The rapid growth in genomic selection data provides unprecedented opportunities to discover and utilize complex genetic effects for improving phenotypes, but the methodology is lacking. Epistasis effects are interaction effects, and haplotype effects may contain local high-order epistasis effects. Multifactorial methods with SNP, haplotype, and epistasis effects up to the third-order are developed to investigate the contributions of global low-order and local high-order epistasis effects to the phenotypic variance and the accuracy of genomic prediction of quantitative traits. These methods include genomic best linear unbiased prediction (GBLUP) with associated reliability for individuals with and without phenotypic observations, including a computationally efficient GBLUP method for large validation populations, and genomic restricted maximum estimation (GREML) of the variance and associated heritability using a combination of EM-REML and AI-REML iterative algorithms. These methods were developed for two models, Model-I with 10 effect types and Model-II with 13 effect types, including intra- and inter-chromosome pairwise epistasis effects that replace the pairwise epistasis effects of Model-I. GREML heritability estimate and GBLUP effect estimate for each effect of an effect type are derived, except for third-order epistasis effects. The multifactorial models evaluate each effect type based on the phenotypic values adjusted for the remaining effect types and can use more effect types than separate models of SNP, haplotype, and epistasis effects, providing a methodology capability to evaluate the contributions of complex genetic effects to the phenotypic variance and prediction accuracy and to discover and utilize complex genetic effects for improving the phenotypes of quantitative traits. Genomic estimation of variance components and associated heritabilities and genomic prediction for quantitative traits using single nucleotide polymorphism (SNP) markers and mixed models have become a widely used approach for genetic improvement in livestock and crop species. The rapid growth in genomic selection data provides unprecedented opportunities to discover and utilize complex genetic mechanisms, but methodology and computing tools are lacking for investigating complex genetic mechanisms using the approach of genomic estimation and prediction. The integration of global low-order epistasis effects and local high-order epistasis effects contained in haplotypes for genomic estimation and prediction is a step forward for the discovery and application of complex genetic mechanisms to improve the phenotypes of quantitative traits.The theory of genetic partition of two-locus genotypic values defines four types of epistasis values: additive × additive (A×A), additive × dominance (A×D), dominance × additive (D×A), and dominance × dominance (D×D) epistasis values . The CocAn epistasis GWAS in Holstein cattle showed that intra- and inter-chromosome epistasis effects affected different traits differently, for example, the daughter pregnancy rate was mostly affected by inter-chromosome epistasis effects, whereas milk production traits were mostly affected by intra-chromosome epistasis effects , and genThe purpose of the multifactorial model in this article is to integrate haplotype effects and epistasis effects up to the third-order for genomic estimation of variance components and associated heritabilities, as well as genomic prediction of genetic and phenotypic values of quantitative traits, to provide a general and flexible methodology framework for genomic prediction and estimation using complex genetic mechanisms and to provide methodology details of the EPIHAP computer package that implements the integration of haplotype and epistasis effects , 2022. TG matrix of G matrix of The mixed model with single-SNP additive and dominance effects, haplotype additive effects, and pairwise SNP epistasis effects in this article is based on the quantitative genetics (QG) model resulting from the genetic partition of single-SNP genotypic values , haplotyui=Wiτiowhere τGenomic relationship matrices are used for genomic estimation and prediction, and the use of genomic relationship matrices results in a reparametrized and equivalent model of the original QG model for genetic values, to be referred to as the RE-QG model, where “reparametrized” refers to the reparameterization of the genetic effects, model matrix, and genetic variance of each effect type; and “equivalent” refers to the requirement of the same first and second moments for the original QG model –5 and thionships  and was ionships , haplotyionships , and paiionships . The neeionships  because ionships . DetaileThe formula of the genomic relationship matrix Si of  is basedmatrices , with thmatrices . AGERM cmatrices , and EGEmatrices .The QG and RE-QG models have the same prediction accuracy due to the equivalence between these two models. The genetic values ui, , 11 and The RE-QG model using genomic relationships –14 has t=kiσio2 , has thee genome . In conttability . MoreoveThe exact relationship between the genetic variance for the y = N×1 column vector of phenotypic observations, Z = b,e = V. The methods described below for genomic estimation and prediction are based on the conditional expectation (CE) method, which is more efficient computationally than the methods based on mixed-model equations (MME) when the number of genetic effects is greater than the number of individuals  > 0.001 and proportion of missing SNP genotypes < 0.100 . The EGEThe methods of genomic epistasis relationship matrices based on the additive and dominance model matrices, GREML, GBLUP and reliability, and estimation of effect heritability are demonstrated using an R program (DEMO.R) and a small artificial sample for the convenience of reading the numerical results .The multifactorial methods with SNP, haplotype, and epistasis effects up to the third-order provide an approach to investigate the contributions of global low-order and local high-order epistasis effects to the phenotypic variance and the accuracy of genomic prediction. Genomic heritability of each effect type from GREML and prediction accuracy from validation studies using GBLUP can be used jointly to identify effect types contributing to the phenotypic variance and the accuracy of genomic prediction, and the GBLUP for the multifactorial model with selected effect type can be used for genomic evaluation. With many capabilities, including the use of intra- and inter-chromosome separately, the multifactorial methods offer a significant methodology capability to investigate and utilize complex genetic mechanisms for genomic prediction and for understanding the complex genome–phenome relationships.


