Genetic analysis of the corolla tube merged degree and the relative number of ray florets in chrysanthemum (Chrysanthemum × morifolium Ramat.)

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Genetic analysis of the corolla tube merged degree and the relative number of ray florets in chrysanthemum (Chrysanthemum × morifolium Ramat.) ⁎

Xuebin Song, Xiaogang Zhao, Guangxun Fan, Kang Gao, Silan Dai , Mengmeng Zhang, Chaofeng Ma, Xiaoyun Wu Beijing Key Laboratory of Ornamental Plants Germplasm Innovation & Molecular Breeding, National Engineering Research Center for Floriculture, Beijing Laboratory of Urban and Rural Ecological Environment, Key Laboratory of Genetics and Breeding in Forest Trees and Ornamental Plants of Ministry of Education, School of Landscape Architecture, Beijing Forestry University, 100083, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Chrysanthemum Corolla tube merged degree Relative number of ray florets Flower type Genetic analysis

Flower type is an important quality trait of ornamental plants. Mastering genetic variation in flower types is of practical significance for breeding improved flower types. Chrysanthemum (non-anemone type) flowers consist of several elements; both ray floret shape and the relative number of ray florets (RNRF) on the capitulum are very important factors. However, until recently, few reports have standardized chrysanthemum flower type evaluations, hindering the development of genetic studies of chrysanthemum flower types. In this study, as an important index of ray floret shape, the corolla tube merged degree (CTMD) was defined as the corolla tube length/ray floret length (CTL/RFL). In addition, the number of ray florets/number of florets (NRF/NF) was used to describe the RNRF on the capitulum. Major gene and polygene mixed inheritance analyses were conducted based on 2 F1 populations from 2 pairs of parents that strongly differed in the CTMD and RNRF. ANOVA revealed that all traits strongly significantly differed among the different hybrids, and correlation analysis revealed that the CTMD and RNRF might have evolved independently. Additionally, according to the Q-mode cluster analysis results, we divided the RNRF into 4 levels: single, semi-double I, semi-double II and double. Genetic analysis revealed that both the CTMD and RNRF could be described by a B-2 genetic model via two additive-dominance major genes. In addition, the heritability of the major genes for these traits was greater than 50%, indicating that the CTMD and RNRF were controlled mainly by genetic factors. These results will provide a new theoretical basis for further improvement and breeding of chrysanthemum flower types.

1. Introduction As valuable flowering plants, chrysanthemums are popular as potted and cut flowers, as groundcover and as garden plant worldwide. Moreover, with their various rich and unique flower types, chrysanthemums are important ornamental plants in the flowering plant kingdom. The study of flower types not only helps improve the understanding of flower shapes but also has practical significance for directing breeding efforts to improve flower types of chrysanthemum cultivars. Chrysanthemum flowers involve many elements, including ray floret shape, ray floret orientation on the capitulum and the relative number of ray florets (RNRF), the latter of which is the proportion of

the number of ray florets (NRF) on the capitulum. For chrysanthemums whose disc florets have not become elongated or colored (non-anemone form), ray floret shape and the RNRF are important with respect to flower type (Dejong and Drennan, 1984; Anderson, 2006; Lim et al., 2014). Ray floret shape also affects petal type, including the corolla tube merged degree (CTMD), the shape of the ray floret tips, and the bending state of the ray florets. The chrysanthemum ray floret shape has often been described as flat, spoon and tubular (Anderson, 2006). On the basis of the CTMD, Dejong and Drennan (1984) divided chrysanthemum petal types into 5 classes: flat, spoon I, spoon II, spoon III and tubular. Most researchers in China consider that the petals of

Abbreviations: ID, inflorescence diameter; CDFD, center disc flower diameter; CDFD/ID, center disc flower diameter/inflorescence diameter; NWRF, number of whorls of ray floret; NWDF, number of whorls of disc floret; NWF, number of whorls of florets; NWRF/NWF, number of whorls of ray floret/number of whorls of florets; NRF, number of ray florets; NDF, number of disc florets; NF, number of florets; NRF/NF, number of ray florets/number of florets; RFL, ray floret length; CTL, corolla tube length; CTL/RFL, corolla tube length/ray floret length; RFW, ray floret width; CTMD, corolla tube merged degree; RNRF, relative number of ray florets ⁎ Corresponding author. E-mail address: [email protected] (S. Dai). https://doi.org/10.1016/j.scienta.2018.07.010 Received 25 April 2018; Received in revised form 9 July 2018; Accepted 11 July 2018 0304-4238/ © 2018 Published by Elsevier B.V.

Please cite this article as: Song, X., Scientia Horticulturae (2018), https://doi.org/10.1016/j.scienta.2018.07.010

