Euphytica (2005) 144: 169–175
DOI: 10.1007/s10681-005-5340-7

C Springer 2005

Optimal sampling strategies for evaluating fruit softening after harvest
in apple breeding
Hiroshi Iwanami1,∗ , Makoto Ishiguro1,2 , Nobuhiro Kotoda1 , Sae Takahashi1 & Junichi Soejima1,3
1

Department of Apple Research, National Institute of Fruit Tree Science, Morioka 020-0123, Japan; 2 Present
address: Yamagata Prefectural Horticultural Experiment Station, Sagae, Yamagata 991-0043, Japan; 3 Present
address: National Institute of Fruit Tree Science, Fujimoto, Tsukuba, Ibaraki 305-8605, Japan(∗ author for correspondence: e-mail: hiwanami@affrc.go.jp)

Received 22 November 2004; accepted 12 April 2005

Key words: environmental variation, Malus × domestica, variance component

Summary
Environmental variance components associated with year, tree, and harvest date were estimated for fruit softening
after harvest in apple (Malus × domestica Borkh.) to determine their relative importance and design optimum
sampling strategies to discriminate genotypes in apple breeding. Fruit were stored after harvest under 20 ± 2 ◦ C
and 80 ± 5%RH. Softening was evaluated by adapting the change in firmness during storage to a linear regression
and defining the regression coefficient as the softening rate. Environmental variances associated with genotype ×
year interaction, among trees, year × tree interaction, and among harvest dates were all very small, namely, 2.7,
0.1, 5.2, and 5.7%, respectively, to the total variance obtained from the analysis of variance for the softening rate.
The variance associated with genotype, at 57.3%, was very large. On the basis of the number of fruit necessary for
firmness measurements, two times harvest is an efficient strategy to determine a genotype mean for the softening.

Introduction
Softening of fruit after harvest is a serious problem
for apple (Malus × domestica Borkh.) growers andflesh markets. Since apples are not always marketed
directly after harvest (Kingston, 1992), growers andmarkets are quite concerned about the length of timethat fruit retains its firmness, which is directly linked
to consumer acceptance. Many studies, consequently,
have attempted to predict changes in fruit firmness fromharvest to after or during storage using regression equations by measuring quality at harvest (Ingle et al., 2000;
Johnson & Ridout, 1998; Blankenship et al., 1997;
Evensen et al., 1993; Ingle & Morris, 1989) or to determine harvest indicators that have a close relationship to
firmness after storage (Ingle & D’Souza, 1989; Knee
& Smith, 1989).
Apples do not always soften continuously during storage, and the extent of softening after harvest
is greatly influenced by the storage period (Iwanami

et al., 2004). Determining how long it takes forfruit to become too soft for market acceptance requires regular evaluation until firmness reaches acertain value, and, consequently, many samples offruit are required when a genotype is likely to havea long storage capability. Therefore, although longshelf life is one of the most important objectives inapple breeding, this important part of the seedlingscreening is ignored in many apple-breeding programs(Alston, 1988). Recently, Iwanami et al. (2004) indicated that the firmness of apple fruit significantly
decreased by 20 days of storage at 20 ± 2 ◦ C and
80 ± 5%RH even in genotypes with a long storage
potential. They proposed a method to evaluate genotype differences in softening using a regression coefficient of change in firmness during storage with restricted fruit samples. By comparing the regression
coefficients of seedlings with those of control cultivars or among themselves, superior genotypes can beselected.