We used whole‐genome information, coupled with image‐based phenotypic data collected over two years, to build the pedigree of the population, assess its genetic diversity, describe growth patterns of ten growth traits and estimate their genetic parameters. Successful parentage assignment of 664 F1 individuals showed that the pedigree consisted of a complex mixture of full‐ and half‐sib individuals, with skewed reproductive success among parents, especially in females. Growth patterns showed seasonal fluctuations  and strong inter‐family differences. Heritability values for growth traits ranged from 0.27 to 0.76. Genetic and phenotypic correlations between traits were high and positive, ranging from 0.57 to 0.94 and 0.50 to 1.00 respectively. The implications of these findings are threefold: first, the best on‐growing conditions are in warmer months, where highest growth peaks can be achieved; second, size‐ and family‐based selection can be used as early selection criterion if pedigree structure and inbreeding risks are closely monitored; third, selection for body length results in concomitant increases in height and weight, traits of paramount importance for aquaculture. It is concluded that there is substantial potential for genetic improvement of economically important traits, suggesting that silver trevally is a promising species for selective breeding for enhanced growth.Aquaculture is the fastest‐growing food production sector worldwide, yet industry has been slow to implement genomic techniques as routine tools. Applying genomics to new breeding programmes can provide important information about pedigree structure and genetic diversity; key parameters for a successful long‐term breeding programme. It can also provide insights on potential gains for commercially important, yet complex, quantitative traits such as growth rate. Here we investigated a population of 1100 captive‐bred F HoweverOne of the most important and well‐studied traits in breeding programmes is growth rate ; Pacific oysters (Crassostrea gigas); and only one finfish species, chinook/king salmon (Oncorhynchus tshawytscha), a species introduced from North America  , a shoaling pelagic species found throughout the coastal waters of southern Australia and around New Zealand .In Aotearoa New Zealand, aquaculture production relies almost exclusively on the farming of the three species: Greenshell™ mussels . The goal of this study was to use genome‐wide data coupled with extensive phenotypic data to provide the first quantitative assessment of growth traits in a population of 1100 captive‐bred F1 trevally. Specifically, we used a mixture of WGS and GBS data to (1) reconstruct the molecular pedigree of the population, (2) calculate inbreeding values within each generation, (3) describe the growth patterns by adding image‐based phenotyping data collected over a period of two years to and finally (4) estimate the heritability and genetic correlations of ten growth traits to determine their potential for enhanced growth performance through a selective breeding programme.In this study, we applied genomic tools to a recently assembled population of silver trevally (22.10 wild broodstock (n = 22) and a captive reared F1 population (n = 1100). F0 individuals were originally captured during two net tows in February 2012 in the North Taranaki Bight (Lat. 3845267–Long.17420626 and Lat. 3851887–Long. 17419780). Live fish arrived two days later at the Wakefield Key Finfish Facility  in Nelson, New Zealand) and acclimated to a single 4400 L tank. Broodstock (remaining n = 19) were later transferred to the Maitai Finfish Facility  in 2014 and were acclimated to a single 13,000 L tank, where all research was subsequently carried out. The Finfish Facility receives ambient seawater from an underground bore, which is filtered using mesh filters and UV treatment. The F1 generation was produced using hormone‐induced mass spawning in December 2015. Induced spawning of F0 individuals was achieved subsequent to an intramuscular injection of human chorionic gonadotropin  at a target dose of 600 IU/kg of bodyweight. Leading up to spawning, surviving parents (n = 19) were fed a specialized diet containing fresh fish and oil supplements. Following injection, two individuals became egg bound and died, most likely before spawning. Spawning occurred 48 h post‐injection of hCG. Fifty grams of eggs were collected each day from the tank outlet over three consecutive days and placed in 450 L hatchery tanks provided with a 12‐h light cycle, gentle aeration and water flow. At seven days post‐hatching, larvae were combined into a single 5000 L tank. The larvae were fed a combination of live rotifers and artemia. At 1 month old, the juveniles were then fed a combination of artemia, O.range (NRD) dry crumbs, and a wet diet consisting of minced fresh fish. At 6 months of age, all fish were transferred into a single 5000 L tank with natural lighting and fed a combination of dry commercial pellets (Skrettings Nutra RC 1.2 mm and 1.8 mm) until 1 year old, and then Ridley pellets  and a wet diet (fish mince or portions of fresh fish). In November 2017, at 2.1 years old, 1100 F1 were randomly selected and transferred to a single 13,000 L tank. During this time, all fish were tagged by inserting a Passive Integrated Transponder (PIT) tag  into the body cavity. To minimize the risk of overcrowding and stunting of growth, F1 was moved for a final