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pseudo-testcross strategies have shown that most important quantitative characteristics of chrysanthemum, such as inflorescence traits in small-flower chrysanthemum, salt tolerance in chrysanthemum, intergeneric chrysanthemum hybrid formation, and branch traits in cut chrysanthemum, are in line with the major gene plus polygene mixed inheritance phenomenon (Zhang et al., 2011; Xu et al., 2013; Peng et al., 2013). Importantly, Zhang et al. (2010a) used the major gene plus polygene mixed model to investigate the inheritance of THE quantitative floral traits of chrysanthemum and reported that the inheritance of some traits (inflorescence diameter [ID], center disc flower diameter [CDFD], the number of whorls of ray florets [NWRF] and the number of whorls of disc florets [NWDF]) were controlled by one or two major genes, with the major gene heritability being greater than 50%. In addition, other traits (ray floret length [RFL] and width) were largely influenced by environmental factors and might be controlled by polygenes. Although mixed model genetic analyses of some quantitative floral traits of chrysanthemum were carried out, descriptions of the CTMD and RNRF are lacking. Hence, we still do not fully understand the inheritance of flower type. It is ultimately necessary to establish accurate evaluation standards for the CTMD and RNRF and to genetic analyze these two traits. This study aimed to establish evaluation standards for the two key elements of chrysanthemum flower type: CTMD and RNRF. In addition, the objective purposes of this study were to better understand the genetic mechanisms that control chrysanthemum flower type and to establish a foundation for the development of genetic markers closely linked to chrysanthemum flower type, both of which would contribute greatly to breeding new flower types and the study of floral organ development.

Chinese large-flowered chrysanthemums can be divided into 5 types (Chinese Chrysanthemum Society, 1993; Zhang and Dai, 2013). The five petal types include flat, spoon, tubular, peculiar (appearing peculiar on the tips of ray florets [TRFs]) and anemone (change in disc florets); the flat, spoon, and tubular classifications are based on the CTMD. Therefore, the CTMD is the most important index of ray floret shape. Accordingly, by analyzing hybrid segregation ratios, researchers have found that the CTMD inheritance depends on the parent types (Dejong and Drennan, 1984) or that the heredity might be matroclinal (Xu et al., 2000). However, the CTMD, as an important trait for determining ray floret shape, has not been clearly defined thus far. Moreover, the description of flower doubleness is mainly based on the RNRF, which has been classified as single, semi-double or double. However, until now, there have been no uniform evaluation criteria for the RNRF; often, criteria have depended on artificial classification. For example, ray florets that extend past the diameter of the capitulum (0–90%) and small cushions of disc florets visible in the center have been defined as semi-double (Lim et al., 2014), while ray florets that extend across 50–75% of the diameter of the capitulum has also been defined as semi-double in other studies (Dejong and Drennan, 1984). Consequently, the genetic analysis of chrysanthemum RNRF is very different. Some research has shown that the single type was partially dominant over the double type (Dejong and Drennan, 1984), and other studies have suggested incomplete dominance is at play for the double type. In conclusion, both the CTMD and RNRF are essential for classifying chrysanthemum flower type. Nevertheless, establishing a unified evaluation standard for both the CTMD and RNRF is necessary. The CTMD and RNRF are two important target traits for developing new varieties of chrysanthemum (Anderson, 2006; Lim et al., 2014). Breeders tend to breed cultivars that have relatively high values of RNRF (such as full-double types) and CTMD (such as tubular types), as these traits increase ornamental value. Moreover, we found that there were significant correlations between the CTMD, RNRF and duration of flowering. In other words, the double type of chrysanthemum has a longer flowering duration than does the single type, and the tubular type has a longer flowering duration than does the flat type. However, compared with the other types, the full-double type and the tubular type often exhibit less heredity (Lim et al., 2014). Therefore, with respect to chrysanthemum breeding, understanding the inheritance of the two traits is very important. These traits clearly are quantitative in nature. Genes controlling the inheritance of quantitative traits are quite different from those controlling the genetic effects of quality traits; these genes might be major genes, polygenes, or both. Consequently, a mixed inheritance model of major genes plus polygenes was proposed (Elston and Stewart, 1973). This mixed inheritance model was first developed for use with humans and animals (Morton and Maclean, 1974; Knott et al., 1991; Shoukri and McLachlan, 1994). Due to the differences in mating systems between plants and animals, the data analysis method for mixed models of plants was developed later (Elkind and Cahaner, 1986; Elkind et al., 1990). Single-generation segregation analysis and joint segregation analysis (JAS) of multiple generations for evaluating the genetic effects of major genes plus polygenes and heritability values in plants have been reported (Gai and Wang, 1998; Zhang et al., 2003; Gai et al., 2003). This method has been widely used to genetically analyze quantitative traits in vegetables and crops, including resistance to agromyzid beanfly in soybean (Wang and Gai, 2001); flowering time in chickpea (Anbessa et al., 2006); flowering time in upland cotton (Hao et al., 2008); the number of seeds per silique in winter rape (Zhang et al., 2010); grain-filling duration in wheat (Khan et al., 2014; Ullah et al., 2014); melon aphid resistance in cucumber (Liang et al., 2015); fruit cracking resistance in melon (Qi et al., 2015); and plant architecture traits of crape myrtle (Ye et al., 2017). These studies have greatly improved the study of the genetic mechanisms of agronomic traits and have improved the breeding of quality traits in crop species. Studies involving the mixed inheritance model method and double-

