Haplotype Bias Detection Using Pedigree-Based Transmission Simulation: Traces of Selection That Occurred in Apple Breeding

43 With the increasing ability to integrate pedigree and genomic data, it is essential to evaluate their potential to uncover 44 valuable genetic insights that can drive the advancement of crop breeding and conservation of genetic diversity. Pedigree 45 analysis remains a fundamental approach for investigating the inheritance of phenotypic traits, exploring evolutionary 46 history, and understanding hybridization processes in crop plants. Among these approaches, gene drop simulations using 47 pedigree and allele origin data enable the construction of genetic maps and provide insights into complex genetic 48 backgrounds. In this study, we developed a new method to identify useful genetic regions associated with single-nucleotide 49 polymorphism (SNP) markers based on gene drop simulations, focusing on 185 Japanese domestic apple cultivars. By 50 performing 10 million gene drop simulations, we generated null distributions for each founder haplotype, which revealed 51 SNP markers with significant frequency biases, which is a potential signal for selection. Frequency biases were identified in 52 eight founder haplotypes that were particularly consistent with genome-wide association studies peaks associated with key 53 fruit traits such as malic acid and fructose content. Gene Ontology enrichment analysis suggested that these SNPs are not 54 only associated with fruit traits but may also play a role in critical biological functions, including stress tolerance and 55 reproductive processes, highlighting their broader relevance to crop resilience. Our integrative approach, which combines 56 founder haplotype analysis with extensive gene drop simulations, effectively detects selection pressure, provides new 57 insights into the genetic basis of apple breeding, and identifies SNP markers with strong potential to improve breeding 58 programs. 59 60 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint

61 Historical breeding materials are of paramount importance for perennial plants such as fruit trees, as they have 62 accumulated rich genetic variation over many years 1. Woody fruit trees, such as apples, are often self-incompatible, 63 leading to well-documented pedigree information compared with crops, such as rice, which have more complex 64 genetic backgrounds owing to selfing 2, 3. Therefore, data-driven breeding approaches that use pedigree information 65 allow for the more effective identification and use of beneficial traits 4. 66 In recent years, advancements in sequencing technology have made it possible to sequence genomes quickly and 67 affordably, extending their capabilities to plant breeding 5. For example, genome-wide association studies (GWAS) 6, 68 which identify candidate genes responsible for traits, such as disease resistance, have been applied to various plant 69 species, including apple 7, 8, 9 , rice 10, wheat 11, maize 12, and citrus 13. This demonstrates that GWAS have become a 70 mainstream method in modern plant breeding. Furthermore, in breeding materials with complete pedigree and single-71 nucleotide polymorphism (SNP) information, founder haplotypes can be visualized and automatically traced 7, enabling 72 breeders to use historical data more effectively. 73 In a study conducted by Minamikawa et al. 7, gene drop simulations 14 were used to validate the non-random 74 transmission of founder haplotypes detected in GWAS. However, the bias detected using this method is not limited to 75 markers significantly associated with the GWAS peaks. In this study, we divided the Japanese domestic apple 76 population based on pedigree information visualized using Helium 15 and expanded gene drop simulations on 77 generational and genome-wide scales. This approach allowed the identification of potential biases in the frequencies 78 of founder haplotypes by comparing them with random transmissions across all markers. By examining genome-wide 79 changes in founder haplotype frequencies without focusing on specific traits, we inferred the occurrence of intended 80 and unintended selections based on these changes. Addition ally, the temporal dynamics of these founder haplotypes 81 were tracked to provide insights into breeding trends during specific periods. 82 To the best of our knowledge, no previous studies have conducted whole-genome gene drop simulations on apples 83 or detected biases in founder haplotypes across markers in other plant species using this method. This study builds on 84 the work of Minamikawa et al. 7 by investigating the underlying reasons for the selection of biased markers and 85 founder haplotypes across the entire genome. Specifically, we compared biased markers with those identified by the 86 GWAS. In cases where there was an overlap between biased markers and GWAS peaks, we analyzed generational 87 changes in the trait, the effect of each founder haplotype on the trait, and frequency changes of the founder haplotypes 88 at the marker to infer the reasons for selection. When no overlap was observed, it suggested the possibility of selection 89 for traits other than those related to fruit characteristics. To explore this further, we combined gene drop simulations 90 with gene ontology (GO) enrichment analysis 16 to gain insight into the reasons for selection beyond the traits targeted 91 by the GWAS. This study employed a quantitative approach to evaluate the impact of breeding-induced biases on 92 gene function and assessed genes by integrating GWAS and GO enrichment analyses. 93 Previous studies have developed gene drop simulations 14 using pedigree and allele information, which have been 94 used to construct genetic maps and understand genetic backgrounds 17, 18. In apples, a similar gene drop simulation was 95 performed using founder haplotypes 19 instead of allele information 20 to validate the non-random transmission of 96 founder haplotypes detected in GWAS 7. However, the biases detected using this method are not limited to markers 97 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint that are significantly associated with GWAS peaks. It is also important to consider when these biases arise because 98 they may reflect the preferences of consumers and breeders at particular times. To address this, we extended the gene 99 drop simulation to the whole genome and ran it across all generations based on pedigree data visualized using 100 Helium15. This allowed us to detect biases independent of the GWAS results. By integrating this approach with GO 101 enrichment analysis 16, we gained insights into selective pressures that may extend beyond the traits traditionally 102 targeted by GWAS. 103 104 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint

105 Detecting frequency bias of founder haplotypes using gene drop simulation 106 To generate a null distribution for the 14 founder haplotypes derived from the seven apple founder cultivars, 10 million 107 gene drop simulations were performed (Supplementary Fig. 1). Two types of null distribution were created: one for the 108 entire population and one for each generation. This generation constitutes a division of the genealogical information 109 inscribed using Helium and approximates the age at which the variety was created. SNP markers with significantly altered 110 frequencies for each founder haplotype were detected by comparing the observed founder haplotypes with null distributions. 111 Frequency bias was identified in eight founder haplotypes (1, 2, 3, 4, 5, 6, 8, and 13) when the entire population was tested 112 (Fig. 1; Supplementary Table.). In tests for individual generations, significant changes in the frequencies of some founder 113 haplotypes were observed starting from the third generation (Supplementary Figs. 2–6). SNP markers detected in the 114 separate-generation tests were identical to those found in the entire population. Hereafter, the results focus on the 115 population-wide test, which is considered to have higher statistical power. 116 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint 117 118 Fig. 1. Detection of frequency bias in the 14 founder haplotypes using gene drop simulations 119 Regions considered to be significantly selected for each founder haplotype are shown. The horizontal axis represen120 the genomic position of SNPs, and the vertical axis shows the value from the simulations. Purple dots 121 indicate significant regions, while blue dots represent non-significant regions. The red dashed lines mark the thresh122 () . 123 124 125 126 ents shold .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Concordance between SNP markers with biased frequencies of founder haplotypes and 127 previously reported GWAS peaks or reference annotation data 128 To investigate the reasons behind the changes in founder haplotype frequencies, we compared SNP markers located on the 129 coding DNA sequence that significantly altered founder haplotype frequencies with previously reported GWAS peaks for 130 fruit traits. The SNP markers with significantly altered founder haplotype frequencies coincided with the GWAS peaks for 131 11 fruit traits (Supplementary Table). SNP markers were grouped according to their corresponding GWAS target traits and 132 loci (Supplementary Table). Subsequently, the markers were divided into 12 blocks based on chromosome and physical 133 position, and the SNP marker with the highest /g3398 log /g2869/g2868 /g4666/g1868 /g4667 value was designated as the representative marker for each block 134 (Supplementary Table; red text cells in the block column). The founder haplotypes that were significant for these markers 135 were then plotted to show their frequency changes over generations, the estimated effect of each founder haplotype on the 136 marker, and the generational evolution of fruit traits associated with the matched GWAS peaks. 137 The results showed that among the 12 blocks, seven exhibited changes in the frequency of the founder haplotype of 138 interest, with consistency between this change and the phenotypic value transition (Supplementary Figs. S7, S9–13, and 139 S16). In contrast, three blocks did not show this consistency (Supplementary Figs. S8, S14, and S15). The two blocks 140 displayed no changes in the relevant phenotypic trends across generations (Supplementary Figs. S17 and S18). For example, 141 the phenotypic value of malic acid tended to decrease over time, but the SNPs associated with it increased significantly in 142 frequency, showing a negative effect in all cases (Supplementary Figs. S10–12). 143 In addition to the above analysis, we compared the annotations assigned to the ‘Golden Delicious’ (GDDH13) reference 144 to explore factors that may have contributed to the selection of these regions beyond fruit traits. This comparison revealed 145 that 68 SNP markers matched 35 genes within the SNP markers identified as founder haplotype biased that associated with 146 previously reported GWAS peaks (Supplementary Table.). These SNP markers may play roles in processes beyond fruit 147 traits, such as cell division, pollen development and germination, drought and salt stress tolerance, reproduction, and the 148 maintenance of vital activities. 149 Moreover, the annotation of apple genes in the gene regions containing the corresponding SNP markers was examined to 150 determine the reason for the bias in the founder haplotype frequencies of SNP markers that did not match previously 151 reported GWAS peaks. In total, 669 SNP markers with biased founder haplotype frequencies corresponded to 351 gene 152 regions (Supplementary Table). These SNP markers, along with those that matched the reported GWAS peaks, may be 153 involved in plant growth processes, such as growth regulation and RNA binding. 