time four months later (March 2018) to a single 50,000 L tank and were maintained under same ambient temperatures and photoperiod for the remainder of the experiment.The trevally population studied consisted of an F2.20 were tagged and fin‐clipped in January 2017. Fin clips were placed directly into chilled 96% ethanol, heated to 80°C for 5 min within 1 h of collection, and then stored at −20°C until needed. Total DNA was extracted as described by Ashton, Hilario et al.  and stored as described above. Total genomic DNA was extracted by SlipStream Automation using the same protocol as for the F0. Genotyping for the F1 was carried out using a modified GBS approach . A gonadal biopsy was taken by inserting a glass cannula  connected to a plastic tubing into the gonopore of the fish and applying gentle aspiration by syringe. A portion of biopsy sample was placed in Ringer's solution , and from this, a wet mount slide was prepared and examined under a compound microscope for the presence of oocytes or sperm.Broodstock sex prediction based on the molecular pedigree was confirmed a posteriori by collecting a gonadal biopsy from each of the 13 F2.5FH) using PLINK. This statistic is equal to Nei's FIS statistic, but is calculated using a different formula:O(Homi) is the observed number of homozygous loci for the ith individual, and E(Hom) is the Hardy–Weinberg expected mean number of homozygous genotypes across m loci . The software extracts the outline of each individual fish from images, locates the XY coordinates of morphometric features on the outline (e.g. upper lip and narrowest cross section of the tail) and then uses those coordinates to make measurements. The measurements were converted from pixels to mm using the length of rulers also present in the images.In total, eight sets of external images were taken for each FFour growth traits were directly extracted from the pictures for each individual fish. Peduncle length (PL) was measured by locating the upper lip and narrowest cross section of the tail and then measuring the distance between these points. Height was measured at three positions along the fish – 25%, 50% and 75% of the way from the upper lip to the narrowest cross section of the tail  from length (L) using the length–weight relationship:b indicates growth in body proportions as the slope of a regression over log‐transformed weight‐at‐length data, and a, the parameter describing body shape, as the intercept of a regression line over log‐transformed weight‐at‐length data. The accuracy of the prediction model was estimated by calculating its R‐square score. The net gain in each trait for each time point was calculated as the difference between the initial measurement in November 2017 and the measure of that month.In addition, six other traits were estimated: weight (EW), and net gains in height at – 25%, 50% and 75% of PL , in peduncle length (ΔPL) and in weight (ΔEW). The weight estimations were done following Froese et al. , using aThe phenotypic correlations between individual traits were measured using Pearson's correlation matrix, which was constructed using all phenotypic measurements in Python v2.7, using the Numpy library  for the F1. After filtering for quality and depth, 17.7 and 1.1 million SNPs were kept for the F0 and F1, respectively. The missing rate per SNP filtering resulted in 17.1 million and 214,700 sites for the parents and the offspring, respectively , generating 21 families  or both parents (3.6%) not genotyped. Although the mating ratios were equal among all females (1:7) and males (1:3), the contributions were skewed among both sexes, particularly so in females, with one of them contributing to up to 60.2% of the total F1 population  was calculated for 13 F0 and 664 F1 individuals with both parents known. The values ranged from a minimum of −0.28 to a maximum of 0.06 with a median of −0.06 for the F0 and from −0.56 to 0.18 with a median of −0.06 for the F1. Variation in the inbreeding values did not significantly differ between the wild‐caught F0 and the F1 generation   to conclude if the means were statistically significantly different from those of the other groups.The inbreeding F statistic  Figure . Most of4 Figure . The mea4 Figure . Familie3.41 trevally cohort occurred roughly every 4 months, from the age of 2.1 to 4.1 years old. Ten growth traits that could either be directly extracted from the images , indirectly measured as in the case of weight, or calculated a posteriori, as in the case of the net gains traits, were recorded across eight time points. The a and b parameters used in the Bayesian hierarchical approach  and moderate to strong correlations were found for the net growth traits (and 0.50 ± 0.00 to 0.98 ± 0.01)  for the measured traits  and moderate (ranging from 0.28 ± 0.07 to 0.68 ± 0.07) for the net gain traits .Strong positive genetic correlations were found between all measured height, length and weight traits throughout the experiment  and between all net gain traits (0.84 ± 0.07 to 1.00 ± 0.03). Although calculations of weights were made using length measurements, such high genetic correlations indicate that the alleles associated have a pleiotropic effect and influence multiple traits simultaneously, Correlation between measurements of height, length, weight and net gain traits were genetically moderate to strong (0.59 ± 0.10 to 0.99 ± 0.00).The genetic variance of each trait increased over time, especially