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

Current Conveyor and Its Application

In this study, a new electronically tunable differential difference current conveyor with translinear circuit principle is proposed. A Capacitance multiplier circuit is used to show functionality of the proposed active block. The designed circuit is simulated by using PSpice program. According to the results of simulation, validation of proposed active block and applied circuit are verified

Current Conveyor and Its Application

In this study, a new electronically tunable differential difference current conveyor with translinear circuit principle is proposed. A Capacitance multiplier circuit is used to show functionality of the proposed active block. The designed circuit is simulated by using PSpice program. According to the results of simulation, validation of proposed active block and applied circuit are verified

The von Bertalanffy growth model for horticulture : Predicting tomato size at harvest

Traditionally, crop load and fruit yield from previous seasons are used as indicators for prediction of fruit size. Disregarding the inevitable biological variation between fruit, von Bertalanffy (1938) described the growth, expressed as length, of virtually any living organism. The model is here extended to include the variation between individuals in a batch. Using this extended model, fruit size and its variation can be predicted, using measurements of a large number of fruit at a single point during early development. The diameter of 200 tomatoes was measured 15 days after full bloom (DAFB). Using the density function derived from the extended von Bertalanffy model, and applying prior knowledge of some of the model parameters, the variation in size at harvest could be predicted. Validation of the results was obtained by comparing the predicted sizes with the diameters of the same tomatoes at harvest

Variation in apple colour and maturity. causes and similarities over orchards, management, cultivars and storage

Proceedings of the International Conference “Environmentally friendly and safe technologies for quality of fruit and vegetables”, held in Universidade do Algarve, Faro, Portugal, on January 14-16, 2009. This Conference was a join activity with COST Action 924.The colour of apples (flesh colour or skin colour) was assessed using the same individual apples repeatedly in time at three different locations, in several seasons for five different cultivars. Two experiments were conducted in the orchard, one experiment during postharvest storage. The same logistic model was applied to analyse the data, separate for each location and cultivar. Non linear mixed effects regression analysis allows to extract not only information on the kinetic parameters like reaction rate constant and potential greenness, but also on the variation present in the data. The rate constant of the decolouration process was found to be largely the same for all combinations (with one exception). The variation in biological shift factor, as an expression for maturity, seems to be independent of orchard location and only slightly dependent on orchard management procedures. The main differences observed are in the potential greenness of the apples (colmin) that vary considerably between successive seasons and between cultivars. The applied technology provides the necessary tools to analyse the effects of season and orchard management, for all locations in the study. It opens wide alleys to investigate more dedicated the effects of weather, season, management and orchard location in growing apples with a constant quality (colour) over the seasons, locations and management procedures

Biological variation in the colour development of Golden Delicious apples in the orchard

BACKGROUND: In managing apple orchards, crop load and rate of nitrogen (N) fertilisation are two factors with a significant influence on fruit quantity and quality, because they affect all physiological processes in the tree. Both factors are strongly related to external and internal fruit quality, especially to skin colour, sugar and acid contents and mineral composition, and consequently to the keeping quality of fruits. The aim of this study was to assess the effects of both factors (three crop load levels and two N fertilisation levels) on the colour development of Golden Delicious apples during the last month on the tree in two consecutive seasons. Data on skin colour (L*, a*, b* values) were analysed using nonlinear mixed effects modelling to extract information on the variation in biological shift factor for colour and to link this variation to the different strategies used concerning N fertilisation and crop load. RESULTS: The major source of information is contained in the a* value. The behaviour of the a* value could be described by a logistic or an exponential model depending on the season and the experimental set-up. Nonlinear mixed effects analysis estimating the biological shift factor (maturity) for each individual fruit (random effect) while estimating the rate constant of the decolouration process in common (fixed effect) resulted in explained parts well over 95%. CONCLUSION: The variation in maturity stage between individual fruits is large. Season has the most profound effect on the estimated values, far more important than that of crop load or fertilisation level. The magnitude of variation in colour due to crop load and N fertilisation is not too large. Its effect on the maturity stage of fruits is more profound: the higher the crop load, the higher the variation. The effect of fertilisation seems to be opposite: the higher the fertilisation level, the lower the variation

Colour development in the apple orchard

Colour is traditionally one of the important appearance features of all fruit for consumers in deciding to buy them. Colour is therefore important in the postharvest supply chain. But where does that colour of fruit come from? Clearly the period of growing and the circumstances during growth are important for developing this important feature. During several seasons (2007-2009), the skin colour of individual apples of different cultivars (‘Braeburn’, ‘Fuji’, ‘Gala’, ‘Golden Delicious’) were measured using a Minolta CR-400 chromameter during the last 40-60 days before (commercial) harvest. By including the biological variation between individual apples in the analyses and applying non linear indexed regression analysis based on process oriented models, explained parts were obtained for the a*-value, all exceeding 90%. The estimated rate constants for the colouration process were remarkably similar for all cultivars (except ‘Fuji’) and growing conditions. That would indicate that the process of colouration is really reflecting the degradation of chlorophyll and not the production of red or yellow coloured blush (anthocyanins). The expected effect of growing conditions (fertilization and crop level, hail net or not, sunny side or shady side of the tree) did change the mechanism nor the kinetic parameter values but could all be attributed to the minimal obtainable skin colour (asymptotic values of the logistic model). This type of information from the production period may constitute an important link to postharvest supply chain management

Development and distribution of quality related compounds in apples during growth

Colour and taste are important attributes of apple fruit quality and have therefore been widely studied. Nevertheless, because of the destructive sampling methods commonly used to obtain the data, and of the subsequent traditional analyses, ignoring the effects of biological variation, the knowledge on the kinetic mechanisms of synthesis and degradation of individual quality components during fruit development and growth is still lacking. Spatio-temporal changes of taste components (sugars: fructose, sucrose, glucose, organic acids: malic, citric, shikimic and fumaric acid) and colour aspects (a) in individual apple fruits were monitored to assess the dynamics and mechanisms of change during development and ripening with respect to location within fruit as a factor and the variation between individual apples. Data were analysed with non-linear indexed regression based on either a logistic or an exponential process oriented model assessing the technical variation simultaneously. The rate constants for colour or taste component were roughly similar between cultivars, suggesting a similar mechanism of development and confirming the generic nature of the model. There was a very large biological variation in individual quality components observed in the raw data (the biological variation), which can be almost exclusively explained by the difference in the maturity stage between individual fruit. The explained parts (R2 adj) were, with one exception, higher than 0.90. The major contribution of this study is the fact that all the herein monitored taste defining components can be analysed and described with the same process-oriented model.</p