2. Materials and methods 2.1. Plant material A total of 461 F1 plants (142 and 319 for cross I and cross II, respectively) were generated from two pairs of parents (after years of asexual reproduction, the traits were stably inherited) that have distinctly different flower types (Fig. 1). In cross I, the flower type (CTMD and RNRF) of the female parent ‘388Q-76’ was double and flat, while that of the male parent ‘Hongchi’ was single and tubular. In cross II, the flower type of the female parent ‘Candy’ was double and flat; the male parent ‘225’, single and tubular. All materials for the experiment were stored at the Nursery of the Beijing Forestry University, Beijing, China. Typical amounts of water and fertilizer were supplied during this period, and plant diseases and insect pests were controlled. The whole growth process took place under natural conditions in the greenhouse, and the chrysanthemums blossomed from September to October. 2.2. Phenotyping Crosses by hand pollination were performed to generate F1 seed during autumn in 2013. The F1 hybrids were grown from seed during the first year, after which they were propagated via cuttings. First, 3 plants of each line were selected randomly to obtain statistical data for this experiment. Second, the inner, middle and outer whorls of the chrysanthemums were measured when there were more than 3 whorls per chrysanthemum, while the entire whorl of the chrysanthemum was measured if it had only one or two whorls. Third, a ray floret at every 120° on each whorl was selected, and the average of 3 ray florets was calculated as the representative of each whorl. Thirteen characteristics of the parents and F1 hybrids were investigated during the flowering periods in autumn of 2015 and 2016 (Table 1 and Fig. 2). In this study, the ratio of the CTL and RFL (CTL/ RFL) was used to describe the CTMD trait. The ratio of the number of ray flowers and NDF (NRF/NDF) was used to describe the RNRF trait. In addition, the ratio of the NWRF and the number of whorls of florets 2

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Fig. 1. Two pairs of chrysanthemum parents and differences in the CTMD and RNRF in the F1 population. (a-1) female parent ‘388Q-76’ of cross I; (a-2) male parent ‘Hongchi’ of cross I; (b-1) female parent ‘Candy’ of cross II; (b-2) male parent ‘225’ of cross II. The scale represents 1 cm.

and ANOVA was performed. Pearson’s correlation analysis and cluster analysis (R-mode) were carried out to analyze the relationships between different characters, and cluster analysis (Q-mode) was performed for all of the cultivars. A cluster method with group linkage, a Euclidean distance reference point, and Z-score data standardization were adopted. The F1 chrysanthemum population was considered a pseudo F2 population for genetic analysis in accordance with the double-pseudo-

(NWRF/NWF) as well as the CDFD/ID ratio could also be used to describe the RNRF (Dejong and Drennan, 1984; Cardoso et al., 2010). 2.3. Data analysis IBM SPSS Statistics 20.0 software was used to calculate and test all statistical data. Mean values, standard deviations, and coefficients of variation (CV % = standard deviations / mean values) were calculated, Table 1 Thirteen floral morphological characteristics and their measurement methods. No.

Traits

Abb.

Measurement methods

C1 C2 C3

Inflorescence diameter/cm Center disc flower diameter/cm Center disc flower diameter/inflorescence diameter Number of whorls of ray florets Number of whorls of disc florets Number of whorls of ray florets/Number of whorls of florets Number of ray florets Number of disc florets Number of ray florets/number of florets

ID CDFD CDFD/ID

The maximal transverse diameter of the capitulum (Fig. 2) The maximal transverse diameter of the center disc florets (Fig. 2) The ratio of the center disc flower diameter and inflorescence diameter (Fig. 2)

NWRF NWDF NWRF/NWF NRF NDF NRF/NF

Ray floret length/cm Corolla tube length/cm Corolla tube length/ray floret length (corolla tube merged degree) Ray floret width

RFL CTL CTL/RFL (CTMD) RFW

The number of whorls of ray florets on the whole capitulum The number of whorls of disc florets on the whole capitulum The ratio of the number of whorls of ray floret and the number of whorls of florets; the number of whorls of florets is the sum of the number of whorls of ray florets and disk florets on the capitulum The number of ray florets The number of disc florets The ratio of the number of ray florets and number of florets; the number of florets is the sum of the number of ray florets and disk florets The maximal length of ray florets (Fig. 2) The distance from the tip of the corolla tube (TCT) to the bottom of ray florets (BRF) (Fig. 2) The ratio of corolla tube length and ray floret length (Fig. 2)

C4 C5 C6 C7 C8 C9 C10 C11 C12 C13

The maximal corolla splitting (flat and spoon type) or the coalescent corolla (tubular type) width

3

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Fig. 2. Schematic plots of the morphological characteristics and measurement methods. Ray floret length (RFL), corolla tube length (CTL), split corolla length (CSL), tip of ray florets (TRF), tip of the corolla tube (TCT), bottom of ray florets (BRF), center disc flower diameter (CDFD), and inflorescence diameter (ID).

When the NWRF was greater than two, these four traits were significantly correlated between the different whorls (r > 0.74) and were linearly correlated with floret whorls (r > 0.92) (Supplemental Fig. 1, Supplemental Table 1). When the NWRF was fewer than 2, the same 4 traits were also significantly correlated between the different whorls, and the correlation coefficients were greater than 0.895 (Supplemental Table 2). Therefore, these characteristics that can describe the ray flower shape tended to decrease linearly from the outer to the inner whorls of the chrysanthemums. Subsequent calculations and analyses were based mainly on the outer whorls of the chrysanthemums.

testcross strategy. A single-generation segregation analysis as described by Gai and Wang (1998); Gai et al. (2003) and Zhang et al. (2011) was used to analyze the mixed inheritance model of chrysanthemum flower type. A total of 11 kinds of genetic models were included; the genetic parameters of each trait were calculated, including the maximum likelihood value (MLV) and Akaike’s information criterion (AIC) (Akaike, 1977). The best-fitting genetic model according to the minimum AIC value was screened and filtered. The selected model was then evaluated by a goodness-of-fit test based on 5 statistical parameters, including U12, U22, U32, Smirnov’s statistics (nW2) and Kolmogorov’s statistics (Dn). In the end, the major gene heritability was calculated based on the equation h2mg = σ2mg / σ2p (σ2mg means major gene variance, σ2p means phenotypic variance). The equation of dominancy was r = h / d (d means the additive effect of major genes, h means the dominant effect of major genes). The analysis software used (SEgregation Analysis [SEA]) was provided by Professor Yuan-ming Zhang, National Key Laboratory of Crop Genetics and Germplasm Enhancement, Soybean Research Institute, Nanjing Agricultural University.

