Dynamic Mapping Based on Single Segment Substitution Lines for Plant Height in Rice

: 1 Background: Dynamic regulations of QTLs still remain mysterious. Single segment substitution 2 lines and conditional QTL mapping, functional QTL mappings are ideal materials and methods to 3 explore epistatic interactions, expression patterns and functions of QTLs for complex traits. 4 Results: Based on single segment substitution lines five QTLs on plant height in rice were 5 identified first in this paper, and then their epistatic interactions, expression patterns and functions 6 were systemmatically studied by tailing after each QTL. Unconditional QTL mapping showed the 7 five QTLs were with significant effects at one or more stages, all of which increased plant height 8 except QTL 1 . They interacted each other as homeostatic mechanisms to regulate plant height with 9 negative effects before 72d after transplanting and positive since then. Conditional QTL mapping 10 revealed the expression quantities and periods for the five QTLs and their epistases. Temporal 11 expression pattern was verified again by selective expressions of QTLs in specific periods. QTL 1 12 expressed negatively while QTL 2 and QTL 4 positively, mainly occurring in the periods from 35 to 13 42d and from 49 to 56d after transplanting. Epistatic expressions were dispersedly in various 14 periods, mainly with negative effects before 35d while positive since then. Functional QTL 15 mapping discovered the five QTLs brought the inflexion point ahead of schedule, accelerated the 16 growth and the degradation, and changed the peak of plant height, while their interactions had the 17 opposite effects approximately. This paper uncovered the dynamic rules of five QTLs and their 18 interactions on plant height systematically, which will be helpful to understand the genetic 19 mechanism for developmental traits. 20 Conclusions: Five single segment substitution lines were tested with significant additive, 21 dominant and epistatic effects of QTLs on plant height. Additive and dominant expressions were 22 mainly in two periods, while epistasis dispersedly. The five QTLs and their interactions 23 significantly regulated the developmental trajectory of plant height.


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Background 1 Plant type of rice, including root type, stem type, leaf type and spike type etc., is one of the 2 main factors to determine yield, and thus shaping of ideotype is an important way to improve rice 3 yield (Peng et al. 2008;Moles at el. 2009;Markel et al. 2020). Plant height is a crucial component 4 of plant type traits. On the one hand plant height is closely related to lodging resistance, plant 5 lodging during maturation surely resulting in the sharp decline of yield and quality of rice (Wang 6 et al. 2014). Development of dwarf and semi-dwarf rice cultivars has greatly increased the 7 capacity of lodging resistance and then the potentiality of yield since 1950s. On the other hand 8 plant height is a major determinant of plant's ability to compete for light because of the close 9 correlation with leaf number and leaf distribution, high stems being usually accompanied by high 10 biomass and then high grain yield (Falster and Westoby 2003;Wang and Li 2006). Given this 11 conflict ideotype suggests that suitable plant height should retain between 90cm and 120cm so as 12 to get the optimal output in cereal crop (Ren et al. 2016). Understanding the genetic basis of plant 13 height makes therefore it possible to find a balance between high yield and lodging. Specially, 14 plant height is one of relatively easily investigated traits, being able to be measured at a serious of 15 stages to allow to dynamically explore the genetic mechanism of development. Thus plant height 16 is often used as one of model traits for the study of developmental behaviors (Yan et al. 1998b;17 Cao et al. 2001;Yang et al. 2006). 18 QTL mapping is one of effective approaches to explore genetic mechanisms of quantitative 19 traits. For developmental traits like plant height, tiller number and leaf number etc., common QTL 20 mapping methods can be summarized as (1) unconditional mapping, (2) conditional mapping and 21 (3) functional mapping etc. (Xu and Zhu 2012). Unconditional QTL mapping usually analyzed 22 directly the phenotypic values measured at various growth stages, and then inferred the dynomic 23 genetic architecture of a developmental trait by longitudinal comparing of the mapping results 24 (Wu et al. 1999). Conditional QTL mapping needs to first estimate the conditional effects 25 for the phenotypic values at time ) (t given the phenotypes at time ) 1 (  t (Zhu 1995;26 Atchley and Zhu 1997), and then to conduct QTL mapping based on these estimations (Yan et al. 27 1998a, b;Wang et al. 1999;Cao et al. 2001 were transplanted to a rice field 20 days later with one plant per hill and the density of 16.7cm 1 16.7cm. Each plot consisted of four rows with ten plants per row. Local standard practices were 2 used for the management of trail. Plant height per hill on 10 central plants were measured in each 3 plot from seven days after transplanting onwards, and data every 7 days once was continuously 4 recorded nine weeks (denoted by 1 t to 9 t ). The averages of plant height in each plot for the 5 nine stages were used as input data for the subsequent analysis. 6 The Wang-Lan-Ding mathematical model 7 The phenotypic performance ) ( y of each plot during the nine measurement times ) (t can 8 be described by the equation (Wang et al. 1982): 9 In the above model, the first term is a logistic model in which the parameter K is the upper 11 limit of plant height, namely the potential maximum of plant height. 0 t is the inflexion point of 12 the logistic curve, or the optimum time. r is the growth rate and c the degradation rate. The

