}+\lambda_{\Omega= \mathrm{el}}\). The default values were \(\lambda_{\Omega=\mathrm{ac}}=0.01\), and \(\lambda_{\Omega=\mathrm{el}}=0.05\). The LAP was typically between 0 (NH) and 1 (deafness). LAP was obtained for stimulus levels of 45 and 65 dB (20 \(\mathrm{\SIUnitSymbolMicro Pa}\)) individually, and the mean was taken. Before the computation of LAP, the spontaneous rates were subtracted from all AN firing rates. The place resolution was 120 nerve fibers, and the time resolution was 1.4 ms.  
The fitting parameters for the acoustic amplification were the frequency-flat and the frequency-sloping components of the low-level gain, i.e., \(\mathrm{L}_{\mathrm{f}}\) and \(\mathrm{L}_{\mathrm{s}}\). The optimal parameters were obtained as \(\left[\mathrm{L}_{\mathrm{f}}^{\mathrm{opt}},\mathrm{L}_{\mathrm{s}}^{ \mathrm{opt}}\right]=\mathrm{argmin}[\mathrm{LAP}(\mathrm{L}_{\mathrm{f}}, \mathrm{L}_{\mathrm{s}})]\), where LAP was obtained with \(\mathrm{AN}_{\Omega=\mathrm{ac}}\). \(\mathrm{L}_{\mathrm{f}}\) and \(\mathrm{L}_{\mathrm{s}}\) were jointly optimized in two loops. In each loop, first \(\mathrm{L}_{\mathrm{f}}\) was optimized using golden-section search with parabolic interpolation, and then \(\mathrm{L}_{\mathrm{s}}\). In the first loop, the minimization was coarse, i.e., with stopping criterion tolerances of 5 dB for both L\({}_{\text{f}}\) and L\({}_{\text{s}}\), and 1% for LAP. In the second loop, L\({}_{\text{f}}\) and L\({}_{\text{s}}\) were fine-tuned, i.e., with stopping criterion tolerances of 0.5 dB and 0.1%, respectively. L\({}_{\text{f}}\) and L\({}_{\text{s}}\) were constraint to 0 and 60 dB, and L\({}_{\text{f}}\leq\) L\({}_{\text{s}}\).  
The fitting parameter of the electrical stimulation was the electrode array's insertion depth D. The optimal insertion depth was obtained as \(\text{D}^{\text{opt}}=\text{ argmin}[\text{r}_{\text{d}}(\text{D})]\). D was optimized using golden-section search with parabolic interpolation, using a stopping criterion tolerance of 0.5 mm. D was constraint to 19 and 29 mm, which corresponded to apex-to-tip distances ranging from 16 to 6 mm in a 35 mm cochlea.