tion with a low temperature − 0.5 – 1°C reduces the biochemical changes associated with respira-
tory metabolism, physical injuries, and physiolog- ical and pathological breakdown Brady and
Romani, 1988; Kerbel et al., 1988; Chavez-Franco and Kader, 1993; Mathooko, 1996. However, an
elevated CO
2
concentration during postharvest storage can cause CO
2
-related injuries such as core breakdown, also called brownheart or
browning Kadam, 1995. This is a physiological disorder characterised by browning and softening
of tissue near the core. It is often coupled with the development of cavities. The time course of inter-
nal browning and appearance of cavities suggests that cavities arise from the brown areas Roelofs
and de Jager, 1997. These authors also found that over-mature ‘Conference’ pears are more sus-
ceptible to core breakdown during storage. A serious breakdown is often observed when the
pears are removed from CA conditions for selling. Late harvested ‘Bartlett’ pears also show an in-
crease in CO
2
in the tissue around the core, until the onset of core breakdown Kadam, 1995. Velt-
man et al. 1999 associated browning in ‘Confer- ence’ pears with the disappearance of ascorbic
acid. Larrigaudiere et al. 1998 and Lentheric et al. 1999 discussed the relation between harvest
date, ascorbic acid concentration and internal browning. The physiological and quality re-
sponses of ‘Bartlett’ pears to modified gas atmo- spheres were studied by Ke et al. 1990. Exposure
of the fruits to O
2
-reduced and CO
2
-enriched at- mospheres resulted in reduced respiration and
increased ethanol and acetaldehyde concentra- tions. Pears stored for a long time under high CO
2
levels showed CO
2
injury. However, the literature concerning the development of this disorder in
other European pear cultivars is scarce. In addi- tion to this, no literature on a statistical modelling
approach to predict core breakdown was found. However, such a predictive model can be valuable
in predicting the susceptibility of pears to core breakdown as affected by their intrinsic quality
attributes soluble solids content SSC, firmness, weight and storage conditions. Storage condi-
tions could then be fine-tuned for a particular fruit lot. A predictive model can also give insight
into the role of interaction between two or more storage parameters.
The specific objectives of this study were 1 to determine the effect of the storage gas composi-
tion, the storage temperature, the storage time, the picking date and quality parameters of ‘Con-
ference’ pears on the incidence of core breakdown as well as to determine the interaction effects
between the storage parameters; and 2 to de- velop a statistical model that can predict brown-
ing
incidence of
pears given
the quality
parameters and the storage conditions. In this way, postharvest storage simulations can be per-
formed. A storage scenario to obtain pears with brownheart, for further research, can be derived
from this statistical model.
2. Materials and methods
2
.
1
. Experimental design Pears used for this experiment were picked
from 40 randomly chosen trees at the Centre for Fruit Culture in Rillaar Belgium. A complete
factorial design was performed, consisting of three picking dates early 991997, optimal 1591997
and late 2391997 and ten CA storage conditions 0.7 CO
2
+ 2 O
2
at − 0.5 and 1°C; 5 CO
2
+ 2 O
2
at − 0.5 and 1°C; 0.7 CO
2
+ 0.5 O
2
at −
0.5 and 1°C; 5 CO
2
+ 0.5 O
2
at − 0.5 and 1°C; 0.03 CO
2
+ 21 O
2
, − 0.5 and 1°C. The optimal picking dates for Belgium were deter-
mined by the Flanders Centre for Postharvest Technology, based on a comparison of refrac-
tometer values, starch index, acidity and Mag- ness-Taylor firmness with historical data. On each
picking date 672 pears were harvested: 32 were analysed for disorders and several quality at-
tributes before CA storage, 640 were stored under the specified CA conditions. After 2, 4, 6 and 8
months of storage, 480 16 pears × ten condi- tions × three picking dates pears were evaluated.
All the pears were conditioned on the 2nd of October 1997. The earliest picked pears were
cooled to − 0.5°C for 3 weeks in air. The pears of the optimal and late picking date were cooled,
respectively, for 2 and 1 weeks. The influence of the cooling time before storage in the appropriate
atmosphere is included in the variable picking
date. Roelofs and de Jager 1997 found that a cooling period of up to 30 days preceding estab-
lishment of CA conditions decreased the incidence of core breakdown without affecting the fruit
quality significantly.
