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 st ructure, like a vertical plant stem, is here extended to cope with organic structures whose morphological or mechanical properties have Weibull freque ncy distributions. This approach is illustrated using the actual length L a nd critical buckling length L-cr of flower stalks (peduncles) collected fro m isogenic garlic (Allium sativum) populations grown under windy field and protected glasshouse conditions. Our analyses of the data indicate that L a nd L-cr of 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 gr own peduncles is 73% higher than that of glasshouse grown plants (i.e. S = 1.73). Comparisons between the S-values computed on the basis of our formul as and on the basis of the quotient of the mean values of L-cr and L for ea ch of the two populations indicate that the statistical method gives biolog ically realistic S-values and that the difference in the S-values for stems grown under protected and unprotected environmental conditions likely refl ects the effects of chronic mechanical perturbation (due to wind-induced dr ag) on normal stem growth and development. (C) 1999 Academic Press.