Plant Breeding 131, 322—328 (2012) 2012 Blackwell Verlag GmbH

doi:10.1111/j.1439-0523.2011.01932.x

Mode of inheritance in fruit acidity in apple analysed with a mixed model of a major
gene and polygenes using large complex pedigree
HIROSHI IWANAMI1, SHIGEKI MORIYA1, NOBUHIRO KOTODA1,2, NAOZUMI MIMIDA1,3, SAE TAKAHASHIS U M I Y O S H I 1 and K A Z U Y U K I A B E 1
1Apple Research Area, National Institute of Fruit Tree Science, Morioka, Iwate 020-0123, Japan, E-mail: hiwanami@aﬀrc.go.jp;
Present address: Citrus Research Area, National Institute of Fruit Tree Science, Shimizu, Shizuoka 424-0292, Japan;
3
Present address: Horticulture Laboratory, Faculty of Agriculture, Iwate University, Ueda 3-18-8, Morioka 020-8550, Japan
2

With 5 ﬁgures and 2 tables
Received April 28, 2011/Accepted November 2, 2011
Communicated by W. E. Weber

Abstract
Fruit acidity is an important characteristic to determine the marketability of apple (Malus · domestica Borkh.). To reveal the mode ofinheritance in fruit acidity and to estimate the genetic parameters, we
performed segregation analysis using a population from an apple
breeding programme. Four models (mixed, Mendelian, polygenic andenvironmental) were compared to ﬁnd the most likely mode of theinheritance of acidity. The phenotypic variance of acidity in the
population was properly explained using a mixed model of a major
gene and polygenes. The genotypic values of the major gene (AA, Aa
and aa) were estimated to be 0.45, 0.52 and 0.92 g/100 ml in titratable
acidity, respectively. The values of the homozygote (AA) and theheterozygote (Aa) were very close and lower than that of the otherhomozygote (aa), indicating that an allele of the major gene appeared
to have complete dominance with a function of lowering acidity. The
estimate of the heritability after accounting for the major gene wasmoderately high, 0.43, in the mixed model. This means that even withremoval of the eﬀect of the major gene, acidity could ﬂuctuateconsiderably by the eﬀect of polygenes. The proportions of progeny
with adequate acidity diﬀered greatly, depending on which genotype
was used as parents for the crossing. Therefore, it is very important toknow the genotypes of parental cultivars before crossing.

Key words: genotype — heritability — Malus domestica —phenotype — titratable acidity
Apples are produced in much of the world and consumed freshand as juice and processed products. Apples can be stored up
to a full year, which supports their mass consumption in theworld market. One important factor that determines thesuitability of a cultivar for dessert or processing purposes is theacidity of the fruit. Because low-acidity apples have a lessdesirable aroma and insipid taste, particularly in processed
products, high-acidity apples are essential for cooking, andlow-acidity apples are used predominantly for desserts. Acidity
also determines whether fruit should be consumed immediately
or not and how long fruit can be stored because acidity
gradually decreases during storage and an excessive decrease inacidity reduces the eating quality of the fruit. Therefore,
acidity is an important characteristic determining the marketability of apples. Consumer acceptability of apples in Europe isclosely correlated with the acid content (Kingston 1992).
Acidity is a characteristic that has been found to segregate
within seedlings, according to early genetic studies of apple.
The acid in a mature apple is almost entirely malic acid. The

