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Postharvest Biology and Technology 90 (2014) 7–14

Contents lists available at ScienceDirect

Postharvest Biology and Technology

jou rn al h om epage: www.elsev ier .com/ locate /postharvbio

odelling batch variability in softening of ‘Hayward’ kiwifruit fromt-harvest maturity measures

bdul Jabbara, Andrew R. Easta,∗, Geoff Jonesb, David J. Tannerc, Julian A. Heyesa

Centre for Postharvest and Refrigeration Research, Massey University, Palmerston North, New ZealandDepartment of Statistics, Institute of Fundamental Sciences, Massey University, Palmerston North, New ZealandZespri International Ltd., Mt. Maunganui, New Zealand

r t i c l e i n f o

rticle history:eceived 16 September 2013ccepted 23 November 2013

eywords:ctinidia deliciosairmnesson-linear mixed effectsomplementary Gompertzime shift

a b s t r a c t

Firmness of kiwifruit (Actinidia deliciosa (A. Chev) C.F. Liang et A.R. Ferguson cv. Hayward) is an importantdeterminant of quality. Batches of fruit vary not only in firmness at time of harvest but also in time to reacheating ripeness (0.5–1.0 kgf). Failure to identify batches with rapid rate of firmness breakdown results ineconomic loss to the industry. Understanding variability in softening rate and its relation with at-harvestmeasures may lead to opportunities for industry to segregate batches for storage potential. The objectiveof this paper was to model batch-specific softening behaviour of kiwifruit and investigate if predictivemodels could be determined from at-harvest maturity measures. Data for ‘Hayward’ kiwifruit softeningat 20 ◦C were collected over 21 d for 108 batches across two seasons (2011 and 2012). In model creation,application of both Complementary Gompertz (CG) equation and a time shift (TSCG) alternative versionresulted in a mean absolute error (MAE) of 0.11–1.55 kgf and 0.14–1.44 kgf respectively for 54 batches.Model parameters were fitted using a non-linear mixed effects procedure. The resulting batch-dependentsoftening description parameters (B, � and �) were best associated with at-harvest firmness and theSSC:firmness ratio. For prediction validation, at-harvest quality indicators of an alternative set of 54batches were used to predict softening descriptive model parameters and subsequent batch-dependentsoftening behaviour at 20 ◦C. When B and � were predicted from firmness and the SSC:firmness ratiorespectively in the validation batches, MAE of firmness prediction by CG ranged from 0.17 to 2.75 kgf

with 46% of the batches having MAE of less than 0.5 kgf. Likewise, when � was predicted from firmness,MAE of firmness prediction by TSCG ranged from 0.17 to 2.78 kgf and approximately 30% of batcheshad MAE less than 0.5 kgf. This paper demonstrates the potential for predicting softening variability ofkiwifruit batches from at-harvest fruit maturity measures. Future work is required to ascertain if a similarmodelling protocol may enable prediction of kiwifruit softening at commercial storage conditions (0 ◦C).

. Introduction

Reducing postharvest losses of fruit and vegetables remains onef the major challenges for the horticultural industry (Kader, 2005).ne of the factors that contributes to these losses is inherent vari-bility between batches which results in variable storage qualitynd makes storage life prediction difficult (Tijskens et al., 2003).his variability results in challenges and opportunities in fresh pro-uce inventory managment. Which batches are sold earlier or lateray have a significant impact on total losses across the stock (East,

011), particularly for kiwifruit where over-softening fruit producearge amounts of ethylene and sound kiwifruit are highly sensitiveo ethylene in the storage environment.

∗ Corresponding author. Tel.: +64 6 356 9099.E-mail address: a.r.east@massey.ac.nz (A.R. East).

925-5214/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.postharvbio.2013.11.008

© 2013 Elsevier B.V. All rights reserved.

Kiwifruit firmness is an important quality determinant (Jacksonand Harker, 1997). At-harvest kiwifruit are hard (6–10 kgf),enabling robustness during picking and initial handling, and thefruit subsequently soften postharvest to eating ripe (approxi-mately 0.5–1.5 kgf). Substantial variation in firmness at-harvest andduring postharvest softening is known to exist between seasons(Woodward, 2006), districts (Kim, 1999) and within (Feng et al.,2003) and between batches or orchards (MacRae et al., 1990b;Benge et al., 2000). Variation in at-harvest firmness has been asso-ciated with orchard management (Tombesi et al., 1993; Pyke et al.,1996; Snelgar et al., 1998) and harvest timing (Mitchell et al., 1992;Costa et al., 1997).