170
On the other hand, softening, estimated by the regression coefficient proposed by Iwanami et al. (2004),
is a quantitative and phenotypic expression of the softening of a genotype, which can be compared with thatof another genotype, can fluctuate depending on environmental factors such as year, location, and samplingdate. Johnston et al. (2002) suggested that one of the
major factors that influence post-harvest softening of
apple fruit at harvest is their maturity. This means that aslight difference in the harvest date could greatly influence the phenotypic expression of the fruit softening ofa genotype. Johnston et al. (2002) also suggested thatfruit from different orchards often differ in firmness
after storage despite being stored under similar conditions. Ingle and Morris (1989) observed that the rate of‘Rome’ apple fruit softening at 20 ◦ C varied from year
to year. These previous reports, however, have not estimated the magnitudes of the environmental variancesof fruit softening.
Environmental variances normally fluctuate depending on the location, climate, and cultural management. Therefore, it is important for apple breeders to
obtain information on the magnitudes of the environmental variances under their cultural management andclimate conditions and the contribution of genetic andenvironmental factors to phenotypic expression. The
objectives of this study were (1) to estimate the environmental variance components of softening specific to apple breeding at the Department of Apple Research, National Institute of Fruit Tree Science (NIFTS) in Japanand (2) to determine the optimum sampling methods
for reducing the environmental variation of fruit softening after harvest.
Materials and methods
Fruit materials
Thirteen apple cultivars and selections (genotypes)
from the orchards at the Department of Apple Researchof NIFTS were selected on the basis of diversity of harvest date (Table 1). The genotypes were used as parents in the NIFTS apple-breeding programs. Two or
three trees from each genotype were used for the experiment. The trees varied in rootstock and years since
planting/top-grafting. Each of 20 to 25 fruit samples
was harvested three times weekly during the maturity
period in 2001 and 2002. The maturity period was determined as the time when most of the fruits were considered to be mature based on ground color, texture,
flavor and starch staining. Fruits of similar size (within

15% of average fruit weight) were harvested randomly
from each tree. Four to five fruits from each harvested
sample were immediately used for the measurement of
firmness and soluble solids concentration (SSC). SSC
was used to assess the degree of maturity of sampling
fruit because SSC tends to increase as apple fruit matureand so it could be a useful maturity index for the fruit(Kingston, 1992). Flesh firmness was measured using
a fruit pressure tester (FT327, McCormick Fruit Technology, Wash.) mounted in a drill press and fitted withan 11.1 mm probe on the pared surfaces of the sunnyand shady sides of each fruit. Data were expressed in
Newton (N). SSC was measured with a digital refractometer (PR-100, Atago, Tokyo) using crude juice extracted with a juicer (MJ-C68, National, Osaka) fromeach fruit that was peeled and cored.
Storage conditions
The remaining fruit was stored in 25-l containers arranged on racks in a chamber controlled at 20 ± 2 ◦ C
and 80 ± 5%RH with constant air circulation. The firmness of four to five fruit was measured at 5-day intervals
until 20 days after harvest. Fruit displaying rot were immediately removed from the containers during storage.
Softening evaluation
Firmness measurements of individual fruit sampledwere subjected to a linear regression on days of storage. Since firmness does not always decrease uniformly
throughout 20 days of storage, the linear regression
for change in firmness was adapted from the harvest
date until firmness decreased by 20%, as described by
Iwanami et al. (2004). When firmness did not decrease
more than 20% within 20 days of storage, the data fromthe full length of storage (20 days) were subjected tolinear regression. The regression coefficient, calculated
by subjecting the firmness measurement to the linear
regression, was defined as the softening rate (N/day).
Softening was evaluated by the softening rate.
Statistical analysis
Comparison of the softening rate among harvest dates
The regression coefficients (softening rate) were compared according to Okuno (1978). Differences in the
regression coefficients among harvest dates were detected by the following F-test:F=

Mean squares among regressions,
Mean squares of regression residual

171
Table 1. Harvest date and storage periods of the fruit from 30 trees of 13 apple cultivars and selections in 2001 and 2002
2001
Storageperiodsb (day)Harvest dateTree agea
Genotype

2002
Harvest date

Storageperiodsb (day)Rootstockin 2001

1

2

3

1

2

3

1

2

3

1

2

3

M.26 EMLA
M.9
M.9
Tsugaru
JM7
M.9
M.9
Akane
M.26 EMLA
Jonathan/M.prunifolia
SilkenM.9
M.9
Himekami S.D./MM.106
S.D./MM.106
SantaroM.26
M.26
Morioka57 JM2
M.26
Jonathan
JM7
M. prunifolia
Kotaro
JM2
M.26
GoldenM.9
Delicious M.9
Orin
JM7
M.9
M.9
Fuji
JM7
M.9
M.9
Ralls Janet M.9
M.9

