Modeling optical properties of 'Braeburn' apples during fruit maturation on the tree

The absorption coefficient of fruit flesh at 670 nm (mu(a)670) non-destructively measured at harvest by time-resolved reflectance spectroscopy (TRS) was shown to be a maturity index for various fruit. In apples mu(a)670 decreased during fruit growth and ripening, with high mu(a)670 fruit (less mature) having lower mass and higher pulp hue at harvest and higher titratable acidity and lower soluble solids after cold storage than low mu(a)670 fruit (more mature). Aiming at modeling mu(a)670 decay during maturation on the tree, a three steps approach was exploited involving the estimate of the rate constant km, the calculation of the biological shift factor (BSF) and then the modeling of mu(a)670 vs. BSF using logistic regression. 'Braeburn' apples were picked 7 times from 149 to 191 days after full bloom (DAFB); at each harvest, 30 fruit were picked near the trunk and 30 from the peripheral part of the tree in order to ensure a mu(a)670 range as wider as possible. Each apple was measured for mu(a)670 by TRS and ranked by decreasing mu(a)670 value (that is increasing maturity) within the same harvest and canopy position, so that fruit ranked 1 was the least mature and that ranked 30 the most mature. The mu(a)670 decreased from (mean +/- standard error) 0.302 +/- 0.014 cm(-1) at 149 DAFB to 0.092 +/- 0.006 cm(-1) at 191 DAFB. The mu(a)670 decay for the whole data set and for the 30 subsets corresponding to the 30 rank positions were modeled using logistic regression based on the biological shift factor (BSF) theory. BSF was computed using the rate constant km of mu(a)670 decay estimated via nonlinear regression considering mu(a)670 value at 149 DAFB and days from the first harvest as independent variables and the fruit mu(a)670 value as dependent variable. The R2(adj) of the logistic model on all data set was 98.6%, while it varied from 99.8% for rank 1 to 97.0% for rank 30. The k(m) decreased from about 0.06-0.078 day(-1) for ranks 1-20 to 0.03-0.05 day(-1) for ranks 21-30 (more mature fruit) confirming that mu(a)670 decreased faster in less mature fruit than in the more mature ones.