Kiwifruit softening is a well documented process (MacRae

et al., 1990a; Benge et al., 2000). Studies of kiwifruit firmnesschanges during storage mainly follow different treatment (pre andpostharvest) effects (Lallu et al., 1989; MacRae et al., 1989, 1990b;Pyke et al., 1996; Davie, 1997; Hertog et al., 2004b) or compare

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ifferent firmness measurement methods (Jackson and Harker,997; McGlone and Kawano, 1998; Schotsmans et al., 2008). Bothenge (1999) and White et al. (2005) suggested that initial firmness

s an important factor affecting kiwifruit postharvest softening. Inontrast, Harker et al. (1997) reported a poor relationship of at-arvest firmness with time to soften or rate of softening. Firmnessariability remains a challenge in the kiwifruit industry, particu-arly for making inventory decisions (Adams et al., 2010). Furthernderstanding of variation between fruit populations (from differ-nt batches) is required for the industry to be able to make morenformed inventory decisions to reduce product losses caused byver softening. While kiwifruit are stored commercially at 0 ◦C,his study investigates difference in kiwifruit softening observedt 20 ◦C. This provision was conducted in order to enable rapid col-ection of a large amount of data, and hence develop the modellingpproach. Should the approach prove positive, adaptation to opti-al air or other different storage temperature regimes could be

uther investigated.Describing and modelling variability in softening between

atches of kiwifruit is rare. Benge et al. (2000) compared differ-nt empirical models to describe softening of kiwifruit from threeatches, and their work assists in selection of softening modelsut lacks the data to enable thorough modelling of variabilityetween batches. Examples of developed models for other fruit thatonsider between batch variability includes colour of cucumberSchouten et al., 2002b, 2004) and decay development in straw-erry (Schouten et al., 2002a; East, 2011).

In contemporary postharvest research, models of quality com-ine two approaches, deterministic and stochastic modellingTijskens et al., 2003). The deterministic models use interpretable

odel parameters for underlying processes (Schouten et al., 1997;ertog et al., 1999), while stochastic models estimate parameters

hrough fitting a model on data (Hertog et al., 2004a; Schoutent al., 2004). Data are required to infer deterministic and stochasticffects, resulting in a post hoc (after the fact) modelling procedure.owever, for successful adoption of a model that considers batch

pecific differences as a tool in industry, there is a need to deter-ine batch specific model parameters a priori (before the fact). Theost likely source of information that can be used to determine

hese model parameters is the at-harvest attributes of each batch.or example, Johnston (2001) modelled variability in softening ofpples caused by different orchard sources with an empirical sig-oidal model, where the model parameter of firmness change (�)as predicted from at-harvest firmness, skin greenness and starch

oncentration. More recently, Van de Poel et al. (2012) used fruitass and colour to determine the biological age of tomatoes and

ubsequently perform model based classification.This study aims to demonstrate the development of a priori

redictive model for kiwifruit softening, in which the batch spe-ific model parameters are based on at-harvest quality attributes.hould this work be successful, adoption to assist in predictingatch specific softening at optimal conditions (0 ◦C) or other con-tant storage conditions may be possible. Such an a priori predictiveodelling tool may assist in the identification of rapidly soft-

ning kiwifruit batches and hence assist in segregation of poortoring batches of fruit and minimisation of in storage industryosses.

. Material and methods

.1. Fruit samples

Three modular bulk packs of (count 36) ‘Hayward’ kiwifruitActinidia deliciosa (A. Chev) C.F. Liang et A.R. Ferguson) from 108ommercial batches were received at Massey University, over the

nd Technology 90 (2014) 7–14

2011 and 2012 harvest seasons from a packing facility in Te Puke,New Zealand. Fruit were sent immediately after the standard com-mercial operations of picking, curing, grading and packing. Uponarrival, fruit from each batch were randomly re-packed into eightsingle layer trays (36 fruit/tray). Seven single layer trays werestored at 20 ◦C in a flow-through system with the remaining trayused to assess at-harvest quality. During storage, firmness of fruitin a single tray was measured at 3 d intervals, resulting in a totalstorage period of 21 d for the final tray measured.

