Precision of herbivore tolerance experiments with imposed and natural damage

Tiffin and Inouye (2000) discussed the use of natural and imposed (controlled) damage in experiments of herbivore tolerance. They constructed a statistical model of the effect of herbivory on plant fitness, including damage level and an environmental factor as the independent factors, in which tolerance is defined as a slope of the regression line when damage level is regressed with plant fitness. They claim that while experiments with imposed damage are more accurate (i.e., they give a more correct estimate of tolerance), experiments with natural damage are more precise under a wide range of parameter values (i.e., tolerance estimates explain a larger part of variation in fitness). I show, however, that experiments with imposed damage are less precise only when an experimenter uses an experimental design that has weaker statistical power than in experiments with natural herbivory. The experimenter can nevertheless control the damage levels to optimize the experimental designs. For instance, when half of the experimental plants are left undamaged and the other half treated with maximal relevant damage level, experiments with imposed damage are almost always much more precise than experiments with natural damage.