3.3. ANOVA of and correlations between 13 quantitative traits The ANOVA results of the 13 quantitative traits within lines showed that there were no significant differences in CDFD/ID, NWRF, NWDF, NWRF/NWF, NRF, NDF, NRF/NF, CTL, or CTL/RFL. These 9 traits were highly consistent within lines, and the environment had little influence on them. On the other hand, very significant differences in ID, CDFD, RFL and RFW occurred within lines (Table 2). These 4 traits presented a low degree of consistency within lines, and environment greatly influenced these traits. The ANOVA results of the 13 quantitative traits between lines showed that highly significant differences occurred among all traits. The CVs of the 13 traits revealed great separation of the quantitative traits of the hybrids (23.98–74.67%); all CVs were greater than 15%. The CV of the NRF (50.93%) was greater than that of the ID (23.98%), suggesting that the NF was more abundant in the morphological variation in flower head shape. In addition, both the RFW (CV = 25.2%) and RFL (CV = 26.98%) values were lower than that of the CTL (CV = 74.67%). These results showed that the variation in CTL is more prominent in the morphological variation in ray flower shape. In addition, the variation in the traits of CTL/RFL (56.28%), NWRF/NWF (46.38%) and NRF/NF (44.11%) was greater than 40% (Table 2). It shows that the variation of RNRF and CTMD in hybrid progeny is very rich. The Pearson correlation analysis revealed that most of the studied traits were correlated with each other, and a strong degree of correlation occurred between some traits. Logical correlations were observed between the ID, RFL and RFW; CTL and CTL/RFL; NWRF, NWRF/NWF, NRF and NRF/NF; and CDFD and NDF, NWDF and CDFD/ID, indicating that a positive connection existed between these correlated traits and

3. Results 3.1. Origins of CTMD and RNRF The morphological variation in ray florets among the hybrids was extremely abundant. We found that, when the RFL, CTL or split corolla length (CSL) was the same, the CTMD (CTL/RFL) was different (Fig. 3), although this occurred only if the measurements of the three traits were unable to fully describe the CTMD. Therefore, CTL/RFL was used to describe the CTMD in this study. Similarly, when the NRF, NDF or NF was the same, the flower doubleness (RNRF, NRF/NF) was different (Fig. 4). Therefore, NRF/NF was used to describe the RNRF in this study. 3.2. Phenotypic variation in ray florets from the outer to the inner whorls on the chrysanthemum capitulum The outer to the inner whorls of the chrysanthemum capitulum of 465 individual plants (all hybrids and their parents) were measured, and the RFL, CTL, CTL/RFL and ray floret width (RFW) were analyzed for possible relationships between different the whorls of the florets. 4

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Fig. 3. Different morphological variation in ray florets among hybrids. (a) equal RFL and different CTL/RFL; (b) equal CTL and different CTL/RFL; (c) equal CSL and different CSL/RFL; (d) equal CTL/RFL. Ray floret length (RFL), corolla tube length (CTL), and split corolla length (CSL). The scale represents 0.5 cm.

CDFD/ID, and NRF/NF were also observed, but these correlations were weak (the correlation coefficients were less than 0.2) (Table 3). Therefore, it is inferred that the CTMD and RNRF might have evolved independently.

that the traits were selected correctly. Significant correlations (correlation coefficient > 0.7) were observed between CDFD/ID, NWRF/ NWF, and NRF/NF, suggesting that the 3 traits had common characteristics that can describe the RNRF. Correlations between CTL/RFL,

Fig. 4. Different morphological variation in flower heads under different NFs. (a) equal NRF and different flower doubleness (NRF/NF); (b) equal NDF and different flower doubleness (NRF/NF); (c) equal NF and different flower doubleness (NRF/NF); (d) equal NRF/NF and equal flower doubleness (NRF/NF). Number of ray florets (NRF), number of disc florets (NDF), and number of florets (NF). 5

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Table 2 Descriptive statistical results of 13 quantitative traits. Traits

Minimum

Maximum

Mean

Std. Deviation

CV %

P-values Between lines

ID CDFD CDFD/ID NWRF NWDF NWRF/NWF NRF NDF NRF/NF RFL CTL CTL/RFL RFW

2.19 0.00 0.00 1.00 0.00 0.10 23.67 4.33 0.11 0.86 0.16 0.10 0.28

8.18 2.00 0.50 13.00 10.00 1.00 290.00 253.00 0.98 4.69 3.70 1.00 1.04

4.57 1.19 0.27 3.82 6.00 0.38 83.89 108.13 0.43 2.13 0.86 0.38 0.53

1.10 0.34 0.08 2.04 1.78 0.18 42.27 41.19 0.19 0.58 0.64 0.21 0.13

Within lines

**

23.98 28.14 28.43 53.49 29.75 46.38 50.39 38.09 44.11 26.98 74.67 56.28 25.20

0.000** 0.000** 0.445 0.401 0.573 0.589 0.345 0.081 0.725 0.000** 0.749 0.054 0.000*

