Detection of QTLs for genotype × environment interactions in tomato seeds and seedlings

Abstract Seed quality and seedling establishment are the most important factors affecting successful crop development. They depend on the genetic background and are acquired during seed maturation and therefor, affected by the maternal environment under which the seeds develop. There is little knowledge about the genetic and environmental factors that affect seed quality and seedling establishment. The aim of this study is to identify the loci and possible molecular mechanisms involved in acquisition of seed quality and how these are controlled by adverse maternal conditions. For this, we used a tomato recombinant inbred line (RIL) population consisting of 100 lines which were grown under two different nutritional environmental conditions, high phosphate and low nitrate. Most of the seed germination traits such as maximum germination percentage (Gmax), germination rate (t50) and uniformity (U8416) showed ample variation between genotypes and under different germination conditions. This phenotypic variation leads to identification of quantitative trait loci (QTLs) which were dependent on genetic factors, but also on the interaction with the maternal environment (QTL × E). Further studies of these QTLs may ultimately help to predict the effect of different maternal environmental conditions on seed quality and seedling establishment which will be very useful to improve the production of high‐performance seeds.


| INTRODUCTION
Tomato is one of the most important agricultural commodities due to the level of production throughout the world (4.8 million hectares with the average yield of 37 ton per hectare [FAOSTAT2016]) (Heuvelink, 2018). Moreover, tomato is of scientific importance as a model organism for fruit-bearing plants (Giovannoni, 2001;Schauer et al., 2006). Tomato producers are attempting to produce plants with high quality fruits as well as with high resistance against stressful environments, such as high temperature (HT) and osmotic stress.
Since tomato is propagated by seed, the first step to improve tomato production is improving the quality of the seeds.
One of the characteristics of seed quality is the ability of the seed to germinate quickly and uniformly, not only under optimal but especially also under stress-full germination conditions (Foolad, Subbiah, & Zhang, 2008). Furthermore, seed quality is not solely determined by germination but also by many other attributes such as genetic purity, vigour, viability and lack of any disease and damages, which all affect seed performance (Hilhorst, Finch-Savage, Buitink, Bolingue, & Leubner-Metzger, 2010;Hilhorst & Koornneef, 2007;Hilhorst & Toorop, 1997). Additionally, these quality parameters may severely affect seedling establishment and further growth of the plant and, ultimately, the success of crop production. In general, low quality seeds, for instance seeds with low vigour, lead to poor seedling establishment and finally lower and non-profitable crop yield (Finch-Savage,-1995). An important determinant of seed quality and performance is the maternal environment (ME) under which seeds develop and mature. The different environmental factors during seed development, such as temperature, light quality and quantity as well as nutrients may affect ultimate seed quality. Therefore, seed quality is defined by both the genetics (G) and the environment (E), as well as their interaction (G × E) (Koornneef, Bentsink, & Hilhorst, 2002;McDonald, 1998).
In tomato, as in many other crops, the domestication process has been accompanied by an attrition of genetic variation and, consequently, loss of many potentially desirable traits (Doebley, Gaut, & Smith, 2006;McCouch, 2004). Therefore, domesticated cultivars are sensitive to nonoptimal germination conditions which limit their production to optimal environments (Foolad et al., 2008;Foolad & Lin, 1997, 1998. However, a large source of genetic variation is found within wild species of tomato, such as Solanum habrochaitis, Solanum pimpinellifolium and Solanum pennellii. As cultivated crops suffer from abiotic stress, such as HT, drought and salinity by increased frequency and severity due to climate change, existing genetic variation could be used to reintroduce lost valuable traits in the domesticated cultivars to cope with these environmental stresses Lippman, Semel, & Zamir, 2007).
Seed dormancy is profoundly affected by the environment (Huo & Bradford, 2015). Seeds perceive their environment and under undesirable conditions they typically do not germinate and become dormant.
Natural variation present in traits such as seed size and weight, as well as dormancy and germination, exhibits a continuous distribution and is considered as quantitative variation likely regulated by multiple quantitative trait loci (QTL) (Argyris et al., 2008;Koornneef et al., 2002). A population of recombinant inbred lines (RILs) may be used for measuring the existing natural variation followed by QTL mapping as a powerful tool to detect loci affecting seed traits (Alonso-Blanco et al., 2009). Many studies have characterized QTLs regulating complex quantitative seed traits in different species, such as Arabidopsis, Tomato and Wheat (Argyris et al., 2008;Joosen et al., 2012;Kazmi et al., 2012;Koornneef et al., 2002;Mathews et al., 2008). However, few studies have been conducted to investigate the interaction between the ME and genetic variation (Dechaine, Gardner, & Weinig, 2009;Elwell, Gronwall, Miller, Spalding, & Durham Brooks, 2011;Geshnizjani et al., 2019;He et al., 2014;Postma & Agren, 2015). In general, final seed performance is determined by the function of several genes and their interaction with the environment.
Using high throughput genetic tools, including QTL mapping, to discover the genotype by environment interaction effects on QTLs affecting these seed traits provides a better understanding of how plants adapt to and cope with new stressful environments and is a prerequisite for crop improvement (Des Marais, Hernandez, & Juenger, 2013;El-Soda, Malosetti, Zwaan, Koornneef, & Aarts, 2014).
In this study we analysed natural variation of several seed and seedling traits including maximum germination percentage and rate of germination under control and stress conditions, as well as fresh and dry weight of seedlings and compare the results with the previously published thermo-dormancy and -inhibition of seed germination characteristics (Geshnizjani et al., 2018). We have used a RIL population derived from two tomato accessions: Solanum lycopersicum (cv. Moneymaker) (MM) and Solanum pimpinellifolium (PI) (Voorrips, Verkerke, Finkers, Jongerius, & Kanne, 2000). From the collection of tomato wild cultivars, S. pimpinellifolium has been used most frequently in breeding programs as it is the most closely related wild species to the domesticated tomato cultivar (S. lycopersicum) and has also the ability to naturally cross with S. lycopersicum. To investigate the existing genetic variation of seed and seedling related traits, we specifically focused on the ME in which seeds develop and mature. We compared the identified QTL for seed and seedling traits between the different nutritional environments of the mother plant. To do so, the RILs were exposed to high phosphate (HP) and low nitrate (LN) environments during seed development and their seeds were tested for seed and seedling related traits. In addition we performed a QTL × E approach to increase the power for detecting the loci affected by the different MEs (Joosen et al., 2012;Malosetti, Voltas, Romagosa, Ullrich, & Van Eeuwijk, 2004;Moreau, Charcosset, & Gallais, 2004;Van Eeuwijk, Malosetti, & Boer, 2007). In this study we show, that the interaction between ME, gemination environment and specific genetic loci can affect seedling establishment.

