The results revealed how the phenotypic expression of the main quantitative traits of interest assessed in five half-sib families was controlled by the additive genetic effects and by non-additive effects of dominance and epistasis. The statistical number of hybrids required to ensure efficient selection increased exponentially with the number of desirable traits. The minimum number of progenies required to obtain a hybrid with associated quantitative traits of agronomic interest was highly variable. For two independent traits essential in selection , but incorporated together in the same hybrid, the statistical number was between about 30 and 300. If three more cumulative traits were added , the limits increased to between 1500 and 18,000. The study highlighted the need for new apple varieties due to the narrowing of the genetic diversity of the cultivated species and how the choice of parents used in hybridizations (as well as the objectives pursued in the selection) can increase the efficiency of apple breeding.Apple breeding is a laborious and long-lasting process that requires qualified resources, land, time, and funds. In this study, more than 5000 F The apple is the primary fruit-bearing species in temperate regions and ranks first in terms of global fruit production. Several factors contributed to the spread of apples over the world, including: the nutritional, gustatory, therapeutic, and prophylactic value of fruits; the specific technological properties and agrobiological characteristics of trees; ecological plasticity; and high economic value ,2. BecauApples are grown on an area of approximately 4 million ha worldwide, with fruit production averaging around 86–87 million metric tonnes per year in recent years . China iM. sieversii and M. sylvestris as well as numerous interspecific and intraspecific hybridizations [The cultivated apple influenced human history, and the apple is considered a symbol of wisdom and love . Apple vizations . Hybridiizations ,15. Thusizations . Among tizations . McIntosizations . Newly cizations ,20,21,22izations .As with any agricultural species, apple quality and production can vary. The apple can also be impacted by variations in consumer preferences, market demands, the processing industry, farmers’ obstacles and difficulties, and other constraints to sustainable apple production ,24,25,261 hybrid populations obtained from intraspecific hybridizations was conducted. Depending on the manner of parental form participation and the type of cross-breeding performed, the results of numerous hybridizations were compared. Additionally, it was investigated how the parental forms utilized for various hybrid combinations and the criteria employed in apple breeding could impact selection efficiency. The biological material in the field did not benefit from the maintenance activities because of the drastically reduced funding. Consequently, data were collected under these circumstances, in a natural context .Even though remarkable results have been obtained in apple breeding (as evidenced by the multitude of cultivars obtained in various countries around the world), the conservation of genetic resources and the creation of new cultivars are processes that have seen a noticeable slowdown or even stagnation in recent years. The global economic and social situation, the global trend of continuously reducing resources allocated for these purposes, and the risk of biodiversity loss and genetic resource restriction can severely impact the efforts to capitalize on genetic resources and counteract possible risk factors for the cultivated species ,39. The 1 apple hybrids showed significant differences. A more accurate evaluation of the outcomes was accomplished by dividing the 25 hybrid combinations into three categories based on the vigor of the maternal parents   and the height of the trees in the 25 hybrid combinations produced by direct crosses between parents with different growth vigor in the Fg vigor) .1 hybrids on average in the experiment was 54.9 cm2, and in hybrid families it ranged between 33.2 cm2 (Ardelean × Ancuța) and 71.2 cm2 (Ardelean × Prima). The difference between the mean values of the two families with the most extreme TCSA levels resulted in a large range of variation. The average of the hybrids from Ardelean × Prima exceeded twice those of Ardelean × Ancuța, which denoted very strong but completely different influences of Prima and Ancuța as fathers in the transmission of a certain vigor in offspring. The hybrid combinations that produced less vigorous seedlings were: Ancuța × Golden spur, Aromat de vară × Ancuța, Starkrimson × Ancuța, Reinette Baumann × Golden spur, and Roșu de Cluj × Ancuța. Depending on the vigor groups of the maternal parents, the lowest vigor of the F1 hybrids was obtained in the maternal parents with low growth vigor. The coefficients of variation (CV%) for TCSA had high values that oscillated between 15.7% (Kinrei × Jonathan) and 71.5% (Ancuța × Roșu de Cluj). When considering the CV% , medium (10–20%), high (20–30%), and very high (over 30%)), only two combinations had medium variation, four had high, and the rest had very high.The cross-sectional area of the trunk in FThe height of the hybrids showed a large amplitude, and there were noticeable differences amongst the examined combinations, thereby demonstrating the strong parental influences on the trait. The average height of the trees for all hybrid combinations was 3.8 m; the extreme values were found in the Ardelean × Ancuța (3.0 m) and Ardelean × Feleac (5.1 m) combinations. Elite plants with a smaller tree height, in addition to other desired traits, were more likely to occur in the following hybrid populations: Ardelean × Ancuța, Ancuța × Golden spur, Roșu de Cluj × Kaltherer Böhmer, Roșu de Cluj × Golden spur, Kinrei × Jonathan, Roșu de Cluj × Ancuța, Ancuța × Mutsu, Aromat de vară × Ancuța, and Prima × Feleac.1 hybrids from the five crosses with a common tester revealed obvious differences depending on half-sib families (1 hybrids’ heights. The testcross with the lowest tester vigor (Starkrimson) was found to have the highest mean TCSA value.The vigor of the Ffamilies  due to t1 hybrids originated from direct and testcross hybridizations with parents of different levels of vigor were arbitrarily classified into three classes .When the parents were divided into three vigor categories to evaluate the combining ability for all crosses, it was discovered that genetic effects of the general combining ability (GCA) were generally more significant than those of the specific combining ability (SCA) both for TCSA and tree height . In accoThe growth and ramification of the trees in some hybrids were rather simply framed in one of the four architectural ‘ideotypes’ established by Lespinasse et al. . Figure In the first two years of their lives, none of the hybrids attained the fruiting period. A relatively small percentage of seedlings (5.7%) produced their first fruit in the third year .The percentage of hybrids that produced fruit increased gradually in consecutive years and reached 11.7% in the fourth year, 22.1% in the fifth, a slightly lower percentage (18.0%) in the sixth, 20.2% in the seventh, 15.5% in the eighth, 5.5% in the ninth, and 1.3% in the tenth. The relationship between the cumulative percentage of hybrids and the year of fruiting indicated the length of the juvenile stage in apple hybrids (seedlings on their own roots). It should be noted that only hybrids that began bearing fruit within the first 10 years of life were examined. However, some of the hybrids analyzed did not bear fruit at the end of the study period (probably due to an extremely long juvenile period or due to sterility). In the direct crosses, hybrids with a high number of fruits per tree were recorded in the following combinations: Reinette Baumann × Golden spur, Cluj Red × Kaltherer Böhmer, Roșu de Cluj × Ancuța, Aromat de vară × Melba, and Golden Delicious × Ancuța .1 apple hybrids was an extremely variable trait. Within the families, the CV% was very high and had limits between 31.5% (Roșu de Cluj × Ancuța) and 92.6% (Kinrei × Jonathan).These hybrid populations have the potential for successful selection of elite plants with profuse fruiting, but this trait must also be coupled to the size of the fruits and other advantageous qualities. The coefficient of variation per experiment (70.9%) demonstrated that the number of fruits per tree in FHybrids with large fruits were obtained in the following families: Aromat de vară × Mutsu, Roșu de Cluj × Kaltherer Böhmer, Ardelean × Prima, Aromat de vară × Reinette Baumann, Aromat de vară × Melba, Kinrei × Ardelean, and Golden Delicious × Ancuța. The coefficient of variation (CV%) fluctuated strongly within the hybrid families between 16.2 and 69.3%.The number of fruits on the tree in the testcrosses  varied w1 hybrids from families resulting from direct hybridizations, a relatively large range of variation was recorded .For the average number of days required for fruit ripening of Frecorded . The ampFruit quality was highlighted in 21 hybrid combinations; some had a significant proportion of offspring with an appropriate taste for the selection. As a result, the hybrid combinations of Prima × Feleac, Ardelean × Feleac, and Prima × Ardelean stood out. Mutsu × Roșu de Cluj, Ardelean × Prima, Roșu de Cluj × Feleac, Golden Delicious × Ancuţa, Roșu de Cluj × Ancuţa, and Kinrei × Jonathan represented other hybrid families with good-tasting fruits that may be of interest for selection.The coefficient of variation for fruit taste in the analyzed families was relatively high, thereby indicating a large diversity of fruit taste in each family. These values suggested the presence of a wide range of genotypes that ranged from low-quality- to high-quality-tasting fruit hybrids. Some hybrids produced fruits with taste comparable to the cultivars in the assortment.1 hybrids to reach physiological fruit maturity varied significantly  was produced when a summer variety (Aromat de vară) and a winter variety (Mutsu as tester) were crossed. It was interesting that by crossing with a winter selection (X–6–64), offspring with an early fruit ripening (110.0 days) were obtained. The hybrids with the latest ripening when Ancuța was used as a tester resulted from the crossing with the DSF 3/80 selection (200.8 days), and a large part of the descendants completed the fruit ripening in storage. As a paternal tester, Prima, which is an autumn variety, induced a relatively late fruit ripening in the progeny (average of 154.7 days of experiment); even though the seven genotypes used as maternal parents contained one (X–13–10) with summer ripening and three  with autumn ripening. Using Starkrimson as a paternal tester (winter variety), an average of 174.3 days was achieved, which was higher than the averages produced by the other testers .When Feleac was used as paternal tester, the differences between the mean scores for the fruit taste of the hybrids in the 13 families were not statistically significant . HybridsIn the ensemble of analyzed hybrids with edifying results