The Fallacy of Ratios and the Testability of Models in Biology

Biological hypotheses framed in terms of ratios of measured variables run the risk of being untestable. Such avoidance of empirical verification results from a substantial widening of the sampling variation of ratios, compared to that of the original variables. Computer simulations show that in order to be testable, models in which ratios are substituted for actual variables would require either substantial magnitudes of the treatment effects, or an unrealistic precision of measurements, or prohibitively large sample sizes. Many theoretical models in biological sciences should be reformulated to facilitate their verifiability by empirical research. Another problem with the use of ratios occurs when the experimental treatment effects are exhibited not as shifts in means, but only in levels of variability of the variables. Focusing on average ratios, rather than allometric relationships between variables, is likely to obscure important biological phenomena. In general, we advocate a multivariate approach, with explicit consideration of the correlation patterns among variables.