2.2. Fruit storage

Kiwifruit are well known as being highly sensitive to ethylene(Ritenour et al., 1999), while only producing substantial amountsof ethylene when fully ripe (Kim, 1999). As batches were receivedover the harvest season, there were opportunities for ethylene con-tamination of later received batches by earlier batches that hadalready softened. Therefore, to ensure batch-independent soften-ing, a flow-through system was developed, that ensured each batchwas ethylene-independent from the other batches. Fruit trays ofeach batch were placed in a sealed 100 L plastic bag and suppliedwith continuous air flow of 1.8 L min−1 delivered by air pumps(Bubbilo DT800, Masterpet Corporation Ltd., Lower Hutt, NewZealand). Air was first passed through a jar filled with KMnO4 eth-ylene scrubber (Purafil® Chemisorbant Media, Purafil Inc., Georgia,USA) before delivering to the bag. Bag outlet flow was deliveredto the room ventilation, ensuring removal of any fruit-generatedethylene from the room. Purafil was also placed within the room tofurther reduce likelihood of ethylene contamination. Ethylene con-centration within the room was monitored regularly and remainedbelow the industry standard 0.03 �L L−1. The room was maintainedat 20 ◦C and 85–90% RH.

2.3. Fruit quality measurement

To assess at-harvest quality, firmness, soluble solids content anddry matter were measured. After storage at 20 ◦C, only firmnesswas assessed. SSC (%) was measured using a pocket refractometer(PAL-1, Atago, Japan). Juice was equally extracted from 15 mm slicesof both blossom and distal ends of the fruit. For dry matter (DM)estimation, a 2–3 mm equatorial fruit slice of known initial (fresh)weight was dried in an oven (60–65 ◦C) for 24 h. After drying, theslice was re-weighed and dry matter calculated as dry weight per-centage of initial fresh weight.

Fruit firmness was measured using a QALink Penetrometer (Wil-lowbank Electronics Ltd., Napier, New Zealand), interfaced to acomputer and fitted with a standard 7.9 mm Magness-Taylor probe.Fruit skin of approx. 1 mm thickness was removed from two loca-tions, at 90◦ orientation to each other, around the equator. Theselocations were then subjected to an 8 mm puncture at a speedof 20 mm s−1, with an average peak force of two measurementsrecorded. Due to the industrial application focus of the work, forcewas recorded as kgf, as this is the common unit terminology usedin industry. Models were also subsequently developed to predictfirmness in kgf for ease of industry adoption. Conversion of kgf tothe SI force unit N can be achieved by multiplication by gravity(9.807 m s−2).

2.4. Fruit softening model development

2.4.1. Choice of modelling approachSoftening of kiwifruit could be described by a number of

models. Benge et al. (2000) applied different empirical models(Complementary Michaelis–Menton (CMM), exponential decay(EXP), Complementary Gompertz (CG), Jointed Michaelis–Menton(JMM) and Inverse Exponential Polynomial (IEP)) and compared

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heir efficiency in describing softening of kiwifruit from threerchards. These empirical models and their parameters provideo biological meaning and are constrained to applications withonstant storage conditions, which remain appropriate for thistudy, with the use of only constant 20 ◦C storage. White et al.2005) modelled softening profiles of different genotypes ofiwifruit with a Boltzmann function and simple EXP model. TheXP model was also used by Feng et al. (2006) to calculate storageife of batches at 0.5 ◦C and Schotsmans et al. (2008) to describeemperature dependent softening of ‘Hort16A’ kiwifruit.

Kiwifruit softening follows a tri-phasic curve (MacRae et al.,990a) with (1) an initial lag phase where softening is slow, (2)

period of rapid decline in firmness, and (3) a late slow phase ofoftening. Due to this tri-phasic nature of the kiwifruit softening,n the author’s opinion, the simplistic EXP model is inappropri-te, due to the inability of this model to describe the initial laghase.

Limiting the model parameters required to describe the soften-ng profile is advantageous in the case of a priori predictions, as each

odel parameter will require independent data to enable estima-ion. As a result, the number of model parameters required to bestimated, has direct implications on the costs required to collectata and allow predictive use of a model. For a useful a priori predic-ion model the value of the results is required to remain higher thanhe effort of data collection and losses required to estimate modelarameters. In an industrial scenario where many batches areequired to be assessed, this puts pressure on minimising data col-ection effort. Among the different empirical models investigatedy Benge et al. (2000) that describe the tri-phasic softening pattern,G, JMM and IEP outperformed the other 2 models assessed. How-ver the JMM model is a 5 parameter model and the IEP model has

parameters, 3 of which seem to have no physical meaning. Alter-atively the CG model has 4 parameters, one of which (Ao) defineshe minimal firmness and hence can be assumed to be the sameor all fruit batches. Given this, the CG model was chosen for itsbility to express the three phases of kiwifruit softening, and withhe knowledge that at the most only 3 parameters would be batchependent.