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DUD (do not use derivatives) method was used to estimate all parameters in the model of the 14 analysis and estimation of QTL effects were carried out with aov() and lm() functions in R 6 language (https://www.r-project.org/). 7 8

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Unconditional QTL mapping on plant height 10 Plant height approximately approached "S" type of growth curve ( Figure 2). The figure drew 11 from all 39 genotypic materials indicated that after slow, rapid growth plant height reached the 12 peak and then started to decrease slightly. Separate analysis of variance at various stages revealed 13 the significant difference of plant height existed among genotypes (Supplementary Table 1), 14 supporting the existence of QTLs on plant height in the mapping population. The contrast tests 15 found that each of the five SSSLs harbored plant height QTLs (Table 2). All carried with additive 16 and/or dominant effects detected at one or more stages (see Table 2). QTL on SSSL S 5 17 (denoted by QTL 5, similarly hereinafter) detected with significant dominant effects just at one of 18 stages perhaps was unreliable. The other QTLs repeatedly appeared guaranteed the truth of them. 19 Only did QTL 1 exhibited negative effects, the others showed to increase plant height. During the 20 early period (from 0 t to 3 t ) few QTLs were detected, while more QTLs presented to the 21 middle-late period. The variations of QTL effects with times implied the dynamicas of expressions 22 for these QTLs. 23 To understand the interaction mechanism among these QTLs, we first aggregated partly two 24 of SSSLs to generate dual segment substitution line (DSSL) and then carried out a half diallel 25 mating scheme to achieve various genotypes required so as to estimate epistasis. Four epistatic 26 components, additive-additive (aa), additive-dominance (ad), dominance-additive (da), and 1 dominance-dominance (dd), were estimated according to configurations of genotypes for seven 2 QTL pairs (Table 3). All seven pairs of j i S S / holding significantly interaction effects further 3 confirmed the prevalence of epistasis (see Table 3). Two epistatic components, 2 1 d d 4 (denoted dd of 2 1 / S S , similarly hereinafter) and 5 1 a a were detected only at one of stages, 5 which reliability was subject to further verification. The other epistatic components were 6 significant at least at two stages, which indicated the validity of these interactions. Negative 7 epistatic effects were major, while positive epistases mainly appeared at the periods of 8 t and 9 t .

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The causes of negative (positive) epistases perhaps were due to positive (negative) additive and 9 dominance effects of QTLs, which will be discussed later. All epistatic effects dynamically 10 changed with developmental stages (see Table 3).

Conditional QTL mapping on plant height 12
To acquire the net effect of a given QTL on plant height during a certain of period, we carried 13 out conditional QTL mapping. The conditional effects  Table   15 2). And then conditional QTL effects, the net effects of QTLs from time 1  t to time t , were 16 calculated based on the conditional effects Table 2). Conditional 17 QTL revealed the quantities and the stages of QTL expressions. QTL 1 had twice expressions, one 18 was in the stage from 5 t to 6 t , exhibiting -6.57 ** additive effect, and the other was from 7 t to 19 1 QTL interactions also exhibited different dynamic models (see Table 3). 2 In the early, middle and late periods, there were six, seven and thirteen significant epistatic 3 expressions, respectively. In the three periods, 3 2 t t  , 5 4 t t  and 7 6 t t  , QTLs hardly 4 expressed. There were 14 significant positive epistatic effects and 12 negative, respectively. 5 Mostly, negative expressions appeared in the early period, while positive in the late period. Some 6 of epistatic components had significant accumulated effects at certain of stages, but their 7 expression periods weren't detected due to dispersed expressing insignificantly. Inversely, some of 8 epistatic components had significant net effects in certain of stages, but didn't detect significant 9 accumulated effects due to reverse expressions. Lots of epistatic expressions were feeble so that 10 fail to be detected, while some large expressions became invisible for the reason of large error. 11 12