154 155 GO enrichment analysis to estimate the reasons for selected regions 156 GO enrichment analysis suggested that GO terms in the biological process category were not significantly ( p < 0.05) 157 enriched within genes containing 669 SNP markers with significantly altered founder haplotype frequencies and unmatched 158 GW AS peaks. GO terms of the Molecular Function (MF) category, ‘transferase activity, transferring phosphorus-containing 159 groups’ and ‘sequence-specific DNA binding,’ were significantly ( p < 0.05) enriched within the genes (Fig. 2(a)). 160 ‘Sequence-specific DNA binding’ had the lowest p-value in the MF category. Additionally, when we analyzed the genes 161 associated with each function in Figure 2(a), HSF4, LOC103416823, and WRKY12 genes were each linked to one function 162 (Fig. 2(b)). Within the network of these genes, the RNA polymerase II transcription regulatory region sequence-specific 163 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint DNA binding appeared to have the greatest downstream function (Supplementary Fig. S19). Furthermore , the cell164 component (CC) category was suggested to be related to organelle and nuclear lumens (Supplementary Fig. S20). 165 166 Fig. 2. Results of gene ontology enrichment analysis in molecular functions (MF) 167 (a) The gene ontology (GO) term within the MF category enriched in genes containing SNP markers with significa168 altered founder haplotype frequencies. The horizontal axis represents the proportion of genes associated with each GO te169 and the size of each dot represents the number of genes. The color of the dots indicates the p-value, with red represen170 statistically significant associations, implying a stronger likelihood of being linked to that function. (b) A figure showing171 genes associated with each GO term. Sequence-specific DNA binding (fifth row from the top), which had the lowest p-va172 was linked to four genes: HSF4, LOC103439953, MADS21, and WRKY12. 173 174 ellular icantly term, enting ng the value, .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint

175 In this study, we introduced an approach based on pedigree and gene drop simulations to identify biases in the frequency 176 of founder haplotypes. Since the frequency of founder haplotypes contributing to valuable phenotypes is expected to 177 increase within breeding populations, the regions identified using this method offer valuable insights for breeding. Focusing 178 solely on founder haplotype frequencies might lead to the conclusion that all founder haplotypes of ‘Fuji’ are beneficial, as 179 haplotypes from ‘Fuji,’ a parent with significant contributions to later generations, would naturally have higher frequencies 180 in the breeding population. However, by comparing the degree of bias in founder haplotypes with random inheritance, our 181 new method enables the evaluation of their contributions to later generations. Unlike traditional methods, such as GW AS 182 and genomic prediction, which rely heavily on phenotypic data, our method does not depend on such data, making it robust 183 and versatile. 184 Previous research has often traced founder haplotypes at a single locus 7 or focused on genetic diversity using 185 gene drop simulations 14; however, a genome-wide method for identifying useful genomic regions through gene drop 186 simulations is lacking. This study aimed to investigate the causes of changes in founder haplotype frequencies at certain 187 SNP markers by tracing them across the whole genome, generation by generation. Additionally, we analyzed the gene 188 regions to determine the possibility that selection may have occurred for unmeasured traits. Therefore, the proposed method 189 offers a unique approach. 190 By investigating the functions of the SNP markers with significantly altered founder haplotype frequencies 191 detected using our method, we aimed to determine the reasons for selecting these regions. For example, in Supplementary 192 Fig. S7 (a) and (b), the founder haplotype 6 from ‘Golden Delicious’ showed a significant change in frequency at the SNP 193 marker SNP_FB_1117728, which coincided with the GW AS peak for fructose. The founder haplotype 6 in this region 194 exhibited a strong positive effect on fructose content, with its frequency increasing significantly above the simulation 195 threshold by the fourth generation (Supplementary Fig. S7 (c)). This suggests that the founder haplotype 6 at 196 SNP_FB_1117728 from ‘Golden Delicious’ may have been selected to increase fructose content. Given that fructose is 197 sweeter than other sugars 21 and consumer preference often leans toward sweeter varieties 22, it is possible that consumer 198 choice may have influenced the selection for increased fructose content. 199 Furthermore, GO enrichment analysis using genes containing SNP markers with significantly altered founder haplotype 200 frequencies, GO terms of the MF category, such as ‘transferase activity, transferring phosphorus-containing groups’ and 201 ‘sequence-specific DNA binding,’ were identified (Fig. 2). Specifically, focusing on sequence-specific DNA binding, four 202 genes, HSF4, LOC103439953, MADS21 and WRKY12 -- were found to be involved in regions with significantly altered 203 founder haplotype frequencies. HSF plays an important role in flavonoid biosynthesis and drought resistance23. Additionally, 204 HSF4 is regulated by cold stress in bananas24, suggesting its potential role in cold and heat tolerance in apples. 205 MADS21 regulates unsaturated fatty acids in the palm by contributing to metabolic genes 25 and is involved in the 206 regulation of fat development and flowering transition in Arabidopsis 26, 27, 28, . The WRKY family is known for its role in 207 abiotic stress responsiveness, including resistance to Alternaria alternata in apple 29. Additionally, WRKY12 exhibited the 208 opposite regulatory effect on flowering under short-day conditions 30. This implies that the regions detected using this 209

