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 properties; biological differences; biodiversity; data analysis; data processing; measurement; apples; tomatoes; statistical methods; mathematics

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Hertog MLATM. 2002. The impact of biological variation on postharvest population dynamics. Postharvest Biology and Technology 26:253–63; DOI: 10.1016/S0925-5214(02)00044-3

Hertog MLATM, Lammertyn J, Desmet M, Scheerlinck N, Nicolaï BM. 2004. The impact of biological variation on postharvest behaviour of tomato fruit. Postharvest Biology and Technology 34:271–84; DOI: 10.1016/j.postharvbio.2004.05.014

Hertog, M.L.A.T.M., Lammertyn, J., De Ketelaere, B., Scheerlinck, N., Nicolaï, B.M. 2007. Managing quality variance in the postharvest food chain. Trends in Food Science and Technology 18, 320-332; DOI: 10.1016/j.tifs.2007.02.007

Lammertyn J, De Ketelaere B, Marquenie D, Molenberghs G, Nicolaï BM. 2003. Mixed models for multicategorical repeated response: modelling the time effect of physical treatments on strawberry sepal quality. Postharvest Biology and Technology 30:195- 207; DOI: 10.1016/S0925-5214(03)00100-5

Lana M.M., Tijskens L.M.M., van Kooten O. (2005): Effects of storage temperature and fruit ripening on firmness of fresh cut tomatoes. Postharvest Biology and Technology 35, 87–95; DOI: 10.1016/j.postharvbio.2004.07.001

Schouten RE, Tijskens LMM, van Kooten O. 2002. Predicting keeping quality of batches of cucumber fruits based on a physiological mechanism. Postharvest Biology and Technology 26:209–20; DOI: 10.1016/S0925-5214(02)00017-0

Schouten RE, Jongbloed G, Tijskens LMM, van Kooten O. 2004. Batch variability and cultivar keeping quality of cucumber. Postharvest Biology and Technology 32:299-310; DOI: 10.1016/j.postharvbio.2003.12.005

Schouten RE, Zhang X, Verschoor JA, Otma EC, Tijskens LMM, van Kooten O. 2009: Development of colour of Broccoli heads as affected by controlled atmosphere storage and temperature. Postharvest Biology and Technology 51:27–35; DOI: 10.1016/j.postharvbio.2008.06.005

Tijskens LMM, Wilkinson EC. 1996. Behaviour of biological variability in batches during post-harvest storage. AAB Modelling Conference: Modelling in Applied Biology - Spatial Aspects. p. 267-8, 24-27 June 1996, Uxbridge, UK

Tijskens LMM, Konopacki P, Simčič M. 2003. Biological Variance, Burden or Benefit? Postharvest Biology and Technology 27:15-25; DOI: 10.1016/S0925- 5214(02)00191-6

Tijskens LMM, Heuvelink E, Schouten RE, Lana MM, van Kooten O. 2005. The biological shift factor. Biological age as a tool for modelling in pre- and postharvest horticulture. Acta Horticulturae 687:39-46

Tijskens LMM, Herold B, Zude M, Schlüter O, Geyer M. 2006. Biological variation in the apple orchard. In: Proceedings COST 924 workshop (ed. J. Ovesná, V. Pouchová, K. Mitrová) From plant to Human genes, p27-34, November 2006, Prague, CZ. ISBN 80- 86555-99-2.

Tijskens LMM, Konopacki PJ, Schouten RE, Hribar J, Simčič M. 2008. Biological variance in the colour of Granny Smith apples. Modelling the effect of senescence and chilling injury. Postharvest Biology and Technology 50:153–63; DOI: 10.1016/j.postharvbio.2008.05.008

Tijskens LMM, Dos-Santos N, Jowkar MM, Obando J, Moreno E, Schouten RE, Monforte AJ, Fernández Trujillo JP. 2009. Postharvest firmness behaviour of near-isogenic lines of melon. Postharvest Biology and Technology 51:320-6; DOI: 10.1016/j.postharvbio.2008.06.001

Tijskens L.M.M., Jacob S., Schouten R.E., Fernández- Trujillo J.P., Dos-Santos N., Vangdal E., Pagán E., Pérez Pastor A. 2010. Water loss in horticultural products. Modelling, data analysis and theoretical considerations. Acta Horticulturae 858, 465-471.

Unuk T., Tijskens L.M.M., Germšek B., Zadravec P., Vogrin A., Hribar J., Simčič M., Tojnko S. 2012, Effect of location in the canopy on the colour development of three apple cultivars during growth. Journal of the Science of Food and Agriculture. 92:2450–2458; DOI: 10.1002/jsfa.5651

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