Non-parametric Statistical Formulas for Factors of Safety of Plant Stems

A previously proposed statistical approach for computing factors of safety (i.e. numerical measures of mechanical reliability) for any load bearing structure, like a vertical plant stem, is here extended to cope with organic structures whose morphological or mechanical properties have Weibull frequency distributions. This approach is illustrated using the actual lengthLand critical buckling lengthLerof flower stalks (peduncles) collected from isogenic garlic (Allium sativum) populations grown under windy field and protected glasshouse conditions. Our analyses of the data indicate thatLandLerof peduncles harvested from both populations have Weibull frequency distributions, that the factor of safety for glasshouse grown peduncles is very near unity (i.e.S=1.03), and that the factor of safety of field grown peduncles is 73% higher than that of glasshouse grown plants (i.e.S=1.73). Comparisons between theS-values computed on the basis of our formulas and on the basis of the quotient of the mean values ofLerandLfor each of the two populations indicate that the statistical method gives biologically realisticS-values and that the difference in theS-values for stems grown under protected and unprotected environmental conditions likely reflects the effects of chronic mechanical perturbation (due to wind-induced drag) on normal stem growth and development.