distribution of seedlings in the malic acid concentration
showed two types of distribution among progeny. One was asimple distribution with one peak, while the other had two
peaks: one below 0.3% (or pH > 3.8) and the other with ahigher range of acidity (Nybom 1959, Visser et al. 1968, Brown
and Harvey 1971). Because low acidity behaved as a recessive
characteristic, medium-to-high acidity was considered to be
dominant, and acidity was assumed to be controlled by amajor gene (Ma). Moreover, a simple distribution wasobserved around the peak within a range of medium-to-highacidity, and polygenes were also suggested to control the malic
acid concentration. Acidity in these early studies was expressedas the malic acid concentration determined by chromatography or as the pH. In modern apple breeding programmes,
however, the acidity of fruit is measured by titration [titratable
acidity (TA)]. Therefore, we cannot refer to the results of theearly studies and take advantage of the results in our own
breeding programmes.
Genetic research on quantitative traits has been restricted instudies on fruit because it is diﬃcult to use trees as
experimental plants. Trees generally require several years after
planting to bear fruit and occupy a large amount of space.
Study on the inheritance of acidity in apples has not advanced
since the early reports. The inheritance of acidity in apple
seems to be explained by three components: the eﬀect of amajor gene of large eﬀect, the residual additive heritable eﬀects
of polygenic loci and the independent random eﬀects of theenvironment. This is commonly referred to as a mixed model.
The most powerful test for the mixed model is a segregation
analysis, which uses information of pedigree to specify theunderlying distributions of phenotypic values (reviewed by
Lynch and Walsh 1998). When a major gene is segregating, thephenotypic distribution can exhibit multimodality, skewness
and/or kurtosis. The segregation analysis is a useful method
because only phenotypic records from a pedigreed population
are required. The objectives of this study were to reveal themode of inheritance in fruit acidity in apple and to estimate thegenetic parameters by segregation analysis.

Materials and Methods
Progeny population: This study was carried out using a populationfrom the apple breeding programme at the National Institute of Fruit
Tree Science (NIFTS), Morioka, Japan. The population consisted of

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Mode of inheritance in fruit acidity in apple
16 cultivars as parents and 408 individuals from 31 families, with one
to 48 unselected individuals per family (Fig. 1). Crosses were madesolely for producing commercial cultivars and therefore had no speciﬁc
mating design. As a result, the frequency of use of a cultivar in crosses
diﬀered greatly among parental cultivars. The pedigree structure of the
16 parental cultivars is shown in Fig. 2. The ﬁrst line of the pedigree
structure indicates the founders. Four of the founders (ÔDeliciousÕ,323
ÔRalls JanetÕ, ÔJonathanÕ and ÔGolden DeliciousÕ) originated in theUSA; two of the founders (ÔCoxÕs Orange PippinÕ and ÔWorcester
PearmainÕ) are from England, and the remainder, ÔIndoÕ, is fromJapan. The other cultivars, except for ÔKiddÕs OrangeÕ and ÔGalaÕ, were
produced from public and private apple breeding programmes inJapan. Progenies were grafted onto dwarﬁng rootstocks and planted in
2000–2002 in an orchard of NIFTS. Trees within a family were planted

Fig. 1: Pedigree structure of progeny used in segregation analysis. The ﬁrst line indicates parental cultivars. n is the number of progenies obtained
from each crossFig. 2: Pedigree structure of parental cultivars used in segregation analysis. The names of the cultivars, acidity and genotype in acidity are
enclosed in rectangles. Acidity is expressed as an average of 3 years of data. The genotype in acidity is estimated by one of the functions equippedin the pedigree analysis package (PAP). The genotype was determined when the probability of the estimation was >90%, computed by PAP. The
dashes in the second and/or third lines of the rectangles indicate that acidity was not measured and the genotype was not accurately estimated.
The cultivars in bold rectangles were used as parents in the population examinedH. Iwanami, S. Moriya, N. Kotoda et al.