for fruit development and ripening both from direct hybridizations and testcrosses (5484 hybrids), the following proportions were obtained for the ripening period of the fruits: summer 12.7%, autumn 53.5%, and winter 33.8% .1 apple hybrids were highlighted by combining all hybridizations in a diallel system with three groups of parents according to the season of fruit ripening   . The res1 hybrids, especially in summer × summer crosses.Interaction effects of dominance and epistasis were significantly positive in crosses with parental forms of the summer × summer type (CSC = +1.1043 **). Contrary, in summer × autumn and summer × winter hybridizations, the non-additive effects significantly prevented the obtaining of offspring with a summer fruit ripening. Thus, significant additive and non-additive effects were involved in the genetic inheritance of the summer ripening of fruits . Therefore, summer fruit ripening was determined either by the combined effect of additivity and dominance and epistasis interactions or solely by the no-additive interactions. These latter effects, although partially non-transmissible, could decisively influence the trait in FVenturia inaequalis (Cke.) Wint.) attack on F1 apple hybrids from 22 direct hybrid combinations highlighted relatively low values of the average scores recorded for most hybrid combinations (Apple scab (inations . HoweverPodosphaera leucotricha (Ell. et Ev.) Salm.) attack. Within the hybrid families, the coefficient of variation of the notes for disease response ranged from small-medium (CV% of 10.2% in Roşu de Cluj × Ancuța) to very high (CV% of 52.8% in Ardelean × Prima). The CV% of powdery mildew noted in the experiment represented by the 22 hybrid combinations was 38.1%.The hybrids of Aromat de vară × Mutsu, Aromat de vară × Ancuta, and Ancuta × Starkrimson provided an appropriate response to the powdery mildew . With Mutsu as a tester, less sensitive hybrids to scab fungus were recorded when the mothers were Ancuța, Aromat de vară, and X–5–71, while the Ancuța tester highlighted the X–17–16 and X–21–20 selections. Prima as the tester highlighted X–5–65 and X–21–20 selections, and Starkrimson two other selections: III–II–17–25 and DSF 1/54.The average notes between half-sibling families based on the tester did not differ significantly for the apple scab attack in the testcrosses, but there were significant differences in each of the five types of testcrosses . Each teThe testcross schemes were also useful in identifying hybrid families in which the selection for resistance or tolerance to powdery mildew could be more efficient. Feleac as a tester indicated the hybrid populations in which the mothers were X–5–71, X–3–8, X–9–70, DSF 7/68, and III–VI–5–26. Mutsu highlighted Aromat de vară, 218/2, X–6–73, and DSF 3/70; Ancuța as the tester highlighted DSF 5/67, X–17–16, and X–9–70. Prima identified the following genotypes: X–5–65, X–21–20, X–6–24, and X–5–52; while Starkrimson as the tester highlighted 218/2, DSF 3/58, and X–6–3.1 hybrids in the half-sibling families depending on the trait and tester used. The genotypic coefficient of variation (GCV) registered large oscillations depending on the tester for the following traits: fruit size—between 2.6 (Feleac) and 41.8 (Prima); fruit taste—between 8.1 (Mutsu) and 49.8 (Prima); and response to powdery mildew attack—between 9.8 (Mutsu) and 41.0 (Prima). For the response of the F1 hybrids to apple scab attack, because the Prima cultivar has a monogenic resistance to disease , the GCV value is only indicative and presented in parentheses. For the same reason, heritability coefficients were also not calculated.The main genetic parameters analyzed within half-sibling families depending on testcrosses are presented in 2) and heritability in the narrow sense (h2) depending on the trait and the tester. For H2, a greater variation in the genotype’s contribution to the trait’s phenotypic expression was observed as follows: fruit size—between 0.531–0.946 (Feleac and Prima); taste of the fruits—between 0.566–0.975, and response to powdery mildew attack—between 0.554–0.891 (Mutsu and Prima). Greater uniformity of H2 values among testers was identified for fruit ripening and tree vigor (TCSA and tree height).There were differences between heritability in the broad sense (H2 = 0.408), for tree height with Mutsu (0.416), for fruit size and fruit taste with Prima , for fruit ripening with Starkrimson (0.427), and for apple scab and powdery mildew attack with Starkrimson . Expected response to selection had relatively high values with Starkrimson for TCSA and the number of fruits per tree and with Prima for fruit size, fruit taste, and response to powdery mildew attack.The genetic effects of additivity played a different role depending on both the tester and the trait analyzed. Thus, the non-additive genetic effects of dominance and epistasis had a more consistent role for TCSA with Starkrimson  but also with Ancuța and Prima and slightly higher with Feleac (9.2%). Overall, a higher proportion of hybrids appropriate for selection were obtained under the hybridization categories for winter ripe fruits, apple scab tolerance, and powdery mildew. Among the testers noted were Ancuța and Feleac (for the ‘large fruit’ trait), Starkrimson and Prima (for tolerance to apple scab), and Mutsu (for weak vigor of the trees).A relatively low percentage (4.6%) was obtained for fruit flavor in direct hybridizations, but an unexpectedly high percentage for the trees’ tolerance to apple scab attack was obtained. In the case of the testers, the percentage of FA principal component analysis (PCA), a multivariate technique for analyzing quantitative data, highlighted a close link between hybridizations when utilizing Mutsu as the tester and direct hybridizations . Ancuța Tolerance to apple scab was the only trait that was placed in a different quadrant from the others. This trait was the most different from the others (quadrant I). In opposition to the adequate response of trees to apple scab attack, the main characteristics of fruit production and fruit quality appeared, namely the number of fruits per tree, large fruits, and high eating taste. On the other diagonal, in quadrant IV there was reduced tree vigor  in an inverse relationship with winter ripeness of fruits and tree tolerance to powdery mildew attack. Of the two main components of the PCA, PC1 captured a very large part of the total variation (90.5%) but PC2 only a small part (6.2%).A UPGMA dendrogram  confirmeIf the arrangement of the vigor elements of the trees together in a common subcluster was to be expected, the positioning of a high number of fruits per tree and high eating taste in a common subcluster appeared quite surprising. The close relationship revealed by the multivariate analysis between these two traits may suggest that hybrids with a larger fruit load in the crown of the trees may produce fruits with a better taste. Similarly, another cluster with two close characters could indicate that the winter ripening of fruits can be associated with larger fruits. These two characteristics would be quite closely related to tolerance to powdery mildew attack.Extreme variation existed in the minimum of progeny required to produce a hybrid with quantitative traits of agronomic interest . RegardlThe average for the entire experiment was at least 122 offspring for the two traits that were crucial in the selection of elite plants (high eating taste and large fruits) and increased to 692 progenies if two more traits of great interest in apple breeding were added (tolerance to apple scab and powdery mildew attacks). If we added a fifth trait (high number of fruits per tree), we reached 6383 hybrids, and then the exponential growth continued to impressive numbers with the addition of the next desired traits.Thus, if we combined the intended fruit ripening period  with the lowered tree vigor , we obtained 259,509 hybrids. Interestingly, if instead of weak vigor as trunk cross-sectional area we included weak vigor as tree height, the minimum number of hybrids was reduced to 166,835. Analysis indicated that among the testers, Feleac and Prima produced the best results for the first five extremely relevant traits .1 hybrid populations derived from direct and testcross hybridizations highlighted the existing differences in the important quantitative traits of seedlings both between families and within the families and depending on the parents and their crossing. The inheritance of the investigated traits followed a predictable quantitative pattern, and the offspring genetically inherited the traits of the parents.The analysis of F1 hybrids .Our results confirmed that the polygenic inheritance of tree vigor ,44,45,461 descendants from the experiment in a certain type of growth and fruiting demonstrated the reduced proportion of spur, weeping, and columnar architectural ideotypes compared to ‘standard’. The spur type included a reduced vigor of the trees and particularities useful for intensive culture that are much desired in modern apple breeding programs [Co) [Co dominant gene [Co allele. This is unlikely because it would have resulted in Mendelian segregation of the columnar offspring. Therefore, there was a greater probability for the hypothesis of a polygenic inheritance of the columnar ideotype because even ‘common’ spur-type varieties can produce offspring with a compact growth that is almost as extreme as the Wijcik type [W) [Even if tree vigor is considered a quantitative trait ,44, the programs ,51. The ams [Co) ,52, but ams [Co) . If the ant gene , in hybrcik type  but withcik type . The rescik type  or implicik type . Spur, ccik type . Similartype [W) ,58.The juvenile period is of great interest in apple breeding because juvenility delays the selection process, increases the costs of tree maintenance, and occupies the land for a certain period ,59,60. IThe size of the fruits along with the number of fruits per tree provided valuable information about the production potential of offspring from various types of crosses subjected to the selection process . Some of1 hybrid populations could be obtained in which hybrids with the desired ripening period predominated and the selection in the respective direction was efficient [1 apple hybrids appeared as a less variable character and as a result were relatively easier to transmit and fixed in the offspring. Apple fruit ripening as well as the flowering period are quantitatively inherited, and deciphering their genetic control is essential for breeding cultivars adapted to growing environments [Breeding objectives aimed at enriching the assortment of apples with varieties of different ripening to ensure fresh fruit throughout the year have lost interest. If in the past the goal was to develop early summer to winter types with good fruit preservation in storage, the significance of these objectives has been diminished by modern storage conditions . Our resfficient . This apronments .The taste of the fruits remains a crucial characteristic in the evaluation of hybrid populations and the selection of elites ,51. AlthVenturia