15
7
7
7
7
7
Unknown
(3)
11
11
(17)
(17)
12
12
11
12
7
43
11
12
7
7
7
7
7
7
7
7
7
7

31 Aug.
31 Aug.
31 Aug.
31 Aug.
31 Aug.
31 Aug.
31 Aug.
31 Aug.
20 Sept.
20 Sept.
14 Sept.
14 Sept.
20 Sept.
20 Sept.
28 Sept.
28 Sept.
5 Oct.
5 Oct.
20 Oct.
20 Oct.
20 Oct.
20 Oct.
20 Oct.
20 Oct.
20 Oct.
2 Nov.
2 Nov.
2 Nov.
9 Nov.
9 Nov.

7 Sept.
7 Sept.
7 Sept.
7 Sept.
7 Sept.
7 Sept.
7 Sept.
7 Sept.
28 Sept.
28 Sept.
20 Sept.
20 Sept.
28 Sept.
28 Sept.
5 Oct.
5 Oct.
11 Oct.
11 Oct.
26 Oct.
26 Oct.
26 Oct.
26 Oct.
26 Oct.
26 Oct.
26 Oct.
9 Nov.
9 Nov.
9 Nov.
17 Nov.
17 Nov.

14 Sept.
14 Sept.
14 Sept.
14 Sept.
14 Sept.
14 Sept.
14 Sept.
14 Sept.
5 Oct.
5 Oct.
28 Sept.
28 Sept.
5 Oct.
5 Oct.
11 Oct.
11 Oct.
20 Oct.
20 Oct.
2 Nov.
2 Nov.
2 Nov.
2 Nov.
2 Nov.
2 Nov.
2 Nov.
17 Nov.
17 Nov.
17 Nov.
22 Nov.
22 Nov.

10
10
10
15
15
15
10
10
10
10
10
10
10
10
10
10
10
10
10
15
10
10
15
15
15
20
20
20
10
10

10
10
10
15
15
15
15
10
10
10
10
10
15
15
10
10
10
15
10
15
10
10
10
10
15
20
20
20
15
10

10
10
10
10
10
10
10
10
10
5
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
20
20
20
15
15

30 Aug.
30 Aug.
30 Aug.
6 Sept.
6 Sept.
6 Sept.
6 Sept.
6 Sept.
13 Sept.
13 Sept.
13 Sept.
13 Sept.
20 Sept.
20 Sept.
27 Sept.
27 Sept.
5 Oct.
5 Oct.
17 Oct.
17 Oct.
17 Oct.
17 Oct.
25 Oct.
25 Oct.
25 Oct.
1 Nov.
1 Nov.
1 Nov.
8 Nov.
8 Nov.

6 Sept.
6 Sept.
6 Sept.
13 Sept.
13 Sept.
13 Sept.
13 Sept.
13 Sept.
20 Sept.
20 Sept.
20 Sept.
20 Sept.
27 Sept.
27 Sept.
5 Oct.
5 Oct.
11 Oct.
11 Oct.
25 Oct.
25 Oct.
25 Oct.
25 Oct.
1 Nov.
1 Nov.
1 Nov.
8 Nov.
8 Nov.
8 Nov.
16 Nov.
16 Nov.

13 Sept.
13 Sept.
13 Sept.
20 Sept.
20 Sept.
20 Sept.
20 Sept.
20 Sept.
27 Sept.
27 Sept.
27 Sept.
27 Sept.
5 Oct.
5 Oct.
11 Oct.
11 Oct.
17 Oct.
17 Oct.
1 Nov.
1 Nov.
1 Nov.
1 Nov.
8 Nov.
8 Nov.
8 Nov.
16 Nov.
16 Nov.
16 Nov.
23 Nov.
23 Nov.

