Mapping QTL affecting the vertical distribution and seed set of soybean[Glycine max(L.) Merr.]pods

Shiping Liu,Hong Xue, Kaixin Zhang, Ping Wang, Daiqun Su, Wenbin Li, Shichao Xu,Jianan Zhang, Zhongying Qi, Yanlong Fang, Xiyu Li, Yue Wang, Xiaocui Tian, Jie Song,Jiajing Wang, Chang Yang, Sitong Jiang, Wen-Xia Li*, Hailong Ning*

Key Laboratory of Soybean Biology,Ministry of Education,Key Laboratory of Soybean Biology and Breeding/Genetics,Ministry of Agriculture,Northeast Agricultural University, Harbin 150030,Heilongjiang,China

Keywords:Soybean Pod number QTL Sowing date Vertical distribution

ABSTRACT Number of pods per plant and number of seeds per pod are quantitative, multigenic traits and important components of yield in soybean[Glycine max(L.)Merr.].Pods are distributed unevenly in the upper, middle, and lower segments of the plant and this distribution is affected by sowing date (SD). A population of four-way recombinant inbred lines (FW-RIL),containing 160 F2:8 individuals, was generated from the cross (Kenfeng 14 × Kenfeng 15) × (Heinong 48 × Kenfeng 19). A linkage map consisting of 275 simple sequence repeat(SSR)markers was used to map quantitative trait loci(QTL)associated with the production of one, two, three, and four seeds per pod in the upper, middle, and lower segments of plants at two SDs,totaling 12 measurements per SD.A wide range of variation in the twelve characteristics was observed among the four parental lines and the FW-RIL population at the two SDs.The effect of SD2(May 17,2016)on pod number was stronger than that of SD1(May 7, 2016) because the heritability of each trait in the SD1 experiment was generally greater than that of SD2. The study identified 76 QTL controlling pod number, with the phenotypic variation explained by each QTL ranging from 1.86%to 13.71%.The numbers of QTL controlling one,two,three,and four seeds per pod were 28,23,23,and 23,respectively.There were 30,28, and 28 QTL controlling the pod number in the upper, middle,and lower segments of the plant,respectively. Forty-five QTL were identified at SD1 and 38 QTL were identified at SD2. Seventeen QTL were associated with pod-number traits. The QTL qPNA1-3 was associated with the number of pods containing one seed in the middle segment of the plant at both SDs. Sixty-three QTL were published QTL (common areas existed when integrating on a map GmComposite2003 of Wm82 based on left and right markers).and 13 QTL related to pod number were newly discovered. These results provide a reference for breeders to improve soybean yield by combining advantageous alleles for these QTL.Future studies may reveal candidate genes for these QTL and identify causal alleles for markerassisted selection.

1. Introduction

Increasing yield is a major breeding objective in many crop species, including soybean [Glycine max (L.) Merr.] [1]. Pod number is a quantitative trait regulated by multiple genes and is an essential component of soybean yield [2], as is seed number per pod [3]. Soybean yield and pod number are also affected by sowing date(SD)[4].

With the development and application of marker-assisted selection (MAS), numerous quantitative trait loci (QTL) that regulate agronomic traits associated with yield have been found. As of July 2018, 48 QTL associated with pod number traits were included in the SoyBase website(https://soybase.org/search) and these QTL mapped to all linkage groups except for B2, D1a, F, and H. Ikeda et al. [5] used a recombinant inbred line (RIL) population composed of 192 lines from the cross Toyomusume × Toyoharuka, to identify three QTL associated with pod number per plant in two different environments, of which one QTL was expressed repeatedly in both environments. Liu et al. [6] used a RIL population from the cross Zhonghuang 24 × Huaxia 3 to identify four QTL associated with the number of full pods and two QTL associated with the number of flat pods on the main stem,as tested in the same location for two years,with four of these QTL detected repeatedly over two years. Shim et al. [7] reported that the number of pods per plant was regulated by two QTL in a RIL population from the cross Jiyu 69 × SS0404-T5-76. Using a RIL population from the cross of Zhongdou 29 × Zhongdou 32, Zhou et al. [8] identified one QTL controlling the production of one seed per pod, three QTL for two seeds per pod, one QTL for three seeds per pod,and two QTL for four seeds per pod; four of these QTL were detected over multiple years. Sun et al. [9] mapped 12 QTL controlling the number of pods on the main stem using a RIL population from the cross Charleston × Dongnong 594.

