COMPARISON AMONG BOLTZMANN AND CUBIC POLYNOMIAL MODELS FOR ESTIMATION OF COMPOSITIONAL NUTRIENT DIAGNOSIS STANDARDS: OPUNTIA FICUS-INDICA L. CASE

Abstract

Compositional Nutrient Diagnosis technique involves a yield target for discriminating between high- and low-yield subpopulations when developing norms. Traditionally, this yield value is estimated by finding the inflection point of the cumulative variance ratio function versus yield relationship through a third-order equation. However, yield targets frequently lie outside of the experimental yield range. A comparison among traditional (unrestricted) and restricted cubic model, and restricted and unrestricted Boltzmann equations was performed using a database (n = 360) of fresh matter yield and nutrient concentrations in one–year old cladodes of Opuntia ficus-indica L. The unrestricted Boltzmann equation resulted to have the best goodness-of-fit. The yield target was 27.01 kg plant⁻¹ associated to the unrestricted Boltzmann equation for phosphorus cumulative variance ratio function versus yield relationship. Proposed nutrient optimum concentrations are: 11.4 g kg⁻¹ for nitrogen (N), 3.4 g kg⁻¹ for phosphorus (P), 42.3 g kg⁻¹ for potassium (K), 42.5 g kg⁻¹ for calcium (Ca), and 16.2 g kg⁻¹ for magnesium (Mg).

Keywords:

• target yield
• nutrient norms
• goodness-of-fit
• cubic models