10
10
10
10
10
10
5
10
10
10
10
10
10
10
5
5
10
10
10
10
10
10
10
10
10
20
20
20
10
10

10
10
10
10
10
10
5
5
10
10
10
10
10
10
5
5
10
10
10
10
5
5
10
10
10
20
20
20
20
15

5
5
10
10
10
10
5
10
10
10
10
10
10
10
5
10
15
10
10
10
10
10
10
10
10
20
20
20
10
10

Sansa

S.D.: Starking Delicious.
a Numeral in parentheses indicates years since top-grafting on intermediate stock.
b Storage continued until the flesh firmness decreased by 20% of harvest firmness or for 20 days when the flesh firmness did not decrease morethan 20% within 20 days of storage.

in whichof the lth harvest date in the jth tree of the ith genotype
in the kth year; (Se)i jkl the sum of squares of regression

Mean squares among regressions
2 h hg t  y h 2
j=1
l=1 (Sx y)i jkl /(Sx)i jkl −l=1 (Sx y)i jkl
l=1 (Sx)i jkl
i=1
k=1
=
,
 g t  y
j=1
i=1
k=1 (li jk − 1)g t  y hj=1
l=1 (Se)i jkl
k=1
i=1
Mean squares of regression residual = g t  y h,j=1
l=1 (m i jkl − 2)i=1
k=1
where (Sx)i jkl is the sum of squares of independent
variables (x: storage day) of the lth harvest date in the jthtree of the ith genotype in the kth year; (Sx y)i jkl the sumof products of variables x (storage day) and y (firmness)

(1)
(2)

residual of the lth harvest date in the jth tree of theith genotype in the kth year; li jk the number of harvest in the jth tree of the ith genotype in the kth year;
mi jkl the number of sampling fruit per harvest of the lth172harvest date in the jth tree of the ith genotype in the kthyear.

σi2jkl . True harvest variation (σh2 ) can be estimated bysubtracting σb2 from the σe2 (Table 4).

Comparison of the softening rates among genotypes,
trees, and years
The regression coefficients from each harvest date were
subjected to analysis of variance (ANOVA). The homogeneity of the variances among harvest dates within atree was tested by Bartlett’s test, and the normal distribution of the residual was tested using Kolmogorov–
Smirnov’s one-sample test. The results of these tests
showed that the homogeneity of the variance and normal distribution was not rejected at P = 0.05, and,
therefore, the model of ANOVA was assumed to be applicable to the data. The model adopted here to express
the phenotypic value is Pi jkl = µ + gi + ti j + yk +(gy)ik + (t y)i jk + h i jkl , where Pi jkl is the regression
coefficient of the lth harvest date in the jth tree of theith genotype in the kth year; µ the overall mean; gi therandom effect of the ith genotype; ti j the random effectof the jth tree of the ith genotype; yk the random effectof the kth year; (gy)ik the interaction between the ith
genotype and the kth year; (t y)i jk the interaction between the jth tree of the ith genotype and the kth year;
and h i jkl , the random effect of the lth harvest date in thejth tree of the ith genotype in the kth year. ANOVA was
performed using a Statistical Analysis System (SASInstitute, Cary, NC, 1989).

Optimum allocation
The variance of a mean of the regression coefficientsin the ith genotype can be expressed ast  y  h  2
j=1
l=1 σi jkl /(Sx)i jkl
k=1
2
σb̄ =
,
(4)
(t yh)2

Estimation of the environmental variance componentsof the softening rate
The ANOVA provided the variance associated withthe genotype (σg2 ), among trees within genotypes (σt2 ),2among years (σy2 ), the genotype × year (σgy), the tree ×2
year (σty ), and among harvest dates within tree and year
(residual variance) (σe2 ) (Table 3). The σe2 contains theerror variance of the regression coefficient. The error
variance is estimated as
g
σb2 =

i=1

where y is the number of yearly replications; t the
number of tree replications; and h the number of harvest replications. Then, the environmental variance ofa genotype mean (σE2 ) can be expressed as
σE2 =

2
σgy

+

y

σty2
σt2
σ2
+
+ h + σb̄2
t
ty
t yh

(5)