| Plant material and growth conditions
The RIL population was derived from a cross between two parental lines: S. lycopersicum cv. Moneymaker and S. pimpinellifolium (accession CGN14498). The population of 100 lines was genotyped in the F 7 using a set of 865 single nucleotide polymorphism (SNP) markers, described in Voorrips et al. (2000). F 8 seeds of this population were grown under controlled conditions in a greenhouse at Wageningen University, the Netherlands with 16 hr light and 8 hr dark. The temperature was adjusted to 25 C during the day and 15 C during the night. All the lines were fertilized uniformly by the same dosage of nutrient until flowering (Tables S1-S10). From the first open flower onwards the lines were transferred to new nutritional conditions and exposed to high and low concentrations of phosphate and nitrate, respectively (HP: 14.0 mM nitrate, 10.0 mM phosphate; LN: 2.4 mM nitrate, 1.0 mM phosphate; Standard: 14.0 mM nitrate, 1.0 mM phosphate used in Kazmi et al., 2012, Table S1).
Afterwards, healthy full ripened fruits were collected and seeds were extracted. To remove the main part of the pulp that is stuck onto the seeds 1% hydrochloric acid (HCl) was used. The seed extract together with diluted HCl was passed through a mesh sieve and then washed with water to remove the residual pulp and HCl. In order to disinfect the seeds, they were soaked in a trisodium phosphate (Na 3 PO 4 ·12H 2 O) solution and then dried on filter paper at room temperature for 3 days and brushed to remove impurities. At the end, the seeds were stored in small paper bags in a cold (13 C) and dry (30% RH) storage room  2.2 | Phenotyping of seeds and seedlings 2.2.1 | Seed size and weight Seed size was measured by using a Nikon D80 camera fixed to a repro stand with 60 mm objective and connected to a PC with Nikon camera control pro software version 2.0 (Joosen et al., 2010). The images of 12-hr imbibed seeds on white filter paper (20.2 × 14.3 cm) were processed by ImageJ (http://rsbweb.nih.gov/ij/) combining colour threshold with particle analysis. For seed weight, a batch of dry seeds was weighed and then divided by the number of the weighed seeds.

