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The authors of Explore Evolution raise another issue, that of variations of clock rates along lineages due to "environmental factors", which if true would be more problematic because they would be harder to control for. However, while mutation rates in individuals can of course change according to environmental factors (e.g radiation exposure), for this change to noticeably affect substitution rates in populations and species (which is what the molecular clock measures), the change in mutation rates would have to be very substantial, to be sustained over many generations, and to affect a very large proportion of individuals in a species. These are not a common occurrence, even on a paleontological scale, and indeed environmental changes are not counted by experts among major hurdles in molecular clock studies. The authors provide the following citations for their statements:
Nowhere in the paper by Valentine, Jablonski and Erwin do the authors find that magnetic field changes and mass extinctions affect clock rates. In fact, while the idea that inversions of the Earth’s magnetic field could correlate with accelerated evolution by effects on cosmic radiation levels was considered early in the 1960s, it was quickly shown to be very unlikely based on physical and biological principles.
Explore Evolution wrongly attributes this idea to Valentine and his collaborators, and gives no basis for this attribution.