Figure 5

Model predicts the shape of the normal and autistic distributions of platelet 5-HT levels. Histograms obtained by simulating a sampling of a very large number of normal and autistic individuals (a million subjects in each group). The distribution of γ was assumed to be (A, B) the beta distribution on the interval [0.8060; 0.9612] with both shape parameters equal to 1.5 (see the text); or (C, D) the normal (Gaussian) distribution with mean 0.8836 (the midpoint of the interval [0.8060; 0.9612]) and standard deviation 0.04 (see the text). The platelet 5-HT levels were calculated by using equation (3), with the values of K, F _C , R _C , α _normal and α _autistic taken from Table 1. In a very large sampling, the number of cases in each histogram bin closely approximates the number of cases predicted by the exact probability distribution functions. The Chi-square test confirmed that the normal and autistic distributions predicted by the model may underlie the distributions reported by Mulder et al. (2004). The following goodness-of-fit results were obtained: = 12.38 (P = 0.26) and = 11.29 (P = 0.19) for the normal and autistic groups, respectively, if γ had the beta distribution; and = 13.36 (P = 0.27) and = 12.21 (P = 0.14) for the normal and autistic groups, respectively, if γ had the normal distribution (bins were pooled if theoretical bins had fewer than 3 cases). It is important that both the normal and autistic distributions had the same underlying distribution of γ and that only one parameter, α, was needed to switch from the normal distribution to the autistic distribution. Also, compare the histograms in C and D, based on the data of Mulder et al. [39], with those in Figure 1 of Coutinho et al. [40].