| Germination experiments
Germination experiments were executed in a randomized design with two replications of around 50 seeds per RIL, as well as the parental lines.
The seeds were sown in germination trays (21 × 15 cm DBP Plastics, http://www.dbp.be) containing one layer of white filter paper (20.2 × 14.3 cm white blotter paper; Allpaper BV, Zevenaar, The Netherlands, http://www.allpaper.nl) and 15 mL of demineralized water for normal and HT conditions, or 15 ml NaCl (−0.5 MPa; Sigma-Aldrich) or mannitol (−0.5 MPa; Sigma-Aldrich) for salt and osmotic stress, respectively. Each germination tray was loaded with three samples using a special mask to ensure correct placement of the seeds. The trays were piled up with one empty tray containing one white filter paper and 15 ml of water at the bottom and top of the pile and a white plastic lid at the top. The trays were wrapped in a transparent plastic bag and stored at 4 C for 3 days and subsequently transferred into a dark incubator (type 5,042; seed processing Holland, http://www.seedprocessing.nl) at 25 C except for the HT condition, which was at 35 C. Germination was scored manually by counting the germinated seeds at 24-hr intervals during 14 following days for salt and osmotic stress and at 8-hr intervals for 1 week in the case of normal and HT conditions. In order to quantify seed vigour, we germinated tomato seeds in water and under three suboptimal conditions; NaCl and mannitol solutions, and HT.

| Seedling phenotyping
Seedling characteristics were measured by sowing around 20 seeds of each seed batch on germination trays containing two blue germination papers (5.6 0 × 8 0 Blue Blotter Paper; Anchor Paper Company, http:// www.seedpaper.com) and 50 ml demineralized water. The germination trays were stored at 4 C for 3 days. Then, they were transferred to an incubator at 25 C without light. The first 10 germinated seeds were placed on circular blue filter papers (9 cm Blue Blotter Paper; Anchor Paper Company, http://www.seedpaper.com) which were placed on a Copenhagen table at 25 C in a randomized complete block design with two biological and two technical replicates, for 10 days. Conical plastic covers with a small hole on top were placed on top of each filter paper to inhibit evaporation. At the end of the 10 days, the seedlings were collected and fresh weight of their shoots and roots was measured (FWSH and FWR respectively). The dry weight of shoots and roots was also measured after incubating them at 80 C for 3 days (DWSH and DWR respectively). Average trait values per RIL per phenotype can be found in Table S2. Since tomato seeds were grown in different nutritional ME and were germinated in several conditions (GE), the seed germination traits were affected by ME, GE and their interactions (ME × GE). To identify the effect of each component on seed performance traits a two-way analysis of variance (ANOVA) analysis was performed using Genstat 18 with a significant threshold of 0.05. The contribution of each environmental component (ME, GE and ME × GE) to an individual trait was presented by the sum of squares (SS).

| Stability of the genotype rankings over two nutritional maternal environments
For each trait the stability of the genotypes over two nutrient MEs was estimated by calculation of Spearman rank correlation. We used the same approach as performed in previous studies to take the G × E interaction affecting traits into account (Becker & Leon, 1988;Oury et al., 2006).

