Methods for calculating factors of safety for plant stems

The concept of a 'factor of safety' is used by biologists and engineers who generally agree that structures must be mechanically reliable, i.e. that structures must be capable of coping with unprecedented loads without failing. These factors can be calculated for individual structures or for a population of otherwise equivalent mechanical structures differing in their load capabilities. Objective methods for quantifying factors of safety for biological structures are nevertheless difficult to devise because (1) actual (working) loads are defined by environmental conditions that can vary widely, (2) breaking loads (capability) of otherwise mechanically equivalent structures can likewise vary as a result of developmental variation, and (3) specific criteria for failure must be determined a priori. In this paper, we illustrate and discuss two methods for computing factors of safety for plants. One method works well for individual stems or entire plants, the other is useful when dealing with a population of conspecifics exhibiting a norm of reaction. Both methods require estimates of the actual and breaking bending (or torsional) moments experienced by stems, and both are amenable to dealing with any biologically reasonable criterion for failure. However, the two methods differ in terms of the assumptions made and the types of data that need to be gathered. The advantage of the first method is that it estimates the potential for survival of an individual stem or plant. The disadvantage is that it neglects natural variation among otherwise mechanically homologous individuals. The advantage of the second (statistical) approach is that it estimates the probability of survival of a population in a particular habitat. The disadvantage of this approach is that it sheds little light on the probability of an individual's survival.