Alternatives to using these empirical models are mechanisticodels that may not only enable suitable prediction, but also fur-

her assist in developing the mechanistic understanding of a fruituality change process. Associating the modelled quality attributee.g. softening) with distinct physiological, biochemical and otherrocesses or conditions is a more complex modelling process thanhe application of empirical models, and typically results in theequirement for multistage Ordinary Differential Equations (ODE)odels that require many parameters. For example, in the recent

ri-phasic apple softening model of Róth et al. (2008), 4 ODE and 1lgebraic equation were required, resulting in 5 batch dependentarameters needing to be estimated. Therefore while mechanisticodels represent the contemporary field for mathematical mod-

ls of fruit quality changes, this work used an empirical model dueo the advantages of reducing the required data collection efforto enable a priori modelling, should the solution be applicable tondustry.

.4.2. Alternative empirical models

.4.2.1. Modelling kiwifruit softening by CG. CG (Eq. (1)) has fourarameters to characterise kiwifruit firmness (FF, kgf) as a functionf time (t, days). Ao (kgf) is a lower asymptotic value and inhis system was defined by the limitations of the penetrometer

easurement and was subsequently set to 0.1 kgf (as a constant).he length of the initial lag phase of slow softening after harvest isefined by ˇ, a horizontal shift factor. Both B (kgf), a scale parameter

nfluencing the upper asymptote, and ̌ dictate the starting

nd Technology 90 (2014) 7–14 9

firmness, while � (kgf day−1) dictates the subsequent softeningrate.

FF = Ao + B(

1 − 1exp( ̌ exp(−�t))

)(1)

Initially firmness curves were fitted with three parameters (B, ˇand �) as batch dependent and one (Ao) as global for all batches. Ini-tial fitting indicated that ̌ values did not vary significantly betweenbatches and thus refitting was conducted with ̌ fitted as a globalparameter. The resulting model was a better representation of thepopulation as indicated by lower Akaike Information Criteria value(data not shown). Therefore, in final curve fitting, only B and � werekept as batch dependent parameters to enable description of thebatch softening differences, while ̌ was fitted as a global parame-ter. The resulting model mimics the work of Johnston (2001), wherethe parameters that described initial firmness and rate of firmnessdecline in an empirical sigmoid model were kept batch dependentin order to model softening of apples from different orchards.

2.4.2.2. Time shift modified complementary Gompertz (TSCG).Assuming all kiwifruit go through similar development, from fruitset to ripening and senescence, the softening behaviour should besimilar for each fruit. However at any point in time, substantial dif-ferences in firmness either within or between populations of fruitare observed. These differences could be attributed to fruit differingin developmental stage or otherwise referred to as biological age(Tijskens et al., 2005). This concept of biological age has alreadybeen applied to describe the variation in within batch postharvestfirmness of apple (Shmulevich et al., 2003) and colour of tomato(Tijskens and Evelo, 1994), cucumber (Schouten et al., 1997) andavocado (Hertog, 2002). These examples demonstrate that differ-ences between individual fruit at any time point can be describedby a standard maturation curve, in which each individual is locatedat a different point on the curve as a result of differences in timing ofmaturity (referred to as biological age). In this work, this ideologyis extended to model the differences observed between batches.Applying this ideology to the CG equation requires the assumptionthat the 4 CG parameters remain constant for all batches with thedifferences explained by a time shift parameter (�, days)· Mathe-matically, addition of � to the CG equation (Eq. (1)) results in Eq.(2).

FF = Ao + B(

1 − 1exp( ̌ exp(−�(t − �)))

)(2)

Algebraic manipulations of Eq. (2) (not shown) revealed that �carries the same effect as ̌ but is independent of any other parame-ter. Given that B defines the upper asymptote for firmness, and thehighest average firmness measured across the set of batches forcalibration was 7.44 kgf then B was changed to the constant valueof 7.34 kgf (i.e. Ao + B = 7.44). Final manipulation results in an equa-tion the authors refer to as the time shift modified complementaryGompertz equation (TSCG, Eq. (3))

FF = Ao + B(

1 − 1exp(exp(−�(t − �)))

)(3)

The equation assumes that all fruit start from the same firm-ness (Ao + B) although some softening may have occurred prior toharvest. This approach assumes that providing the same environ-mental conditions after harvest, all fruit have the same softeningrate (�). Therefore, applying Eq. (3) to describe batch dependentsoftening, Ao and B remained as set constants, � was fitted as a globalparameter while � was fitted as a batch dependent parameter.