Previously identified QTL for pod number were detected based on the total number of pods per plant,or on the number of seeds per pod,separately,or on the numbers of full and flat pods. The advantage of these traits is that they are easy to evaluate. However, pods are unevenly distributed in the upper, middle, and lower segments of the soybean plant.Indeed, Schou et al. [10] found significant differences in the vertical distribution of pods. Wiebold et al. [11] studied the distribution of pods in eleven determinate soybean varieties and found that 53% of pods were in the upper, 40% in the middle,and 7%in the lower segment of the plant.Johnston et al.[12]studied Amsoy,an indeterminate soybean variety,and found that more than half of the pods were produced in the middle segment of the plant. Ning et al. [13] studied two RIL populations sharing a common parent, found several QTL associated with the production of one, two, three, and four seeds per pod, and identified QTL associated with number of seeds per pod in the upper,middle,and lower segments of the plant.

SD strongly influences the number of pods in soybean.Ahmed et al.[14]studied the number of pods of three soybean varieties, G-2, PB-1, and PS-5, using five SDs and found that pod number was significantly affected by SD as well as by the interaction of SD and variety. Li et al. [15] studied threesoybean varieties using four SDs and found that late sowing affects the number of pods containing two seeds and that this trait was significantly negatively correlated with plant yield.

Table 1-Characteristics measured in this study.

Biparental populations, such as F2, RIL, and introgression lines, are commonly used for identifying QTL. However, because only two alleles at any locus can be distinguished with biparental populations, it is difficult to identify QTL with similar additive effects, resulting in low stability of QTL and QTL identified number less than multiple parents population. A method for QTL mapping using populations from four-way (FW) crosses among inbred lines was first introduced by Xu [16] in 1996. More genetic differences can be estimated using populations of multiple crosses,which can increase the marker number of the genetic map. Qin et al. [17] identified QTL for yield and fiber content by analysis of a FW-cross population of upland cotton (Gossypium sp.). Ning et al. [18] constructed a genetic map of soybean from a FW-RIL population and identified 29 QTL for seed protein content and 39 for seed oil content in eight environments.

In this study, we used a FW-RIL population planted at two SDs to investigate the vertical distribution of pod number in the plant and the numbers of pods containing different numbers of seeds. Our objective was to identify QTL for pod number and provide a reference for breeders to increase soybean yield by altering the number of pods and increasing the numbers of pods with three or four seeds.

2. Materials and methods

2.1. Plant materials

The soybean varieties Kenfeng 14, Kenfeng 15, Heinong 48,and Kenfeng 19 differ substantially in morphology.In 2008,we crossed inbred lines of these parents in the following combinations, Kenfeng 14 × Kenfeng 15 and Heinong 48 × Kenfeng 19, and obtained two F1populations. In 2009,we crossed selected F1progeny from these two populations to obtain F1progeny of the FW-RIL population. We then performed five generations of inbreeding using the singleseed descent method, in which each plant from each generation is selfed and one seed is randomly taken from each selfed plant of each generation to reproduce a single plant of the next generation. By this method, we obtained a FW-RIL population containing 160 unique homozygous individuals.

Fig.1-The genetic linkage map and positions of QTL identified in this study.The labels in red indicate QTL with multiple effects and those in green indicate QTL without multiple effects.LG,linkage group;Chr,chromosome.

Fig. 1(continued)

2.2. SSR analysis and map construction

For DNA extraction,200 mg of leaf tissue from juvenile plants of each line at the four-leaf stage was collected, frozen in liquid nitrogen, and ground into powder with a mortar and pestle.Total genomic DNA was extracted by the CTAB method[19].Genetic map construction was conducted following Ning et al. [20], but an additional 121 pairs of polymorphic primers were added. In total, 638 simple sequence repeat (SSR)markers were selected based on the common map of soybean published by Cregan et al. [21] and Song et al. [22], and synthesized according to the primer sequences published on SoyBase (https://soybase.org/dlpages/index.php#ssrprimer).Among all markers, 275 showed polymorphisms among the four parents.