inaequalis (Cke.) Wint., which causes apple scab, and Podosphaera leucotricha (Ell. et Ev.) Salm., which causes powdery mildew, are the pathogens that causes the greatest damage to apple crops [1 offspring was generally high, thereby indicating the presence in most of the analyzed combinations of some plants with a different response to the pathogens: from not attacked or weakly attacked (resistant or tolerant) to medium or strongly attacked (susceptible or even very sensitive to the disease). Testcrosses highlighted cultivars and selections with good combinatory ability to obtain resistant or tolerant progeny to both diseases.Among the apple diseases, le crops ,73. AttaVf (Rvi6) gene for resistance to apple scab derived from Malus floribunda 821 [Vf, which was transmitted to approximately half of its offspring, Prima produced hybrids with an average score for apple scab attack that was halved compared to the other testers. Because of monogenic resistance, the genetic parameters specific to the characters with polygenic inheritance were not calculated for Prima half-siblings. It was obvious that obtaining hybrids with good resistance or at least tolerance to apple scab attack was relatively easy to achieve by using suitable parents  [Vf gene  group) resulted in obtaining a higher percentage of hybrids with genetic resistance to apple scab according to Mendelian reports. Hybrids with a proper response to apple scab attack were obtained by crossing the X–21–20 selection, which was derived from a cross between an interspecific hybrid of Reinette Baumann × Malus niedzwetzkyana (see It is well known that Prima was the first apple cultivar in a series to carry the unda 821 . Due to parents) ,76,77. Cyana see  with PriIn the direct hybridizations, offspring with reduced susceptibility to powdery mildew were obtained in the following crosses: Aromat de vară × Mutsu, Aromat de vară × Ancuţa, and Ancuţa × Starkrimson. Some parents (Aromat de vară and Ancuța) produced hybrids that were both resistant (or tolerant) and sensitive to powdery mildew, which illustrated the important role of the hybridization partner or the hybrid combination. The difference between direct and reciprocal hybrids of Ancuța and Roşu de Cluj led to the hypothesis that the sensitivity to powdery mildew of Roşu de Cluj (previously reported as a carrier of polygenic resistance to apple scab ) is tran1 hybrids (in about one-fourth of the offspring). It was found that the statistical size of the hybrid population required to find at least one hybrid that possessed all of the desirable characteristics at a high level increased exponentially with the number of traits of interest associated with that hybrid (and subsequently a new variety). As an average for all hybrids, this number was 122 for two traits (high eating taste and large fruits), 692 for four traits (if resistance/tolerance to apple scab and to powdery mildew attack were added to the first two), and 6383 (if the fifth trait (the high number of fruits per tree) was added). If the winter ripening of fruits was also added, a very high value of 21,292 hybrids needed was reached. Adding low tree vigor resulted in 259,697 hybrids (when considering TCSA) and 166,872 hybrids (when considering tree height). A similar study has not been reported since the one conducted by Williams, who showed that one of 6250 hybrids will possess a combination of five quantitative traits independently from one another with a reasonable level of expression [The broad- and narrow-sense heritability calculated in this study varied within the limits of the majority of apple breeding experiments for normally distributed variables. Like in other investigations, the parental forms, the type of cross-breeding, the traits examined, and their scale influenced the heritability values . Overall, it was confirmed that the additivity effects of polygenes were more important than the non-additive effects ,46,61. H1 phenotypes probably was influenced due to a certain inbreeding of the parents involved obtained at HRS. As shown in The results regarding the complexity of the breeding process through hybridization and the extremely large number of descendants required for the selection of valuable descendants, which accumulate favorable characteristics expressed at a higher level ,85, appeIf 10,000 varieties of wheat were cultivated in China in 1949 and by the 1970s the number was reduced by 90%, Goland and Bauer  showed tMalus has a wide genetic diversity, cultivated apples have a narrow genetic background due to the common origin of many cultivars, the selection process, and heterozygosity maintained by continuous vegetative propagation [Internationally, the multitude of cultivars indicates how significant apple culture is in terms of food, nutrition, diet, health, social, and economic considerations ,3,18,34.pagation ,103. Manpagation ,98,104.Rvi6 (Vf) to scab  from ornamental or Japanese apple  [Vf gene [The widespread use of the resistance gene ribunda) ,107,108 ribunda) . More th[Vf gene . Many ap[Vf gene . To impr[Vf gene ,88,111.Malus genus as effectively as possible and obtaining ‘durable’ varieties with a good response against diseases and pests, biological potential, and ecological adaptability combined with the very high quality of fruits can result in the creation of new varieties [Climate change, the intensification of agriculture, the increase in the number of phytosanitary treatments and the diversification of products to combat diseases and pests, and the emergence of new pathogens or insects or their physiological or virulent races and strains accentuate the vulnerability of the apple to new challenges . Proposearieties ,112,113.arieties ,115. In arieties ,111. HRSFinally, based on the findings of this study, it can be concluded that the hybrids from the combinations with the highest scores for fruit taste provided the greatest proportion of clonal selections from the investigated hybrid populations. Some of these selections were obtained not just from ancestors represented by high-quality varieties but also from offspring obtained through free pollination. Because the open pollination in the latest case occurred in experimental fields with thousands of genotypes , it is probable that in the future they could represent a broad genetic base beneficial to new breeding projects. In addition, favorable outcomes may be produced in the future by combining the valuable traits from parents represented by these clonal selections and creating double or complex hybrids, thereby diversifying the genetic background of the new cultivars.The research was carried out at the Horticultural Research Station (HRS) in Cluj-Napoca, North West Romania. The station was founded in 1953 and has produced more than 20 new apple and pear cultivars. The main apple breeding objectives were reduced tree vigor, productivity, fruit quality, and disease resistance. The HRS pome tree breeding sector produced 10,000–20,000 hybrids annually and followed selection procedures in the field . The expSite and soil preparation, fertilization, and planting were standard and similar to those recommended in commercial orchards. However, due to a lack of funding and resources allocated to HRS in the last two decades, phytosanitary treatments, fertilization, and pruning or other interventions were not applied after planting to the hybrids included in this study. Thus, the hybrids had a natural vegetative growth, branching, crown, and fruiting; consequently, tree architecture, fruiting, and disease attacks were evaluated in the field without technological and phytosanitary interventions.1 apple hybrids in this study were obtained from intraspecific crosses with different cultivars or selections as parents as part of a breeding cycle in a standard and traditional scheme described by Wannemuehler et al. [All Fr et al. . The dat1 hybrids from testcrosses were derived from crossing a variety used as a paternal tester with different cultivars or selections (elites) obtained at HRS used as maternal parents. In the five testcrosses, the testers used were represented by the following cultivars: Feleac, Mutsu (included as an exception in the experiment for data comparison because it is a triploid variety), Ancuţa, Prima, and Starkrimson. In the direct hybridizations, hybrids were originated from 21–25 hybrid combinations (families). The parents were some well-known apple cultivars that included Jonathan, Golden Delicious, Starkrimson, Starking, Reinette Baumann, Kaltherer Böhmer, Melba, Golden spur, Mutsu, Prima, etc.; or cultivars created at HRS: Roşu de Cluj (in English: red of Cluj), Aromat de vară (in English: flavored of summer), Feleac, Ancuţa, and Ardelean. Some hybrids resulted from direct and reciprocal crosses . FIn the study, the data recorded in HRS observation registers were processed. In each hybrid family, the number of offspring as individuals (plants) was extremely variable and ranged from 7 to 178 seedlings. There were no seedlings removed before the data were recorded. All the offspring of the examined hybrid combinations were considered for the study regardless of their positive or negative traits. Due to the limited planting distances (3.0 m between rows and 1.0 m between plants per row) in the hybrid fields due to the terrain economy, the hybrids had an obvious tendency to increase in height. Although the branching of the trees was also influenced, it was assumed that all hybrids had the same uniformity of conditions. Due to the absence of tree cutting and fungicide treatments, the evaluation of the response of the hybrids to the attack of diseases was performed under natural conditions of infection using data from all years processed. The evaluation of the hybrids was performed based on the UPOV recommendations  and the The observations, measurements, and inferences were focused on the key elements of growth vigor, yield, fruit quality, and response to the main diseases of the species. In general, these factors are also considered while choosing elite plants for hybrid fields. Furthermore, assessments were made on the length of the juvenile stage, the type of growth and fruiting, and the fruit’s ripening time.2. Depending on the height and the TCSA, the vigor of the hybrids was arbitrarily considered as low (less than 3.5 m or 38.5 cm2), medium (between 3.5–4.5 m or 38.5–78.5 cm2), or strong (over 4.5 m or 78.5 m2).In order to assess the vigor of plant growth, measurements were made of the height and thickness of the trunk. The study considered data registered at the end of the 12th year of life in the autumn after the hybrids had finished their vegetation. The height of the trees was measured from the ground level to the top of the trees and expressed in meters; the diameter of the trunk was measured at 20 cm above ground in the row direction. Based on these data, the trunk cross-sectional area (TCSA) was calculated and expressed in cmAfter the hybrids entered the fruitification period, their productivity was analyzed via observations made on two essential elements of productivity: the number of fruits per plant and