This phenomenon may give rise to an apparent dependence of α on μ. It is possible that the shape of the dispersion-mean fit for the Bottomly data (Figure 1A) can be explained in that manner: the asymptotic dispersion is α0≈0.01, and the non-zero slope of the mean-dispersion plot is limited to the range of mean counts up to around 100, the reciprocal of α0. However, overestimation of α in that low-count range has little effect on inference, as in that range the variance v is anyway dominated by the α-independent Poisson component vP. The situation is different for the Pickrell data: here, a dependence of dispersion on mean was observed for counts clearly above the reciprocal of the asymptotic dispersion α0 (Figure 1B), and hence is not due merely to estimation bias. Simulations (shown in Additional file 1: Figure S25) confirmed that the observed joint distribution of estimated dispersions and means is not compatible with a single, constant dispersion. Therefore, the parametrization (6) is a flexible and mildly conservative modeling choice: it is able to pick up dispersion-mean dependence if