The genetic map was constructed in three steps: grouping markers into linkage groups, ordering all markers for each linkage group, and rippling the ordering results. First, using the public map GmComposite2003 (https://www.soybase.org/sbt/)anchor markers were placed in linkage groups.Then,the nnTwpOpt algorithm (nearest neighbor was used for tour construction and two-opt was used for tour improvement)was applied to sort the nearest-neighbor markers on each linkage group(the minimum value of nnTwpOpt algorithm in each of mapping unit), and marker distances were calculated from the estimated recombination.Rippling was then used to fine-tune the ordered linkage groups according to the SAD(Sum of Adjacent Distances) for eight SSR markers in a window, using the PLM function of GAPL 1.0 [23]. Finally, all pairs of adjacent markers in the resulting map separated by agenetic distance ≥40 cM were disconnected, reducing the length of the map.

Table 2-Statistical analyses of soybean pod numbers for four parents and their recombinant inbred line (FW-RIL)population at two sowing dates.

2.3. Field experiment

In 2016, the FW-RIL population and the parental lines were planted in double rows on ridges with length 3 m and spacing 0.7 m with a plant spacing of 0.07 m. The seeds were planted on different SDs in Harbin city, Heilongjiang Province, China(45°43′N, 126°45′E). The field experiment was laid out in a randomized block design with two replications. The first sowing date(SD1)was May 7 and the second(SD2)May 17.The chernozem soil contained (208.0 ± 24.0) mg kg-1of available potassium, (51.0 ± 2.1) mg kg-1of available phosphorus, and(118.0 ± 7.2)mg kg-1of alkali-hydrolyzable nitrogen and had a pH of 6.5. Field management followed local standards of production for soybean.

2.4. Trait measurements

Fig.2-Frequency distribution of pod location and pod type(1-4 seeds).A.number of pods in each of three(upper,middle,and lower)segments of the inflorescence;B.numbers of pods containing different numbers of seeds(1,2,3,or 4 seeds per pod);The error bars represent the standard deviation of pod-number of 160 families.

Five mature plants of the 160 lines and their parents were measured randomly in the middle of each row after the beginning of maturity and before harvest in the field for each replication.The numbers of pods containing one,two,three,and four seeds on each node from the growing point of the stem tip to the cotyledon node of the main stem were recorded. The main stem was then divided into upper,middle, and lower segments based on the total number of nodes divided by three, following Ning et al. [13] If the remainder was one, the extra node was allocated to the middle section; if it was two, one additional node was allocated to the top and the other to the lower section so that the ratio of nodes in the upper, middle, and lower segments of the plant was x: x ± 1: x. The vertical distribution of the twelve pod-number characteristics was obtained by counting the pods containing one, two, three, and four seeds in the three segments.A mean of five replications was used as the phenotypic value for the identification of QTL.The upper, middle, and lower segments of the plant were abbreviated as U,M,and L,respectively,and pods containing one, two, three, and four seeds were represented as A, B, C,and D, respectively (Table 1).

2.5. Data analysis

A general linear model(GLM)was used for analysis of variance(ANOVA)of the pod number x with the following model:

where μ is the grand mean,p is the effect of pod location on the soybean plant (upper, middle and lower), t is the effect of pod type(one-,two-,three-,and four-seed pods),G is the effect of genotype(line),p × t is the interaction effect of pod location and pod type, p × G is the interaction effect of pod location and genotype, and t × G is the interaction effect of pod type and genotype.The mixed linear model was used to estimate the variance components. The heritability of single environments was then calculated by the following formula:

where h2is broad-sense heritability,is the variance of genotype,is the variance of error, and r is the number of replications.