the size of the fruits. The number of fruits per tree was assessed by grading them with notes as follows: 1 = small number of fruits per tree (less than 6–8 regardless of fruit size); 4 = average number of fruits per tree (between 6–8 and 20–30); 7 = large number of fruits per tree (between 20–30 and 60–70); and 10 = very large number of fruits per tree (over 60–70). The size of the fruits was also assessed by grading them (for the same reasons of expeditiousness) with notes as follows: 1 = very small fruits (less than 50 g); 4 = small fruits (between 50–85 g); 7 = medium-sized fruits (between 85–125 g); and 10 = large fruits (over 125 g). For the ripening period of the fruit, the number of days from the beginning of flowering to the physiological maturity of the fruit was considered. The ripening of the fruit was considered to be summer if the apples had reached the maturity of consumption until September 1; autumn if the optimal time of consumption and fruits preserved capacity period was in the autumn months of September, October, and November; and winter if the optimal time of consumption and fruits preserved capacity period was in the winter months (even in the spring). In the assessment of ripening for late autumn and especially winter apples, the storage time  was also considered and was given as the number of days from the beginning of flowering to the moment when the fruits reached optimal consumption maturity.The taste of the fruit was appreciated by tasting and grading with the following notes: 2 = weak; 6 = medium; and 10 = good. The hybrids marked with 10 bore fruit at the quality level of most cultivated varieties, including very good or excellent quality. Those marked with 6 had fruits below the level of the lowest rated varieties in terms of the taste quality of apples, and those in grade 2 had fruits that were unfit for consumption (non-edible).Venturia inaequalis) and powdery mildew (Podosphaera leucotricha)—was appreciated in the natural conditions of infection; in the hybrid fields, the fungicide treatments was excluded. Each year, scab and powdery mildew incidence was assessed two times: in the first week of July and August and based on scab attack on leaves and powdery mildew on shoots. For expedition, a scale of 0 to 5 was used that followed the standard diagram corresponding to an attack index or attack degree (AD%) as follows: 0 = no attack, which represented a ‘zero’ apple scab and/or powdery mildew attack degree (AD% = 0); 1 = very weak attack (AD% = 0.1–1); 2 = weak attack (AD% = 1.1–5.0); 3 = medium attack (AD% = 5.1–15); 4 = strong attack (AD% = 15.1–20); and 5 = very powerful attack (AD% > 20.1) [The response of hybrids to the attack of the main diseases of the species—apple scab ( > 20.1) . The datThe data were summarized as means and standard deviations for each analyzed trait and hybrid combination. Statistical analysis of the experimental data was performed by applying the analysis of variance (ANOVA). When the value of the ratio F was greater than the appropriate critical distribution F at α = 0.05, the null hypothesis was rejected when considering that at least one of the means was significantly different from the other means. In this case, a post hoc test using Duncan’s multiple range test (α = 0.05) was performed.2) and narrow-sense heritability (h2) were calculated, and genetic variances were partitioned based on the relationship between the half-siblings [G = VGA + VGD + VGI). The genetic variance, environmental variance, and genetic × environmental interaction variances were divided into the overall phenotypic variance’s constituent parts (VP = VGA + VGD + VGI + VE + VG*E). All siblings were thought to have exposure to the same technology and life environment. Using the equation H2 = VG/VP (where VG represents genotypic variation and VP represents phenotypic variance), broad-sense heritability was computed. According to the equation h2 = VGA/VP (where VGA stands for additive genetic variance and VP stands for phenotypic variance), narrow-sense heritability was computed. Methods based on half-sibling variance were used to calculate H2 and h2; this took into consideration that the proportion of half-siblings’ shared genes (or their degree of relatedness) was equal to 25% (or 1/4 of the additive variance) [Both broad-sense heritability  .G) by the trait mean of half-sib families depending on the tester , 1 hybrids from each testcross combination of half-siblings, and h2 = narrow-sense heritability) [The genotypic coefficient of variation (GCV) was calculated by dividing the genotypic standard deviation (Sability) ,121. As ability) . The datability) .1 hybrids that exhibited the quantitative traits expressed individually at an optimal level for selection, the minimum number of offspring was calculated that would have accumulated and associated the desired quantitative features. The Williams procedure [Based on the percentage of Frocedure  was usedOur results illustrated the complexity of apple breeding using hybridization as well as the opportunities for breeders to achieve breeding goals, which must be associated with the current problems facing humanity. The expansion of the world’s population, the need to protect humanity’s food resources, climate change, and other risk factors for cultivated species are all arguments that must be considered in the future. The apple is one of the most important fruit species, and the reduction in funds allocated to research for the development of varieties and the conservation of genetic resources can dramatically amplify the vulnerability of the species to various stress factors. New hybridizations using parental forms with a different genetic dowry from most of the well-known and widespread varieties in the world could widen the genetic base of the new varieties. In this way, the genetic vulnerability of the cultivated apple and the risk of catastrophes  would decrease.


Skewed X chromosome inactivation (XCI-S) has been reported to be associated with some X-linked diseases, and currently several methods have been proposed to estimate the degree of the XCI-S (denoted as  X chromosome inactivation (XCI) is an important epigenetic phenomenon. Under the XCI, one of two X chromosomes in females is silenced in the early stage of embryonic development to ensure that the transcriptional dosage of X chromosomes in females and that in males are balanced . GeneralThe skewness of the XCI can reflect, or cause, biological consequences for females . The clovariants ,28. Overvariants . Single-variants ,31,32,33variants . The varvariants , has thevariants . Therefovariants  put forwvariants  improvedvariants , is not Except for testing the association between the genes on the X chromosome and the traits under study, it is also important to develop methods to measure the corresponding degree of the skewness of the XCI  . So, modFor quantitative traits, As for qualitative traits, As such, we obtain By assuming that the degree of the skewness of the XCI at the Note that g et al. , we haveTherefore, the It should be noted that even in the case of As mentioned above, we construct g et al. , we propg et al.  because Note that the point estimates  ,46,47. Wg et al. , Basu et …, 100) ,47, wherWe only consider a covariate o be 0.5 ; |βj|=e| jth SNP ,34,36, wAll of the parameters are the same as when simulating the quantitative trait, except that we need to set the case-control ratio to be 1:1.After simulating the genotypes and the trait values, we use model (4) to obtain the estimates of http://r-project.org, accessed on 5 January 2022). For each simulation setting, the number of the replicates is fixed to be 500, and for each replicate, the true value of The above simulation steps are all implemented in the R software  for The MSEs of the four point estimates . The dataset includes 2183 families and 7377 participants . Among them, only 5960 subjects have both the phenotypic and genotypic data, while others do not have phenotypic data or do not have genotypic data. There are five quantitative traits included in this dataset: the nicotine composite score, the alcohol consumption composite score, the alcohol dependence composite score, the illicit drug composite score and the non-substance use related behavioral disinhibition composite score. To avoid the influence of family structure on the results, we exclude offspring from the real data application. At the same time, we only need the information of female subjects, so we also exclude male subjects from the analysis. Meanwhile, 12,354 SNPs on the X chromosome are included in the dataset. We use the following quality control criteria to filter the SNPs [p value of the Hardy–Weinberg equilibrium test being less than https://uswest.ensembl.org/, accessed on 25 February 2022) reference, we use the “getBM” function in the R package “biomaRt” to match the SNPs to the genes on the X chromosome [The MCTFR Genome-Wide Association Study of Behavioral Disinhibition is a family-based epidemiological study of substance abuse and related psychopathology. The dataset can be made available from the database of Genotypes and Phenotypes with accession numbers 86747-6 and 95621-5  romosome . As suchNote that estimating ait data . Furtherait data . Due to ait data  to test TMEM47, statistically significantly associated with the alcohol dependence composite score  included in the gene. The estimated MAFs of these two SNPs are 0.1407 and 0.0998, respectively, which means that both SNPs only contain common variants. It has been confirmed that TMEM47 is located in the NC_000023.11 region and includes three exons. Studies have shown that the gene is expressed in the bladder, adipose and 23 other tissues and found that the overexpression of TMEM47 may induce resistance in patients to certain chemotherapy drugs [TMEM47 on the alcohol dependence composite score may be the XCI-R or the XCI-E. By comparing the interval widths of these four interval estimation methods, we find that the width of the CI obtained by the PF method is the shortest, followed by the HPDI obtained by the GBN method, and the longest is the CI yielded by the Fieller’s method.We finally identify only one gene, py drugs ,52. The In this paper, we propose four point estimates , and can be used to estimate the degree of the skewness of the XCI for genes through the proposed methods in this paper. This R package also allows researchers to specify the prior distribution of each unknown parameter from their own research backgrounds. Fourthly, the Bayesian methods use the HMC algorithm for the sampling, which is not affected by the correlation between unknown parameters. Therefore, to improve computational efficiency, we assumed that all the unknown parameters are independent. However, the Bayesian methods, taking the correlation between the parameters into account, should have better performance, which is our future work. Fifthly, if the HPDIs or CIs we get contain 1, which means that the XCI pattern for the gene is the XCI-R or the XCI-E, our proposed methods cannot distinguish them. Therefore, in our future study, we will consider including males’ information to distinguish the XCI-R from the XCI-E. Finally, the proposed methods are only applicable to independent female subjects, and we will extend them in future so that they could accommodate the family data.Last, but not least, there are still some issues in our proposed methods which need to be discussed. Firstly, we would like to further discuss the effect of the truncation by the interval 0,  on the pWe propose four point estimates and four interval estimation methods to estimate


