Probability distributions for concentrations of nine nutrient elements in the foliage of black walnut (Juglans Nigra L.) in a New Zealand population

Abstract

Black walnut foliage samples collected from a wide range of sites during a national survey of the New Zealand (NZ) resource conducted in 1979 were analysed for N, P, K, Ca, Mg, B, Fe, Mn, and Zn. Provisional American standards applied to the foliar data indicate that only very small proportions of the field population (individually 1 to 2%) have foliar levels of N, P, Fe, Mn, or Zn rating deficient. For K, Ca, Mg, or B foliar levels consistently exceeded the deficiency threshold. The proportions of the population rating intermediate were very large (40 to 95%) for certain elements (P, Mg, Fe, Zn), and fairly large (16 to 27%) for the remainder. In this transitional bracket response to fertiliser is uncertain. As the applicability of the American criteria to NZ conditions is unproven, this evaluation must remain tentative.

To study the distributions for the foliar concentrations of the elements determined, two functions of the Weibull distribution were used ‐ one for cumulative density and the other for probability density. The cumulative density function fitted the arrayed data for each nutrient very closely (R = 0.992 to 0.998). Quartile values for cumulative probability are given for each nutrient; these allow a preliminary ranking of individual foliar analyses as an aid in assessing nutrient status relative to the expected NZ norm. Estimated parameters of the same function are given for each nutrient so that percentile values can easily be calculated.

Keywords:

• Foliar analysis
• Juglans nigra L.
• Weibull distribution