The Biological Shift Factor: Biological Age as a Tool for Modelling in Pre- And Postharvest Horticulture

Abstract

Individuals differ in development stage or biological age. This difference can be taken into account when modelling the quality behaviour of various fruits and vegetables. Even on a batch level, the same principle can be applied, provided the variation within a batch is not too large. By applying the biological shift factor, i.e. a shift in calendar time, the effects of different growing and harvesting condition can be included in modelling quality behaviour, which widely opens alleys for producing models applicable in the entire globalised food chain. The variation in biological shift factor over individuals in a batch and over several batches seems to exhibit a normal distribution pattern. INTRODUCTIONThe concept of biological age has been subject of many discussions and developments over the past decades. Especially in the pre-harvest period, this concept was developed as a normalising approach for products grown under different conditions and scenarios of temperature, light, fertilisation and other management issues (e.g. Heuvelink and Marcelis, 1989). Application of these viewpoints in research and practice was however always hindered not only by the lack of a suitable definition, but especially because biological age could not be measured or determined in a quantitative way.The advantage of thinking in biological age is that it does not matter how long it takes in calendar time to reach a certain stage. Once the produce reaches that stage, it will be identical (at least highly comparable) to all other individuals at that stage, no matter how that stage is reached. For purposes of modelling and understanding product behaviour, this is a very powerful and useful concept. Temperature (during growth or storage), light, fertilisation etc. do no longer reflect on the product behaviour or state, only on the calendar time necessary to reach that state. This concept also allows to link pre-and postharvest phases, which is essential for understanding the sometimes erratic behaviour during postharvest stage and handling (Heuvelink et al., 2004). In Fig. 2 an example is given, based on a logistic behaviour as is frequently encountered in colour development.The concept of biological age as a substitute for calendar time closely resembles the system of dimensionless representations of behaviour, frequently encountered in the field of engineering and physics. In this paper, some examples are provided based on measured data of several quality attributes for several products, and based on the modelling and analysis of these data. In this paper, the biological shift factor is introduced that can serve as a quantitative estimate for the biological age of individuals or batches of individuals. At the same time the biological shift factor of individuals in a batch do express the variation that exists in that batch.

Biological Variation in Ripening of Nectarines

“…Measuring the absorption of the fruit flesh by Time Resolved Spectroscopy (TRS) at 670 nm, provide information on the ripening stage and the variation in ripening stages of batches of fruit. Since each individual fruit is harvested and measured at some arbitrary stage of development, the analysis of the data gathered was based on the system of the biological shift factor (Tijskens et al 2005) applying non-linear mixed effects regression analysis. The results show that µ a , and therefore also the fruit flesh colour and chlorophyll content, change according a sigmoidal pattern, which was approximated with a symmetrical logistic function.…”

“…2a. On many occasions, the estimated biological shift factor was normally distributed (Tijskens et al 2005, Hertog et al 2004. Based on this assumption, and on the appropriate model for the quality property under study, the distribution and the dynamics of the distribution of μ a in time can be deduced (Hertog et al 2004, Schouten 2004.…”

How to Choose Criteria to Harvest Apples. The Dynamics of Maturity

“…And also assume both variables change according to a sigmoidal behaviour, frequently modelled with the logistic model (Eq. 1), here expressed in the notation for biological shift factor ∆t (Tijskens et al, 2005).…”

Modelling for Globalisation

“…When these differences are taken into account, we are basically dealing with biological variation. Lately reports were published dedicated to that subject (Hertog, 2002(Hertog, , 2004Schouten et al, 2004;Tijskens et al, 2003Tijskens et al, , 2005a. Hertog (2006) will speak more dedicated to that subject.…”

“…The effects of harvest maturity on product behavior can be manifold. In its simplest form it induced a mere shift in the biological time, without altering fundamentally the behavior of the aspect studied (Tijskens et al, 2005a). Based on a simple exponential decay (Eq.…”