Between-group heritability and the status of hereditarianism as an evolutionary science

Hereditarianism is a school of thought that contends there are substantial evolved cognitive and behavioral differences among groups of humans which are both resistant to environmental intervention and are a root cause of differential social outcomes across groups. The relationship of between- group heritability ( h2B ) to within-group heritability ( h2W ) is one of the key theoretical components of hereditarianism and forms one of the bases for its claim to be an evolutionary science. Here, we examine the relationship between h2B and h2W and its application to problems in the hereditarian literature from an evolutionary genetic perspective. We demonstrate that the formulation of the relationship between h2B and h2W used in the hereditarian literature has no evolutionary content. By re-writing the relationship between h2B and h2W in a novel evolutionary framework, we demonstrate that there is no way to predict h2B using h2W without considerable additional theory that is absent from the hereditarian literature. Furthermore, we demonstrate that the hereditarian technique that uses h2B and h2W as a means of judging whether a given difference between groups may be plausibly ameliorated through environmental intervention is mathematically flawed. Lastly, we fill a gap in the hereditarian literature by writing out a means of using h2B to predict the absolute difference between groups under a neutral evolutionary model and find that it is much smaller than claimed by hereditarians. In conclusion, we propose a path forward for the study of human variation that moves us past the ill-conceived nature vs. nurture question and allows us to focus on more productive issues. ### Competing Interest Statement The authors have declared no competing interest.