0.000 0.000** 0.000** 0.000** 0.000** 0.000** 0.000** 0.000** 0.000** 0.000** 0.000** 0.000** 0.000**

Note: * indicate significant difference at 0. 05 probability level, ** indicate significant difference at 0.01 probability level. Inflorescence diameter (ID); center disc flower diameter (CDFD); center disc floret diameter/inflorescence diameter (CDFD/ID); number of whorls of ray floret (NWRF); number of whorls of disc floret (NWDF); number of whorls of ray floret/number of whorls of florets (NWRF/NWF); number of ray florets (NRF); number of disc florets (NDF); number of ray florets/ number of florets (NRF/NF); ray florets length (RFL); corolla tube length (CTL); corolla tube length/ray floret length (CTL/RFL); ray floret width (RFW). Same as Table 3 below. Table 3 Pearson correlation analysis results of 13 traits.

ID CDFD NWRF NDFW NRF NDF RFL CTL RFW CDFD/ID NWRF/NFW NRF/NF CTL/RFL

Note:

*

ID

CDFD

NWRF

NDFW

NRF

NDF

RFL

CTL

RFW

CDFD/ID

NWRF/NFW

NRF/NF

CTL/RFL

1 0.442** −0.159** −0.109* 0.006 0.205** 0.943** 0.646** 0.744** −0.339** −0.058 −0.095* 0.143**

1 −0.708** 0.630** −0.640** 0.773** 0.413** 0.227** 0.258** 0.663** −0.734** −0.773** 0.118*

1 −0.691** 0.864** −0.684** −0.171** −0.114* −0.056 −0.606** 0.933** 0.851** 0.021

1 −0.697** 0.760** −0.121** −0.182** −0.219** 0.715** −0.870** −0.802** −0.039

1 −0.652** −0.012 0.081 0.089 −0.663** 0.845** 0.906** 0.077

1 0.168** 0.031 0.059 .613** −0.761** −0.872** 0.028

1 0.683** 0.767** −.321** −0.050 −0.074 0.136**

1 0.736** −.266** −0.001 0.060 0.133**

1 −.320** 0.062 0.045 0.086

1 −0.700** −0.719** −0.175**

1 0.902** 0.039

1 0.124**

1

indicate significant difference at 0. 05 probability level,

**

indicate significant difference at 0.01 probability level.

and semi-double I (50) types were more frequent than semi-double II (26) and double (8) types. In addition, the CTMD was divided into 3 classes based on the CTL/RFL: spoon (81) was more frequent than tubular (57) and flat (4) types. In cross II, the 319 F1 progenies for RNRF were divided into 4 classes based on the NWRF/NWF: single-type (141) and semi-double I (128) types were more frequent than semidouble II (39) and double (11) types. In addition, the CTMD was divided into 3 classes based on the CTL/RFL: spoon (180) type was more frequent than flat (113) and tubular (26) types.

3.4. Classification and distribution of the CTMD and RNRF in the F1 populations Classification of the CTMD was conducted in accordance with our previous study, which included flat, spoon and tubular types (Song et al., 2018). In addition, the CTL/RFL of flat, spoon and tubular types ranged from 0 to 0.2, 0.2 to 0.6 and 0.6 to 1.0, respectively. The following discussion mainly centers on the evaluation of the RNRF. As mentioned above, three traits, CDFD/ID, NWRF/NWF and NRF/NF, could be used to describe the RNRF. The Q-mode cluster analysis based on the three traits of 465 chrysanthemums classified the RNRF of chrysanthemums into four types (at the grading line of 10, Supplemental Fig. 2): single, semidouble I, the semidouble II and double (Fig. 5). The distribution range of each RNRF parameter is shown in Table 4. The cluster analysis results showed that NWRF/NWF and NRF/ NF could be clearly divided into 4 classes and that the boundaries between the 4 classes did not overlap each other; however, the CDFD/ID was excluded (Supplemental Fig. 3). Therefore, compared with the other indices, the NWRF/NWF and NRF/NF were determined to be more suitable as important indices for measuring the RNRF of chrysanthemums. In accordance with the abovementioned classification method, the number of progenies for the CTMD and RNRF traits in crosses I and II were counted (Fig. 6). In cross I, the 142 F1 progenies for the RNRF were divided into 4 classes based on the NWRF/NWF: single-type (58)

3.5. Selection of a best-fitting genetic model for inflorescence traits The frequency distribution of inflorescence traits of the F1 population showed that the RNRF (NRF/NF) and CTMD (CTL/RFL) behaved as continuous multimodal and skewed distributions with clear quantitative genetic characteristics (Fig. 7), which was the same for the other traits (Supplemental Fig. 4). The inheritance of quantitative traits was in line with a mixed major gene plus polygene model. In accordance with the major gene plus polygene mixed inheritance model of the quantitative traits of the single-generation segregating method, the AIC values of 11 models of chrysanthemum flower traits were calculated (Supplemental Table 3). According to the AIC minimum criteria (i.e., the genetic model close to the minimum AIC and the minimum AIC value were used for the candidate model) and goodness-of-fit test results (Supplemental Table 4), candidate models for cross I and cross II 6

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Fig. 5. Differences in the CTMD and RNRF among F1 hybrid chrysanthemums. Relative number of ray florets (RNRF), Corolla tube merged degree (CTMD). The scale represents 1 cm.

