Time for a regular reminder that logarithmic transformation is often necessary in biology for biological (and not just statistical reasons).. .thread 1/x @KerkhoffLab https://www.sciencedirect.com/science/article/abs/pii/S0022519308006681?via%3Dihub

Why transform? Most biological phenomena - growth, reproduction, sensation, & metabolism are inherently multiplicative, rather than additive, & it is proportional rather than absolute variation that matters, especially across the range of data spanned by most biological analyses

Folks often think log transformation is only done for statistical reasons (normality assumptions etc.) but there are biological reasons and these issues are deeper and based on the conflict between arithmetic & geometric (or multiplicative) assumptions about biological variation

But this is not new. We seem to have a deep rooted assumption that biological variation operates only on arithmetic scales. This debate is perhaps one of the longest in biology - see Galton 1879 "The geometric mean in vital and social statistics." https://royalsocietypublishing.org/doi/10.1098/rspl.1879.0060

The default status of the additive error model is perhaps based on the deeper assumption that arithmetic scales are somehow truer or more intuitive, and that log-transformat- ion thus represents a distortion of the ‘‘real’’ data. However, recent research strongly challenges this.

Gingerich (2000) points out that our evolved senses (e.g. eyes, ears) measure the world geometrically, based on proportional changes but our constructed measurement devices (rulers, balances) generally do so arithmetically, like counting on our fingers. https://www.sciencedirect.com/science/article/abs/pii/S0022519300920083

Biology (many other physical & social sciences) multiplicative error is often the appropriate model of variation. But as noted by Galton (1879) an additive error model assumes equivalent deviations differ by equal amounts, multiplicative error assumes differ by equal proportions

Log-transformation is not simply a statistical convenience. It is indeed a non-linear transformation, but it places numbers into a geometric domain in which proportional deviations are represented consistently, independent of the scale and units of measurement.

But more importantly, log-transformation often appropriate in biology because many biological phenomena (e.g. growth, reproduction, metabolism, sensation) are fundamentally multiplicative, and likely conform more closely to a geometric error model.

Not convinced? As noted by Calder (1984), measures of metabolic rate vary by about 20% in mammals from shrews and elephants, corresponding to about 0.175 units on a (base-10) logarithmic scale....

For a shrew metabolic rate varies by only about 0.035W, while elephant metabolic rate can vary by 284W. Thus, despite the fact that variation in both animals is proportionally the same, elephants appear to be much more variable on an arithmetic scale...