may have undergone significant changes in founder haplotype frequencies owing to selection for traits such as 210 growth, disease resistance, and environmental adaptation, which are often not measured in phenotypic assessments. 211 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Unconscious selection by breeders, reflected in regions with significantly altered founder haplotype frequencies, likely 212 led to an increase in the number of haplotypes associated with beneficial effects on physiological functions. Unconscious 213 selection in breeding processes has rarely been explored, making our methodology a pioneering contribution to our 214 understanding of the historical context and unintentional decisions made during the breeding of apple varieties. 215 In recent years, serious diseases such as Alternaria fungus31 and burn diseases have had a significant impact on apple 216 breeding. For example, among the seven ancestral Japanese apple varieties (Founder cultivar; ‘Ralls Janet’, ‘Delicious’, 217 ‘Golden Delicious’, ‘Jonathan’, ‘Worcester Pearmain’, ‘Indo’, ‘Cox’s Orange Pippin’) 17, ‘Indo’ and ‘Delicious’ are 218 particularly susceptible to Alternaria alternata , and this low resistance has been inherited by many of their offspring. 219 Additionally, ‘Fuji’ is prone to burn, a disease that often causes wilting 32. Marker-assisted selection is available for these 220 diseases33. However, although such methods are highly accurate, they are labor-intensive for the comprehensive 221 identification of resistance genes. Our method may not only allow for the detection of gene regions potentially associated 222 with resistance to such diseases but also provide a comprehensive approach to identifying useful gene regions that might be 223 useful for resistance against severe diseases that have not yet been extensively studied, potentially opening new possibilities 224 for future breeding efforts. Furthermore, this method is not limited to apples and is applicable when the pedigree is limited 225 and founder haplotype information is complete. This adaptability makes it a valuable tool for other fruit tree species such as 226 citrus34 and peach35. 227 In conclusion, our method, based on genealogical information and gene drop simulations of founder haplotypes, is a 228 valuable tool for detecting biases in founder haplotype frequencies, while minimizing the influence of breeding parents with 229 substantial contributions to subsequent generations, such as ‘Fuji.’ By comparing these detected biases with the GW AS 230 peaks, we inferred the selective intentions behind the selection of specific regions, offering insights into the often-231 unexplored realm of breeder decisions. Additionally, by comparing regions with significantly altered founder haplotype 232 frequencies with annotated regions, we identified useful genetic regions that may not have been directly targeted by 233 breeding programs. Because our method does not require phenotypic measurements, it allows the exploration of a wider 234 range of valuable genetic regions, providing new opportunities for future breeding efforts. 235 236 237 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint

238 Plant materials 239 Data obtained from 185 domestic Japanese apples ( Malus domestica Borkh.) varieties 7 w e re u s e d i n th i s s tu d y . Th e s e 240 varieties originated from seven founder cu ltivars: ‘Ralls Janet’, ‘Delicious’, ‘Golden Delicious’, ‘Jonathan’, ‘Worcester 241 Pearmain’, ‘Indo’, ‘Cox’s Orange Pippin’. All the materials mentioned above were cultivated at the Apple Research Station, 242 Institute of Fruit Tree Science, NARO, Japan. 243 Pedigree information, genotypes, and phenotypes 244 Pedigree information for 185 domestic Japanese apple varieties was used in this study. SNP genotypes for 11,786 markers 245 (Illumina Infinium array) were obtained, and sporadic missing SNP genotypes were imputed using Beagle ver. 4.0 21, as 246 reported by Minamikawa et al. 7. The SNP data of the varieties were characterized by 14 founder haplotypes derived from 247 seven founder cultivars, as detailed in the same publication. The phenotypic data for 23 fruit traits evaluated over multiple 248 years7 were included in this study. 249 Gene drop simulation to detect the frequency bias of founder haplotypes 250 The genome-wide haplotype composition of a population reflects the effects of selection and mating during breeding, 251 particularly around gene regions related to the target trait. This study focused on the usefulness of pedigree-based gene drop 252 simulation10 to account for bias created by breeding parents. We combined this approach with founder haplotype 253 information that represents the origin of SNP alleles. The aim of this study was to identify regions that have undergone 254 intended and unintended selection during the breeding process. Because the apples used in this study were diploid (2n = 2x 255 = 34), this gene drop simulation assumed the null hypothesis that one of the two founder haplotypes at an SNP locus was 256 randomly selected with a probability of 1/2 in subsequent generations. Therefore, the transmission of the founder haplotype 257 at a locus was equivalent to performing a Bernoulli trial with /g1868/g34041 / 2 . In this study, multiple founder haplotypes were 258 assumed, and the frequency distribution of the founder haplotypes in the later population followed a multinomial 259 distribution instead of a binomial distribution as follows: 260 /g2279 /g4666 /g2206 /g1508 /g2760, /g1866 /g4667 /g3404 /g1866! Π /g3038/g2880/g2869 /g3012 /g1876 /g3038 ! Π /g3038/g2880/g2869 /g3012 π /g3038 /g3051 /g3286 where /g2206/g3404/g4668 /g1876 /g2869 ,/g1876 /g2870 ,/g1710,/g1876 /g3038 /g4669 is the number of times about founder haplotype has been obtained, /g2760/g3404/g4668 π /g2869 ,π /g2870 ,/g1710,π /g2921 /g4669 261 is the probability of obtaining a combination of founder haplotypes, n is the number of haplotypes (2/g3400 population size), and 262 k is the number of possible combinations of founder haplotypes in the population. where /g2250 and /g1824 satisfy ∑ /g1876 /g3038 /g3012 /g3038/g2880/g2869 /g3404/g1866 , 263 ∑ /g2024 /g3038 /g3012 /g3095/g2880/g2869 /g34041 . Although it is possible to obtain the frequency of founder haplotypes analytically, as described above, it is 264 difficult to do so for all individuals in this study’s apple population, which consisted of 14 founder haplotypes and 185 265 parental varieties. To address this, we simulated the spread of founder haplotypes in later generations by creating empirical 266 frequency distributions of founder haplotypes using 10 million gene drop simulations based on pedigree informati on. This 267 simulation assumed that founder haplotypes were obtained randomly when breeders did not select them as a null hypothesis. 