Use of the elliptical mathematical formula to estimate the surface area of cladodes in four varieties of Opuntia ficus-indica


  • Martín E. Tiznado-Hernández
  • Judith Fortiz-Hernández
  • Ángel J. Ojeda-Contreras
  • Armida Rodríguez-Félix


Ellipse figure, days after sprout, cladode area, „Atlixco?, „Copena F–1?, „Milpa Alta?, „Jalpa?.


Estimation of cladode area in Opuntia spp. can be a valuable tool for estimating plant growth, development and productivity for either physiological studies or commercial purposes. The objective was to develop an easy, non destructive and inexpensive protocol to estimate the area of cladodes at different stages of development in four varieties of Opuntia ficus–indica. The study was carried out by tagging 300 buds of „Atlixco? and „Copena F–1? varieties and 180 of „Milpa Alta?. Further, not tagged buds of „Jalpa? variety were sampled only once. Sampling of buds in „Atlixco? and „Copena F–1? was done at 10, 17 and 23 days after sprout (DAS), whereas for „Milpa Alta? the sampling was done only at 10 DAS. In the „Jalpa? variety, sampling was done randomly. The determination of the real cladode area (RCA) was carried out by computer analysis of the digitalized cladodes circumference drawn on a paper sheet and the estimated cladode area (ECA) was done by measuring the minor and major axes, and using the formula of the ellipse. It was found that cladodes of „Copena F–1? showed a higher growth from 10 to 17 DAS than from 17 to 23 DAS. In contrast, „Atlixco? showed a constant growth from 10 to 23 DAS. Regression analysis did not allow concluding whether the cladodes growth phenomena follows a straight or exponential behavior. Scatter plots of RCA and ECA recorded a coefficient of determination of 0.94 and 0.96 for „Atlixco? and „Copena F–1? varieties, respectively. However, statistical analysis found differences (p<0.05) between the RCA and ECA. It was concluded that the area estimated in „Atlixco?, „Copena F–1?, „Milpa Alta? and „Jalpa? varieties with the ellipse mathematical formula is very close to the real cladode area, although not completely accurate.





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