| Correlation analysis
In each ME pairwise Spearman correlation analysis was done between all seed, seedling and seed performance traits using the cor function in R. The values of the correlation and statistically significant level of the correlations was represented as correlation value and false discovery rate (FDR), respectively. Correlation values with FDR ≤ 0.05 were selected to generate a correlation network using Cytoscape v.3.4.0.
The NetworkAnalyser tool in Cytoscape was used to obtain further characteristics of the networks.
The correlation between the mean values of each RIL for each trait between two MEs was also calculated using the rcorr R package.

| Linkage analysis
We use the genetic linkage map by Kazmi et al. (2012), in which they used 5,529 SNPs to genotype the RIL population. SNP markers with identical values were removed, leaving 2,251 polymorphic markers.
Furthermore, co-segregating markers were also removed. The remaining 865 unique markers were used for generating the genetic linkage map, which contains 12 individual linkage groups corresponding to the 12 chromosomes of tomato. This map has been constructed using JoinMap 4 (Van Ooijen and Voorrips, 2001) based on recombination frequency and Haldane's mapping function and integrating the existing SNP marker data set for the RILs   (Table S3).

| QTL detection
The mean values per RIL of the seed-, seedling-and seed performancetraits were used for QTL detection. QTL analysis was carried out by genome scan with a single QTL model (scanone) using the r/qtl package (Broman, Wu, Sen, & Churchill, 2003). The Logarithm-of-Odds (LOD), physical position, related marker and additive effects of each detected QTL together with phenotypic variation explained by each QTL (explained variance, EV%) were determined. The genome-wide significant LOD threshold (≥2) was estimated using 10,000 permutation tests (Broman et al., 2003;Doerge & Churchill, 1996). The physical position of the related markers and other characteristics of the QTLs affecting the traits measured for the RIL population grown in the two different MEs are summarized in Table S9. The QTLs for thermotolerance (Th-T), thermo-inhibition (Th-I) and thermo-dormancy (Th-D) were previously mapped (Geshnizjani et al., 2018).

| QTL × E analysis
The QTL by Environment effect was determined by an ANOVA model in which for each germination trait the model includes; the genetic background (GB), GE, ME and marker under study and their interactions (Phenotype ME * GE * marker + GB). The GB was defined by the RIL identifier. In this way the differences between environments for each individual RIL were taken into account. Phenotype = numerical scored trait (mean value per RIL), ME (LN or HP), GE (Water, NaCl, Mannitol or HT), marker = the ith marker from the genetic map (MM or PI) and GB = RIL identifier as the same RILs were measured in the different environments and thus controlling for the RIL background variation.
All calculations were done in R and visualised using the R package ggplot2 (Wickham, 2010). Thresholds for QTL by environment effects were determined by permutations (1,000 randomly sampled phenotypic values in the same mapping model). For an additive single maker effect the 0.05 −log10(p) threshold was between 3.6 and 3.9, depending on the trait (3.4-3.5 for 0.1 threshold). For the interaction between the ME and a marker the 0.05 −log10(p) threshold was between 3.3 and 3.6, depending on the trait (3.0-3.3 for 0.1 threshold). For the interaction between the GE and a marker the 0.05 −log10(p) threshold was between 3.2 and 4.2, depending on the trait (3.1-3.3 for 0.1 threshold).
For the threeway interaction between the ME, the GE, and a marker the 0.05 −log10(p) threshold was between 3.7 and 3.8, depending on the trait (3.2-3.3 for 0.1 threshold). For convenience the commonly used threshold of −log10(p) > 3 was used, to show significant QTLs in figures.

| RESULTS
To identify the loci involved in variation in tomato seed-and seedling-traits in interaction with different maternal nutritional conditions, HP and LN, we used a population of RILs derived from a cross between a wild (Solanum pimpinellifolium [PI]) and a domesticated (Solanum lycopersicum, cv. Moneymaker [MM]) tomato species (Voorrips et al., 2000). We mapped QTLs for five seed germination traits under four different GEs, three seed thermo-dormancy traits (Geshnizjani et al., 2018), two seed morphology traits and four seedling traits (Table 1).

