The ever extensively cultivated “860” variety of S.japonica and the species S.longissima were selected as parents for the mapping population. Variety “860” usually has blade length of 240.2±23.1 cm and a blade width 25.4±3.0 cm; S.longissima usually has blade length of 5~8 m and blade width of 15~25 cm (Zhang et al., 2007; Zhang et al., 2015). Morphology of S.japonica and S.longissima in the wild has been described (Kawashima, 2012). The mapping population used in this study for genetic linkage maping and QTL mapping for S. japonica has been reported (2018). In brief, the male gametophytes of “860” and the female gametophytes of S. longissima were crossed to produce F₁ hybrid generation. After cultured F₁ sporophytes in the laboratory reached 1~2 cm in blade length, seedlings were moved to outdoor cultivation in the sea at Shandong Gaolv Aquatic Farm (E122°62´, N37°22´). Subsequently, one mature F₁ sporophyte was selected for self-fertilization in the laboratory to produce the F₂ mapping population. The F₂ population was cultivated in the same sea farming area as the F₁ population. Blade length and width of individual sporophytes were measured at different observation days during cultivation, with blade length measured from the top of stipe to the blade tip and blade width measured at the widest part of the blade.

DNA extraction for samples was according to established method (Wang et al., 2004). 182 simple sequence repeat (SSR) markers selected from over 2000 SSRs were used for a genetic linkage map ( Table S1 ). Selected SSR markers could produce polymorphic and expected reproducible DNA bands between two parents as well as from F₂ individuals. Some of the selected markers have been reported (Shi et al., 2007; Zhang et al., 2015; Zhang et al., 2015a) and 128 markers were developed by our group (Li et al., 2016). SSR marker analysis was via an ABI PRISM 3730 sequencer (Applied Biosystems, USA). Marker alleles were sized using GeneMapper ID v3.2 (Zhang et al., 2017).

JoinMap 5 (van Ooijen, 2018) was used for genetic linkage map construction. Segregation on each SSR marker locus from the expected 1:2:1 Mendelian segregation ration was checked by a χ²–test (p=0.05). Loci with significantly distorted segregation were removed. LOD score of >4.0 was set as the linkage threshold for grouping markers. Haldane mapping function was adopted for calculating map distance between markers.

SSR markers on the genetic linkage map were aligned with assembled kelp pseudo-chromosomes (NCBI: MEHQ00000000) with BLASTN (Altschul et al., 1990). Based on BLAST analysis with right and left primers anchored on the same pseudo-chromosome and with expected length of ePCR products, SSR markers were assumed to be located on the targeted pseudo-chromosome.

JoinMap 5 (van Ooijen, 2018) was used to integrate the SSR-based genetic linkage map with the previously constructed SNP-based genetic linkage map (Wang et al., 2018). QTL IciMapping (Li et al., 2007) and MapQTL 6 (van Ooijen, 2009) were applied to blade length and width based on the integrated genetic linkage map. The inclusive composite interval mapping (ICIM) model in software QTL IciMapping, and the interval mapping (IM) model in MapQTL6.0 were used for QTL mapping. The genome-wide significant threshold of each trait was determined by permutation test of more than 1,000 times at P< 0.05 in MapQTL 6 (van Ooijen, 2009).

Candidate genes for QTL were analyzed by established method (Wang et al., 2018). In brief, primer sequences corresponding to marker in the mapped QTL were used in a BLAST analysis and compared with kelp assembled genome sequences (MEHQ00000000). Candidate genes were annotated and analyzed via the NCBI database (http://www.ncbi.nlm.nih.gov). SjPT (registered as ON872174 in NCBI) and the other orthologous proteins ( Table S5 ) were phylogenetically analyzed by software MEGA 11 (Tamura et al., 2021). The phylogenetic tree was generated by maximum likelihood (ML) with best LG+G5 model, complete deletion of gap and 1000 bootstrap (Tamura et al., 2021). Online server TMHMM (https://services.healthtech.dtu.dk/service.php?TMHMM-2.0) was used to predict transmembrane helics ( Table S5 ). PIs and molecular weight (MW) were deduced by the ExPASyProParam (https://web.expasy.org/protparam/) ( Table S5 ). Cellular localization of SjPT was predicted with online server Cellon (http://cello.life.nctu.edu.tw).

RNA extraction and RT-qPCR analysis were by established method (Wang et al., 2018). Sporophyte blades of the “90-1” S.japonica strain (Zhang et al., 2007) cultivated at Shandong Gaolv Aquatic Farm (E122°62´, N37°22´) were collected on five observation days for RNA extraction. Meristematic tissue in the joint between blade and stipe was used to extract RNA. Primer pairs specific to SjPT for 150-bp amplicon region were in the Table S6 . Transcript profiling of SjPT was examined according to the method described by Lu et al. (2020). T ranscriptome data used (NCBI: PRJN512328) was reported by Shao et al. (2019). RSEM software (Li and Dewey, 2011) was used to analyze gene abundance and expression levels were normalized by fragments per kilobase of transcript per million mapped reads (FPKM). EdgeR package was used to identify differentially expressed genes (Robinson et al., 2010).