Pears for model validation were picked in the orchards of Velm Nationale Proeftuin voor
Grootfruit, Zellik commercial orchard and Ril- laar Fruitteeltcentrum in Belgium at three pick-
ing dates early 991997, optimal 1591997 and late 2391997. All pears were held at − 0.5°C
for 1 week before CA establishment. CA condi- tions were 2 O
2
+ 0.7 CO
2
at − 0.5°C and 2 O
2
+ 5 CO
2
at − 0.5°C. After 2, 4, 6 and 8 months of storage, 240 pears from each orchard
40 pears × two conditions × three picking dates were analysed for physiological disorders as de-
scribed above. No quality measurements were performed on these pears. To test the model
validity over a year, pears were picked in 1998 in Velm and Zellik at 2481998 early, 3181998
optimal and 191998 late. After 1 week of cooling − 0.5°C the pears were stored at the
same conditions as in 1997 and after 2, 4, 6 and 8 months of storage, for each orchard 480 80
pears × two
conditions × three picking
dates pears were analysed for core breakdown and
quality attributes.
2
.
2
. Quality measurements Each pear was weighed g and the largest
diameter mm was measured with a caliper. The soluble solids content SSC was measured °Brix
with a refractometer PR-101, ATAGO, Japan. A standard colour card Golden Eurofru, CTIFL,
Paris was used to assign a colour score between 1 dark green and 8 yellow. A Magness-Taylor
Gullimex, Germany penetrometer with a 8 mm diameter probe was used to measure the firmness
of the fruit N. Finally, each pear was cut in two and the absence or presence of the disorder was
coded with 0 and 1, respectively. The proportion of disordered pear events in a set of pears that
were picked at the same date and had been stored in the same conditions, was calculated.
2
.
3
. Statistical analysis
2
.
3
.
1
. Logistic regression Logistic regression is a statistical method used
to analyse binary and binomial response data. It is based on the construction of a statistical model
describing the relationship between the observed response and explanatory variables, also called
independent variables Hosmer and Lemeshow, 1989; Collett, 1991. The dependence of the prob-
ability of disorder on explanatory variables is modelled as follows
logitp
i
= log p
i
1 − p
i
= a +
m j = 1
b
j
x
ij
1 A batch is a set of pears with the same values x
ij,
for the set of m explanatory variables e.g. 2 O
2
, 0.7 CO
2
, − 0.5°C, early picking date, etc.; i and j indicate the number of the batch and the number
of the explanatory variable see Table 1, respec- tively; p
i
is the probability defined by the propor- tion of disordered pear events in batch i, and a is
an intercept parameter. The b
j
parameter relates to the jth explanatory variable; it describes the
importance of the jth explanatory variable. Since a logit transformation of a proportion is dimen-
sionless, the units of b
j
are the reciprocal units of the corresponding explanatory variable x
ij
. The logit function transforms the probability
scale from the range 0, 1 to − , + . Other transformations are possible, but the logit trans-
formation leads to coefficients b interpretable in terms of odds ratios which is a measure of associ-
ation that is widely used, especially in epidemiol- ogy
Greenland and
Rothman, 1998.
All statistical analyses in this report were performed
using the SASSTAT software, version 6.11 SAS Institute Inc., Cary, NC, USA.
To study the hypothesis that internal browning is followed in time by the development of cavities,
and thus both are symptoms of core breakdown disorder, a generalized logits model needs to be
fitted. A different coding system to describe the disorder was used: absence of both disorders was
coded as 1, occurrence of internal browning with- out cavities as 2. Pears with both browning and
cavities were coded with 3, and those with only cavities with 4. The ordinal response variable with
Table 1 Summary of the logistic regression analysis of factors influencing internal brown and cavity development in ‘Conference’ pears
a
Wald confidence limits Parameter
Odds ratio Explanatory variable
Parameter
b
estimate Lower
Upper a
Browning external parameters
a 4.98
1.91 8.06
– Intercept
Carbon dioxide −
1.87 −
2.81 −
0.946 0.156
b
1
− 1.71
− 0.525
− 1.12
0.321 LogStorage time [logdays]
b
2
− 7.95
b
3
− 10.5
− 5.36
3.20e-4 Oxygen
− 2.84
− 1.92
Picking I 0.0921
b
4
− 2.38
1.03 1.61
1.31 3.73
b
5
Picking II 0.394
b
6
0.220 0.571
1.49 Temperature °C
b
7
1.43 0.968
1.91 4.21
LogStorage time.Oxygen [logdays.] 0.261
0.63 0.452
1.57 b
8
LogStorage time.Carbon dioxide [logdays.] b
9
LogStorage time.Oxygen.Carbon dioxide −
0.351 −
0.495 −
0.211 0.702
[logdays..] 0.895
Oxygen.Carbon dioxide [.] 2.33
b
10
5.02 1.61
− 2 Log L: 2215 intercept only, 1333 intercept and covariates. AIC: 2217 intercept only, 1355 intercept and covariates.