QTL mapping was performed by inclusive composite interval mapping (ICIM) [24,25] following Ning et al. [26]First, important markers were selected by stepwise regression using all the marker information and their effects were estimated. Then, the phenotypic data were adjusted by the linear model with stepwise regression. Finally, additive effect QTL were identified by one-dimensional scanning using a scan step of 1 cM and a LOD threshold of 2.5. The analysis of QTL mapping method mentioned above was implemented by the PLQ function of GAPL. QTL naming followed McCouch et al. [27]

3. Results

3.1. Genetic map

The soybean genetic map covered a total genomic length of 3636 cM and included 20 linkage groups(LGs).The locations of the 275 SSR markers and the order of most markers were consistent with the common genetic map.Each LG contained six to 20 markers. The genetic length of each LG ranged from 49.4 cM(LG D1a)to 319 cM(LG D2).The mean genetic length of LGs was 181.8 cM. The shortest distance between adjacent markers was 0.01 cM,the longest was 33.93 cM,and the mean interval length was 15.47 cM(Fig.1).

3.2. Phenotypic variation

The range of phenotypic variation in the FW-RIL population was higher than that of the four parents, indicating transgressive segregation of these traits(Table 2).Pod number showed significant differences in pod type and plant position.In general, seed numbers in pods followed the order three seeds ＞four seeds ＞two seeds ＞one seed and the pod number followed the order middle ＞upper ＞lower segment (Fig. 2).The kurtosis and skewness of the statistical analyses fell mostly between 0 and 1, suggesting that the population was suitable for ANOVA of related traits. An F test showed significant (P ＜0.01) differences in most of the 12 traits among the different genotypes, suggesting that the genetic variation of this population could be applied in mapping QTL for these traits(Table 2,Fig.S1).

There were large differences of heritability of each trait between the two SDs, showing that SD influenced podnumber traits (Table 2). The ANOVA revealed significant variation in pod location, pod type, and the interaction between pod location and pod type. These results showed that the number of pods per plant segment and the number ofseeds per pod are controlled by complex genetic mechanisms(Table 3).

Table 3-Analyses of variance of soybean pod numbers for four parents and their recombinant inbred line (FW-RIL)population at two sowing dates.

Table 4-Identification of QTL for soybean pod number at two sowing dates.

Table 4(continued)

3.3. QTL analysis of the distribution of pod number in plant segments

A total of 76 QTL were associated with the two SDs(Table 4,Fig.1).Among them,45 QTL were associated with SD1 and 38 with SD2 (Fig. S2). There were 17 QTL controlling more than two pod number characteristics at the same time(Fig.3).The QTL were classified according to the number of seeds per pod.Twenty-eight QTL controlling one seed per pod were detected on 14 LGs and explained 3.11% to 10.8% of phenotypic variation. Twenty-three QTL associated with two seeds per pod were identified on 16 LGs and explained 1.85%-13.1% of phenotypic variation. Twenty-three QTL associated with three seeds per pod were detected on 14 LGs, and a single QTL explained 2.01%-10.7% of phenotypic variation. Twentythree QTL associated with four seeds per pod were distributed on 16 LGs, and a single QTL explained 2.24%-10.8% of phenotypic variation(Fig.1).

The QTL were linked in 8 of 24 pod number-related traits.The phenotypic variation explained (PVE) of non-linked QTL was used to estimate the QTL detection efficiency of this population (PNUA2, PNUB1, PNMA1, PNMA2, PNLA1, PNLB1,PNLC2, and PNLD1, where the upper, middle, and lower segments of the plant are abbreviated U, M, and L, respectively,and pods containing one,two,three,and four seeds are abbreviated A, B, C, and D, respectively, and the numbers indicate SD1 and SD2.). The phenotypic variation explained (PVE)of non-linked QTL could be used to estimate the QTL detection efficiency of a traits.Among 12 traits in two sowing densities,some QTL underlying 8 traits, including PNUB, PNMA, PNLA, PNLB and PNLD in SD1,PNUA,PNMA and PNLC in SD2,were linked in same linkage group. For QTL controlling PNUB, PNUD, PNMB and PNLC detected in SD2,the total PVE were closest to their heritability,which indicated that the variation of these traits is derived largely from the QTL identified in this study. In other words, the QTL detection capacity of this population is greater for these four traits than for other traits.Also,the total PVE of QTL for PNUC in SD2 and PNLC in SD1 was greater than their heritability,suggesting that the QTL for these traits were likely to interact.