When the regression residual variances σi2jkl are assumed to be equal to σ 2 and the number of samplingtimes for measuring firmness during storage and thenumber of fruit for each measurement are the same((Sx)i jkl = Sx) for all regressions, Eq. (4) becomesσb̄2 = σ 2 /(Sx)t yh. Moreover, the sum of squares ofan independent variable (Sx) can be expressed in thisstudy condition as
Sx =

N


(xi − x̄)2 = f d 2 C;

i=1

C=


n

2

n
(i − 1) −i=1

2i=1 (i − 1)

n

,

(6)

where f is the number of fruits per firmness measurement; d the interval of firmness measurement (5days); and n the number of sampling times for firmness measurement during storage. Consequently, theenvironmental variance of a genotype mean can be y h  2
σi jkl /(Sx)i jkl (m i jkl − 2)
j=1
l=1
k=1
,
g t  y hj=1
l=1 (m i jkl − 2)
k=1
i=1

t

where σb2 is the weighted average of the error varianceof the regression coefficient; σi2jkl the regression residual variance of the lth harvest date in the jth tree of
the ith genotype in the kth year; (Sx)i jkl is referred toabove; σi2jkl /(Sx)i jkl the error variance of the regression coefficient of the lth harvest date in the jth treeof the ith genotype in the kth year; m i jkl is referred toabove; and (m i jkl − 2) the degree of freedom of the(3)

rewritten as
σE2 =

2
σgy

y

+

σty2
σt2
σ2
σ2
+
+ h +
.
t
ty
t yh
f d 2 Ct yh(7)

Each variance component in Eq. (7) has been obtained from Table 4, and the regression residual variances (σ 2 ) were estimated by Eq. (2). The optimum
allocation can then be determined under a particular173
level of environmental variance by changing the number of years (y), trees (t), harvest dates (h), and sampling
number of fruit (f) for each firmness measurement.
Results and discussion
The difference in the regression coefficient from harvest dates from one tree was significant at the 5% level(Table 2). The difference indicated that the softening
rate was not equal in fruit harvested in subsequent harvest dates. For this study, fruits were harvested froma total of 30 trees of 13 genotypes in a year, and theexperiment was repeated in 2 years (Table 1). When the
ANOVA for the regressions obtained from three harvest
dates was conducted for each tree separately, significant differences were detected in five trees of 30 trees
in 2001, and in only one tree out of 30 trees in 2002.
The genotype was different in all six trees, in which
the softening rate was significantly different according to the harvest date. This means that the significant
difference does not depend on the genotype.
Stow and Genge (2000) suggested that the picking date did not affect the softening rate during storage of the ‘Royal Gala’ apple, in which the difference in the picking date was 20 days, although thesamples harvested later were always softer than theearlier ones. Moreover, in several studies, firmness at
harvest was highly correlated with firmness after storage when fruit was harvested on several dates (Marmoet al., 1985; Knee & Smith, 1989). The correlation,in other words, indicated that the softening rate during storage was uniform regardless of the harvest datewhen the fruit was commercially mature. On the other
hand, Ingle and Morris (1989) observed that a significant positive correlation coefficient was evident between firmness at harvest and changes in firmness during storage at 20 and 0 ◦ C in the ‘Rome’ apple. Ingle
and D’Souza (1989) also observed the same correlationin the ‘Red Delicious’ apple stored at 0 ◦ C. Johnston
et al. (2002) observed that fruit harvested later began
to soften sooner than fruit harvested earlier although
Table 2. Analysis of variance for regression among harvest
and test for the significance of differences in the regression
coefficient
Source of variationdf

Mean squares

Among regression coefficientson each harvest date
Regression residual

120

36.981∗2476

28.148∗ Significant at P < 0.05, using F-test.