| Variability and heritability of seed and seedling traits
In both suboptimal nutritional conditions (HP and LN) most of the traits displayed wide variation for the parental lines MM and PI, as previously observed (Geshnizjani et al., 2019). For the seed germination traits G max and AUC the difference between MM and PI increased under suboptimal germination condition HT, NaCl and Mannitol ( Figure 1, Table 2). For most of the traits MM was affected more by suboptimal germination conditions than PI, which confirms the higher susceptibility of MM to stressful conditions, as previously also observed (Geshnizjani et al., 2019) (Figure 1, Figure S1). parental lines were differently affected by the HP and LN nutrient environments ( Figure 2).
Moreover, considerable phenotypic variation for some of the traits was found in the RILs for each nutritional environment, this was reflected in the CV ranking from 12 to 120% under HP and 13 to 190% under LN conditions (Figures 1 and 2, Table S4). The largest variation in CV values was perceived in Th-D followed by AUC and The hinges correspond to the first and third quartiles (the 25th and 75th percentiles). The whisker extends from the hinge to the largest value no further than 1.5 * IQR from the hinge (where IQR is the interquartile range, or distance between the first and third quartiles). Points indicate outliers beyond the IQR has most negative alleles. In a few cases, such as G max water in both nutritional environments, substantial transgression was observed, due to poorly germinating RILs (Figure 1; Table 2).
Broad sense heritability (H 2 ) calculated for each trait in both maturation environments was high for most of the traits (with most traits >80% in both environments; ranking from 49 to 91% in HP and 54 to 93% in LN) ( Table 2). Taken together this shows that substantial genetic variation exists for these seed traits interacting with the germination as well as the ME.

| Genotype ranking and its stability over different nutritional maternal environments
In order to investigate how consistent the phenotypic rankings of the RILs are between the MEs and how large the effect is of the interaction between the genotype and the environment (G × E), the Spearman rank correlation coefficient (Oury et al., 2006) between two suboptimal nutritional MEs was calculated (Table 3, Tables S5 and S6).
For phenotypic traits, such as SS and SW, rankings of the genotypes T A B L E 2 Averages and broad-sense heritability of seed germination and seedling traits of RILs and their parental accessions Solanum lycopersicum (cv. Moneymaker) and Solanum pimpinellifolium grown in high phosphate (HP) and low nitrate (LN) conditions were stable from one ME to another and, thus, Spearman rank correlation values were also high for these traits, which suggests a relatively moderate effect of maternal G × E on seed size and seed weight.

| Germination environments versus maternal environments
By germinating the tomato seeds in optimal (water) and suboptimal conditions, such as salt-stress (NaCl), osmotic-stress (Mannitol) and HT stress (35 C), the seed germination traits were affected by their ME, their GE, and their interaction (ME × GE) (Table 4). In comparison to the optimal GE, seed germination traits showed higher variability in suboptimal GE in both MEs (Table 2). For instance, CVs for G max and AUC in water were 12% and 17%, respectively, while they showed significantly higher values in salt-(33 and 60% respectively), osmotic-(31 and 56% respectively) and HT-(35 and 44% respectively) stress (

| Trait by trait correlation
To obtain a comprehensive visualization of possible correlations among the phenotypic traits, a correlation network has been generated for each ME (Figure 4). In general, the mean value of all phenotypic traits showed a positive significant correlation between the two suboptimal nutrient environments (HP and LN) (Table S7) condition. In addition, seed and seedling quality traits showed negative association with seed germination traits including G max , AUC and U 8416 −1 , especially in the HT GE, which became visible at the LN condition ( Figure 4, Table S8). On the other hand, in both correlation networks, thermo-dormancy (Th-D) was negatively correlated with most of the germination traits, including G max , AUC and t 50 −1 under different GEs (such as water, NaCl and HT). However, they were much more correlated under the high-phosphate than the low-nitrate condition ( Figure 4, Table S8).