Functional QTL mapping on plant height 13
Functional QTL mapping is an appropriate method that passes a mathematical equation to 14 describe a biological developmental process with the genetic mapping framework (Ma et al. 2002). 15 We first applied the Wang-Lan-Ding model (Wang et al. 1982) to fit curves of plant height and to 16 estimate four functional parameters--the optimum time ) ( 0 t , the growth rate ) (r , the maximum 17 value ) (K and the degradation rate ) (c (Supplementary Table 3). And then based on these 18 estimations we carried out QTL mapping (Table 4). The five SSSLs were found to harbor QTLs 19 with additive and/or dominance to regulate the four parameters. Any one of SSSLs was associated 20 with two functional parameters at least, for which pleiotropy or close linkage of genes were 21 responsible. S 1 and S 5 involved in all of four parameters, and S 2 , S 3 and S 4 regulated 0 t or K 22 and c . For the parameter 0 t QTLs shortened the time of inflexion point on a curve. For r and 23 c , QTLs improved not only the growth rate but also the degradation rate. The impact of QTLs on 24 parameter K differed, enabling the potential of plant height to increase or decrease.

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All pairs of S i /S j held interaction effects significantly, involving in one or more parameters by 26 various epistatic components. Interactions between QTL 2 and QTL 3 , QTL 4 , QTL 5 influenced one, 1 two and three parameters, respectively. While epistatic interactions between QTL 1 and the other 2 QTLs were associated with all of the four parameters. Epistases always regulated 0 t and K 3 positively, while r and c negatively ( Table 4). The relationship that positive (negative) 4 epistasis were always derived from the interaction of negative (positive) QTLs was confirmed 5 once again. Conditional QTL mapping on the indirect estimations of conditional phenotypes can provide net 11 expression of QTLs in a time interval and the stages of QTL expressions (Wang et al. 1999;Zhu 12 1999). And functional QTL mapping on the parameters defined in a mathematical function that 13 describes the trait variation with biological significance can reveal the QTLs regulating the shape 14 and the trajectory of developmental curve (Ma et al. 2002;Wu et al. 2004Wu et al. , 2006Cui et al. 2006Cui et al. , 15 2008. In this paper we carried out systematical analysis for the dynomics of QTLs regulating the 16 developmental behavior of plant height in rice. We detected that the five SSSLs carried with 17 significant additive and/or dominant effects of QTLs on plant height at multiple developmental 18 stages. These QTLs were credible due to their repeatability of appearing. Except for QTL 1 19 exhibiting negative effects in the middle-late periods, the other QTLs showed the effects to 20 enhance plant height (see QTL(t) in Table 2). These QTLs interacted each other to form genetic 21 network to regulate plant height. Seven pairs of SSSL combinations tested were all with one or 22 more significant epistatic components to mostly reduce plant height (see QTL(t) in Table 3). QTLs 23 were characterized by temporal expression, selectively appearing significant effects in specific 24 stages of development. The five QTLs turned on mainly in the middle-late periods (see QTL(t|t-1) 25 in Table 2), whereas the seven QTL interactions dispersely in various periods (see QTL(t|t-1) in 26 Table 3). Some expressions were too small to be statistically detected. Plant height varied 27 followed by the logistic curve of the Wang-Lan-Ding model approximately (Figure 1), which was 28 determined by the parameters of 0 t , r , K and c (Wang et al. 1982). These parameters 1 changed the trajectory of growth curve of plant height including the inflection point, the growth 2 rate, the peak value and the degradation rate. Our research indicated that the four functional 3 parameters were regulated by the QTLs and the QTL interactions on the five SSSLs, each of 4 which regulated two parameters at least (Table 4). 