were obtained, and the possible optimal genetic model of each trait was ultimately determined (Table 5). Thus, the NWRF, NWRF/NWF, NRF, NRF/NF, CTL and CTL/RFL traits all belong to B-2 model. The two RFL and NDF traits fit A-0 model, which shows that their inheritance is controlled by polygenes. Some differences in the inheritance of the two NWDF and CTL/RFL traits were observed in different cross combinations. Theoretically, the number of populations of cross II (319) is much more than cross I (142), indicating the results of genetic analysis of flower traits based on cross II will be more reliable. Therefore, we use the results of cross II, NWDF belongs to B-1 model and CTL/RFL belongs to B-2 model. In addition, the genetic models of NWRF/NWF and NRF/NF are the same, indicating that both traits can be used to describe the RNRF.

Table 4 Distribution range of four kinds of double flowers. RNRF

CDFD/ID

NWRF/NWF

NRF/NF

Class

Single Semi-double I Semi-double II Double

(0.23,0.5] [0.23,0.35) [0.13,0.23) [0,0.13)

[0.1,0.3) [0.3,0.5) [0.5,0.75) [0.75,1.0]

[0.1,0.35) [0.35,0.55) [0.55,0.8) [0.8,1.0]

1 st class 3rd class 4th class 2nd class

Note: Center disc floret diameter/inflorescence diameter (CDFD/ID); number of whorls of ray floret/number of whorls of florets (NWRF/NWF); number of ray florets/ number of florets (NRF/NF); corolla tube length/ray floret length (CTL/ RFL).

Fig. 6. Number of progenies for the RNRF and CTMD in crosses I and II. Relative number of ray florets (RNRF), Corolla tube merged degree (CTMD). 7

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Fig. 7. Frequency distribution of inflorescence traits among the F1 population derived from two crosses. Number of ray florets/number of florets (NRF/NF), relative number of ray florets (RNRF), corolla tube length/ray floret length (CTL/RFL), and the corolla tube merged degree (CTMD); female (F), male (M).

3.6. Estimation of genetic parameters for the best-fitting model of CTMD and related traits

3.7. Estimation of genetic parameters for the best-fitting model of RNRF and related traits

In cross I, the inheritance of CTL was controlled by 2 pairs of additive-dominant major genes; the additive effect was 0.505, the dominant effect was 0.405, and the degree of dominance (ha/da and hb/db) was -0.711 and -1.712, respectively. The first pair of genes was negatively partially dominant, and the second pair was negatively overdominant. The inheritance of CTL/RFL was controlled by 2 pairs of additive major genes, whose additive effects were 0.095 and 0.246 (Table 6). The estimation of the genetic parameters of cross II was analyzed in the same way. The inheritance of CTL was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively overdominant, and the second pair was negatively partially dominant. In addition, the inheritance of CTL/RFL was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively overdominant, and the second pair was negatively partially dominant (Table 6).

Estimation of the genetic parameters of the RNRF and related traits was analyzed in the same way. In cross I, the inheritance of the NWRF was controlled by 2 pairs of additive-dominant major genes: the first pair was negatively overdominant, and the second major gene was negatively partially dominant. The inheritance of the NWDF was controlled by 2 pairs of equally dominant major genes, and the inheritance of the NRF was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively overdominant, and the second pair was negatively partially dominant. The inheritance of the NWRF/NWF was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively overdominant, and the second pair was negatively partial dominant. Last, the inheritance of the NRF/NF was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively partially dominant, and the second pair was negatively overdominant. In cross II, the inheritance of the NWRF was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively overdominant, and the second pair was negatively 8

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Table 5 Test for fitness of the genetic models of the inflorescence traits of two generations derived from two crosses. Traits

Cross I Cross II Candidate Model

Optimal Model

The genetic effects of major gene

NWRF

B-2

B-2

B-2

NWDF

B-6

B-1

B-1

NWRF/ NWF NRF

B-2

B-2

B-2

B-2

B-2

B-2

NDF NRF/NF

A-0 B-2

A-0 B-2

A-0 B-2

RFL CTL

A-0 B-2

A-0 B-2

A-0 B-2

CTL/RFL

B-3

B-2

B-2

Two major genes, additivedominance Two major genes, additivedominance-epistasis Two major genes, additivedominance Two major genes, additivedominance Polygenes Two major genes, additivedominance Polygenes Two major genes, additivedominance Two major genes, additivedominance

Table 7 Main genetic heritability of inflorescence traits in two generations derived from two crosses. Traits

Cross combination

σ2mg

h2mg(%)

σ2p

NWRF

Cross Cross Cross Cross Cross Cross Cross Cross Cross Cross Cross Cross Cross Cross

2.867 3.587 1.78 1.517 0.031 0.022 1073.657 1442.582 0.025 0.022 0.281 0.084 0.036 0.026

81.82 81.59 60.46 53.81 83.17 78.15 69.30 79.99 63.81 71.45 66.13 85.14 95.41 85.77

3.503 4.396 2.956 2.819 0.037 0.028 1549.288 1803.453 0.039 0.031 0.425 0.099 0.037 0.031

NWDF NWRF/NWF NRF NRF/NF CTL CTL/RFL

I II I II I II I II I II I II I II

Note: σ2p: phenotypic variance; σ2mg: major-gene variance; h2mg: major-gene heritability.