324
in plots at a spacing of 0.5 m within a row with 3 m between rows.
Parental plants were grown in adjacent ﬁelds.
Fruit materials and measurement of acidity: Three fruit samples wererandomly harvested from a tree of each progeny when most of the fruit
was determined to be mature by sensory evaluations based on groundcolour, texture, ﬂavour and starch staining in 2005. In parental
cultivars, ﬁve fruits were sampled at commercial maturity from August
to November 2003, 2004 and 2005, and the phenotypic values of eachparental cultivar were expressed as an average of the 3-year data.
Acidity was measured as the TA. Crude juice was extracted with ajuicer (MJ-C68; National, Osaka, Japan) from each fruit. After
ﬁltration, 2 ml of juice was titrated with an autotitrator (AUT-301;
TOA Electronics, Tokyo, Japan) to pH 8.0 with 0.1 N NaOH.
Titration results are calculated as malic acid (in grams) per 100 ml of
the sample juice.
Segregation analysis: According to Snow and Wijsman (1998), we
compared four models that can be ﬁt to observed pedigree data to ﬁnd
the most likely mode of inheritance of acidity:
Mixed model: yi ¼ l þ gi þ ai þ ei
Mendelian model: yi ¼ l þ gi þ ei
Polygenic model: yi ¼ l þ ai þ ei
Environmental model: yi ¼ l þ ei
Where yi is the TA of ith progeny, l is the population mean, gi is theeﬀect of the major gene of ith progeny (the oﬀset from l for the majorgene genotype of ith progeny), ai is the polygenic component of ithprogeny, and ei is the random environmental component of ithprogeny. For founders, the ai is assumed to be distributed ð0; r2a Þ,
where r2a is the additive genetic variance after removing the genetic
variance contributed by the major gene. Non-founders are distributed
N ðafather þ amother =2; r2a =2Þ. The ei is distributed N ð0; r2e Þ. Heritability(h2) was deﬁned as h2 ¼ r2a =ðr2a þ r2e Þ, which is commonly used in thecontext of segregation analysis. First, the observed pedigree data wereanalysed with the mixed model, and the frequency of the major geneand genotypes of the major gene in each parental cultivars were
estimated. Then, the analysis was restarted to maximize the likelihoodof the other three models (Mendelian, polygenic and environmental
model) with the frequency of the major gene ﬁxed. Comparisons of themodels were made with likelihood ratio tests. The analysis was
performed with pedigree analysis package (PAP) software (Hasstedt2008) version 6.0. Segregation analysis, implemented in the PAP, hasbeen widely used for estimating the parameters and computing or
approximating the likelihood for the mixed model, especially in human
genetics (Neuman et al. 1995, Snow and Wijsman 1998, Almasy andWarren 2005).

Results
Acidity in progeny populations was distributed continuously
from 0.1 to 1.6 g/100 ml with a peak around 0.5 g/100 ml.
Mid-parent values of acidity were very close to family meansof that in most of all crosses (Table 1). Acidity in progenies
from crosses among cultivars with acidity of 0.3–0.4 g/100 ml
was distributed around the mid-parent value, showing atypical normal distribution (Fig. 3a). In crosses in which theacidity of one parent on a cross was in a higher category (from0.4 to 0.8 g/100 ml), the distribution of acidity shifted towards
a higher category (Fig. 3b–c). Progenies with low acidity werealso obtained, even though the mid-parent values became
higher. These frequency distributions suggested that acidity
would be a quantitative trait controlled by polygenes as well as
by some major genes with a large eﬀect that made acidity low(<0.3 g/100 ml) or high (>0.6 g/100 ml).
The likelihood ratios of the genetic models (mixed, Mendelian and polygenic) to the environmental model were tested,

Table 1: Mid-parent values and family means of acidity in 31 apple families examined
Cross
Tsugaru · Delicious
Sansa · Delicious
Orin · Sansa
Tsugaru · Sansa
Fuji · Delicious
Kitaro · Tsugaru
Fuji · Orin
Fuji · Kotaro
Fuji · Tsugaru
Senshu · Kotaro
Sansa · Shinsekai
Kitaro · Shinsekai
Toko · Kotaro
Fuji · Sansa
Senshu · Sansa
Senshu · Shinsekai
Fuji · Morioka #54
Senshu · Morioka #54
Fuji · Megumi
Toko · Morioka #54
Akane · Orin
Fuji · Morioka #57
Fuji · Himekami
Sansa · Akane
Senshu · Himekami
Kitaro · Akane
Fuji · Akane
Senshu · Akane
Jonathan · Delicious
Akane · Megumi
Jonathan · Sansa

Mid-parent
value (g/100 ml)

Progeny
evaluated (no.)