268 This empirical frequency distribution was used as the null distribution. The p-value of the observed founder haplotype 269 frequency in each genetic region was defined as the difficulty of occurrence in the simulation (Supplementary Figure 1). 270 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint This method detected SNP markers as regions that may have been selected by setting the threshold to 271 detecting significant changes in the frequency of founder haplotypes when the value exceeds the threshold272 this study, because the focused founder haplotypes were tested using the percentage of all founder haplotypes, the horizo273 axis in Supplementary Figure 1 corresponds to k of the multinomial distribution and the vertical axis to . Additionally274 tested the bias in each generation because we considered that founder haplotypes that increased or decreased in the e275 generation might not have been detected by testing the whole population. The pedigree drawing software Helium was u276 to separate generations (Fig. 3) 15 . The generations were then separated into rows. Generation 1 consisted of the se277 founder cultivars. Because this study compared the simulation results with actual founder haplotype frequencies, it is lik278 that the simulation results will be biased if the number of individuals being compared is small. Herein , the combination279 columns fifth and sixth is defined as Generation 5 because there are few rows corresponding to Generation 6. 280 281 Fig. 3 Generational partitioning of apple varieties based on the pedigree chart drawn using Helium 282 This diagram shows the generations and contributions of 185 Japanese varieties. Each node represents a variety , and283 dark gray nodes indicate uninformed parent individuals. Each row shows the generation partitioned using the pedig284 visualization tool Helium. The sizes of the nodes indicate their contribution as parent s to subsequent generations. The la285 nodes representing ‘Fuji’ reflect its significant role in breeding, as ‘Fuji’ was used extensively for mating and has the lar286 contribution to subsequent generations. 287 288 289 Comparison of SNP locus, in which the frequency bias of founder haplotypes was detected, with290 previously reported GW AS peaks 291 SNP markers that significantly changed the frequency of founder haplotypes using the previous method were compa292 with previously reported GW AS peaks for fruit traits14 to determine whether the regions were selected based on fruit tra293 Specifically, when the SNP marker with a significant change in founder haplotype frequency matched the SNP mar294 and old. In izontal lly, we early s used seven likely tion of nd the digree e large largest ith pared traits. arker .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint detected in the GW AS, we tracked the change in the founder haplotype frequency of the marker and the phenotypic 295 transition by generation. Furthermore, we estimated the effects of each founder haplotype on the marker using BayesB with 296 MCMC 36, 37. Marker regression models, such as BayesB, assume that genotypic values /g1873 are determined by a linear sum of 297 marker effects, as follows: 298 /g1873 /g3036 /g3404/g3533 γ /g3037 /g3533/g3435/g1876 /g3036/g3037/g3039 /g3397/g1876 /g3036/g3037/g3039 ’ /g3439β /g3037/g3039 /g3013 /g3285 /g3039 /g3011 /g3037/g2880/g2869 where J represents the total number of markers, and /g1838 /g3037 represents the number of founder haplotypes at the j-th marker. The 299 variable /g1876 /g3036/g3037/g3039 (/g1876 /g3036/g3037/g3039 ’ ) denotes the maternal (paternal) haplotype of marker j for variety i and equals to 1 if the maternal 300 (paternal) haplotype is the l-th haplotype ( /g1864 /g3404 1,2, /g1710 , /g1838 /g3037 ) and 0 otherwise. The parameter γ /g3037 indicates the posterior 301 probability of the j-th marker having a quantitative trait locus, while β /g3037/g3039 represents the genetic effect associated with the l-th 302 founder haplotype at marker j. The effect β /g3037/g3039 is assumed to follow a Gaussian distribution /g2280/g4672 0 ,σ /g2962 /g3285 /g2870 /g4673 , as described by 303 Minamikawa et al. 7. This study identified the combinations of SNP markers and founder haplotypes that exhibited 304 significant increases or decreases in frequency. The markers were compared with GW AS peaks for fruit traits, and the set of 305 markers that may have undergone selection based on fruit traits was narrowed. We then tracked the frequency of founder 306 haplotype in each generation that was divided by Helium and combined with the founder haplotype effect β /g3037/g3039 , investigated 307 that the markers and founder haplotypes may be strongly associated with selection on fruit traits. 308 Inferring reasons for changing of founder haplotype frequency via gene set enrichment analysis 309 The methods described above detected SNP markers showing significant changes in the frequencies of specific founder 310 haplotypes. These markers were compared with the GW AS results for fruit traits to identify the regions potentially selected 311 for fruit traits. However, markers that are unrelated to fruit traits may not have been detected. It is possible that these SNP 312 markers were selected based on unmeasured traits. Therefore, we investigated SNP markers associated with these traits. 