| QTL identification for each trait
To determine the large effect loci regulating seed, seedling and seed performance traits, QTL analysis of the tomato RIL population was performed. Concerning all traits, with the exception of chromosomes 2, 3, 5 and 12, all chromosomes contain QTLs of which many are colocated ( Figure 5, Table S9). We found 16 QTLs affecting G max under optimal and sub-optimal GEs of which six were detected in seeds of HP and 10 in LN maternal conditions. For AUC in all GEs, 13 QTLs were found of which nine were co-locating with the ones affecting G max on chromosomes 1, 4, 5, 10 and 11. With the exception of two QTLs on chromosome 6 and 10 discovered for the HP environment, all other QTLs regulating AUC were associated with the LN maternal condition. The result showed that t 10 −1 and t 50 −1 in all GEs and both MEs are regulated by almost the same QTLs which is not surprising as they are highly correlated traits. In total 18 QTLs were detected for t 10 −1 and t 50 −1 on chromosomes 2, 4, 6, 7, 8 and 11 which are also largely related to the LN ME ( Figure 5, Table S9).
For SS and SW, three and four QTLs were found respectively.
The co-locating QTLs for these two seed traits for the HP ME were detected on chromosome 1. A co-located QTL was also found for seedling quality in the same ME. Furthermore, another QTL related to seedling quality on chromosome 9 is co-locating with seed traits such as SW.
There is a strong QTL on chromosome 1 regulating thermodormancy traits in both MEs. This QTL affects both Th-T and Th-I traits in the same direction, while antagonistically regulating Th-D ( Figure 5, T A B L E 4 Effect of maternal environment (ME), germination environment (GE) and their interaction (ME × GE) on germination traits of tomato seeds

| QTL by environment
Generally, when different environments are studied simultaneously, detected QTLs can be affected by several environments. The QTL by Environment interaction (QTL × E) can describe such effects. In this study seeds were grown under two MEs, HP and LN and germinated in optimal (water) and three suboptimal conditions: osmotic (NaCl and mannitol) and HT stress. Therefore, in each seed germination trait the environmental component of QTL × E can be explained by either the ME or the GE and their interaction (ME × GE). We identified the QTLs affected by the environments and also decomposed the environmental effect into the different environmental components; GE, ME and their interaction (Figure 6). Figure 6a shows the QTLs regulating the seed germination traits independently from the environments. Those  Figure S2). On the other hand, some of the QTLs regulating seed germination traits are significantly influenced by the environment. For example the QTL located near the top of chromosome 2, which regulates AUC, was significantly affected by GE and to a lesser extent by ME (Figures 6 and   7, Figure S2). We have observed that GE showed generally more effects on QTLs than the ME. This result is in accordance with the observed variance between ME and GE in which seed germination traits showed higher variance in different GEs in comparison with different MEs. GE affects QTLs related to t 10 −1 and t 50 −1 , located on chromosomes 3, 6 and 11. Some QTLs affecting U 8416 −1 on chromosomes 8 and 11 were also affected by the GE (Figure 6, Figure S2). In comparison with GE, ME showed a less pronounced effect on the QTLs. Although the detected QTLs were sometimes affected by either maternal or GEs, we only found a suggestive interaction of a QTL, GE and ME (Figure 6, Figure S3). Comparing the QTLs found in the stressfull MEs, HP and LN, to QTLs found in control conditions from Kazmi et al. (2012) (Figure 7) shows that the majority of QLTs is ME specific. The QTLs are often shared between GE yet many QTLs occur only in specific combinations of maternal and GE.

