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 length L and critical buckling length Lerof flower stalks (peduncles) collected from isogenic garlic (Allium sativum) populations grown under windy field and protected glasshouse conditions. Our analyses of the data indicate that L and Lerof 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 the S -values computed on the basis of our formulas and on the basis of the quotient of the mean values of Lerand L for each of the two populations indicate that the statistical method gives biologically realistic S -values and that the difference in the S -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. Copyright 1999 Academic Press.