313 First, the gene regions assigned to the ‘Golden Delicious’ doubled-haploid tree (GDDH13) reference and their annotations 314 were downloaded from Phytozome database38. Using the 669 SNP markers detected using the above method, gene regions 315 containing these markers were extracted. The extracted 271 genes were then subjected to gene set enrichment analysis using 316 the R package “ClusterProfiler”39. The GO terms of these genes were analyzed in three categories: biological processes, MF, 317 and CC. 318 319 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Acknowledgments 320 We thank all members of the Laboratory of Biometry and Bioinformatics of The University of Tokyo for their advice 321 regarding this study and all members of the NARO Institute of Fruit Tree Science for maintaining the apple trees. This 322 research 541 is supported by a grant from MAFF commissioned project study on “Smart breeding 542 technologies to 323 Accelerate the development of new varieties toward achieving “Strategy for 543 Sustainable Food Systems, MIDORI”” and 324 JST SPRING grant number JPMJSP2108. 325 326 Data availability 327 Data supporting the findings of this study are available from the corresponding author, H.I., upon reasonable request. 328 329 Conflict of interests 330 The authors declare that they have no conflict of interests. 331 332 Competing financial interests 333 The authors declare no competing financial interests. 334 335 Author Contributions 336 The study was conceptualized by H.M., M.F.M., K.H., and H.I.. The experimental design was implemented by M.K., S.M., 337 Y .K., and T.Y ., who extracted DNA, and performed SNP genotyping. S.M. performed the phenotyping. M.F.M., M.K., and 338 H.I. traced the founder haplotypes. M.F.M. and K.N. performed the GW AS. H.M., M.F.M., and K.H. performed gene drop 339 simulations. H.M. and M. F. M. checked the annotation and performed GO enrichment analysis. M.F.M, K.H., and H.I. 340 provided technical help for the statistical analysis. H.M., M.F.M., and H.I. drafted the manuscript. All the authors have read 341 and approved the manuscript. 342

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Nat. Genet. 49, 1099–1106 (2017). 438 [39] Yu, G., Wang, L.-G., Han, Y . & He, Q.-Y . clusterProfiler: an R package for comparing biological themes among gene 439 clusters. OMICS 16, 284–287 (2012). 440 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Supplementary Figure 1; Test of Founder haplotype frequency using the null distribution. This figure shows the null distribution (grey) used to test the founder haplotype frequency. The stars indicate the position of the observed frequency of the founder haplotype at an SNP locus, and the red area shows the probability (= 𝑝-value) of an event being rarer than the observed frequency of the founder haplotype in the simulation. Frequency of founder haplotype Number of simulations .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Supplementary Figure 2; Detection of bias in the frequency of the 14 founder haplotypes in the gene drop simulation in the first generation of divided generations. No gene drop simulation was performed in the first generation because of the origin of founder haplotype. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Supplementary Figure 3; Detection of bias in the frequency of the 14 founder haplotypes in the gene drop simulation in the second generation of divided generations. Since the gene drop simulation assumes a half inheritance of each founder haplotype combination from both parents, there were no SNP markers with significantly altered founder haplotype frequencies until the second generation. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Supplementary Figure 4; Detection of bias in the frequency of the 14 founder haplotypes in the gene drop simulation in the third generation of divided generations. SNP markers with significantly altered founder haplotype frequencies were detected in founder haplotypes 1 and 2. Both of these SNPs were located on chromosome 1. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Supplementary Figure 5; Detection of bias in the frequency of the 14 founder haplotypes in the gene drop simulation in the fourth generation of divided generations. As in the third generation, there was a SNP marker on chromosome 1 of the founder haplotype 2 that significantly changed the frequency of the founder haplotype. Moreover, the founder haplotype 3 also had significantly altered the frequency of founder haplotype associated with SNP markers on chromosome 15. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Supplementary Figure 6; Detection of bias in the frequency of the 14 founder haplotypes in the gene drop simulation in the fifth generation of divided generations. In this generation, SNP markers significantly altering the frequency of founder haplotypes were present on chromosome 13 of founder haplotype 8. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 7; Relationship between the bias in the frequency of founder haplotype 6 from 'Golden Delicious’ and fructose content of apple fruits. (a) Detection of bias in the frequency of founder haplotype 6 from 'Golden Delicious'. (b) GW AS