For the upper segment of the plant,30 QTL for pod number were detected, including eight QTL for PNUA on seven LGs with PVE ranging from 4.37%to 8.14%,12 QTL for PNUB on 11 LGs accounting for 2.24%-13.06% of phenotypic variation, 10 QTL for PNUC on nine LGs accounting for 3.62%-13.71% of phenotypic variation, and nine QTL for PNUD on eight LGs explaining 2.24%-10.58% of phenotypic variation. Of all QTL associated with the upper segment of the plant, four QTL contributed over 10% of the total variation and thus could be considered major QTL(Table 4).For all QTL,there were 13,13,14, and 14 synergistic allelic genotypes which contained alleles that cause an increase in pod number in Kenfeng 14,Kenfeng 15, Heinong 48, and Kenfeng 19, which could be associated with increased pod number(Table S1, Fig.S3).

For the middle segment of the plant, 28 QTL were associated with pod number, including 14 QTL for PNMA on nine LGs accounting for 3.10%-10.82%of phenotypic variation,seven QTL for PNMB on seven LGs explaining 4.92%-8.58% of phenotypic variation, four QTL for PNMC on four LGs accounting for 2.75%-9.60% of phenotypic variation, and five QTL associated with PNMD on five LGs explaining 4.05%-6.50%of phenotypic variation(Table 4).For all QTL,there were 15, 10, 14, and 10 synergistic allelic genotypes in Kenfeng 14,Kenfeng 15, Heinong 48, and Kenfeng 19, respectively, which could be associated with increased pod number(Table S1,Fig.S3).

For the lower segment of the plant,28 QTL were associated with pod number. They consisted of seven QTL for PNLA on six LGs accounting for 3.13%-7.52% of phenotypic variation,five QTL for PNLB on four LGs contributing 1.85%-9.55% of phenotypic variation,11 QTL for PNLC on nine LGs explaining 2.01%-9.29% of phenotypic variation, and nine QTL for PNLD on seven LGs explaining 3.63%-10.81%of phenotypic variation(Table 4).For all QTL,there were 14,10,11,and 14 synergistic allelic genotypes in Kenfeng 14, Kenfeng 15, Heinong 48, and Kenfeng 19, respectively, which could be associated with increased pod number(Table S1, Fig.S3).

Fig.3-Putative pleiotropic or closely linked QTL. PN, number of pods in the upper (U), middle (M), or lower (L) segments of the inflorescence,with 1(A),2(B),3(C),or 4(D)seeds per pod.For the different QTL,the phenotypic variation explained(PVE)by each QTL for each trait is represented by a different color and the log-odds score (LOD) is represented by the size of the circle.

Among the 76 intervals, 17 controlled multiple traits, 10 two traits,six three traits,and one four traits(Fig.3).

4. Discussion

4.1. The difference in heritability between total pod number and component traits

Heritability shows the extent to which genetics influence the variation of traits. The number of pods and the number of seeds per pod are important components of yield. The heritability of these traits depends on genotypic effects, but is subject to environmental variation. Heritability was estimated vary widely among studies, owing probably to differences in experimental design or population selection.For total number of pods per plant, Vieira et al. [28] reported a heritability of 18.7% in a RIL population of 118 individuals derived from the cross BARC-8 × Garimpo. Shim et al. [7]estimated a heritability was 35% in a RIL population of 200 individuals from the cross Jiyu 69 × SS0404-T5-76. Dargahiet al.[29]reported a heritability of 66%in a F2:3population of 135 individuals from the cross RI8500 × MJ0004-6.In this research we found the heritability was 49.60%for total number of pods per plant. By comparison, we could found FW-RIL showed higher heritability for total number of pods per plant than biparental RIL populations.