| DISCUSSION
In this study we have used the genetic variation in a tomato RIL population to study how the genotype, ME and GE, including their interactions affects seed-and seedling-quality traits. A tomato RIL population was , Reciprocal time to reach 50% of maximum seed germination; Water, NaCl and HT are the seed germination environments water, salt and high temperature, respectively; Th-T, Thermo-tolerance; Th-I, Thermo-inhibition; Th-D, Thermodormancy; SS, Seed size; SW, Seed weight; FWSH, Fresh weight of shoot; DWSH, Dry weight of shoot; FWR, Fresh weight of root; DWR, Dry weight of root [Colour figure can be viewed at wileyonlinelibrary.com] grown in two different MEs with suboptimal nutritional conditions, low nitrogen and HP. The seed produced in these environments were used to study the effect of genetic variation and variation in the ME on seed quality and seedling establishment related traits. Nitrogen and phosphorus are two key elements required for plant growth (Schachtman, Reid, & Ayling, 1998;Urbanczyk-Wochniak & Fernie, 2004). Hence, their nonoptimal concentrations in mother plants may seriously affect the produced seed and the seedlings from those seeds. Moreover, the effect of the GE on the seedling establishment was further studied by observing these traits in four different GEs.
Although several studies have been conducted previously on the effect of abiotic stresses, such as drought and salt stress on seed quality (Asins, Raga, Roca, Belver, & Carbonell, 2015;Foolad, 2004;Foolad, Zhang, & Subbiah, 2003), studies of the effect of maternal nutritional conditions on the produced seed and seedling traits are scarce (Geshnizjani et al., 2019;He et al., 2014). By exploiting the natural variation observed in a tomato RIL population obtained from a cross between Solanum lycopersicum (cv. Moneymaker) and Solanum pimpinellifolium, we identified several loci controlling seed and seedling traits related to suboptimal nutritional seed maturation conditions, as well as suboptimal germination conditions. 4.1 | How are seed and seedling traits correlated?
Breeders and producers often are interested in seed traits such as t 50 −1 and seedling traits such as ability to produce normal and healthy seedlings. Furthermore, traits such as germination percentage and uniformity of germination, may also pose an important focus for breeders. The AUC (combining germination rate [t 50 ] and percentage [G max ]) will determine how fast seeds will germinate to a certain level, which directly affects further establishment of seedlings. On the other hand, seedling properties such as shoot and root weight determine how fast seedlings can penetrate the soil and start nutrient uptake and how fast the above ground tissues develop to provide required assimilates through photosynthesis. All together these factors determine seed and seedling vigour. Correlation of seed traits (SS and SW) with seed performance (rate of seed germination and uniformity) and with seedling traits have been studied before. Many studies have implied a direct relation between SS and SW and better seedling growth (Doganlar, Frary, & Tanksley, 2000;Khan et al., 2012;Nieuwhof, Garretsen, & Oeveren, 1989). This can be due to the amounts of reserve food which are deposited in seeds during seed development and maturation. Bigger tomato seeds produce seedlings with higher weight (Geshnizjani et al., 2019;Khan et al., 2012;Nieuwhof et al., 1989). Our results confirm the relation of SS and SW with seedling quality and establishment. In both suboptimal nutritional maternal conditions SS and SW were significantly influencing seedling quality traits. However, this correlation was most obvious in the LN nutritional condition. Such a strong correlation between seed and seedling traits suggests a similar genetic architecture, whereas the environment can partially affect such relations. In the former study in which the same RIL population was grown in standard conditions, similar correlations have been found between seed and seedling size. However, there was no obvious correlation between SS and seed germination traits . This contradicts our findings in which significant negative correlations were found between SS and seed performance traits such as G max , t 50 −1 , AUC and U 8416 −1 in both nutritional conditions. Such a negative correlation was even more apparent if seeds were germinated at HT. Such a discrepancy may be caused by the MEs under which seeds developed and matured. Khan et al. (2012) grew the RILs under optimal environment while suboptimal maturation environments were used in this study. Hence it is postulated that the stressful environments that we used affect the correlation of the seed size and seed germination traits such as G max and t 50 −1 .
The negative correlation that we found between SS and seed performance has been reported previously in tomato. The inheritance of germination time factors (e.g. t 50 −1 ) was negatively correlated with SS, implying that smaller seeds take longer to germinate (Whittington, 1973).
We also have found collocated QTLs for SS and seed performance traits such as G max and t 50 −1 on chromosome 11 which antagonistically affected the traits under study. Such co-locating QTLs might be an indication for the same regulatory mechanism for these traits.