Antidepressants are a first-line treatment for depression. However, only a third of individuals experience remission after the first treatment. Common genetic variation, in part, likely regulates antidepressant response, yet the success of previous genome-wide association studies has been limited by sample size. This study performs the largest genetic analysis of prospectively assessed antidepressant response in major depressive disorder to gain insight into the underlying biology and enable out-of-sample prediction.nremit = 1852, nnonremit = 3299) and percentage improvement (n = 5218) was performed. Single nucleotide polymorphism–based heritability was estimated using genome-wide complex trait analysis. Genetic covariance with eight mental health phenotypes was estimated using polygenic scores/AVENGEME. Out-of-sample prediction of antidepressant response polygenic scores was assessed. Gene-level association analysis was performed using MAGMA and transcriptome-wide association study. Tissue, pathway, and drug binding enrichment were estimated using MAGMA.Genome-wide analysis of remission  but not for percentage improvement . Better antidepressant response was negatively associated with genetic risk for schizophrenia and positively associated with genetic propensity for educational attainment. Leave-one-out validation of antidepressant response polygenic scores demonstrated significant evidence of out-of-sample prediction, though results varied in external cohorts. Gene-based analyses identified ETV4 and DHX8 as significantly associated with antidepressant response.Neither genome-wide association study identified genome-wide significant associations. Single nucleotide polymorphism–based heritability was significantly different from zero for remission (This study demonstrates that antidepressant response is influenced by common genetic variation, has a genetic overlap schizophrenia and educational attainment, and provides a useful resource for future research. Larger sample sizes are required to attain the potential of genetics for understanding and predicting antidepressant response. Major depressive disorder (MDD) is the third leading cause of years lived with disability worldwide  and is aIn 2011 to 2014, 12.7% of individuals in the United States 12 years of age and over reported antidepressant medication use . AntidepPharmacogenetic studies were expected to uncover loci with large effects on drug response and adverse events due to effects of pharmacokinetic or pharmacodynamic mechanisms. While associations between antidepressant plasma levels and drug-metabolizing enzymes CYP2D6 and CYP2C19 have been identified , 11, 12,Several genome-wide association studies (GWASs) have been performed to identify genetic predictors of antidepressant response. Although no robustly replicated associations have been detected to date , 18, 19,In this study, we analyze genome-wide genetic data on clinically assessed antidepressant response from 5843 patients treated for MDD, combined from 13 international research studies. Using this novel data resource, we perform GWAS of remission and percentage improvement after receiving antidepressant medication, and undertake extensive post-GWAS analyses, made feasible through this increased sample size. This study aims to elucidate the genetic architecture of antidepressant response and use polygenic scores to establish the relationship between antidepressant response and mental health outcomes. We find, for the first time, a replicable polygenic signal of antidepressant response across studies.This study analyzed 13 cohorts . Ten cohTwo measures of antidepressant response were defined: remission and percentage improvement. Remission is a binary measure attained when a patient’s depression symptom score decreases to a prespecified threshold for the rating scale .All analyses included covariates of the first 20 principal components of population structure, age, and gender. Analyses using the remission measure of response also included the baseline symptom score as a covariate, to control for depression severity.Each cohort underwent standard quality control and 1000 Genomes Project phase 3 imputation using the RICOPILI pipeline on the LISA server  Supplem.GWAS was performed using the RICOPILI pipeline  separateGene associations were estimated using MAGMA  and tranp values. The analysis was based on genetic variants and linkage disequilibrium in the 1000 Genomes Project phase 3 dataset available on the MAGMA website (g1000_eur.bed/bim/fam). SNPs were assigned to genes using the MAGMA NCBI37.3.gene.loc file with a 10-kb window. False discovery rate (FDR) correction was used to control for multiple testing. See The MAGMA v1.06b SNP-wise mean model (±10-kb window) was used to perform gene-level association analysis based on the remission and percentage improvement GWAS http://gusevlab.org/projects/fusion/) and precomputed multi-SNP predictors of gene expression based on data collected from multiple specific brain regions, thyroid tissue, pituitary gland, liver, and blood  in the software GCTA  ,28. The p values were used to assess statistical significance, as we are testing the one-sided hypothesis that the polygenic score has a positive association with the outcome in the target sample.To determine whether polygenic scores derived from the remission and percentage improvement GWAS summary statistics predict antidepressant response in an independent sample, a leave-one-out polygenic scoring approach was used. This involves calculating polygenic scores within each cohort based on GWAS summary statistics derived using all other cohorts. Polygenic scores were calculated using PRSice V2  Supplem. One-sidWe tested for evidence of genetic overlap between antidepressant response measures and seven mental health phenotypes: major depression , bipolarp-value thresholds to estimate genetic covariance between antidepressant response and the eight mental health phenotypes. AVENGEME parameters are provided in AVENGEME aggregates polygenic score association results across N = 190, remission rate = 11.8%)      , the Dou= 23.6%) , and the= 52.4%)  prospect = 2455)  assessedIndividual-level data were available for Generation Scotland enabling estimation of genetic covariance between TRD and mental health-related phenotypes using AVENGEME, as described above. Analyses in Generation Scotland were controlled for age, gender, and 20 principal components of population structure. When estimating genetic covariance between TRD and major depression, we used major depression GWAS summary statistics excluding Generation Scotland to avoid sample overlap.Descriptive statistics for the cohorts used in this study are available in Across the 10 European studies, 5151 individuals with remission data (1852 [36.0%] patients remitting) and 5218 participants with percentage improvement data were available. No variants were significantly associated with remission or percentage improvement . There wN = 527) (No significant associations were identified in the East Asian GWASs (N = 527) . A compaETV4 with both remission (pFDR = .016) and percentage improvement (pFDR = .016). Within the same region, DHX8 was also significantly associated with remission (pFDR = .046). The SNP associations within this region span multiple genes (MAGMA identified a significant association on chromosome 17 for le genes . Full MAp < 2.51 × 10−6). Further inspection of TWAS associations within the chromosome 17 region implicated by MAGMA highlighted SNP-associations with upregulation of BRCA1  and upregulation of TMEM106A . Colocalization analysis of these associations indicated shared casual variants for these genes’ differential expression and antidepressant response. Full TWAS results are given in TWAS identified no association achieving transcriptome-wide significance , whereas the SNP-based heritability for percentage improvement was not significantly different from zero   showed remission to have a significant nonzero SNP-based heritability ( = .303) .Figure 1h2 = 0.396; SE = 0.153; 95% CI, 0.096 to 0.696; p = .010, liability scale assuming population prevalence of 0.357) and percentage improvement   were significant for both remission ( = .041) . See FigSee p-value thresholds associated at nominal significance.Leave-one-out polygenic score analysis provided evidence that polygenic scores derived using remission and percentage improvement GWAS results could both explain a statistically significant amount of variance out-of-sample . Both reR2 = 0.8%, p = .015) and a nonsignificant association for the percentage improvement score   showed nominally significant evidence of association for the remission polygenic score (maximum liability  = .091) . ResultsBoth remission and percentage improvement showed a significant negative genetic covariance with schizophrenia, and significant positive genetic covariance with educational attainment . PercentGenetic overlap estimates between TRD in Generation Scotland and mental health phenotypes were congruent with results from primary samples, showing that genetic risk for schizophrenia was greater among individuals with TRD, and educational attainment genetic propensity was greater among individuals with non-TRD .Antidepressants are a common and effective strategy for treating MDD; however, remission rates are typically low, and factors affecting antidepressant response are poorly understood. This study is the largest genetic investigation of antidepressant response based on clinically defined cohorts. For the first time, we identify a polygenic profile for antidepressant response, which can predict across cohorts, and shows genetic correlations with traits that reflect clinical observations.This study finds significant evidence that antidepressant response is influenced by common genetic variation. Meta-analysis of SNP-based heritability estimates within each cohort indicates that 20% to 40% of the variance in antidepressant response is attributable to common genetic variation, consistent with a previous analysis of a subset of these studies , 31, 32.This study provides novel insight into the shared genetic basis between antidepressant response and mental health phenotypes. We show an association between high genetic liability of psychiatric disorders and poorer response, which mirrors conclusions of clinical studies . The schR2 = 0.1%) and p values are close to the nominal significance threshold, this result is encouraging given the sample size of this study. For example, a recent GWAS of MDD explains only 1.9% of the variance in MDD, despite having a sample size 100 times greater than this