Green mathematics: Benefits of including biological variation in your data analysis
Biological variation is omnipresent in nature. It contains useful information that is neglected by the usually applied statistical procedures. To extract this information special procedures have to be applied. Biological variation is seen in properties (e.g. size, colour, firmness), but the underlying issue is almost always to the variation in development or maturity in a batch of individuals generated by small scale environmental differences. The principles of assessing biological variation in batches of individuals are explained without putting emphasis on mathematical details. Obtained explained parts increase from about 60 to 80 % for the usual approach to 95 when the biological variation is taken into account. When technical variation or measuring error is small even 99 % can be achieved. The benefit of the presented technology is highlighted based on a number of already published studies covering the colour of apples during growth and storage and the firmness of cut tomatoes during storage.
Biological variance in the colour of Granny Smith apples: Modelling the effect of senescence and chilling injury
Abstract The colour of ‘Granny Smith’ apples, harvested from three orchards at two stages of maturity, was measured individually using the CIE L*a*b* system during storage in regular atmosphere at three temperatures: 1, 4 and 10 °C. A model was developed based on a simplified mechanism to describe the development of the apple colour during storage as affected by senescence (aging) and chilling injury. Monitoring of individual apples made it possible to include and to describe the biological variance of colour in batches of apples and to correct the colour of each apple individually for its own biological shift factor (biological age; random effect). The biological shift factor is related to the initial condition and range of colour change. The rate of the colour development was estimated in common (fixed effects) for all batches using non-linear mixed effects regression analysis. The variance accounted for by the developed model, including effects of temperature, harvest maturity and orchard location, was more than 95% on 3211 observations. The overall reaction rate constant of decolouration, combining the effects of senescence and chilling injury, was found to depend on temperature. The temperature that showed the lowest overall reaction rate of decolouration is 8 °C, which is in contrast with the currently recommended storage temperature for ‘Granny Smith’ apples.
Fruit pigmentation of four green apple cultivars responds to urea sprays but not to nitrogen fertilization
Four green apple (Malus domestica Borkh.) cultivars, 'Granny Smith', 'Mutsu', 'Newtown', and 'Shamrock', were subjected to a factorial experiment of two rates of nitrogen fertilization and three concentrations of foliar urea sprays for 4 years. The higher rate of N (160 kg N/ha) had no effect on ground color or fruit quality relative to the lower rate of 80 kg N/ha. Urea sprays enhanced green pigmentation in 'Granny Smith' and 'Newtown' at harvest and retarded yellowing of fruit in all cultivars during air storage at 0C. Response was similar for urea at 0.5% and 1%, and urea sprays did not adversely affect quality. Urea sprays increased fruit N by 23% and 47% for the 0.5% and 1% concentrations, respectively.