| Breeding of crops
In general, a breeding strategy is highly dependent on genotype by environment interactions and the heritability level. Detection of a high correlation between the performance of genotypes in the different MEs may simplify the breeding strategy as it is then not required to select different genotypes for implementation into a breeding program. It has been mentioned previously that genotype re-ranking per trait in different environments is an indication of genotype by environment interaction (G × E) (Oury et al., 2006). Considering this, good breeding traits are the ones with the lower G × E effects. The results of the Spearman correlation analysis show that genotype re-ranking for most of the studied traits did not occur, therefore traits were limited affected by G × E (

| QTL and QTL × E detection
In general, QTL detection depends on several factors such as trait heritability, population type, number of lines and genetic map quality QTLs, regulating seed and seed performance traits, as well as seedling characteristics. In this, we have discovered more QTLs with high explained variance at LN ME as compared to HP (Figures 5 and 7).
Such a result could indicate that more physiological mechanisms and, subsequently, more genes are involved in plant adaptation to a LN environment. Many of the identified QTLs in this study have been reported previously for the same population, but under standard conditions only Khan et al., 2012) (Figure 7). For example the QTL that we have found at the end of chromosome 6, predominantly regulating the t 50 −1 trait in both MEs, was also detected in the standard condition. In addition, we have identified more environment-specific QTLs which were detected exclusively in one of the environments. These QTLs are more interesting from scientific point of view, however, QTLs detected in all different environments which may be considered as robust QTLs are the most interesting ones for further analysis for breeders and producers. These stable QTLs could regulate the traits independent from the growth environment. Further analysis, such as fine mapping, would ultimately result in identification of gene(s) regulating the analysed traits. As an example, many studies carried out so far to identify the genetic loci regulating SW in tomato have resulted in the identification of several QTLs (Doganlar et al., 2000;Grandillo & Tanksley, 1996;Khan et al., 2012;Tanksley, Medina-Filho, & Rick, 1982;Weller, Soller, & Brody, 1988). An interesting QTL which is common in different reports, and for which the causal gene has been identified, is present on chromosome 4 Orsi & Tanksley, 2009). A colocating QTL also appeared in our population grown under LN nutritional condition. Under HP nutritional condition the QTL was just below threshold ( Figure 5).
Studies of the interactions of QTL by environment have been carried out previously in different crops including tomato and rice taking a relatively simple strategy (Lu et al., 1997;Paterson et al., 1991). Plants were grown in different environments, QTL analysis was performed for individual environments and finally the results obtained from the different environments were compared with each other. In this study we also report the interactions between the QTLs, the nutritional environment, and the GE. We used a more complex strategy which has been applied previously for other species and/or environments (Des Marais et al., 2013;Snoek et al., 2015;van Eeuwijk, Bink, Chenu, & Chapman, 2010). In this method QTLs are directly studied in several environments. Although there is considerable overlap between the simple and more complex strategies, the second method enhances the statistical analysis resulting in higher LOD values and higher chances of finding significant QTLs (Tétard-Jones, Kertesz, & Preziosi, 2011).
According to our results ( Figure 6) we have detected some QTLs with significant QTL × E. The interaction between QTLs and environment are mostly applied by GEs, which indicates that most QTLs are regulating the tomato seed germination traits independently from the MEs.
Therefore, we conclude that in comparison with the nutritional ME, the GE must be considered as the more important factor for seed performance in tomato. Nevertheless, also some QTLs show interaction with the ME and even some suggestive QTLs in which the interaction between the ME and GE could play a role.

T A B L E 5
The 10 genotypes with the highest value per trait within two nutritional maternal environments [Colour table can be viewed at wileyonlinelibrary.com] Taken together, our results provide the genetic architecture of the effects of the ME on seed and seedling traits. These results could be further implemented in tomato breeding programs. We also suggest fine mapping of detected QTLs to narrow down the quantitative genetic loci and ultimately identify the causal gene(s). These can be the start to investigate more in-depth details of the molecular regulation of seed germination performance under different maternal and GEs.