study  induced hippocampal dendrite development and plasticity (DHX8 has a less clear mechanistic link to antidepressant response with a broader function in messenger RNA splicing (This study provided limited insight into the biological underpinnings of antidepressant response implicating one locus on chromosome 17 surrounding asticity , congrueasticity . DHX8 hasplicing . ReplicaCYP2D6 and CYP2C19, which have previously been robustly associated with antidepressant plasma levels (In addition, no association was detected with genetic variation within classical pharmacokinetic candidate genes, such as a levels . AlthougOwing to a limited sample size, it was not possible to estimate genetic correlations between longitudinally assessed antidepressant response and TRD defined using electronic health records. However, comparison of shared genetic etiology with other mental health phenotypes indicated that these distinct measures of antidepressant response have a shared genetic basis. Further comparison and integration of these two approaches is warranted and may prove fruitful given the large gains in sample size that electronic health record–derived phenotypes can provide.There are several limitations to this study that should be addressed in the future. First, large sample sizes are essential for robust identification of associated genetic variation and out-of-sample prediction. However, combining independently collected datasets inevitably introduces heterogeneity. Obtaining large homogeneous samples is particularly challenging for pharmacogenetic studies, as heterogeneity is driven not only by patient characteristics such as diagnosis and patient ascertainment, but also by differences in treatment such as the drug, dosage, duration, and co-pharmacotherapy. Although the cohorts within this study have many features in common, heterogeneity in antidepressant treatment is present. As sample sizes grow, analyses stratified by these factors will become more feasible, enabling detection of genetic effects relevant to each antidepressant, antidepressant class, or other treatment characteristics. Second, an important question to consider is whether the variance in depressive symptoms after treatment is due to antidepressant response or to other variables altering the course of depression. Although antidepressants have a significant effect on depressive symptoms, and their administration is the core feature of participants in this study, individuals may vary in depressive symptoms due to other factors affecting disease progression, such as clinical and sociodemographic variables and placebo response. This is a difficult issue to resolve but should be considered when interpreting the results. Future genetic studies incorporating the placebo arm of clinical trials may help identify genetic associations specific to antidepressant response. Third, this study has focused on changes in total depressive symptoms without considering symptom domain-specific changes or the presence of side effects. Given the wide range of depressive symptoms and the influence side effects can have on efficacy, consideration of these features may provide additional insights. Fourth, although this study included three cohorts of East Asian ancestry, further inclusion of cohorts with diverse ancestries is an important area. Genetic analysis within diverse populations helps to ensure that the findings are applicable to worldwide populations and can help fine-map causal variants underlying genetic associations.In summary, this study identifies a polygenic profile for antidepressant response that predicts across studies and is negatively correlated with genetic susceptibility to schizophrenia, which could be used for prognostic purposes. While the current results have no clinical utility as a pharmacogenetic test, they indicate that studies with larger sample sizes could provide predictions explaining a substantial proportion of antidepressant response. We note that a prognostic test that enables even a modest increase in the proportion of patients that respond to antidepressants would have a substantial impact on recovery for many patients, given the high prevalence of depression. We hope that this study prompts both replication and extension to accelerate the development of pharmacogenetic testing for psychiatry.


PED) and genomic (FROH and FGRM) inbreeding in a representative number of Italian sheep and goat populations. Indeed, even though it has been widely studied in cattle, there is still little knowledge about the relationship between these coefficients in small ruminants, which are characterized by a different population structure, often with unconnected farms. Mean inbreeding values were low, FROH being the highest, with breed differences due to different managements; the correlation between FPED and FROH was the strongest and directly related to pedigree depth. Moreover, we estimated FPED from FROH using a linear regression model. Since massive genotyping is not affordable to small ruminant breeders, it is important to understand the distinction and relationship between differently calculated inbreeding coefficients, also in view of the introduction of genomic enhanced breeding values. Our study highlights the importance of accurate pedigree information and, especially if not obtainable, of genotyping animals. Correct data contribute to mitigate inbreeding depression and loss of genetic variability.The inbreeding coefficient is relevant for managing livestock and safeguarding biodiversity, especially in small populations. Small ruminant breeders mainly rely on pedigree information, but genomics is increasingly gaining ground as a tool to face possible pedigree inaccuracies. This study investigates pedigree-based (FPED), as well as two genomic inbreeding indexes, using runs of the homozygosity (FROH) and genomic relationship matrix (FGRM). The correlation between the inbreeding coefficients was assessed. A linear regression model (LRM) was fitted for estimating FPED from FROH. After quality control on genomic data, we retained 5085 animals. Mean inbreeding values were low, with higher FROH than FPED and FGRM. Breed differences can partially depend on different managements. The correlation between FPED and FROH was the highest and directly related to pedigree depth. The best LRM was chosen for FullGen ≥4 and ≥6 for goats and sheep, respectively; after excluding animals with extreme residuals, a new refined regression equation was calculated. Since massive genotyping is not affordable to small ruminant breeders, it is important to understand the distinction and relationship between differently calculated inbreeding coefficients, also in view of the introduction of genomic enhanced breeding values. Our study highlights the importance of accurate pedigree information and, especially if not obtainable, of calculating genomic-based inbreeding coefficients. A better estimation of animals’ relatedness contributes to improve animal breeding and conservation.The inbreeding coefficient is an important parameter for livestock management. Small ruminant breeders and associations mainly rely on pedigree information, but genomic tools are gaining relevance, overcoming possible pedigree inconsistencies. This study investigates the relationship between pedigree-based and genomic inbreeding in two goat and four sheep dairy breeds. Pedigree and genomic data (medium-density SNPchip) were obtained for 3107 goats and 2511 sheep. We estimated pedigree depth  and inbreeding (F The accurate estimate of the inbreeding value of an individual could be of extreme importance for all the domesticated species, both for commercial and conservation purposes ,2,3. WitToday, genomic data obtained by high-throughput SNP genotyping represent a new instrument that should be integrated with the traditional pedigree information to more precisely estimate the relationship between individuals . MoreoveROH) [There are different ways to calculate inbreeding using SNP chip data, and those based on runs of homozygosity (ROH) and the genomic relationship matrix (GRM) are among the most used ,13. ROH ROH) . Indeed,ROH) .PED and pedigree depth and the genomic inbreeding FROH and FGRM in six Italian small ruminant populations focusing, in particular, on FPED and FROH.Even if SNP genotyping has been routinely implemented in dairy cattle , its cosFor this work, we selected a total of six breeds, namely four local dairy sheep breeds—Comisana, Delle Langhe, Massese and Sarda—and two cosmopolite dairy goat breeds—Camosciata delle Alpi and Saanen. All the breeds are mainly used for cheese production, being both representative of different production systems and geographical areas. The official herd books of these breeds are managed by the Italian Sheep and Goat Breeders Association , hereinafter referred to as Asso.Na.Pa. In all the breeds, male selection candidates are DNA-tested for parentage assignment. Artificial insemination (AI) is used mainly in Camosciata delle Alpi and Saanen breeds, where from 10 to 15% of annual births are from semen of foreign AI bucks. All breeds are officially milk-recorded, and a routine genetic evaluation for milk yields is in place. The selection scheme for Comisana and Massese sheep breeds is based on two different closed nucleus flocks reared at the Genetic Center of Asciano ; instead, the Sarda sheep is managed using a pyramidal scheme, with a nucleus flock at the apex . FinallyPedigree records and genomic data were obtained from the ‘Conservation, Health and Efficiency Empowerment of Small Ruminant’ (CHEESR) repository project, a database created by Asso.Na.Pa. in the framework of the Italian National Rural Development Plan (PSRN)—sub-measure 10.2 project and supported by the European Agricultural Fund for Rural Development (EAFRD). In total, we analyzed 3107 goats (2164 Camosciata delle Alpi and 943 Saanen) and 2511 sheep . All animals were genotyped with the medium density chip, Ovine SNP50 BeadChip for ewes and Goat SNP50 BeadChip for goats. A quality control analysis was performed on both species fitting the same parameters and using PLINK 1.9 software [optiSel package of the R software [PED), the number of fully traced generations , the number of maximum generation (MaxGen), the number of equivalent complete generations (EquiGen), the percentage of animals with a complete first generation and the effective size for each sheep or goat breed according to Wright’s formula [All the pedigree analyses were carried out using the software . The fun formula .ROH) in each individual. The FROH coefficients were computed using the following equation:ROH is the sum of the total length of ROH in individual i and LAUTO is the total length of the autosomes covered by the SNPs [ROH are expected to correspond to the ancestral population dating 50 (1 < ROH < 2), 20 (2 < ROH < 4), 12.5 (4 < ROH < 8), 6 (8 < ROH < 16) and 3 (ROH > 16) generations ago [We used the function ‘--homozyg’ of PLINK 1.9 for the calculation of the ROH applying the following criteria: (i) a sliding window of 20 SNPs, (ii) no heterozygous genotype allowed, (iii) no more than two