The fallacy of ratios and the testability of models in biology

Biological hypotheses framed in terms of ratios of measured variables run t he risk of being untestable. Such avoidance of empirical verification resul ts from a substantial widening of the sampling variation of ratios, compare d to that of the original variables. Computer simulations show that in orde r to be testable, models in which ratios are substituted for actual variabl es would require either substantial magnitudes of the treatment effects, or an unrealistic precision of measurements, or prohibitively large sample si zes. Many theoretical models in biological sciences should be reformulated to facilitate their verifiability by empirical research. Another problem wi th the use of ratios occurs when the experimental treatment effects are exh ibited not as shifts in means, but only in levels of variability of the var iables. Focusing on average ratios, rather than allometric relationships be tween variables, is likely to obscure important biological phenomena. In ge neral, we advocate a multivariate approach, with explicit consideration of the correlation patterns among variables.