b Browning
external and intrinsic parameters Intercept
1.54 a
9.02 –
5.28 −
2.87 −
0.945 0.155
Carbon dioxide b
1
− 1.89
− 1.46
− 0.227
− 0.843
0.432 LogStorage time [logdays.]
b
2
− 8.54
b
3
− 11.2
− 5.87
1.14e-4 Oxygen
− 3.05
− 2.09
Picking I 0.0771
b
4
− 2.57
1.06 1.66
1.36 3.90
b
5
Picking II 0.458
b
6
0.272 0.644
1.58 Temperature °C
1.54 b
7
1.06 2.04
4.69 LogStorage time.Oxygen [logdays.]
0.258 0.639
0.448 1.56
LogStorage time.Carbon dioxide [logdays.] b
8
− 0.370
− 0.512
− 0.230
LogStorage time.Oxygen.Carbon dioxide 0.699
b
9
[logdays..] 0.988
2.46 b
10
5.60 1.72
Oxygen.Carbon dioxide . Firmness N
0.0197 0.00448
0.0349 1.021
b
11
− 0.401
− 0.111
− 0.257
0.772 b
12
Sugar °Brix 0.00876
b
13
0.00505 0.0122
1.01 Weight g
− 2 Log L: 2215 intercept only, 1289 intercept and covariates. AIC: 2217 intercept only, 1317 intercept and covariates.
c Ca6ities
external parameters −
7.58 Intercept
− 4.81
a –
− 6.19
b
1
0.166 0.0743
0.257 1.18
Carbon dioxide 0.717
LogStorage time [logdays] 1.256
b
2
2.68 0.987
− 0.339
− 0.152
− 0.246
0.782 b
3
Oxygen −
2.01 b
4
− 2.54
− 1.49
0.133 Picking I
b
5
1.46 1.17
1.76 4.32
Picking II −
0.122 −
0.0133 −
0.0678 0.935
b
6
Oxygen.Carbon dioxide . −
2 Log L: 1939 intercept only, 1307 intercept and covariates. AIC: 1942 intercept only, 1321 intercept and covariates. d
Ca6ities external and intrinsic parameters
− 9.70
− 6.11
– Intercept
a −
7.90 0.0696
0.253 0.161
1.18 b
1
Carbon dioxide 1.03
b
2
0.760 1.30
2.80 LogStorage time [logdays]
− 0.326
− 0.138
Oxygen 0.793
b
3
− 0.232
− 2.58
− 1.52
− 2.05
0.130 Picking I
b
4
1.50 b
5
1.20 1.791
4.47 Picking II
− 0.122
Oxygen.Carbon dioxide . −
0.0134 b
6
0.934 −
0.0679 0.00216
0.0318 0.0170
1.018 Firmness N
b
7
Table 1 Continued Explanatory variable
Parameter
b
Parameter estimate Wald confidence limits
Odds ratio Lower
Upper Weight g
b
8
0.00367 0.000104
0.00723 1.01
− 2 Log L: 1939 intercept only, 1298 intercept and covariates. AIC: 1941 intercept only, 1316 intercept and covariates.
a
All variables entered in the models met the 0.05 level of significance. Not directly interpretable odds ratio.
b
The units of the parameter are the reciprocal of the corresponding explanatory variable.
four levels was modelled by performing a logistic regression on the generalized logits. The general-
ized logit is defined as:
logit
k
= log
p
ik
p
i1
= a
k
+
m j = 1
b
kj
x
ij
2 where k is 2, 3, 4 three logits correspond to four
response levels, p
ik
is the proportion of pears in batch i which developed the kth-stage of the
disorder given a set of m explanatory variables, a
k
is the intercept parameter of the kth logit, b
kj
is the parameter of the kth logit for the jth explana-
tory variable, x
ij
is the value for the jth explana- tory variable in batch i.