missing genotypes, (iv) a minimum number of SNPs in a ROH equal to 20, (v) a minimum ROH length of 1 Mb, (vi) a minimum SNP density of 1 SNP per 500 kb and (vii) a maximum gap of 500 kb between two consecutive homozygous SNPs. In order to minimize false positives discovery within regions of low marker density, rather stringent criteria were selected. ROH distribution was characterized for each breed by estimating the number of individuals without ROH, the mean number of ROH per individual, the mean total length of ROH per individual, the mean length of a ROH per individual and the genomic inbreeding coefficient . This calculation was performed on all the individuals of both species together considering increasing FullGen classes .Using the functions ‘cor’ and ‘lm’ implemented in the R base package, we calculated the correlation coefficient between FPED and FROH and the highest linear model R2. After that, we applied the coefficients of the chosen FullGen model to estimate the FPED value only on the individuals of the correspondent species with the selected minimum FullGen. We calculated the standardized residuals  and excluded all the animals with a standardized residual falling under the 1st or over the 3rd quartile. Lastly, we recalculated the linear model using only the retained subjects and re-estimated their FPED values with the coefficient of this last refined model. Then, for each species, we chose the linear model of the FullGen class that maintained at least 600 individuals of the species of interest and, at the same time, had both the highest correlation coefficient between FGRM, FROH or FPED were excluded. Therefore, the final dataset used for estimating the correlation coefficients and the linear model included 5085 animals (3028 goats and 2057 sheep)  individuals and 51,097 markers for goats, and 2484  individuals and 46,723 markers for sheep. All the 485 individuals for which we could not calculate F7 sheep) . The resPED, FGRM and FROH for different ROH length classes. An FPED value equal to 0 was observed in less than 1% of sheep and 37% of goats. As shown in ROH values were higher than the other inbreeding coefficients in both the species. Instead, FPED values were higher than FGRM in sheep, whereas the two were similar in goats. It is worth noticing that FGRM showed some negative values in all the breeds and a particularly spread distribution in the Delle Langhe breed. For each sheep and goat breed, we calculated FROH distribution per ROH length class (ROH classes apart from the one derived from ROH > 16 Mb (suggesting recent inbreeding), which was higher in Saanen than in Camosciata delle Alpi. In the sheep species, Sarda and Delle Langhe breeds presented the highest FROH value and proportion of long ROH classes. In any case, all inbreeding coefficients were relatively low in both species, with the highest values in the Sarda sheep.Regarding the Fth class c, the twGRM, FROH and FPED were much higher in sheep than in goats, and, in particular, in the Sarda breed. In addition, the correlation between FPED and FROH was higher than between FPED and FGRM; therefore, we decided to use a linear regression model to estimate FPED from FROH . Based on these results and the assumptions explained in the material and methods section , we identified the model calculated for FullGen ≥ 4 as the best one for the goats, and the one calculated on Fullgen ≥ 6 as the best for the sheep.The correlation coefficients between FPED values   b.PED from FROH for all the goats with FullGen ≥ 4, and for each 0.05 class of estimated definitive FPED, we calculated the corresponding mean and range of FROH   and applied them on the 927 sheep with a FullGen ≥ 6 to calculate the estimated FD values a. We sta× 10−16) b.PED intervals and relative FROH means and ranges for all the sheep with FullGen ≥ 6 are reported in ROH corresponding to an estimated FPED of 0.00–0.05 and 0.05–0.10: Comisana had the lowest FROH values, followed by Massese, while Delle Langhe and Sarda present the highest values. As shown in PED classes (>0.20).The estimated FThe inbreeding coefficient is a fundamental tool for livestock husbandry: It is necessary for increasing the accuracy of the genomic and genetic breeding value of animals and the consequent improving of the breeds ; it is oPED and genomic inbreeding coefficients (FGRM and FROH), as well as their relationship, in a representative number of animals belonging to six differently managed Italian dairy small ruminant breeds.Nevertheless, the genotyping costs, although consistently reduced in recent years, cannot yet be afforded by the breeders of small ruminants. This makes it necessary to understand how to correctly interpret and compare inbreeding coefficients calculated from different data. Therefore, the present study aimed to explore the FGRM values tend to be more variable with respect to the other inbreeding parameters because they are highly influenced by the rare allele variants frequencies [PED values identified by the analysis, we know that goat pedigrees are less complete compared to other species, similar to a lot of animals  with FPED = 0, often due to lack of genealogic information. For the same reason, the correlation between FROH and FPED coefficients is lower in goats. Regarding the percentage of FROH per ROH length class, the different management of the breeds can account for a portion of the observed variability: For example, the higher level of recent inbreeding found in Saanen compared with Camosciata delle Alpi could partially depend on the higher use of AI in the former . The inbreeding estimated on these subjects was, for the most part, low. The lack of very inbred animals could be considered a limitation of the present study, but it should also be considered that this can depend either on good management of the population or from the low level of connection of the Italian small ruminant farms, with a minimal exchange of animals except when the breeders make use of the AI or receive animals from a genetic center. The diffusion of AI is still limited in both species; however, it is rising in goats due to the commercialization of foreign, mainly French, semen. Avoiding an excessive increase of inbreeding is a main goal of the breeders and their associations to prevent inbreeding depression, especially in small-sized populations, whose survival would be in danger if a reduction of the number of the breeding animals occurred. If the genomic inbreeding could be estimated for all the animals of a farm, or at least a representative number, it would be possible to warn the breeders who are at risk of inbreeding-related issues.Our results showed that there were some differences in the variability distribution of inbreeding coefficients, both within and among breeds. As we know from the literature, Fquencies ; moreovePED in a population varies based on the considered pedigree depth , the use of unknown parent groups and the involved computational algorithm [ROH can be estimated starting from sliding (as in the present study) or consecutive (not overlapping regions) ROH, both varying according to the parameters used to define the regions. In the literature, results about this parameter have also considerably changed within the same breed. One example is the Sarda dairy sheep: In this study, the average FROH for this breed was 0.135 using sliding regions, whereas Cesarani et al. (2019) [ROH of 0.041. In the latter study, the authors reported FROH values also for Delle Langhe (0.080 vs. 0.099 in this study), Comisana (0.016 vs. 0.044 in this study) and Massese (0.055 vs. 0.067 in this study). The different values between Cesarani et al. (2019) [GRM values change according to the method used to create the genomic relationship matrix [PED and FGRM estimated with this fixed frequency are extremely high.The comparison of inbreeding coefficients with those reported in literature is hampered by the several different parameters that can be defined to estimate them. The average Flgorithm , some oflgorithm . FROH ca. (2019)  reported. (2019)  estimate. (2019)  and the p matrix ,36,37 inp matrix , this kiPED was generally higher with FROH (0.30 in goats and 0.82 in sheep) than FGRM , especially when the pedigrees were more complete. The results of our analyses are consistent with those previously reported in other studies [PED and FGRM in Comisana and Massese breeds and that already reported in the literature for other species [ROH and FPED; this means that in order to estimate FPED accurately, between four and six full generations should be known. It would be important to bring this information to the attention of the breeders, who should especially genotype those animals with a small number of known ancestors. We used a simple regression model that aims to estimate a more accurate pedigree-based inbreeding coefficient on the basis of FROH and can be useful for the breeders to compare the inbreeding of genotyped and non-genotyped animals. This regression model could obviously be improved using a larger sample size per breed and including highly related animals. We noticed that goats had shallower pedigrees and a higher number of inbreeding coefficients equal to zero. For this reason, since the two species share several characteristics, such as similar management and production aptitude (milk and cheese) and they are often raised together, the initial model included both species. The results of the model also highlighted that different breeds had different mean FROH per estimated FPED class. This aspect should be considered when implementing the genomic inbreeding in the animal evaluation, for example, through the estimation of genetic breeding values. Indeed, previously published works have attempted to propose a new model based on ROH for the computation of genomic breeding values in cattle (GROH), finding quite high levels of accuracy [The analysis of the relationship among inbreeding coefficients showed that the correlation of F studies ,39. Of i species . Pedigreaccuracy . This coPED and genomic data FROH, particularly in goats (0.30). Indeed, FPED values equal to zero  occur often due to a lack of genealogic information. Excluding subjects with likely erroneous or too shallow pedigrees while keeping an adequate sample size allowed us to better estimate a reliable correlation between the two inbreeding coefficients. These results underline the importance for small ruminant breeders and associations to improve the accuracy of the collection of pedigree information and, especially when it is not possible, the significant advantages of estimating a genomic inbreeding coefficient. The correctness of the data, indeed, allows to improve small ruminant breeds in different ways: having more reliable EBV and creating better mating schemes in order to improve welfare, production and health-related traits; minimizing the risk of inbreeding depression; and better understanding the effect of their management on inbreeding trends. On the contrary, inaccurate information might limit the breed’s genetic progress and lead to the reduction of the genetic variability, which is essential to safeguard livestock biodiversity and to face future climate challenges.Pedigree information is the most used source of data to compute inbreeding coefficients, especially in small ruminants, due to the still high cost of genotyping. As emerged from our analyses on Italian sheep and goat populations, when all data were included, there were low values of correlation between inbreeding calculated from pedigree F