The seed set in pods in each segment of the plant can be regarded as a component trait in a compound trait of total pod number per plant. Wang et al. [30] found that the heritability of the sum of multiple traits is approximately the sum of the heritability of the component traits for independent QTL,whereas the genetic effect of compound traits is more complex than that of component traits influenced by linked QTL. In other studies, pod number was assessed by different classification methods and heritability was calculated separately. Palomeque et al. [31] estimated the heritability of the total number of pods per plant and the number of pods per node using 98 RIL families derived from the cross OAC Millennium × Heinong 38. The heritabilities of number of pods per plant and number of pods per node ranged from 54%to 96% and from 52% to 80%, respectively. Using a RIL population composed of 165 families from the cross of Zhongdou 29 × Zhongdou 32, Zhou et al. [8] reported that the heritabilities of the total number of pods per plant, the number of pods on the main stem, the number of pods on secondary branches,and the numbers of pods containing one,two, three, and four seeds were 45.60%, 49.04%, 58.04%,48.00%, 76.77%, 84.28%, and 92.25%, respectively. In the present study, the heritability for the grand mean of pod number per plant in each environment was 49.60%,while the heritability of single component traits ranged from 21.25% to 65.63%. The above studies found, in summary, that there are differences in heritability between the total number of pods per plant and its component traits.Thus,it may be possible to design a breeding scheme to select pods with the preferred seed-set type in the various plant segments,and this scheme could combine alleles for four-seed pods in upper,middle,and lower segment together to increase seed yield.

4.2. The advantage of identifying QTL with populations generated from multiple parents

Populations constructed from multiple parents can increase the power of detecting QTL. Compared with the narrow genetic pool of RIL populations constructed using two parents,populations generated from four-way crosses can overcome the limitation of limited genetic information,and increase the statistical power and space[16].More polymorphic molecular markers could be used in our genetic map of the FW-RIL population, increasing the number of markers of the map than bi-parental population. In terms of the efficiency of QTL detection,populations generated from four-way crosses were also superior to RIL constructed by crossing two parents. The number of QTL for pod-number traits identified by bi-parental populations ranged from three to eight in previous studies[32-34].The number of QTL from a four-way cross population was significantly increased by taking advantage of the allelic differences among the four parents[17].It would be difficult to identify many of these QTL from a population constructed from two parents with the same or similar additive effects.For example,for the QTL qPN-N-1,the additive-effect values of the four parents were - 0.25, 1.16, -0.25, and - 0.67. Given that the same additive-effect values appeared in Kenfeng 14 and Heinong 48, this QTL would be difficult to identify using the biparental population derived from the cross of Kenfeng 14 × Heinong 48. The additive-effect values of qPN-O-1 of the four parents were 1.08, -0.72, 1.09, and - 1.46. A similar situation occurred in the population from the cross of Kenfeng 14 × Heinong 48.

Fig.4- The target genotypic design using QTL mapping results for three and four-seed pods.Yellow shading represents the origin of synergistic QTL.Green shading represents the target genotype of the design.Red shading represents the QTL of the three lines that fit the target genotype.Only QTL whose PVE was ≥5%in the study are included in this fig.A indicates that the superior(in terms of highest pod number)allele for the QTL comes from Kenfeng 14;B indicates that the superior allele for the QTL comes from Kenfeng 15;C indicates that the superior allele for the QTL comes from Heinong 48;D indicates that the superior allele for the QTL comes from Kenfeng 19.

4.3. Suitability of identifying QTL in multiple environments

Because the phenotypic values used to identify quantitative traits are affected by genotype, environment, and interaction between genotype and environment, the results of QTL mapping of the same trait can change in different environments. Fulton [35] reported that QTL detected in multiple environments which measured in different genetic backgrounds or under different environmental conditions were more stable than QTL with high effect values detected in a single environment,and were more useful for breeding.Eight QTL associated with pod number were identified in three environments in chromosome segment substitution lines(CSSLs)by He et al.[33],and two of those QTL were expressed simultaneously in all three environments. Six QTL for pod number traits were identified in nine environments with different planting densities over three years by Liu et al. [36],but only one QTL was detected in multiple environments.The present study was performed with different SDs in the hope that stable QTL that are not affected by SD could be identified.However, QTL for pod number traits showed poor reproducibility at different SDs, and only one QTL (qPN-A1-3, LG: A1,46.45-71.39 cM) was identified at both SDs. These results showed that the expression of QTL for pod-number traits was influenced by SD.