Smallest value inthe progeny (g/100 ml)

Largest value in theprogeny (g/100 ml)

Family mean
(g/100 ml)

0.32
0.34
0.34
0.35
0.36
0.36
0.36
0.36
0.37
0.37
0.38
0.38
0.39
0.39
0.40
0.40
0.45
0.46
0.47
0.47
0.47
0.49
0.50
0.51
0.51
0.51
0.52
0.53
0.57
0.59
0.60

37
37
4
13
11
3
3
11
4
28
11
7
5
15
16
13
14
13
16
5
10
1
1
22
8
48
7
9
16
16
4

0.12
0.13
0.16
0.24
0.22
0.42
0.37
0.36
0.40
0.17
0.32
0.35
0.24
0.19
0.11
0.27
0.25
0.31
0.20
0.26
0.15
0.78
0.90
0.14
0.20
0.27
0.24
0.17
0.17
0.41
0.59

0.49
0.56
0.48
0.72
0.62
0.58
0.54
0.85
0.61
0.82
0.64
0.73
0.83
0.74
0.83
0.75
0.94
0.71
0.73
0.68
0.83
0.78
0.90
1.16
0.86
1.27
0.80
0.68
1.06
1.17
1.62

0.31
0.34
0.37
0.43
0.36
0.51
0.47
0.53
0.51
0.51
0.45
0.55
0.41
0.45
0.46
0.50
0.55
0.47
0.46
0.39
0.44
0.78
0.90
0.51
0.51
0.62
0.49
0.38
0.59
0.76
1.06

Mode of inheritance in fruit acidity in apple

325

Fig. 3: Frequency distributions of acidity in progeny obtained from crosses (a) between parents with TA at 0.3–0.4 g/100 ml, (b) between parents
at 0.3–0.4 g/100 ml and 0.4–0.5 g/100 ml, and (c) between parents at 0.3–0.4 g/100 ml and 0.6–0.8 g/100 ml. The arrows indicate the acidity ofthe parents. Each group consists of progeny from (a) seven crosses (ÔSansaÕ · ÔDeliciousÕ, ÔTsugaruÕ · ÔDeliciousÕ, ÔSansaÕ · ÔShinsekaiÕ,ÔSansaÕ · ÔTsugaruÕ, ÔSansaÕ · ÔOrinÕ, ÔKitaroÕ · ÔShinsekaiÕ and ÔKitaroÕ · ÔTsugaruÕ); (b) nine crosses (ÔFujiÕ · ÔDeliciousÕ, ÔFujiÕ · ÔKotaroÕ,ÔSenshuÕ · ÔShinsekaiÕ, ÔFujiÕ · ÔSansaÕ, ÔSenshuÕ · ÔKotaroÕ, ÔSenshuÕ · ÔSansaÕ, ÔFujiÕ · ÔTsugaruÕ ÔFujiÕ · ÔOrinÕ and ÔTokoÕ · ÔKotaroÕ); (c) ﬁve
crosses (ÔSansaÕ · ÔAkaneÕ, ÔAkaneÕ · ÔOrinÕ, ÔKitaroÕ · ÔAkaneÕ, ÔJonathanÕ · ÔDeliciousÕ and ÔJonathanÕ · ÔSansaÕ)and all tests were highly signiﬁcant, indicating that thephenotypic variance of acidity was a result of genetic control.
Moreover, the likelihood ratio tests for the mixed model vs.
Mendelian and polygenic models were also highly signiﬁcant,indicating that the mixed model was accepted as the modelthat best ﬁts the observed pedigree data. Therefore, theexistence of a major gene was veriﬁed in the inheritance ofacidity.
When the mixed model was applied to the pedigree data, thegenotypic values of the major gene (A1A1, A1A2 and A2A2)
were estimated to be 0.45, 0.52 and 0.92 g/100 ml, respectively(Table 2). The values of the homozygote (A1A1) and theheterozygote (A1A2) were very close and lower than that of theother homozygote (A2A2), indicating that an allele (A1) of the
major gene behaved as a completely dominant gene with thefunction of reducing acidity. Therefore, we designated the A1
and A2 alleles as A and a, respectively. Genotypes of the major
gene in 15 of 19 parental cultivars were accurately estimated(probability of the estimation was >90%) (Fig. 2). The
estimate of heritability after accounting for the major gene
was moderately high, 0.43, in the mixed model. This meansthat even with removal of the eﬀect of the major gene, acidity
could ﬂuctuate considerably by the eﬀect of polygenes. The
phenotypic values of AA and Aa genotypes in parental