Genome-wide association studies (GWAS) are an integral tool for studying the architecture of complex genotype and phenotype relationships. Linear mixed models (LMMs) are commonly used to detect associations between genetic markers and a trait of interest, while at the same time allowing to account for population structure and cryptic relatedness. Assumptions of LMMs include a normal distribution of the residuals and that the genetic markers are independent and identically distributed—both assumptions are often violated in real data. Permutation-based methods can help to overcome some of these limitations and provide more realistic thresholds for the discovery of true associations. Still, in practice, they are rarely implemented due to the high computational complexity.permGWAS, an efficient LMM reformulation based on 4D tensors that can provide permutation-based significance thresholds. We show that our method outperforms current state-of-the-art LMMs with respect to runtime and that permutation-based thresholds have lower false discovery rates for skewed phenotypes compared to the commonly used Bonferroni threshold. Furthermore, using permGWAS we re-analyzed more than 500 Arabidopsis thaliana phenotypes with 100 permutations each in less than 8 days on a single GPU. Our re-analyses suggest that applying a permutation-based threshold can improve and refine the interpretation of GWAS results.We propose permGWAS is open-source and publicly available on GitHub for download: https://github.com/grimmlab/permGWAS.Bioinformatics online. GWAS-Flow (Genome-wide association studies (GWAS) are an integral tool to detect associations between genetic markers within a population of individuals and a complex trait or disease that is measured in the same population . HoweverpermGWAS, an efficient permutation-based linear mixed model (LMM) to compute adjusted significance thresholds that are able to account for correlated markers and skewed phenotypic distributions without the need to arbitrarily transform phenotypes. To account for multiple hypotheses, correlated markers and skewed phenotypes, we compute permutation-based significance thresholds based on the maxT method proposed by Arabidopsis thaliana phenotypes to underpin its benefits.We propose We will first provide the necessary background of LMMs for GWAS, the multiple hypothesis testing problem and how to empirically estimate the FWER using the Westfall–Young permutation testing procedure . Finallyn be the number of samples and m the number of genetic markers. Then for each genetic marker we consider a LMM of the formP-value of the F-test is below a predefined significance threshold α (e.g. 5%).Let Since we have to test thousands to millions of markers simultaneously, we have to take these multiple tests into account, otherwise we would obtain thousands of false positive associations deemed to be significant.2.2.1δ for each hypothesis, such that the FWER(δ) The FWER is the probability of making at least one type-1 error . One has to find an appropriate corrected significance threshold α by the number of simultaneous tests, i.e. Evaluating this optimization problem in closed form is not possible in general. For this purpose, the widely used Bonferroni approximation  can be u2.2.2δ). One could either approximate the null distribution by using permutations to then compute adjusted P-values or use the unadjusted P-values and provide a permutation-based significance threshold based on the maxT permutation-method proposed by P-values and adjusted significance thresholds.Permutation-based methods can help to overcome some of these problems, by empirically estimating the FWER and b the batch size. Let b copies of the phenotype vector b copies of C. Then, the linearly transformed data is given byDenote by NP xj∈ℝn . Let Xjbtor y∈ℝn . Furtherb SNPs starting at the b SNPs:b copies of the residual sum of squares of the null model. Once we have computed the test statistics for all SNPs, we can sequentially calculate all P-values.Now, we can compute the coefficients 2.3.2q denote the number of permutations. Then for each permutation y with k and let q copies of y, we estimate associated variance components k and again linearly transform the data. Let k. Then, we can transform the data viaWhen performing GWAS with permutations, let additionally s of Xjb . Now forq permutations and b SNPs at once:b copies of the RSS of the null model for each permutation.Now similar to above, we compute the coefficients permGWAS framework is implemented in Python3 using commonly used libraries for scientific computing, such as numpy  are used. permGWAS can be used as a standalone command line tool or directly within Python. Our implementation allows both, the usage of multi-core CPU architectures with and without GPU support. To ensure a smooth experience on different environments and machines, we provide a standardized Docker environment. Our framework supports several common genotype and phenotype file formats, including HDF5, CSV and PLINK  if any SNP in a 50 kbp window around the causative marker was significant. In addition, each phenotype was classified as false positive (FP) if any SNP outside the 50 kbp window around the causative marker was significant. In this way, a phenotype can be true positive and false positive at the same time. We define the phenotype-wise FDR as FDR := P-value thresholds based on both, the Bonferroni and permutation-based thresholds.Artificial phenotypes were simulated for 200 random permGWAS with respect to runtime and statistical power using simulated data, as well as more than 500 public available phenotypes from the model species A.thaliana.In the following, we evaluate 3.1.1permGWAS with respect to (i) the number of markers, (ii) the number of samples and (iii) the number of permutations. For all runtime experiments, we used data from a flowering time related phenotype in A.thaliana, FT10   , and dow4 and permGWAS (the GPU and CPU version) outperforms both, the binary implementation of EMMAX and FaST-LMM. Our dockerized Python implementation of permGWAS is almost one order of magnitude faster than the C/C++ implementation of FaST-LMM . The advantage of the GPU architecture becomes most obvious when using permutations, as illustrated in permGWAS is at least an order of magnitude faster than the CPU version of permGWAS. More importantly, permGWAS (GPU) is more than one order of magnitude faster than EMMAX and more than two orders of magnitude faster than FaST-LMM. Even for 1000 samples, 106 SNPs and 500 permutations permGWAS (GPU) takes less than 1.8 h. In contrast, EMMAX would require at least more than 2.7 days, while FaST-LMM might take more than 11 days for 500 permutations. Results for environments with 8 cores are summarized in Finally, to compare the runtime of the permutation-based approach, we fixed the number of samples to 1000 and the number of SNPs to 10A.thaliana phenotypes with 100 permutations each on a single GPU (Nvidia RTX A5000 with 24 GB RAM) in less than 8 days. The respective runtimes are shown in In addition, we re-analyzed over 500 permGWAS is more efficient than the commonly used state-of-the-art LMMs, such as EMMAX and FaST-LMM, due to its tensor-based and batch-wise reformulation. Especially when performing GWAS with more than a few hundred of samples and permutations, EMMAX and FaST-LMM take several days to weeks to compute the results, while our implementation only needs a few hours. Although the GPU implementation of permGWAS is faster than the corresponding CPU implementation, the CPU version still outperforms existing methods.In summary, 3.1.2Our simulations show that the phenotype-wise FDR increases, if the respective phenotypes become more skewed. Using a static Bonferroni threshold, the phenotype-wise FDR increases from 30% for slightly skewed phenotypes to 50% in the most extreme case . The latP-values can arise randomly. This will get controlled by permutations that can account for model violations, as underlying assumptions are also violated in a model without genetic signal. Hence, permutations can control for false associations that arise through non-normal phenotypic distributions.Noticeably, the permutation-based threshold becomes more and more stringent, if the phenotypic distribution becomes more skewed , therebyOn the other hand, for normally distributed phenotypes, the permutation-based threshold is less stringent compared to the Bonferroni threshold  and incrP-value > 0.05, indicating a normal distribution  have a significant association. Using the permutation-based threshold, these numbers change to 53 and 15, respectively  for some cases, a less stringent permutation-based threshold will identify a significant signal that would not have been significant using the Bonferroni threshold  We hreshold  and (3) hreshold . Most phhreshold .Although follow-up experiments would be needed to confirm that associations deemed positive in the scenarios (1) and (3) are true positives, anecdotally many of this candidates seem plausible.3.3A.thaliana phenotypes. One phenotype is nearly normally distributed, while the other is markedly skewed  versus several days for EMMAX and FaST-LMM for 1000 samples, 106 markers and 500 permutations]. These reformulations enable performing permutation-based thresholds in practice.We introduced ll–Young  to compuA.thaliana that the use of a permutation-based threshold has many advantages compared to the classically used Bonferroni threshold. Bonferroni correction is thought as a very conservative way to control false positives in GWAS, and indeed for normal distributed phenotypes, we could show that the permutation-based threshold is less stringent and can identify more true positive associations. Further, for non-normally distributed phenotypes, as often observed in biological data, the permutation-based threshold is quite often even more stringent. Here, our data suggest that we could reliably control false positives under those scenarios. A sensible next step would be to investigate how to extend permGWAS to Generalized LMMs, e.g. to properly handle the analysis of binary traits. To summarize, we highlight that the use of permutation-based thresholds should be considered the default choice in any GWAS and with permGWAS we provide the tool to enable this.We demonstrated through simulations and the re-analyses of publicly available data from the model plant species This paper was published as part of a special issue financially supported by ECCB2022. The work was supported in parts by funds of the Federal Ministry of Education and Research (BMBF), Germany .Conflict of Interest: none declared.btac455_Supplementary_DataClick here for additional data file.