This models implies that there are separate intercept parameters a
k
and different sets of regression parameters b
k
for each logit. Instead of estimating one set of parameters for one logit
function, as in logistic regression for a dichoto- mous response variable, sets of parameters for
multiple logit functions are estimated. By fitting Eq. 2 three times for each value of k and by
using the fact that the sum of all probabilities is one, it is possible to calculate the probability that
a pear belongs to a certain disorder stage.
2
.
3
.
2
. Dependent and independent 6ariables The absence and presence of the storage disor-
der was coded, respectively, with 0 and 1. In the predictive models, the occurrence of internal
browning and occurrence of cavities were consid- ered as two separate disorders. However, in real-
ity both phenomena are expected to be associated, and therefore a joint model for browning and
cavities was constructed. The factor picking date was considered a discrete explanatory variable,
which could only take on three values: early, optimal and late. The cell reference coding system
Agresti, 1996 was used to enter this discrete variable in a regression model. The effect of pick-
ing date on the incidence of the disorder was modelled by means of two dummy explanatory
variables, picking I j = 4 and picking II j = 5 see Table 1. Both variables can only take value
0 or 1. Eq. 1 becomes
logitp
i
= a + b
1
x
i1
+ ··· + b
4
x
i4
+ b
5
x
i5
+ ··· + b
j
x
ij
3 Assume, for instance, that batch i was picked
early, x
i4
and x
i5
were coded as 1 and 0, respec- tively. The contribution of picking date to the
logitp
i
is equal to b
4
. In the case of the optimal picking date x
i4
and x
i5
were coded as 0 and 0, resulting in no contribution to logitp
i
of b
4
+ b
5
. For the late picking date x
i4
= 0 and x
i5
= 1, giv-
ing a contribution of b
5.
The explanatory variables were divided into two groups. The first group contained all the
external variables like storage time, O
2
and CO
2
concentration, temperature and picking date. The second group contained the intrinsic variables:
soluble solids content, firmness, size, weight and colour. For both response variables, brown and
cavity, models were built with the external vari- ables and with the variables of both groups, to
investigate whether the addition of intrinsic parameters improved the model.
2
.
3
.
3
. Model selection criteria In order to select an appropriate subset of
important explanatory variables, the calibration set 2016 observations was used to generate ten
different data sets of 1816 observations. The sets were constructed by a random elimination of 200
observations of the calibration set. On each of the
ten data sets and on the complete calibration set a stepwise, a backward and a forward multiple lo-
gistic regression procedure was performed. The most important variables were selected automati-
cally. Biologically important variables e.g. tem- perature were entered manually in the model.
The − 2 Log Likelihood statistic − 2 Log L and the Akaike Information Criterion AIC
Akaike, 1973 were used to compare the models. For both measures, lower values indicate a more
desirable model. Since − 2 Log L can only de- crease when including more explanatory variables,
it tends to select models overfitting the available data. The AIC criterion however includes a
penalty term for model complexity and therefore is more reliable to select good models McCullagh
and Nelder, 1989.
The odds ratio was used for the interpretation of the influence of the different variables on the
storage disorder. The odds ratio, associated with an explanatory variable, expresses by which factor
the odds of the event increases or decreases for a unit increase e.g. O
2
concentration increases from 2 to 3 of a particular explanatory variable,
keeping other variables constant. The odds of an event is defined as the ratio of the probabilities of
event to non-event and is calculated by exponenti- ating the parameter estimate for the explanatory
variable Agresti, 1996. An odds ratio can range between zero and infinity. A value of 1 indicates
that the variable has no influence on the incidence of the disorder. For instance, an odds ratio of 1.5
for the variable O
2
indicates that when the O
2
concentration is increased with one unit e.g. from 2 to 3 the odds corresponding with 2 O
2
needs to be multipled by 1.5 to obtain the odds for 3 O
2
.
3. Results and discussion