for length and weight traits , showing that variation between individuals increases as fishes get bigger.40 and 1100 F1 and to investigate the inbreeding levels in each generation and within families. Phenotyping data collected over 2 years were added to assess the quantitative genetic architecture of 10 growth traits. The results of this study will support breeding efforts in trevally, as well as inform more generally genomic work on other teleost species.Here, we applied, for the first time, a genomics‐informed approach to study a captive trevally population in New Zealand. Data from different genotyping methods were pooled to reconstruct a two‐generation pedigree of 13 F1 offspring. However, reproductive contributions were skewed, particularly among females. Skewed contributions have been reported from a wide range of captive fish populations, including closely related species such as the yellowtail kingfish   may have influenced their ability to spawn, or limited gamete availability. Second, different survival rates of progeny could have skewed family representations (note: DNA sampling of the F1 was conducted at 2.1 years of age). Third, courtship and mating behaviour might have been at play. This has been documented in yellowtail kingfish . Although the average inbreeding rates did not vary between generations, some slight differences could be observed between families in the F1 generation. Values were similar to the ones found in other wild‐caught marine species such as orange clown fish (Amphiprion percula) (0.018)  (0.054–0.247)  compared with the colder months (T°~ 11°C). This can be explained by an increase in metabolism during summer as water temperature rises and day length increases . We found that families which had initially higher values in growth traits remained larger throughout the experiment. However, some smaller families showed higher net gains compared with the larger families, demonstrating that the bigger fish were not necessarily the fastest growing proportionally and could also indicate some degree of compensatory growth. Finally, growth showed a pattern of being strongly influenced by seasonal temperatures. An increase in growth rate was observed during the warmer months of the year    ranged from 0.26 .In trevally, like in other teleost, seasonal effects have a significant influence on the realized growth rate. This finding has important implications for the selection of aquaculture locations and monitoring of optimal rearing temperatures; holding fish in a warmer environment could increase the growth rate and reduce the time taken to reach harvesting size. Our study showed that families exhibiting larger measurements initially, remained the largest individuals in the population throughout the duration of the experiment. Early removal of small individuals can thus be a useful hatchery‐management method to maximize the realized growth potential overall. However, if there is no accompanying genetic management plan, it can result in a genetic bottleneck as often only a few families are selected, which increases the risk of inbreeding depression over several generations Kincaid, . The impThe results of this research indicate that trevally have skewed parental contributions, which may be a consequence of uncontrolled tank‐based spawning or subsequent family‐specific mortality. A cohort mating strategy could be used to increase the number of parents contributing to even out the mating differences. Tank‐based spawning of broodstock selected based on genotype data could help select less closely related individuals in the next generation. This approach, also called walk‐back selection, can be mixed with additional steps that reduce skewed contribution, such as holding the broodstock in multiple tanks and standardizing the volumes of fertilized eggs from each tank. However, these techniques introduce environmental variation, which would need to be accounted for in downstream analyses. If walk‐back selection were to be implemented, further research would also be needed to determine its effectiveness in controlling inbreeding over multiple generations.The high heritability estimates found in this study highlight that there is potential for making strong genetic improvements via selective breeding. Phenotypic and genotypic correlations between traits were all positive and moderate to strong. A breeding objective for increased fish length is thus expected to produce a positive response on the other traits measured in this study, provided that they have the same allometric relationship later in life. Future work on this species could focus on a single trait such as length, as it can be easily measured using high‐throughput phenotyping methods and has been shown to be highly genetically correlated with other commercially relevant traits. Indeed, the speed of phenotyping will become increasingly more important as the range of locations for image‐based phenotyping grows wider. Using correlated traits like length and body shape from images to move into high frequency underwater environmentally linked measurements will enable more complete Genotype × Environment × Phenotype studies rather than single point Genotype × Phenotype studies in the future. Taken together, these results suggest that trevally is a suitable future candidate for enhanced growth.The authors declare no conflict of interest.Supplementary MaterialClick here for additional data file.