the rate of rapid softening did not differ according to
the harvest dates in the ‘Royal Gala’ and ‘Cox Orange
Pippin’ apples.
To determine the cause of the difference in the softening rate according to the harvest date, the relationship between the variance of fruit firmness according
to the harvest date and the variance in the softening
rate according to the harvest date was calculated forall entries. In addition, the relationship between thevariance of SSC according to the harvest date and thesoftening rate was calculated. These calculations werenecessary because of the probability that genotypes
with a large difference in the physiological stage ofmaturity of fruit harvested 2 weeks after the first harvest date had a tendency to have large differences insoftening rates. The results were that the relationships
were low (r = 0.2019, 0.0887, respectively). Moreover, there was not a tendency for the fruit to soften
faster or more slowly when the fruit was harvested
later (data not shown). Therefore, the significant difference in the softening rate according to the harvest
date, which reached the 5% level, could not have been
induced by some particular genotype, or by the large
difference in the physiological stage of maturity.
The length of the harvest period depends on the
genotypes, and the harvest period may last a few weeks.
Therefore, an ANOVA was conducted using the regression coefficient by defining the variance in the regression coefficient among three harvest dates at weeklyintervals as the error variance to determine the significance of the effects of tree, year, and its interactions on
the softening rate. The result of the ANOVA showedthat the effects of genotype and year were highly significant at p < 0.01 (Table 3). On the other hand, theTable 3. Analysis of variance for the regression coefficient of fruit
softening during storage using 13 genotypes with 2 or 3 trees per
genotype for 2 years
Source of variation
Genotypedf

MS

Expected mean squares

12

5.560∗∗

2σe2 + 3σt2y + 6σt2 + 6.9σgy+13.8σg2Year

2 + 90σ 2
1 8.202∗∗ σe2 + 3σt2y + 7.2σgyyGenotype × year2
12 0.364NS σe2 + 3σt2y + 6.9σgy

Among trees
within genotype

17 0.249NS σe2 + 3σt2y + 6σt2

Year × tree

17 0.243∗

Among harvest within 120 0.140
tree and year

σe2 + 3σt2yσe2

NS: Non-significant.
∗ ,∗∗ indicates significance at P < 0.05 and P < 0.01, respectively.

174
Table 4. Estimates of variance components and their percentage to thetotal variance obtained from the analysis of variance for the regression coefficient of fruit softening during storage using 13 genotypes
with 2 or 3 trees per genotype for 2 years

Table 5. Softening rates of 13 apple cultivars and selection averaged from three harvest dates from two or
three trees of each genotype for 2 years
Softening

Environmental

Variance components

Genotype

rate (N/day)deviationa ( σE2 )Silken

2.850

0.186

Himekami

2.546

0.175

Akane

2.464

0.178

Morioka57

2.445

0.207

Kotaro

2.091

0.192

Sannsa

2.083

0.158

Jonathan

1.929

0.191

Orin

1.927

0.152

Ralls Janet

1.847

0.169

Golden Delicious

1.834

0.173

Santaro

1.478

0.169

Tsugaru

1.382

0.147

Fuji

0.498

0.135

Estimates

Genotype

σg2

0.376

57.3%

Year

σy2

0.087

13.3%

Genotype × year

2
σgy

0.018

2.7%

Among tree within genotype

σt2

0.001

0.1%

Year × tree

σty2
σe2
σh2
σb2

0.034

5.2%

0.140

21.4%

Among harvest
True harvest varianceError variance of regression coefficient
Total

0.037

5.7%

0.103

15.7%

0.656

100%

effects of trees within genotype and genotype × year
were nonsignificant.
The variance associated with genotype (σg2 ) was
the largest, namely, more than half of the total variance(Table 4). The variance among harvest dates was next,
being 21% of the total variance. The variance among
harvest dates, however, contained the error variance ofthe regression coefficient. The error variance of the regression coefficient was 75% of the variance among
harvest dates (Table 4). Therefore, the environmental
2
variance components associated with year (σgy, σty2 ),tree (σt2 ), and harvest date (σh2 ) were all very small
though the variance associated with years (σy2 ) was
large (13% of total variance).
In apple breeding, using trees that are planted in thesame year or grafted on the same rootstock for comparison of genotypes is not always possible (Durel et al.,
1998; Hampson et al., 2000). For this study, therefore,
trees of various ages and rootstocks were examined todetermine how environmental variances contributed to
the genotype means. Since the variance components
associated with trees and other environmental factors
were small despite the fact that trees of various types
had been used, this method appears to be efficientfor the comparison of genetic differences in softening
by using regression coefficients. Although fruit of all
genotypes except ‘Fuji’ softened within a storage period of approximately 10 days (Table 1), the softening
rates of the genotypes varied from 1.38 to 2.85 (Table 5)
and were significantly divided into six groups by calculating ±1.96 σE2 as the 95% confidence interval.
The environmental variance (σE2 ) can be reduced
and, thus, the precision of estimates for the genotype mean of softening rate can be increased mosta Calculated using Eq. (5).