125 S.japonica individuals were genotyped with 182 SSR markers. Segregation and mapping analysis resulted in 15 SSR markers being excluded or unmapped due to segregation distortion or duplication. The remaining 167 SSR markers were mapped on 27 linkage groups ( Table 1 ; Figure S1 ) that included 5 doublets (Lg4, Lg20, Lg21, Lg26, Lg27) and 3 triplets (Lg3, Lg19, Lg25). Linkage group lengths ranged from 2.09 cM (Lg20) to 281.45 cM (Lg1), with average length 13.07 cM and total length 2069.07 cM. Between 2 and 20 markers were mapped on each linkage group, with an average of 6.2 markers per group. Yielded map density of the marker loci was 1 per 12.39 cM.

Compared with the previous genetic linkage map (Zhang et al., 2015), 13 pairs of genetic linkage groups may have been from the same chromosome ( Table 2 ) but pairs Lg9 and LG28, Lg13 and LG24, Lg25 and LG20 exhibited only one common SSR marker.

27 linkage groups were mapped on the 23 pseudo-chromosomes in S. japonica ( Table 3 ). No. 3 and No. 5 linkage groups were co-mapped on chr12, No. 7 and No. 27 were on chr02, No. 4 and No. 18 were co-mapped on the chr03. No. 22 was not anchored on any pseudo-chromosomes. 127 SSR markers in the linkage map were anchored on assembled pseudo-chromosomes ( Table 3 ). SSR marker locations on the pseudo-chromosomes are in Table S2 . Right and left primers of M43, M1140, M768 and M200 from the Lg1 ( Figure S1 ) were not verified in chr06; only the right primer of M37 was anchored to chr06 ( Table S2 ). M284 were mapped on two locations in chr06 ( Table S2 ). Some linkage groups had the same marker order as the corresponding pseudo-chromosome, such as M88-M114-M78-M2048—M30-M1907 in Lg11 ( Figure S1 ), which was consistently anchored to the chr11 except M58 and M220 ( Table S2 ). The two SSR markers at the end of linkage groups was inverse order compared to the same markers in corresponding pseudo-chromosomes, such as M374-M1445 on Lg13 ( Figure S1 ) and M1445-M374 on the chr16 ( Table S2 ). Physical distance per cM was not uniform in the linkage group, such as in Lg7 with 7.8 cM genetic distance between M1878 and M1679, less than 22.2 cM between M1101 and M128, but 153433 bp per cM between M1878 and M1679 was larger than 77968 bp between M1101 and M128.

7627 SNPs and 182 SSRs were used to integrate a linkage map with 3397 markers (3224 SNPs and 173 SSRs) mapped to 33 linkage groups, of which No. 32 and No. 33 included only SSR markers while No. 13 and No. 28 merely had SNP markers ( S1 ; Table S3 ). Seven ungrouped SSR markers (M2102, M439, M1237, M1236, M1699, M2219, M151) in the SSR-based genetic linkage map were successfully mapped to the new integrated linkage groups, such as M1236 and M1699 on No. 20. A verage genetic distance between markers in the merged map was 2.87 cM in terms of Haldane map function. Table S3 shows collinearity of the integrated genetic linkage groups with SSR-based linkage groups, assembled pseudo-chromosomes and previous SNP-based linkage groups.

Blade length and width observed on May 8^th, May 22^nd and June 9^th, were the same as in our previous report ( Table 2 , in Wang et al., 2018). Frequency distribution patterns of blade length and width of the mapping populationat three observation days appear in Figure S2 . Before QTL mapping, the genome wide significant LOD threshold for detecting QTLs for each trait was calculated by permutation test in MapQTL6.0 ( Table S4 ). 30 QTLs were detected by the ICIM (inclusive composite interval mapping) method for QTL IciMapping ( Table 4 ; Figure S3 ). According to the calculated significant LOD threshold ( Table S4 ), few significant QTLs were mapped such as the QTL in the interval of Marker1203S-Marker1895S ( Table 4 ). Similarly, Marker1895S was found to be closely associated with blade length and width at three observation days by the interval mapping (IM) method in MapQTL 6.0 ( Figure 1 ).

SjPT was annotated in the QTL closely associated with M1895S, which could explain phenotype variations of blade length from 10.68% ~ 12.55% and blade width from 17.92% ~ 19.96% ( Table 4 ). Figure 2 shows right and left primer positions of M1895S and five exons and introns of SjPT. The sequence of right primer of M1895S located at the 356-378 bp interval of the first exon. SjPT coding sequence was 1422 bp coded one protein for presumed high affinity phosphate transporter with 473 aa, 8 transmembrane helices, 50.24 kDa molecular weight, and 5.75 isoelectric point. Table S5 shows biochemical characters of SjPT with other counterparts. Phylogenetic relationship between SjPT and others analyzed by MEGA11 ( Figure 3 ) showed that high plants with canonical 12 conserved membrane-spanning domains cluster together and non-canonical 8 transmembrane helixes exist in S. japoncia and other group ( Table S5 ; Figure 3 ).

Evaluation at different observation days based on RNA-Seq data and fragments per kilobase of exon model per million mapped reads (FPKM) showed that SjPT transcriptions obviously increased with growth in blade length and width ( Figure 4C ), especially from May to June ( Figure 4A ). qRT-PCR detection exhibited similar tendencies from March to April ( Figure 4B ).