Postharvest Biology and Technology 43 (2007) 78–88 The impact of biological variation on postharvest behaviour of Belgian endive: The case of multiple stochastic variables Maarten L.A.T.M. Hertog a,∗ , Nico Scheerlinck a , Jeroen Lammertyn a , Bart M. Nicola¨ ı a,b a BIOSYST-MeBioS, Katholieke Universiteit Leuven, W. de Croylaan 42, B-3001 Leuven, Belgium b Flanders Centre of Postharvest Technology, W. de Croylaan 42, B-3001 Leuven, Belgium Received 1 February 2006; accepted 23 July 2006 Abstract Data generated in postharvest research is often characterised by its large biological variation. This variation generally obscures the behaviour of interest, complicating both the statistical and conceptual interpretation of the data. This paper outlines a general model approach of how to account for the propagation of biological variation when analysing experimental postharvest data. Previous work on the case of a single stochastic variable was extended to the situation of two stochastic variables. The proposed technique was applied to experimental data on stem growth of Belgian endive. By explicitly using the information on biological variation, the number of model parameters to be estimated (only two) did not change while the fitness of the model to describe the experimental data was improved tremendously as compared to the traditional fitting of a model without stochastic variables. The model could describe the complex behaviour of a batch showing propagation of biological variation in stem length of Belgian endive as a function of time and temperature during postharvest storage. Differences between batches could not be related directly to either grower, harvest or culture type but probably depends on a complex interaction with preharvest factors. © 2006 Elsevier B.V. All rights reserved. Keywords: Batch behaviour; Belgian endive; Biological variation; Chicory; Modelling; Multivariate distribution; Probability; Stochastic kinetic model; Witloof 1. Introduction Postharvest product behaviour is inherently affected by the omnipresent biological variation. The variation in postharvest storage behaviour can be interpreted as the expression of the same generic product behaviour with some of the product parameters varying per individual. If all fruit and vegetables would be harvested at the same developmental state, variation at harvest would be negligible and would remain negligible throughout the postharvest period. As fruit and vegetables are not harvested at such a homogenous stage, variation at harvest cannot be prevented. Depending on the underlying mechanism the amount of variation observed at harvest may remain the same during postharvest storage or will be altered. In the case of a linear process the shape of the distribution of ∗ Corresponding author. Tel.: +32 16 322376; fax: +32 16 322955. E-mail address: Maarten.Hertog@biw.kuleuven.be (M.L.A.T.M. Hertog). quality remains the same and only shifts towards lower qual- ity levels, while in the case of a non-linear process the shape of the distribution of quality will be altered as a function of time while shifting to lower quality values. This move- ment of the distribution of a certain quality aspect with time, moving to lower quality levels, and depending on the under- lying mechanism also changing shape is what is referred to as propagation of biological variation. In a previous paper (Hertog et al., 2004) a mathemat- ical approach was outlined to interpret postharvest batch behaviour combining kinetic models describing postharvest behaviour with the concept of biological age modelled by a random variable. In this approach, postharvest propagation of biological variation in tomato colour was modelled as a func- tion of a single stochastic variable (biological age) assuming all other parameters constant. Colour of tomato was mea- sured non-destructively on individual tomatoes providing a clear picture of the different sources of variation. Parallel efforts to get a grip on the effects of biological variation on 0925-5214/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.postharvbio.2006.07.007