2.4.3. Model parameter fittingInclusion of experimental variation of both fixed (or global)

and random (or batch dependent) effects into models is possible

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Fig. 1. At-harvest average fruit firmness (A), soluble solids content (SSC, B) anddry matter (DM, C) of 108 kiwifruit batches from 2011 (solid) and 2012 (empty)harvest seasons as influenced by harvest date (ISO day). Each data point representsan average of 30 fruit for firmness and SSC; and 15 fruit for DM.

ISO day

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0 A. Jabbar et al. / Postharvest Bio

sing mixed effects models. A mixed effects model is a statisticalechnique which simultaneously enables characterisation of mainffects and the components which cause variability (i.e. randomffects) to a particular problem (Pinheiro and Bates, 2000). Thisype of model has successfully been used previously for firmnesshange of apple (Tong et al., 2013), tomato (De Ketelaere et al.,004) and mango (De Ketelaere et al., 2006). Mixed effects mod-ls enable independent parameterisation for each batch within theramework of the same model and acknowledge that each individ-al batch is part of a larger population. In this case, all batches haveommonality, in being ‘Hayward’ kiwifruit stored at 20 ◦C. Consid-ring each batch as a member of a population, the batch dependentarameters are expected to have a normal distribution.

The 108 batches from two harvest seasons were divided into tworoups (54 batches each), having equal representation across botharvest seasons in each group. For one population of 54 batches (thealibration data set) both CG (Eq. (1)) and TSCG model (Eq. (3)) weretted to collected firmness data using the nlme (non-linear mixedffects) procedure in R (version 2.15.1, cran.r-project.org, Pinheirot al., 2013). For CG, Ao remained constant, ̌ was fitted as a globalarameter for all batches while B and � were batch dependent. Tot TSCG model (Eq. (3)), Ao and B remained constant; � was fitteds a global parameter while � was batch dependent.

Errors of fit between the models and the data were assessed byalculating Mean Absolute Error (MAE, Eq. (4)).

AE = 1n

n∑i=1

|Oi − Pi| (4)

here n is the number of observations, i is the observation number, is the observed value and P is the predicted value. Distributionf the resulting batch dependent parameter values of both modelormats was assessed with an Anderson–Darling test in Minitabersion 16 (Minitab Inc., State College, PA, USA).

.5. Model parameter prediction

Predictive models require estimation of model parameters ariori. Fitted batch dependent model parameters from the calibra-ion data set were correlated with at-harvest DM, SSC, firmness,SC:firmness ratio and ISO day of harvest (as a measure of seasoniming). Relationships between batch at-harvest quality attributesnd model parameters were described with a simple straight linet.

.6. Model prediction validation

Validation of the a priori predictive capability of the models as result of parameter estimation from at-harvest measures wasested on the remaining set of 54 batches (the validation data set).rrors of prediction were also assessed by calculating the MAE (Eq.4)).

. Results and discussion

.1. At-harvest fruit quality and softening

During the kiwifruit harvest season, firmness decreased (Fig. 1A)hile SSC increased (Fig. 1B) and DM displayed no obvious trend

Fig. 1C). These results emulate expected seasonal progression orhange in at-harvest quality as previously observed (Mitchell et al.,992; Jabbar et al., 2013; Burdon et al., 2013).

Firmness data of 54 batches (the calibration population) dis-layed a variety of softening curves (Fig. 2A). While at-harvestrmness of the kiwifruit decreased throughout the harvest sea-on, most batches continued to display an initial slow softening lag

Fig. 2. Raw data (A), CG fitted (B) and TSCG fitted (C) softening curves of 54 kiwifruitbatches from harvest season of 2011 (blue) and 2012 (red). Raw data comprises of8 data points (mean of 36 fruits) at 3 day interval.