5 6 Dynamic patterns of QTL expressions 7 One of major goals in developmental genetics is to explore gene expression (Zhu 1995;8 Atchley and Zhu 1997). Conditional QTL mapping makes this possible, which can estimate the 9 net expression of QTL in a certain of time interval (Wang et al. 1999;Zhu 1999). In theory, 10 unconditional QTL effect at time point t is the accumulation effect of QTL from initial time to 11 time t , which can be divided into several conditional QTL components, i.e.
Where conditional QTL effects were independent 13 each other, and thus were additive. According to the formula, it is possible to generate following a 14 few of cases at stage t , both were significant. The relationship between unconditional QTLs and 16 conditional QTLs was discussed in a our previous paper (Zhou et al. 2020) and was well validated 17 by the results estimated in this paper. The correlation coefficient between QTL effects at the 18 final stage 9 t and the sum of all conditional QTL effects before 9 t reached 0.9379 ** in the 19 previous paper (Zhou et al. 2020) and 0.7208 ** in this paper, respectively(data not shown). Where 20 only did a series of conditional QTLs truly reflected the expression periods and quantities of a 21 QTL throughout the whole developmental stage. Conditional QTL mapping had widely been 22 applied to reveal gene dynamic patterns for developmental traits (Yan et al. 1998a, b;Wang et al. 23 1999;Gao et al. 2001;Jiang et al. 2008;Liu et al. 2010b;Zhou et al. 2020). There were four 24 representative patterns for the genetic control of growth trajectories, permanent QTLs, early QTLs, 25 late QTLs and inverse QTLs (Wu et al. 2006). This knowledge derived from the accumulated 26 effects of QTLs, QTLs being permanent, early, late and inverse when one genotype was better than 27 the other in entire growth process, at early stages, at late stages and one genotype showed inverse 1 effects with the other since a particular stage, respectively. However, accumulated effects of QTLs 2 couldn't reflect the expression stages and quantities of QTLs. This paper indicated that QTLs on 3 plant height expressed all of additive, dominant and epistatic effects according to temporal 4 expression pattern (see QTL(t|t-1) in Table 2 and Table 3). QTLs and their interactions expressed 5 significant effects only in one or more periods, and sometimes even hadn't significant expression 6 periods while remained silent all the time. Permanent expression of QTLs was rare. QTL 1 and 7 QTL 2 expressed mainly in the late period, QTL 4 in the middle period, while QTL 3 and QTL 5 were 8 not detected significant expression periods (see QTL(t|t-1) in Table 2). Similarly, QTL 1 /QTL 2 , 9 QTL 1 /QTL 3 , QTL 1 /QTL 5 and QTL 2 /QTL 3 expressed mainly since the period 5 t , QTL 1 /QTL 4 and 10 QTL 2 /QTL 4 dispersedly in various periods, and QTL 2 /QTL 5 with inverse effects between the early 11 period and the late period (see QTL(t|t-1) in Table 3). In fact, QTLs and their interactions 12 expressed net effects in various stages, just some of which reached the levels of significance 13 statistically. Small expressions of QTLs were considered as no expressing or experimental error. 14 15