cultivars were 0.31–0.56 g/100 ml and 0.37–0.83 g/100 ml,
respectively (Fig. 2). Both genotypes had large variation in
the phenotypic value, and it is diﬃcult to distinguish the two
genotypes only by the phenotypic values. When the eﬀect ofthe major gene was integrated into the eﬀect of polygenes(Polygenic model), the estimate of heritability became higher,
0.73 (Table 2).
The frequency distributions of progeny were estimated using
the parameters obtained (Fig. 4). The progeny of each acidgenotype was assumed to be distributed according to a normal
distribution deﬁned by the genotypic value and the re, shownin Table 2, as the mean and standard deviation, respectively. A
translocation of the distributions from the genotypic meancaused by the eﬀect of polygenes was corrected by the mean
phenotypic value of parents, expressed as a deviation from the
genotypic mean of the parents, being multiplied by theheritability (gp þ h2  fðpf  gf Þ þ ðpm  gm Þ=2g; where pf, phenotypic value of father; pm, phenotypic value of mother; gf,
genotypic value of father; gm, genotypic value of mother; gp,
genotypic value of the progeny; h2, heritability). Frequent
distributions estimated from the genotypic and phenotypicvalues of parents were well ﬁtted to the distributions ofprogeny actually obtained from the parents. The reason thatprogenies with both high and low acidity were obtained from

H. Iwanami, S. Moriya, N. Kotoda et al.

326
Table 2: Genetic parameters in mixed and polygenic models estimatedby the segregation analysis
Heritability

Genotypic
value (g/100 ml)

Standard
deviation

Model

h2

A1A1 (AA) A1A2 (Aa) A2A2 (aa)

re

Mixed
Polygenic

0.43
0.73

0.45
—

0.52
—

0.92
—

0.201
0.270

crosses between parents with low and high acidity can be
explained by the fact that both parents are heterozygotes (Aa)in acidity (Fig. 4d).
The proportion of progeny with adequate acidity,
0.35–0.45 g/100 ml, for dessert use was estimated using theparameters obtained when the mid-parent value was changedin the range of 0.2–0.6 g/100 ml. Because a diﬀerence in the
genotypic value of acidity was not large between AA and Aa
genotypes, there could be cultivars in which the phenotypicFig. 4: Comparison of the frequency distributions of acidity in progeny actually obtained with those estimated by genetic parameters reported inTable 2. The progeny was classiﬁed into four groups on the basis of the phenotypic and genotypic values of the parents in acidity; (a) from crossesof AA · AA genotypes with acidity at 0.3–0.5 g/100 ml; (b) from crosses of AA · Aa genotypes with acidity at 0.3–0.5 g/100 ml; (c) from crossesof AA · Aa genotypes with acidity at 0.3–0.4 g/100 ml and 0.6–0.8 g/100 ml; (d) from crosses of Aa · Aa genotypes with acidity at 0.3–0.4 g/
100 ml and 0.6–0.8 g/100 ml. The arrows indicate the acidity of the parents. Each group consists of progeny from (a) seven crosses(ÔTsugaruÕ · ÔDeliciousÕ, ÔKitaroÕ · ÔShinsekaiÕ, ÔKitaroÕ · ÔTsugaruÕ, ÔFujiÕ · ÔDeliciousÕ, ÔSenshuÕ · ÔShinsekai, ÔFujiÕ · ÔTsugaruÕ and ÔFujiÕ · ÔOrinÕ); (b) six crosses (ÔSansaÕ · ÔDeliciousÕ, ÔOrinÕ · ÔSansaÕ, ÔSansaÕ · ÔShinsekaiÕ, ÔSansaÕ · ÔTsugaruÕ, ÔSenshuÕ · ÔSansaÕ and ÔFujiÕ · ÔSansaÕ); (c)four crosses (ÔAkaneÕ · ÔOrinÕ, ÔFujiÕ · ÔAkaneÕ, ÔSenshuÕ · ÔAkaneÕ and ÔJonathanÕ · ÔDeliciousÕ); (d) three crosses (ÔSansaÕ · ÔAkaneÕ,ÔKitaroÕ · ÔAkaneÕ and ÔJonathanÕ · ÔSansaÕ)Mode of inheritance in fruit acidity in apple