A. Jabbar et al. / Postharvest Biology and Technology 90 (2014) 7–14 11

0 5 10 15 20

0

2

4

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0 5 10 15 20 0 5 10 15 20

Β = 5.92κ = 0.72τ = 3.41

MAECG = 0.24

MAETSCG = 0.43

Β = 2.85κ = 0.82

τ = −2.04MAECG = 0.26

MAETSCG = 0.14

Β = 3.93κ = 0.70τ = 0.34

MAECG = 0.27

MAETSCG = 0.33

Fir

mnes

s (k

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Time (days)

0

2

4

6

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Β = 7.04κ = 0.15

τ = 22.29MAECG = 0.19

MAETSCG = 0.34

Β = 6.12κ = 0.65τ = 4.12

MAECG = 0.26

MAETSCG = 0.56

Β = 6.85κ = 0.37

τ = 10.10MAECG = 0.25

MAETSCG = 0.59

A B

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F data s( sent th

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ig. 3. Change in ‘Hayward’ kiwifruit firmness of six batches from the calibration

solid) and TSCG (dash). Batches were selected from a 54 batch population to repre

hase at the beginning of the postharvest period. The differences inhe initial lag phase between batches seemed independent of har-est timing (ISO day) or initial at-harvest firmness. Some batchest the start of the season, with an at-harvest firmness (>6 kgf) didot maintain a substantial initial lag phase, while other initiallyofter batches from the middle of the season seemed to have laghases of 6–9 days at 20 ◦C prior to rapid softening. The longest laghase observed in this dataset was 18 days. No substantial differ-nces in softening trends were observed between the two harvesteasons.

The variability between different batches in softening behaviournder the same conditions emulates the previous reported effects

f growing locations or orchards (Mitchell et al., 1992; Arpaia et al.,994; Benge, 1999) and at-harvest firmness (Crisosto et al., 1984;enge et al., 2000; Ghasemnezhad et al., 2013). This observed vari-tion in the softening trends among batches demonstrates the

MAE of fitted firmness (kgf)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

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0

5

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350

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ig. 4. Histogram of mean absolute error (MAE) of fits by (A) CG and (B) TSCG for the cali

et. Dot points represent average data (n = 36) and lines represent model fits by CGe range of different softening trends.

industrial challenge of making inventory decisions based on thesoftening behaviour of kiwifruit.

3.2. Model fitting and parameter estimation

The CG model appropriately characterised kiwifruit softening(Fig. 2B) with the global parameter for all batches ̌ having a valueof 57.37. Use of the model with a tri-phasic nature was requiredwith the CG fits expressing all softening stages to look similar tothe data (Fig. 2A). Example CG fits for six batches demonstrate howthe dependent parameters B and � can accurately characterise therange of softening patterns observed in the data (solid line, Fig. 3).

CG described most stages of softening in the example curves excepton occasions in which a less dominant lag phase was present in thedata (Fig. 3B and E). This effect of the horizontal shift parameter (ˇ)resulting in too much initial lag phase on some occasions was also

MAE of predicted firmness (kgf)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

D

C

TSCG

CG

bration data set; and prediction by (C) CG and (D) TSCG for the validation data set.

12 A. Jabbar et al. / Postharvest Biology a

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of less than 0.5 kgf. Batches with no initial lag phase had lowest

ig. 5. Histogram of batch dependent parameters (A) B, (B) � and (C) � for thealibration data set.

bserved by Benge et al. (2000). Prediction of more rapid softeningo the lower asymptote was also evident on some occasions (e.g.ig. 3D and F).

The MAE of the fitted CG curves varied from 0.11 to 1.55 kgf,ith an average of 0.35 kgf across all batches (Fig. 4A). Approxi-ately 87% of batches had MAE less than 0.5 kgf. The highest MAE

1.55 kgf) was found for a batch that demonstrated inconsistentrmness decrease over the storage time (i.e. an observed increase

n average firmness between two measurement points), a resulthat can occur on occasions when destructive methods of firmness

easurement are used. Parameter estimates for B varied from 2.85o 7.14 kgf while � ranged from 0.15 to 0.88 kgf day−1 (Fig. 5A and). Both B and � populations were not significantly different from

normal distribution (p > 0.05).The TSCG model resulted in a single shape model being applied

o all batches with variability in softening trends being describedy the shift in time (Fig. 2C), when fitted with � (0.23 kgf day−1) aslobal and � as batch dependent. The resulting model, while able toescribe the difference in timing of rapid softening of each batch,as clear deficiencies in the ability to describe the observed laghase in softening immediately after harvest, especially in the latereason fruit (>150 ISO days) which were less firm at harvest. Exam-le TSCG fits demonstrate a complete lack of description of a laghase in those batches in which the initial firmness <7 kgf (dashed

