## 2 Models
### Statistical Methods
A summary of these results can be found in the third column of Table 1 where the average values \(\bar{\chi}_{\rm all}\) and the 95% CI of the distributions shown in Figure 4 are given for the four models and the two MTS samples. In the light of these results, the following facts deserve a comment:  
1. For all models, the distributions corresponding to sample #2 were wider than those of sample #1. This is seen in Figure 4 and also in Table 1. The sizes of the 95% CI quoted in the table for sample #2 are larger than those of sample #1 by factors between \(\sim\)2 for the G-model and \(\sim\)5 for the P-model. In addition, the \(\bar{\chi}_{\rm all}\) found for sample #2 is larger than the corresponding for sample #1, the increase ranging between 0.2% and 17% for the G- and B-models, respectively. The variability in the AMB parameters that was considered in the simulation generating sample #2 produces more different growth shapes of the MTS and this results in better (those with smaller \(\chi_{\rm all}^{2}\) values) and worst (those with larger \(\chi_{\rm all}^{2}\)) fits occuring independently of the specific mathematical model considered. 2. In general, the best fits to the whole growth curves were provided by the G-model. As shown in Table 1, the \(\bar{\chi}_{\rm all}\) obtained for this model are an order of magnitude smaller than those corresponding to the other models considered. In the case of sample#1, the  
Figure 3: In (**a**), the fits of the exponential model to the simulated ABM data of the MTS #1 of sample #1 are shown. Solid black circles indicate the volumes of this spheroid along the whole time period studied. Dotted red, dashed green, and solid blue lines display the results obtained when the fit involves the data in the time intervals [10-40] day, [40-60] day, [40-60] day, and [30-50] day, respectively; (**b**) shows the corresponding semi-logarithmic plot to emphasize the MTS volume behavior. 95% CI obtained for the G-model is clearly below those found for the other models. For sample #2, there is a slight overlap between the CI of the G- and P-models. 3. It is noticeable the large \(\chi_{\rm all}\) values obtained for the L-model. The \(\bar{\chi}_{\rm all}\) values are above 170 in both samples, and the respective 95% CI begin at 139 and 56, respectively. This again points out the fact already discussed in connection to Figure 2 about the difficulties of this model to describe the whole MTS growth. 4. A curiosity of these results is that all the distributions are skewed to the right (to high \(\chi_{\rm all}\)) except that found for the P-model in the case of sample #1 where an almost Gaussian behavior is observed. The predictive capabilities of the models were analyzed by looking at how well the models, fitted to reproduce a part of the growth curves, described the remaining volume data. The \(\chi\) distributions obtained are shown in Figures 5 and 6 and summarized in Table 1 in terms of the corresponding values of \(\bar{\chi}\) and of the 95% CI. In the two figures, the distributions shown in the left panels are those found in the fits, while those calculated for the predicted data are plotted in the right panels. Again, the distributions shown with light colors correspond to sample #2 while those with dark colors were obtained for sample #1. The results obtained deserve several comments:  
1. The best fits were now much better than those found when all volume data were included. The maximum \(\bar{\chi}^{\rm fit}\) was \(\bar{\chi}^{\rm fit}_{\rm pro}=3.75\), which corresponds to the L-model. These relatively low values are due to the fact that the number of data fitted is now 21 instead of the 55 considered before. It is worth noting that also the low limits of the 95% CI of \(\chi^{\rm fit}\) were much lower than in the case of \(\chi_{\rm all}\). In all cases, the values obtained are close to 1, with the only exception of the 1.97 found for the L-model in the prospective prediction (see Table 1).