4.4. Authenticity and selection of QTL

The QTL used in this study were integrated into the common map GmComposite2003, and compared with the corresponding QTL in the SoyBase website. The QTL for podnumber traits identified in this study showed high overlap with pod-number QTL identified in previous studies[13,28,37-43] (Fig. S5). Among the 76 QTL in this study, 63 crossed (shared a common region and did not share unique regions),overlapped(shared the same left and right markers),or covered (shared a common region, with only one QTL showing a unique region)QTL for pod number traits found in previous studies. The genomic regions of the other 13 QTL,qPN-A1-2, qPN-A1-5, qPN-B1-2, qPN-D2-5, qPN-G-2, qPN-K-3,qPN-K-5, qPN-M-2, qPN-M-3, qPN-N-1, qPN-N-2, qPN-O-1, and qPN-O-4, were not found in previous studies, and these QTL were assigned as new QTL for pod-number traits.

Seventeen QTL were associated with two or more pod number traits in this study (Fig. 3). Moncada et al. [44]suggested that there might be linkage or epistatic effects in regions associated with multiple traits. More traits could be explained by this kind of QTL.These QTL could speed up MAS by enabling a one-selection, multiple-effects strategy in soybean breeding.

Six QTL with PVE ＞10.0% were identified: qPN-A1-3, qPND2-5, qPN-F-3, qPN-F-4, qPN-K-3, and qPN-N-1, and were assigned as main-effect QTL.All of these QTL were associated with two or more pod-number traits.Among them,the PVE of qPN-F-3 in controlling PNUC and PNUD was higher than 10%(Table 4, Fig.S4).

4.5. Phenotypic predictions after use of QTL in breeding

The vertical distribution of pod number differed among the four parents in this study. Many of the twelve pod-number traits measured in this study showed transgressive segregation among the four parents and synergistic and subtractive(contained alleles that cause a decrease in pod number) QTL for these traits were scattered among the four parents. This finding suggests that target genotypes could be designed to meet breeding objectives. Increasing the numbers of pods with three and four seeds per pod would be a suitable breeding objective to improve yield. Nineteen QTL associated with three and four seeds per pod with PVE ≥5% were selected from the results of this study (Fig. S4). According to the QTL mapping and the values of the additive effects of each parent, we designed the genotype most suitable for this breeding objective (Fig. 4) according to a formula predicting the pod number of a genotype:

where G is the phenotypic value of a hybrid, b is the phenotypic mean of the population, n is the number of QTL,aiis the additive effect value of the ith QTL, and xiis an indicator variable for the ith QTL.

Finally, we selected the lines with target genotypes from the 160 individuals of the FW-RIL population according to the results of genotype prediction.Because it would be impossible to synthesize the target genotypes using only two lines in the population, we selected three lines from the population: FWRIL-14,FW-RIL-33,and FW-RIL-40(Fig.4).These lines could be used as parents to prepare hybrid combinations, and then MAS could be performed to combine alleles expected to increase the numbers of pods containing three and four seeds.

5. Conclusions

A total of 76 QTL were identified using 160 lines of a FW-RIL population. Among them, 30, 28, and 28 QTL were associated with pod-number traits in the upper, middle, and lower segments of the plant, respectively. The number of QTL associated with one, two, three, and four seeds per pod was 28,23,23,and 23,respectively.The expression of the QTL qPNA1-3 was stable under both SDs used in this study.Sixty-three QTL used in this study overlapped or crossed previously identified QTL. Thirteen new QTL associated with podnumber traits were identified.

Supplementary data for this article can be found online at https://doi.org/10.1016/j.cj.2019.04.004.

Declaration of Competing Interest

Authors declare that there are no conflicts of interest.

Acknowledgments

The authors gratefully acknowledge the financial support for this study provided by grants from the Natural Science Foundation of Heilongjiang Province, China (LC201610) to Hailong Ning.