QTLs regulated developmental trajectories of temporal traits 16
Developmental theory considers if different genotypes at a given QTL correspond to different 17 developmental trajectories, the QTL must affect the differentiation of this trait (Wu et al. 2006). 18 Therefore, by estimating the functional parameters that define the trait curve of each QTL 19 genotype and testing the differences in these parameters among genotypes, one can determine 20 whether a QTL affects the formation and expression of a trait during development. In the 21 Wang-Lan-Ding model, there were four parameters to regulate the growth curves of 22 developmental traits, which might change the inflexion point ( 0 t ), the upper limit ( K ), the rise 23 speed ( r ) and the descent speed ( c ) of curves (Wang et al 1982). In this paper genotypes of five

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SSSLs differed from that of HJX74 at a given QTL (Figure 3), implying that a putative QTL 25 existed on each of SSSLs. Both unconditional QTL mapping and conditional QTL mapping 26 confirmed the existence of QTLs (Table 2). How did these QTLs affect the development of plant 27 height? Functional QTL mapping based on the estimations of the four parameters indicated that 28 QTL 1 and QTL 5 regulated all of the four parameters by additive and/or dominant effects, and the 1 other three QTLs influenced two of them, 0 t or K and c , respectively. These QTLs brought 2 the inflexion point ahead of schedule, and accelerated the growth and the degradation of plant 3 height. QTL 1 and QTL 5 made the maximum plant height shorter, while QTL 3 and QTL 4 higher 4 (Table 4). Similarly, the interactions among these QTLs also influenced the four parameters, 5 which always regulated 0 t and K positively, while r and c negatively by various epistatic 6 components (Table 4).  (Tanksley, 1993;Eshed andZamir, 1995, 1996). On the one hand target QTL can be 22  (Table 2), and then four components of epistases were estimated via analysis of 27 pyramiding materials derived from two SSSLs ( Table 3). The information is reliable due to the 28 repeated emergence of putative QTLs and their interactions at multiple stages of development. All 1 of seven pairs of SSSLs were tested with two or more significant effects of four epistatic 2 components, further confirming the prevalence of epistasis (Table 3). Epistasis may be brought 3 about by modification of gene function due to alterations in the signal-transducing pathway. 4 Epistatic genes are more deleterious in combination than separately, which are often accompanied 5 by inverse epistatic interactions as homeostatic (that is, canalizing) mechanisms (Mackay et al. 6   2014). This role of epistasis was first observed by Eshed and Zamir (1996) when they found 7 less-than-additive interactions between QTLs in tomato. We also confirmed inverse epistastic role 8 on yield traits in rice that the negative epistasis derived mainly from the interactions between 9 positive QTLs while the positive epistasis from negative QTLs (Wang et al. 2018;Zhou et al. 10 2020). In this paper, most of QTLs were detected with positive additive and/or dominance, thus 11 the estimations of epistatic components were mainly negative. Only after the stage of 6 t 12 occurred positive epistasis since negative QTLs appeared since then (Table 2 and Table 3). The 13 property of epistasis was stipulated by the calculated formula Additionally, one QTL always interacted with multiple other QTLs, forming genetic network. In 18 this paper five QTLs were detected to interact each other with one or more significant epistatic 19 components (Table 3). Of seven combinations of SSSLs set, QTL 1 , QTL 2 interacted with the other 20 four QTLs respectively, while QTL 3 , QTL 4 , QTL 5 at least with the other two QTLs. Five QTLs 21 were with various interaction magnitudes, displaying different epistatic intensities. QTL 2 and 22 QTL 4 seemed to be larger average epistatic effects and greater interoperability than the other 23 Table 4). Of four epistatic components, average estimation of dd was 24 seemingly larger than those of the others (Supplementary Table 4). Knowledge of epistatic 25 interaction will improve our understanding of genetic networks and mechanisms that underlie 26 genetic homeostasis, and improve predictions of response to artificial pyramiding breeding for 27 quantitative traits in agricultural crop species. In the future, we must assess the effects of pairwise 28 and higher order epistatic interactions between polymorphic DNA variants on molecular 29 interaction networks and, in turn, evaluate their effects on organismal phenotypes to understand 1 the mechanistic basis of epistasis (Mackay et al. 2014). Only then will we be able to go beyond 2 describing the phenomenon of epistasis to predicting and testing its consequences for genetic 3

systems. 4
Conclusions 5 Based on single segment substitution lines we systemmatically analyzed dynamic regulations 6 of five QTLs on plant height in rice. The five QTLs were with significant effects at one or more 7 stages, all of which increased plant height except QTL 1 . They interacted each other as homeostatic 8 mechanisms to regulate plant height with negative effects before 72d after transplanting and 9 positive since then. QTL 1 expressed negatively while QTL 2 and QTL 4 positively, mainly occurring 10 in the periods from 35 to 42d and from 49 to 56d after transplanting. Epistatic expressions were 11 dispersedly in various periods, mainly with negative effects before 35d while positive since then.   dd QTL(t) -10.96 ** -12.21 ** -9.67 ** -15.07 ** -14.47 ** -8.18 * -9.97 ** -9.28 * QTL(t|t-1) -10.96 ** -6.19 * -6.36 * S 2 /S 5 ad QTL(t) -12.02 ** -13.03 ** -9.56 ** -8.77 ** -8.13 ** -7.87 * QTL(t|t-1) -12.02 ** -6.43 * 6.14* dd QTL(t) -14.16 ** -11.71 ** -9.40 ** -11.66 ** -8.37 ** QTL(t|t-1) -14.16 ** 1 2  Figure Legend 2 Figure 1 The approximate lengths and locations of substitution segments on chromosomes. Chr 3 was the abbreviation of chromosome, which was followed by chromosomal number. Genetic 4 distance (cM) and marker codes were listed on the left and the right of Chr, respectively. The 5 vertical lines on the right of Chr represented substitution segments with serial number i S . The approximate lengths and locations of substitution segments on chromosomes. Chr was the abbreviation of chromosome, which was followed by chromosomal number. Genetic distance (cM) and marker codes were listed on the left and the right of Chr, respectively. The vertical lines on the right of Chr represented substitution segments with serial number Si.

Figure 2
The growth curves of 39 genotypes for plant height over time. ti represented ith stage measured, interval of 7 days. Unit of plant height was in cm.

Figure 3
Different trajectories corresponding to different genotypes at a given QTL. S0 represented the genotype (aa) of HJX74, while Si and Hi indicated the genotypes (AA and Aa) of ith single segment substitution line. ti indicated various developmental stages, the difference of 7d. Unit of plant height was in cm.

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