This correspondence concerns a publication by Malmstrøm in Nature Genetics in October 2016. Malmstrøm made an important contribution to fish phylogeny research by using low-coverage genome sequencing for comparison of 66 teleost (modern bony) fish species, with 64 of those 66 belonging to the species-rich clade Neoteleostei, and with 27 of those 64 belonging to the order Gadiformes. For these 66 species, Malmstrøm estimated numbers of genes belonging to the major histocompatibility complex (MHC) class I lineages U and Z and concluded that in teleost fish these combined numbers are positively associated with, and a driving factor of, the rates of establishment of new fish species (speciation rates). They also claimed that functional genes for the MHC class II system molecules MHC IIA, MHC IIB, CD4 and CD74 were lost in early Gadiformes. Our main criticisms are (1) that the authors did not provide sufficient evidence for presence or absence of intact functional MHC class I or MHC class II system genes, (2) that they did not discuss that an MHC subpopulation gene number alone is a very incomplete measure of MHC variance, and (3) that the MHC system is more likely to reduce speciation rates than to enhance them. Furthermore, their use of the Ornstein-Uhlenbeck model is a typical example of overly naïve use of that model system. In short, we conclude that their new model of MHC class I evolution, reflected in their title "Evolution of the immune system influences speciation rates in teleost fish", is unsubstantiated, and that their "pinpointing" of the functional loss of the MHC class II system and all the important MHC class II system genes to the onset of Gadiformes is preliminary, because they did not sufficiently investigate the species at the clade border.