The variance in the genetic data
Kammerer explicitly states that he predicts Mendelian ratios to apply for the offspring in his crossing experiments (Kammerer, 1911). Actually, the numbers of water- and land-breeding F2 -offspring provided by Kammerer (1911:101-104) are remarkably close to the expected 3 to 1 Mendelian ratio. In the four Alytes-experiments, with sample sizes in the 20-28 range, the differences between the observed values and those suggested by the Mendelian ratio are -0.5, 0, 0 and 0.5 (see Appendices I and II). However, for unbiased sampling at sample sizes of ≥ 20 the expected deviates (|observation minus the mean|) have an average well in excess of unity. This raised our suspicion as to the nature of Kammerer's data. We hence investigated other results of which Kammerer said they were in support of the 3 to 1 Mendelian ratio and found 11 observations on crosses of different phenotypes of the fire salamander, namely the spotted ‘typical form’ and the striped ‘taeniata’ form (Kammerer, 1913:131), that are currently known as the subspecies Salamandra salamandra salamandra Linnaeus, 1758 and Salamandra salamandra terrestris Lacépède, 1788. The argument is reminiscent of the Mendel-Fisher controversy and for all possible intricacies and subtleties involved in the conscious or unconscious mechanisms operating in data gathering that could explain certain biases we refer to Franklin et al. (2008) and references therein. As for Kammerer's results, we found our concern vindicated (Figure 2). The chance for finding results as close as observed to the Mendelian ratio are 0.510, i.e. P<0.001 for the fire salamander and 0.514, i.e. P<0.0001 for the two data sets combined. We propose that there can be no reasonable doubt that Kammerer's data are too good to be genuine.
Figure 2. Cumulative probabilities of the binomial distribution for the 3 to 1 Mendelian ratio at sample sizes ≤ 40. Published data are shown by open square symbols (N=4, midwife toad; Kammerer, 1911:101-104) and by open round symbols (N=11, fire salamander; Kammerer, 1913:131). Unbiased data would be equally distributed over the four quartiles, whereas the given data all fall in the second and third quartiles (light shading) and none in the first or fourth quartile (dark shading), suggesting an anomaly of kinds. The small solid dots represent a data ambiguity, presumably a typographical error (for an explanation see Appendix II).