Lukas Kratochvil

Media, social scientists and public health researchers often present comparisons across countries, and policy makers use such comparisons to take evidence-based action. For a meaningful comparison among countries, one often needs to normalize the measure for differences in population size. To address this issue, the first choice is usually to calculate per capita ratios. Such ratios, however, normalize the measure for differences in population size directly only under the highly restrictive assumption of a proportional increase of the measure with population size. Violation of this assumption frequently leads to misleading conclusions. We compare per capita ratios with an approach based on regression, a widely used statistical procedure that eliminates many of the problems with ratios and allows for straightforward data interpretation. It turns out that the per capita measures in three global datasets (gross domestic product, COVID-19-related mortality and CO 2 production) systematically overestimate values in countries with small populations, while countries with large populations tend to have misleadingly low per capita ratios owing to the large denominators. Unfortunately, despite their biases, comparisons based on per capita ratios are still ubiquitous, and they are used for influential recommendations by various global institutions. Their continued use can cause significant damage when employed as evidence for policy actions and should therefore be replaced by a more scientifically substantiated and informative method, such as a regression-based approach.

Small erythrocytes might be beneficial for blood rheology, as they contribute less to blood viscosity than large erythrocytes. We predicted that rheological disadvantages of larger erythrocytes could be alleviated by relatively smaller nucleus size in larger cells allowing higher flexibility and by more elongated shape. Across squamate reptiles, we found that species with larger erythrocytes tend to have smaller ratio of nucleus size to cell size (N : C ratio), but that larger erythrocytes tend to be rounder, not more elongated. Nevertheless, we document that in fact nucleus area changes with erythrocyte area more or less linearly, which is also true for the relationship between cell length and cell width. These linear relationships suggest that nucleus size and cell size, and cell width and cell length, might be constrained to largely proportional mutual changes. The shifts in widely used N : C ratio and elongation ratio (cell length/cell width) with cell size might be misleading, as they do not reflect adaptive or maladaptive changes of erythrocytes, but rather mathematically trivial scaling of the ratios of two variables with a linear relationship with non-zero intercepts. We warn that ratio scaling without analyses of underlying patterns of evolutionary changes can lead to misinterpretation of evolutionary processes.