efficiently by reducing the contributions of σty2 , σh2 , andσb̄2 , which were relatively large (Table 4). Since boththe year and tree replications can equally reduce thecontributions of the σty2 , σh2 , and σb̄2 (Eqs. (4) and (5)),
year and tree replications are more efficient than harvest replications or increasing the number of harvest
fruit.
The cost for breeding depends on the space in thefield and the speed of selection (Yamada et al., 1993).
Tree replication reduces the number of genotypes thatcan be evaluated in a restricted breeding field, and thetrees continue to occupy the field during yearly repeatedevaluations. Thus, yearly repetitions or tree replications
are costly and time-consuming, and a comparison between yearly repetitions and tree replications should
be primarily considered (Sato et al., 2000). Yamada
et al. (1993), however, indicated that, unless the variance associated with trees within a genotype (σt2 ) ismarkedly greater than the variance associated with the2genotype × year interaction (σgy), it is disadvantageous
to increase the number of tree replications while sacrificing yearly repetitions in every breeding situationin which seedlings cannot bear fruit in the first year ofplanting. In this study, the year replications appeared tobe more efficient for estimating the genotype mean of
the softening rate than the tree replications because the2
σt 2 was considerably smaller than the σgy.
The genotype differences in the softening rate
among 13 cultivars and selections were evaluated with

175
about two trees from each genotype and two annual
repetitions. Since the tree replications are disadvantageous in a breeding situation, alternative allocationsof the repetitions were then examined as a means ofdetecting significant differences in the softening rate
among genotypes with the same accuracy as in the current study. Equation (7) was solved for f under various replications of years, trees, and harvest times. The
standard environmental variance ( σE2 ) was defined as
0.2, which was about the highest value obtained in thisstudy. C in Eq. (6) was calculated by substituting three
for n; this means that the firmness measurement is carried out three times at 5-day intervals from the harvest
date until 10 days after storage, since fruit from almost
all of the genotypes in this study soften within approximately 10 days of storage.
The number of fruit necessary for firmness measurements to obtain 0.2 in standard environmental variance is given in Table 6. The results demonstrate that
14 fruits are necessary when fruit are harvested at threetimes from a single tree of each genotype for 2 years,
while 0.2 in standard environmental deviation cannot
be obtained when fruit are harvested at one time. When
fruits are to be harvested at one time from a single tree,
the evaluation of softening needs to be continued for
3 years, and 21 fruits are necessary for each measurement for each year. On the other hand, only six fruits
are necessary when fruits are harvested twice under
the same conditions. Therefore, although harvest on
several dates is likely to be more costly, at least two
harvests are necessary to determine a genotype mean
for the softening rate.
Estimations of the variance component generally
depend on the experimental populations and could vary.
However, the environmental variance components estimated in this study were all small, although genotypes
Table 6. Comparisons of the number of fruit for firmness measurements for some alternative replications of years, trees,and harvest dates when the standard environmental deviation( σE2 ) was defined as 0.2 for the genotypes in which the fruit
softened after 10 days of storage
No. of fruit for measurement
harvest replications

No. of year
replications

No. of tree
replications

1

2

3

2

1

–

37.8

13.7

2

11.0

4.0

2.5

3

1

20.4

6.1

3.6

2

4.3

1.9

1.2

of relatively wide variation were used with trees undervarious conditions. Therefore, this method for evaluating softening is stable and may be useful for otherbreeding locations and apple populations.
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