value was the same but the genotype was diﬀerent: AA and Aa.
All progenies from crosses AA · AA or AA · Aa have a lowacid allele A, and the proportion of progeny with 0.35–0.45 g/
100 ml in acidity is 19–20% when the mid-parent value isaround 0.4 g/100 ml (Fig. 5). On the other hand, the proportion decreased to 14–15% when progenies were obtained fromthe cross Aa · Aa. This is because a quarter of the progeny
from the cross is the high-acid genotype (aa).

Discussion
To the best of our knowledge, a segregation analysis using PAP
was not previously conducted in populations of plant breeding.
The segregation analysis successfully revealed that fruit acidity
in apple was governed by polygenes as well as a major gene. In
early studies, a discontinuity was observed in the distributionof acidity in progeny around pH 3.8 or 0.3% in malic acidconcentration (Nybom 1959, Visser et al. 1968, Brown andHarvey 1971). The segregation ratio between low-acid(pH > 3.8) and moderate-to-high acid (pH < 3.8) was presumed to be 1 : 3, and the conclusion was that acidity was
governed by a major gene, with moderate-to-high acidity being
dominant, designated Ma. On the other hand, although Visser
et al. (1968) observed discontinuous distribution in someprogeny, they questioned the segregation ratio 1 : 3 because
the segregation ratios varied greatly in the progeny. Afterwards, Visser and Verhaegh (1978) indicated that the mode ofinheritance of acidity could be explained by an additive genetic
action model (polygene). In our study, no distinct discontinuity
in the distribution of acidity was observed in the low-value
range, around 0.3 g/100 ml in TA (Fig. 3). One possibility isthat parent cultivars used for making crosses in the earlystudies diﬀer largely from those in our study. Both excessively
sweet (<0.2% in malic acid) and sour (>0.9%) parent
cultivars were used in the early studies (Brown and Harvey1971). Those are old cultivars that have not been used inmodern breeding programmes because of the low quality of the
fruit. In our study, TA in parental cultivars ranged from 0.31–
0.83 g/100 ml (=%) (Fig. 2). Therefore, acidity in the progeny

Fig. 5: Proportion of progeny having titratable acidity (TA) at 0.35–
0.45 g/100 ml obtained from three combinations of acid genotypes
with mid-parent values in the range of 0.2–0.6 g/100 ml TA. The
proportion was estimated from the genetic parameters reported inTable 2