for fructose content. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_1117728; block5) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on fructose content. Founder haplotype 6 (red) has the largest positive effect on fructose content. (d) Changes in frequency of founder haplotype 6 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of fructose content in each generation. Fructose content tends to increase over generations. This marker showed an increased frequency of founder haplotype 6 with a positive effect on fructose content. There was also an increasing trend in fructose content per generation. As a result, marker effect and founder haplotype frequency matched the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 8; Relationship between the bias in the frequency of founder haplotype 13 from ‘Cox’s Orange Pippin’ and fructose content of apple fruits. (a) Detection of bias in the frequency of founder haplotype 13 from ‘Cox’s Orange Pippin’. (b) GW AS results for fructose content. Green dashed line in (a) and (b) indicate SNP locus (RosBREEDSNP_SNP_AG_10716913_Lg6_MDP0000302895_MAF10_MDP0000302895_exon2; block3) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on fructose content. Founder haplotype 13 (red) has a fifth negative effect on fructose content. (d) Changes in frequency of founder haplotype 13 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of fructose content in each generation. Fructose content tends to increase over generations. This marker showed an increased frequency of founder haplotype 13 with a negative effect on fructose content. There was also an increasing trend in fructose content per generation. As a result, marker effect and frequency did not match the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 9; Relationship between the bias in the frequency of founder haplotype 13 from ‘Cox’s Orange Pippin’ and fructose content of apple fruits. (a) Detection of bias in the frequency of founder haplotype 13 from ‘Cox’s Orange Pippin’. (b) GW AS results for fructose content. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_0666725; block4) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on fructose content. Founder haplotype 13 (red) has a third positive effect on fructose content. (d) Changes in frequency of founder haplotype 13 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of fructose content in each generation. Fructose content tends to increase over generations. This marker showed an increased frequency of founder haplotype 13 with a positive effect on fructose content. There was also an increasing trend in fructose content per generation. As a result, marker effect and frequency matched the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 10; Relationship between the bias in the frequency of founder haplotype 2 from ‘Ralls Janet’ and malic acid content of apple fruits. (a) Detection of bias in the frequency of founder haplotype 2 from ‘Ralls Janet’. (b) GW AS results for malic acid content. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_0436910; block1) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on malic acid content. Founder haplotype 2 (red) has a third negative effect on malic acid content. (d) Changes in frequency of founder haplotype 2 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of malic acid content in each generation. Malic acid content tends to decrease over generations. This marker showed an increased frequency of founder haplotype 2 with a negative effect on malic acid content. There was also an increasing trend in malic acid content per generation. As a result, marker effect and frequency matched the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 11; Relationship between the bias in the frequency of founder haplotype 6 from ‘Golden Delicious’ and malic acid content of apple fruits. (a) Detection of bias in the frequency of founder haplotype 6 from ‘Golden Delicious’. (b) GW AS

for malic acid content. Green dashed line in (a) and (b) indicate SNP locus (RosBREEDSNP_SNP_CT_16509379_Lg8_324685_MAF40_324685_exon1; block10) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on malic acid content. Founder haplotype 6 (red) has a fifth negative effect on malic acid content. (d) Changes in frequency of founder haplotype 6 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of malic acid content in each generation. Malic acid content tends to decrease over generations. This marker showed an increased frequency of founder haplotype 6 with a negative effect on malic acid content. There was also a decrease trend in malic acid content per generation. As a result, marker effect and frequency matched the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 12; Relationship between the bias in the frequency of founder haplotype 6 from ‘Golden Delicious’ and malic acid content of apple fruits. (a) Detection of bias in the frequency of founder haplotype 6 from ‘Golden Delicious’. (b) GW AS

for malic acid content. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_0746410; block6) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on malic acid content. Founder haplotype 6 (red) has a fourth negative effect on malic acid content. (d) Changes in frequency of founder haplotype 6 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of malic acid content in each generation. Malic acid content tends to decrease over generations. This marker showed an increased frequency of founder haplotype 6 with a negative effect on malic acid content. There was also a decrease trend in malic acid content per generation. As a result, marker effect and frequency matched the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 13; Relationship between the bias in the frequency of founder haplotype 3 from ‘Delicious’ and Harvest time (PickDay) of apple fruits. (a) Detection of bias in the frequency of founder haplotype 3 from ‘Delicious’. (b) GW AS results for PickDay. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_0303417; block11) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on PickDay. Founder haplotype 3 (red) has a sixth negative effect on PickDay. (d) Changes in frequency of founder haplotype 3 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of PickDay in each generation. PickDay tends to decrease over generations. This marker showed an increased frequency of founder haplotype 3 with a negative effect on PickDay. There was also a decrease trend in PickDay per generation. As a result, marker effect and frequency matched the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 14; Relationship between the bias in the frequency of founder haplotype 5 from ‘Golden Delicious’ and PickDay of apple fruits. (a) Detection of bias in the frequency of founder haplotype 5 from ‘Golden Delicious’. (b) GW AS