Note: Number of whorls of ray floret (NWRF); number of whorls of disc floret (NWDF); number of whorls of ray floret/number of whorls of florets (NWRF/ NWF); number of ray florets (NRF); number of disc florets (NDF); number of ray florets/ number of florets (NRF/NF); ray florets length (RFL); corolla tube length (CTL); corolla tube length/ray floret length (CTL/RFL). Same as Tables 6 and 7 below.

4. Discussion 4.1. Establishment of evaluation criteria for the CTMD and RNRF Several evaluation methods have been developed for defining the CTMD and RNRF. For example, the CTMD has been divided in accordance with the percentage of corolla splitting on the ray florets (Dejong and Drennan, 1984), and the RNRF has been based on the NWRF and the percentage of ray florets extending past the diameter of the capitulum (Dejong and Drennan, 1984; Lim et al., 2014). Moreover, in some other Compositae species, the percentage of the CDFD on the capitulum can also describe the RNRF (Cardoso et al., 2010). However, the CTMD and the RNRF have been distinguished as qualitative traits by direct observations for a long time; there can be a strong degree of subjectivity and identification errors in the results, which have caused many problems in subsequent classification studies and genetic analyses. In actuality, we can infer that the CTMD is the ratio of the CTL of the ray florets (or corolla split length) and RFL according to the definition above. In addition, the RNRF is the difference in the NRF or the NWRF on the capitulum; therefore, it is the ratio of the NRF and NF, the ratio of the NWRF and NWF, or the CDFD. In our study, we found that the first two ratios were better than the last index. In addition, the results of the Pearson correlation analysis in this study suggested that the CTMD and RNRF might have independently evolved. Similarly, Dejong and Drennan (1984) also reported no linkage relation between

partially dominant. The inheritance of the NWDF was controlled by 2 pairs of additive-dominant epistatic major genes, and the two pairs of major genes were positively partially dominant. Similarly, the inheritance of the NRF was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively overdominant, and the second pair was negatively partially dominant. The inheritance of the NWRF/NWF was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively overdominant, and the second pair was negatively partially dominant. Similarly, the inheritance of the NRF/NF was controlled by 2 pairs of additive-dominant major genes: the first pair of genes was negatively partially dominant, and the second pair was positively overdominant. (Table 6). In conclusion, the inheritance of the CTMD was controlled by 2 pairs of additive-dominant major genes (B-2), and the major gene heritability was greater than 80%. The inheritance of the RNRF was controlled by 2 pairs of additive-dominant major genes (B-2), and all the major gene heritability was greater than 60% (Table 7).

Table 6 Estimates of the genetic parameters of the inflorescence traits of F1 populations from two crosses. Cross combination

CrossI

Cross II

Traits

Model

m

da

db

ha

hb

i

jab

jba

l

ha/da

hb/db

NWRF NWDF NWRF/NWF NRF NRF/NF CTL CTL/RFL NWRF NWDF NWRF/NWF NRF NRF/NF CTL CTL/RFL

B-2 B-6 B-2 B-2 B-2 B-2 B-3 B-2 B-1 B-2 B-2 B -2 B-2 B-2

5.089 4.049 0.549 120.044 0.5601 1.976 0.555 6.314 5.711 0.537 120.855 0.5215 0.940 0.518

1.616 1.076 0.166 26.050 0.1291 0.505 0.095 2.378 1.178 0.173 42.952 0.1744 0.367 0.201

1.301

−2.275 \ -0.234 −36.663 −0.1805 −0.711 \ −3.347 0.581 −0.244 −60.451 −0.245 −0.517 −0.283

−0.761 \ -0.078 −22.695 −0.076 −0.237 \ −0.712 0.149 −0.052 −14.624 0.0253 −0.117 −0.070

\ \ \

\ \ \

\ \ \

\ \ \

−1.407

−0.585

\

\

\

\

\ \ −1.164 \ \

\ \ −0.149 \ \

\ \ −0.572 \ \

\ \ 0.441 \ \

\

\

\

\

-1.407 −1.407 0.715 −0.711 \ −1.407 0.493 −1.408 −1.407 −0.712 −1.407 −1.408

-0.582 −0.723 −1.584 −1.712 \ −0.473 0.128 −0.473 −0.505 1.439 −0.489 −0.511

0.134 31.380 0.1204 0.405 0.246 1.505 1.166 0.110 28.942 0.0364 0.239 0.137

Note: (m) population mean square variance; (da) the first major-gene additive effect; (db) the first major-gene additive effect; (ha) the second major-gene dominant effect; (hb) the second major-gene dominant effect; (i) epistatic effect value between da and db. (jab) epistatic effect value between da and hb; (jba) epistatic effect value between ha and db. 9