327

obtained from the parents with moderate acidity has a compact
range relative to that in the early studies, and excessive lowacid genotypes had probably not been segregated. Kouassi
et al. (2009) estimated a heritability of TA at 0.79 using 2207
pedigreed genotypes with 132 founders from breeding programmes in six European countries. In our study, when theeﬀect of a major gene was included in the polygenes, theheritability of TA was 0.73 (Table 2) and nearly identical to theestimate above. One of the reasons is that the constitution ofcultivars used in our breeding was similar to that in Europe. All
the original parental cultivars in our study are also used in thebreeding programmes in Europe, except for ÔIndoÕ, which
originated in Japan. Noiton and Alspach (1996) analysed thepedigrees of 50 apple cultivars produced from modern breeding
programmes around the world and reported that ÔCoxÕs
Orange PippinÕ, ÔGolden DeliciousÕ, ÔRed DeliciousÕ, ÔJonathanÕ
and ÔMcIntoshÕ were the most frequent ancestors. One of the
ﬁve cultivars was also an ancestor of each of the progenies usedin our study. Therefore, our results are adaptable to modern
apple breeding programmes throughout the world.
Recent studies of molecular markers and genetic linkage
maps have tried to identify loci closely related to acidity andthe positions of the loci on apple linkage maps. Maliepaard
et al. (1998) evaluated acidity using pH-indicator paper in aseedling population from ÔPrimaÕ · ÔFiestaÕ under the following assumptions: pH values lower than 3.8 were considered toindicate the presence of the Ma gene; and genotypes with pH
values >3.8 were considered to be of the mama recessive
genotype and the parents, heterozygous Mama. The Ma gene
was then mapped to the distal end of the linkage group (LG)
16. Liebhard et al. (2003) indicated that fruit from trees
carrying two acidity alleles on LG8 and LG16 showed anaverage of 1.12% in TA and fruit from trees carrying no
acidity allele showed an average of 0.58% in TA. The values
were close to our data that the genotype means of high-acidand moderate-acid types were 0.92 and 0.45–0.52 g/100 ml(%), respectively (Table 2).
Malic acid accumulates in young fruit up to about 1.5 g/
100 g fresh weight and decreases during growth and ripening(Ulrich 1970). The diﬀerence in malic acid content between ahigh-acid genotype and a low-acid genotype was unrelated toeither malic acid synthesis or the degradation activity of malic
enzyme (Beruter 2004). The low content of malic acid in the
low-acid genotype was suggested to be the result of a restrictedability to accumulate malic acid in parenchyma cells. Yao
et al. (2007) isolated a gene, Mal-DDNA, expressed diﬀerently
between a low- and a high-acid genotype, and the transcriptionof the Mal-DDNA was much higher in genotypes with low
acidity than in those with high acidity, indicating that the MalDDNA was related to the low-acid characteristic. Yao et al.
(2009) recently revealed that the activity of malic enzyme, bywhich malic acid is degraded, was higher in ripening fruit of
the low-acid genotype than in that of a high-acid genotype.
These results indicate that malic acid is down-regulated byseveral genetic factors during the ripening stage. A dominant
allele of the major gene involved in making acidity lower,
estimated in our study, may regulate the ability to accumulate
malic acid in parenchyma cells or may promote the degradation of malic acid.
The estimated distributions of acidity were not signiﬁcantly
diﬀerent between the AA and Aa genotypes (Fig. 4). However,the proportions of progeny with adequate acidity weresigniﬁcantly diﬀerent depending on which genotype was used328

as parents for the crossing (Fig. 5). In other words, theproportion will be lower when progenies are obtained from across of Aa · Aa. Therefore, it is very important to know the
genotypes of parental cultivars before crossing. To estimate thegenotypes of many parental cultivars, the segregation analysis
performed in our study using a large complex pedigree fromthe breeding population is useful for breeders because only
phenotypic records from a pedigreed population are required.
The identiﬁcation of QTL for many characteristics has beenthoroughly reported in fruit tree studies. However, molecularmarkers that are close to the genes underlying the characteristics are only developed using restricted populations derived
from crossing between a few cultivars. Therefore, it isuncertain whether the markers can be useful to other cultivars
and whether the QTL localized to the maps of a particular
cultivar are valid for other cultivars.
In this study, crosses between high-acid genotypes (Aa · aa
or aa · aa) were absent because the objective of our breeding
programme was to produce dessert apples. To verify theaccuracy of the acid genotypes estimated, it will be necessary
to incorporate high-acid cultivars into the pedigree population
analysed.