for PickDay. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_0246031; block9) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on PickDay. Founder haplotype 5 (red) has a third negative effect on PickDay. (d) Changes in frequency of founder haplotype 3 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of PickDay in each generation. PickDay tends to decrease over generations. This marker showed a decrease frequency of founder haplotype 5 with a negative effect on PickDay. There was also a decrease trend in PickDay per generation. As a result, marker effect and frequency did not match the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 15; Relationship between the bias in the frequency of founder haplotype 8 from ‘Jonathan’ and PickDay of apple fruits. (a) Detection of bias in the frequency of founder haplotype 8 from ‘Jonathan’. (b) GW AS results for PickDay. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_0164463; block8) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on PickDay. Founder haplotype 8 (red) has a largest positive effect on PickDay. (d) Changes in frequency of founder haplotype 8 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of PickDay in each generation. PickDay tends to decrease over generations. This marker showed an increase frequency of founder haplotype 8 with a positive effect on PickDay. There was also a decrease trend in PickDay per generation. As a result, marker effect and frequency did not match the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 16; Relationship between the bias in the frequency of founder haplotype 13 from ‘Cox’s Orange Pippin’ and PickDay of apple fruits. (a) Detection of bias in the frequency of founder haplotype 13 from ‘Cox’s Orange Pippin’. (b) GW AS results for PickDay. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_0654632; block2) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on PickDay. Founder haplotype 13 (red) has a second negative effect on PickDay. (d) Changes in frequency of founder haplotype 13 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of PickDay in each generation. PickDay tends to decrease over generations. This marker showed an increase frequency of founder haplotype 13 with a negative effect on PickDay. There was also a decrease trend in PickDay per generation. As a result, marker effect and frequency matched the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 17; Relationship between the bias in the frequency of founder haplotype 8 from ‘Jonathan’ and fruit weight (W eight) of apple fruits. (a) Detection of bias in the frequency of founder haplotype 8 from ‘Jonathan’. (b) GW AS results for Weight. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_0160784; block7) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on Weight. Founder haplotype 8 (red) has a seventh positive effect on Weight. (d) Changes in frequency of founder haplotype 8 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of Weight in each generation. Weight has no trend over generations. This marker showed an increase frequency of founder haplotype 8 with a positive effect on Weight. There was also a no trend in Weight per generation. As a result, marker effect and frequency did not match the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint (a) (b) (c) (d) (e) Supplementary Figure 18; Relationship between the bias in the frequency of founder haplotype 8 from ‘Jonathan’ and Weight of apple fruits. (a) Detection of bias in the frequency of founder haplotype 8 from ‘Jonathan’. (b) GW AS results for Weight. Green dashed line in (a) and (b) indicate SNP locus (SNP_FB_1063136; block12) detected in both (a) and (b). (c) Effects (𝛽) of each of the 14 founder haplotypes locating at this marker locus on Weight. Founder haplotype 8 (red) has a seventh negative effect on Weight. (d) Changes in frequency of founder haplotype 8 against the generation. The upper and lower red dashed lines indicate the frequencies in the point of upper or lower −log10 𝑝 = 4, respectively, in the null distribution obtained by the simulation. The blue dashed line represents the average frequency in the simulation. (e) Box plot of Weight in each generation. Weight has no trend over generations. This marker showed an increase frequency of founder haplotype 8 with a negative effect on Weight. There was also a no trend in Weight per generation. As a result, marker effect and frequency did not match the transition of phenotypic values. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Supplementary Figure 19; MF gene network drawing by go-plot in ClusterProfiler The result of gene set enrichment analysis in MF. Arrows indicate relationship between functions. MF had two type of function and its separated binding and catalytic activity. In catalytic activity, the transferase activity, transferring phosphorus-containing groups had lowest adjusted p-value. Additionally, the protein kinase activity is most down- stream function. Moreover, in binding function, sequence-specific DNA binding had lowest adjusted p-value. The most down-stream function of binding is RNA polymerase II transcription regulatory region sequence-specific DNA binding. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint Supplementary Figure 20; CC gene network drawing by go-plot in ClusterProfiler The result of gene set enrichment analysis in CC. The solid arrows indicate relationship between functions and the dashed arrows indicate part of the function is included. The function related to nuclear lumen is most down-stream and significant. The function CC related to the SNP markers, associated with biased founder haplotype frequency, may be related to nuclear lumen. .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 17, 2025. ; https://doi.org/10.1101/2025.03.16.643583doi: bioRxiv preprint