ine, Fig. 3D–F). In addition, slow speed of transition between thepper and lower asymptotes (�) results in a consistent under pre-iction of firmness initially and over prediction of firmness at the

ater period of softening (e.g. Fig. 3B–D). The nature of the TSCGodel results in the batches with the initially highest firmness tak-

ng the longest time to soften to the lower asymptote and henceakes the initial assumption that initial firmness and time to soften

to a desired point) are correlated, which was not the case.The MAE of individual batch fitted curves varies from 0.14 to

.44 kgf, with an average of 0.57 kgf for all batches (Fig. 4B). Approx-mately 46% of batches had MAE less than 0.5 kgf. The highest MAE

f fit by TSCG (1.44 kgf) occurred for the same batch as for CGith the inconsistent softening pattern in the firmness data. � var-

ed from −2.04 to 22.29 days with an average of 4.61 days. The

nd Technology 90 (2014) 7–14

distribution of � values was significantly different from a normaldistribution (p < 0.01, Fig. 4C) with 3 outlier batches representingthose that did not complete softening during the 21 days at 20 ◦Cand hence expressed an extended initial lag phase (e.g. Fig. 3A).

3.2.1. Model parameter predictionFor a successful model to be used in industry, model parameters

that assist in describing individual batch behaviour are requiredto be determined a priori. Model parameters were correlated withat-harvest quality indicators of the batches (Fig. 6). The B parame-ter was most strongly correlated with at harvest quality, especiallywith firmness (r = 0.95, Fig. 6M) and with SSC, SSC:firmness ratioand ISO days (r = −0.79, −0.90 and −0.76 respectively). The highassociation of B with at-harvest firmness is not surprising giventhat it represents the scaling parameter that assists in defining theupper asymptote of the prediction.

The best association of model parameter � was with firmnessand SSC:firmness ratio (r = −0.38 and 0.32 respectively); batcheswith a low initial firmness are unlikely to have a low � (Fig. 6H).DM, SSC and ISO days were found to have no relationship with�. When Johnston (2001) used at-harvest quality attributes fora priori model parameter prediction, scale parameter (B) waspredicted from firmness and TSS while firmness change parameter(�) was predicted from firmness, DM and glucose concentration.

Fitted values of � were positively associated (r = 0.67) with firm-ness and negatively associated with SSC, SSC:firmness ratio andISO days (r = −0.54, −0.60 and −0.50 respectively) while havingno association with DM. When Van de Poel et al. (2012) createda method for determining biological age to perform classificationof tomatoes, fruit mass and colour were used.

Overall, at-harvest fruit quality indicators showed some poten-tial to define batch dependent parameters for CG and TSCG. In orderto predict batch model parameters from at-harvest quality mea-surements, simple straight line regression equations were usedto describe the most promising relationships. At-harvest firmness(FF0, kgf) and SSC:firmness ratio (SSCFR, % kgf

−1) were used as pre-dictors of B and � for the CG model respectively (Eqs. (5) and (6)),while at-harvest firmness was also used to predict � for the TSCGmodel (Eq. (7)).

B = (0.8936)FF0 + 0.2090 (5)

� = (0.07559)SSCFR + 0.4316 (6)

� = (2.743)FF0 − 11.13 (7)

3.2.2. Model validation from at-harvest dataTo validate prediction of batch dependent parameters (of both

CG and TSCG) from at-harvest quality, the validation data set of 54batches was used. Model parameters for each batch predicted fromat-harvest attributes (Eqs. (5)–(7)) were then applied to the soften-ing models (Eqs. (1) and (3)). For the CG model, MAE of predictedsoftening ranged from 0.17 to 2.75 kgf with an average of 0.73 kgffor the population of batches (Fig. 4C). Around 46% of batches hadMAE of less than 0.5 kgf. Batches that demonstrated all 3 phases ofsoftening (in the data) tended to have the smallest MAE (Fig. 7Aand B) while batches that did not demonstrate this behaviour, byeither not softening rapidly (Fig. 7C) or not ever softening (Fig. 7D),had the worst prediction (highest MAE).