References
Almasy, L., and D. M. Warren, 2005: Software for quantitative trait
analysis. Hum. Genomics 2, 191—195.
Beruter, J., 2004: Carbohydrate metabolism in two apple genotypes
that differ in malate accumulation. J. Plant Physiol. 161,
1011—1029.
Brown, A. G., and D. M. Harvey, 1971: The nature and inheritance ofsweetness and acidity in the cultivated apple. Euphytica 20, 68—80.
Hasstedt, S. J., 2008: Pedigree Analysis Package. University of Utah,
Salt Lake City.
Kingston, C. M., 1992: Maturity indices for apple and pear. Hortic.
Rev. 13, 407—432.
Kouassi, A. B., C. E. Durel, F. Costa, S. Tartarini, E. van de Weg,
K. Evans, F. Fernandez-Fernandez, C. Govan, A. Boudichevskaja,
F. Dunemann, A. Antoﬁe, M. Lateur, M. Stankiewicz-Kosyl,
A. Soska, K. Tomala, M. Lewandowski, K. Rutkovski, E.
Zurawicz, W. Guerra, and F. Laurens, 2009: Estimation of genetic

H. Iwanami, S. Moriya, N. Kotoda et al.
parameters and prediction of breeding values for apple fruit-quality
traits using pedigreed plant material in Europe. Tree Genet.
Genomes 5, 659—672.
Liebhard, R., M. Kellerhals, W. Pfammatter, M. Jertmini, andC. Gessler, 2003: Mapping quantitative physiological traits in apple(Malus · domestica Borkh.). Plant Mol. Biol. 52, 511—526.
Lynch, M., and B. Walsh, 1998: Genetics and Analysis of Quantitative
Traits. Sinauer Associates, Sunderland, MA.
Maliepaard, C., F. H. Alston, G. van Arkel, L. M. Brown,
E. Chevreau, F. Dunemann, K. M. Evans, S. Gardiner, P. Guilford,
A. W. van Heusden, J. Janse, F. Laurens, J. R. Lynn,
A. G. Manganaris, A. P. M. den Nijs, N. Periam, E. Rikkerink,
P. Roche, C. Ryder, S. Sansavini, H. Schmidt, S. Tartarini, J. J.
Verhaegh, M. Vrielink-van Ginkel, and G. J. King, 1998: Aligning
male and female linkage maps of apple (Malus pumila Mill.) using
multi-allelic markers. Theor. Appl. Genet. 97, 60—73.
Neuman, R. J., J. M. Kwon, L. Jilek-Aall, H. T. Rwiza, J. P. Rice, and
P. J. Goodfellow, 1995: Genetic analysis of Kifafa, a complex
familial seizure disorder. Am. J. Hum. Genet. 57, 902—910.
Noiton, D. A. M., and P. A. Alspach, 1996: Founding clones,
inbreeding, coancestry, and status number of modern apple cultivars. J. Am. Soc. Hort. Sci. 121, 773—782.
Nybom, N., 1959: On the inheritance of acidity in cultivated apples.
Hereditas 45, 332—350.
Snow, G. L., and E. M. Wijsman, 1998: Pedigree Analysis Package(PAP) vs. MORGAN: model selection and hypothesis testing on alarge pedigree. Genet. Epidemiol. 15, 355—369.
Ulrich, R., 1970: Organic acids. In: A. C. Hulme (ed.), The
Biochemistry of Fruits and their Products, vol. 1, 89—118.
Academic Press, London.
Visser, T., and J. J. Verhaegh, 1978: Inheritance and selection of somefruit characters of apple. I. Inheirtance of low and high acidity.
Euphytica 27, 753—760.
Visser, T., A. A. Schaap, and D. P. de Vries, 1968: Acidity andsweetness in apple and pear. Euphytica 17, 153—167.
Yao, Y. X., M. Li, Z. Liu, Y. J. Hao, and H. Zhai, 2007: A novel
gene, screened by cDNA-AFLP approach, contributes to lowering the acidity of fruit in apple. Plant Physiol. Biochem. 45,
139—145.
Yao, Y. X., M. Li, Z. Liu, C. X. You, D. M. Wang, H. Zhai, andY. J. Hao, 2009: Molecular cloning of three malic acid related genes
MdPEPC, MdVHA-A, MdcyME and their expression analysis inapple fruits. Sci. Hortic. 122, 404—408.