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the improvement of breeding efforts in accordance with gene effects is effective. A strong additive effect of quantitative traits is easier for obtaining breeding effects during early-generation selections. In addition, dominant effects are closely related to heterosis in the crossed generation. Epistatic effects are generated by the interactions of nonallelic genes, which play an important role in controlling the inheritance of quantitative traits. The dominant effects of the first major genes for the CTMD and RNRF were essentially the same as the additive effects or were slightly greater than the additive effects, indicating that the CTMD and RNRF exhibited heterosis in the hybrid generations and that efficient selection for such traits should be carried out in early generations. In addition, by comparing the heritability of the major genes involved in every flower trait of the two hybrid combinations, we found that both the CTMD ( h2 > 80%) and RNRF ( h2 > 60%) had high heritability ( h2 > 50%). This finding indicated that CTMD and RNRF, each of which had high heritability, were slightly influenced by the environment, which means making individual selections is better in early generations than in later ones; this finding also has implications for the directional breeding of novel flower shape characteristics in chrysanthemum. Because chrysanthemum plants are self-incompatible and highly heterozygous, the F1 population was used as a “pseudo F2” population to analyze the quantitative traits of inflorescences via singlegeneration segregation analysis, although the variation in polygenes could not be distinguished from the environmental variation. However, two parental combination pairs that greatly differ in flower type were selected, and after a comparative analysis of the two combinations, an optimal genetic model for each flower trait was obtained. In addition, we screened a large number of hybrid lines that presented high-quality plant and flower types as well as color, which may be expected to become new popular cultivars for use as potted ornamentals or groundcover.

them. 4.2. Inheritance of important inflorescence traits constituting chrysanthemum flower type The Asteraceae, whose members have a typical capitulum, is the largest family of flowering plants. In previous studies, the inheritance of flower type-related traits in the Compositae family was based mainly on the phenotypic segregation ratio of the progenies. Some studies have reported that flower doubleness in Callistephus chinensis was determined by a recessive allele (Wit, 1937; Raghava and Negi, 2001). However, Kloos et al. (2004) reported that an incomplete dominant gene controlled flower doubleness in Gerbera hybrida; this result was similar in both Helianthus annuus (Chapman et al., 2012) and Chrysanthemum × morifolium (DeJong and Drennan, 1984; Lim et al., 2014). Notably, other researchers reported wide variation in flower doubleness in the progenies of the Compositae and that they observed characteristics of quantitative characters whose inheritance was affected by excess genes (Crane et al., 1947; Samata, 1958; Serrato, 1990; Dejong and Drennan, 1984). Additionally, some researchers consider that the ray florets of the Compositae exhibit a change from bilateral asymmetry to radial symmetry, such as the change from flat (similar to lateral symmetry) to tubular (similar to radial symmetry) types in chrysanthemum ray florets. Therefore, those researchers focused on floral symmetry. For example, some studies have suggested that the genes of CYC-like played an important role in floral symmetry in Helianthus annuus (Fambrini et al., 2011; Mizzotti et al., 2015), Gerbera hybrida (Broholm et al., 2008; Juntheikki-Palovaara et al., 2014), Aster hispidus (Nakagawa and Ito, 2014) and Senecio vulgaris (Kim et al., 2008). However, many intermediate types exist between flat and tubular in chrysanthemum, that is, the ratio of CTL and RFL continuously varies among chrysanthemum groups. Given that quantitative traits can be controlled by polygenes, the genetic mechanism is complex. It is therefore necessary to study the inheritance of quantitative traits for high-quality breeding and to provide a theoretical basis for the clear and reasonable selection of generations. Unlike that of crop and vegetable species, the genetic improvement of chrysanthemum lags behind, which is attributable to its characteristics, including its complex genome, high degree of heterozygosity, inbreeding depression and self-incompatibility; therefore, it is difficult to obtain pure chrysanthemum lines (Anderson et al., 1988; Anderson and Ascher, 2000; Zhang et al., 2010b). To establish available genetic populations, a pseudo-testcross population of which the plants present high heterozygosity is often used for genetic analysis (Hemmat et al., 1994; Weeden et al., 1994; Kriegner et al., 2003; Isobe et al., 2012; Taniguchi et al., 2012; Cai et al., 2015; Zhang et al., 2015). In the present study, a single-generation segregation analysis was used to genetically analyze the CTMD and RNRF. The results showed that both the CTMD and RNRF were quantitative traits that fit a mixed inheritance model. The inheritance of both the CTMD and RNRF was controlled by 2 pairs of additive-dominant major genes. To our knowledge, this is the first report of a genetic study of the CTMD and RNRF in chrysanthemum.

5. Conclusion In the present study, we tried to establish evaluation standards for the RNRF and CTMD, two main elements that constitute chrysanthemum flower type. In addition, we found that the CTMD and RNRF might have evolved independently. Moreover, we divided the RNRF into 4 levels (single, semi-double I, semi-double II and double), which were then accurately defined. Additionally, we found that both the CTMD and RNRF were quantitative traits controlled by major genes. These results will lay a theoretical foundation for QTL studies of chrysanthemum flower type and will provide a basis for further realization of directed breeding efforts of chrysanthemum flower types in the future. Acknowledgements This study was performed under the National Natural Science Foundation of China (NO. 31530064), National Natural Science Foundation of China (NO. 31471907) and Special Research Fund for the Doctoral Program of Higher Education of China (NO. 20130014110013). We are particularly indebted to Beijing Dadongliu Nursery for providing test sites. We thank YuShan Ji and Shuo Wang for their guidance on plant material cultivation.

4.3. Application of the major gene plus polygene mixed inheritance model in chrysanthemum breeding

Appendix A. Supplementary data The major gene plus polygene mixed inheritance model shows that the related quantitative traits of flower type fit with major genes or polygenes and that both the calculated major gene effects and heritability contribute to the understanding of the genetic model of flower type. For example, when the related quantitative traits of flower type were affected by major genes, hybridization or backcrosses can be used for select target traits. In addition, some markers closely linked to these major genes can discovered by quantitative trait locus (QTL) analysis for marker-assisted breeding to improve breeding efficiency. Moreover,

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