The MAE for predicting firmness using the TSCG model, inwhich � was determined from initial firmness, ranged from 0.17to 2.78 kgf with an average of 0.86 kgf for population of batches(Fig. 4D). Approximately 30% of batches in the population had MAE

MAE of prediction (Fig. 7E and F) while batches that did not showsubstantial softening had the worst prediction (Fig. 7G and H). Addi-tionally the TSCG did not predict well in cases where the data

A. Jabbar et al. / Postharvest Biology and Technology 90 (2014) 7–14 13

κ v

alues

0.3

0.6

0.9

τ v

alues

0

8

16

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ISO day

135150165180

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345678

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2

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691215

SSC:firmness ratio

1234

AB C D E

F G H I

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dd

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ig. 6. Relationship of fitted batch dependent parameters B, � (CG) and � (TSCG) wialibration data set. Straight lines are fitted only to the data used for predictive mod

emonstrated an initial lag phase, resulting in an increased pre-iction error (examples not shown).

Overall, both model formats resulted in similar a priori pre-ictive ability of the batch dependent softening behaviour. TheG model has the lower average MAE of prediction (0.73 kgf) and

larger percentage of the batches were more closely modelled46% with a MAE < 0.5 kgf). For both models a number of batcheshat were observed to not soften rapidly or have an extended laghase prior to softening (i.e. potentially have the best storage life)ere most poorly predicted (Fig. 7). Investigation of these batches,

nd the reasons why they are able to maintain firmness for thisxtended period of time, may provide beneficial knowledge foraintaining kiwifruit firmness in storage.This work attempted to use standard industry at-harvest quality

ndices to predict batch dependent softening. Techniques beyondhe standard at-harvest quality attribute measures such as NIRMcGlone and Kawano, 1998), X-ray (Mondragon et al., 2011;rejo-Araya et al., 2013), mineral composition (Feng et al., 2006),on-destructive measurements (Feng et al., 2013) or metabolomicsechniques (Hertog et al., 2011) may be required to gatherdditional data that enable better characterisation of the batch dif-erences in softening behaviour and subsequently offer a solutiono obtaining better a priori batch specific parameter estimation andence model predictive ability.

In this study softening trends of kiwifruit batches were evalu-ted under ambient conditions (20 ◦C in air), in order to ascertainhe potential for a priori model parameter prediction to define batch

20151052001510502015105200151050

0

2

4

6

8

0

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CG

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Β =4.88κ =0.59

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ΜΑΕ=2.75

Β =6.65κ =0.53ΜΑΕ=2.45

τ =−2.38ΜΑΕ=0.17

τ =−0.10ΜΑΕ=0.24

τ =2.25ΜΑΕ=2.23

τ =2.03ΜΑΕ=2.7 8

Β =3.5 7κ =0.69

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A B C D

E F G H

ig. 7. Measured (symbols) and predicted (lines) softening of example batches pre-icted by CG (A–D) and TSCG (E–H). Batches were selected from a population of 54o represent the two extremes for best (A–B, E–F) and worst (C–D, G–H) predictions determined by the MAE. Each measured data point represents an average of 36ruit.

t quality and ISO day at-harvest. Each data point represents a single batch from the. Equations for these lines are provided in Eqs. (5)–(7).

dependent softening. A substantial body of work is required tofurther adapt these models to enable description of batches perfor-mance at optimal storage (0 ◦C), while adoption of a mechanisticapproach will be required should a more sophisticated model thatcan account for changes in environmental conditions (atmosphereand temperature) be desired. Existing models for firmness changein apples (Gwanpua et al., 2012) and kiwifruit (Hertog et al., 2004b)as a function of temperature and modified atmosphere storage con-ditions are suitable examples.

4. Conclusion

This paper developed a modelling system to enable use of at-harvest quality attribute information for a priori batch specificprediction of kiwifruit softening. The ability to predict batch spe-cific performance a priori has potential to significantly contributeto reducing storage losses of crops with substantial storage periods.However in order to achieve this, balancing of the model complex-ity that enables sufficient predictability with the effort required toobtain data to inform model parameter prediction is required.

Acknowledgments

Abdul Jabbar gratefully acknowledges the Higher EducationCommission of Pakistan for his Ph.D. scholarship. The first authoris highly appreciative of Zespri International Ltd., New Zealandfor providing project resources and a research scholarship. Manythanks to Sue Nicholson, Peter Jeffery and Thamarath (An)Pranamornkith for their help in experiment planning and data col-lection.

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