A century after the first twin and adoption studies of behavior in the 1920s, this review looks back on the journey and celebrates milestones in behavioral genetic research. After a whistle-stop tour of early quantitative genetic research and the parallel journey of molecular genetics, the travelogue focuses on the last fifty years. Just as quantitative genetic discoveries were beginning to slow down in the 1990s, molecular genetics made it possible to assess DNA variation directly. From a rocky start with candidate gene association research, by 2005 the technological advance of DNA microarrays enabled genome-wide association studies, which have successfully identified some of the DNA variants that contribute to the ubiquitous heritability of behavioral traits. The ability to aggregate the effects of thousands of DNA variants in polygenic scores has created a DNA revolution in the behavioral sciences by making it possible to use DNA to predict individual differences in behavior from early in life. Although the history of heredity and behavior can be traced back to ancient times Loehlin , the firThe most important development during this century of behavioral genetic research has been the synthesis of the two worlds of genetics, quantitative genetics and molecular genetics. Quantitative genetics and molecular genetics both have their origins in the 1860s with Francis Galton Galton , 1869 anAntipathy between the two worlds of genetics followed because of the different goals of Mendelians and Galtonians. Mendelians, the predecessors of molecular geneticists, wanted to understand how genes work, which led to the use of induced mutations and a focus on dichotomous traits that were easily assessed such as physical characteristics rather than behavioral traits. In contrast, Galtonians, whose descendants are quantitative geneticists, used genetics as a tool to understand the etiology of naturally occurring variation in complex traits selected for their intrinsic interest and importance, with behavioral traits, especially intelligence, high on the list. The resolution to the conflict could be seen in Ronald Fisher’s quantitative genomics. Second, the results of GWA studies were used to create polygenic scores that predict individual differences for complex traits. Third, GWA genotypes facilitated new approaches to causal modeling of the interplay between genes and environment. Together, when applied to behavioral traits, these advances could be called behavioral genomics. This synthesis of the two worlds of genetics, the journey from behavioral genetics to behavioral genomics, is the overarching theme of this whistle-stop tour celebrating a century of research in behavioral genetics.  studies of complex traits. In addition to finding DNA variants associated with complex traits, GWA genotypes led to three far-reaching advances in genetic research. First, GWA genotypes were used to estimate directly the classical quantitative genetic parameters of heritability and genetic correlation, which could be called The first 50 years of quantitative genetic research, from 1920 to 1970, started off well with family studies Jones , twin stNonetheless, a few studies of IQ appeared in the 1930 and 1940 s, such as the first study of identical twins reared apart  . In 2011, the first new method was devised to estimate heritability and genetic correlations since twin and adoption designs in the early 1900s. GCTA  uses GWA genotypes for large samples of unrelated individuals to compare overall SNP similarity to phenotypic similarity pair by pair for all pairs of individuals  Regression. In 2015, a second quantitative genomic method, LDSC, was published which estimates heritability and genetic correlations from GWA summary effect size statistics for each SNP, corrected for linkage disequilibrium between SNPs . In 2019, a third quantitative genomic analysis completed the arc from quantitative genetics to quantitative genomics by combining quantitative genetic structural equation model-fitting, routinely used in twin analyses, to LDSC heritabilities and genetic correlations  weighted by the SNP’s effect size on the target trait as indicated by GWA summary statistics. In 2001, polygenic scores were introduced in plant and animal breeding (Meuwissen et al. The most predictive polygenic scores in the behavioral sciences are for cognitive traits, especially educational attainment and intelligence. Early GWA studies of cognitive traits were underpowered to detect the small effects that we now know are responsible for heritability (Plomin and von Stumm The next milestone will be to narrow the gap between heritability explained by polygenic scores and SNP heritability. A more daunting challenge will be to break through the ceiling of SNP heritability to reach the heritability estimated by twin studies. Reaching both of these destinations will be facilitated by even larger GWA studies and whole-genome sequencing (Wainschtein et al. Polygenic scores are unique predictors because inherited DNA variations do not change systematically during life – there is no backward causation in the sense that nothing in the brain, behavior or environment changes inherited differences in DNA sequence. For this reason, polygenic scores can predict behavioral traits from early in life without knowing anything about the intervening pathways between genes, brain, and behavior.Polygenic scores have brought behavioral genetics to the forefront of research in many areas of the life sciences because polygenic scores can be created in any sample of unrelated individuals for whom GWA genotype data are available. No special samples of twins or adoptees are needed, nor is it necessary to assess behavioral traits in order to use polygenic scores to predict them.Although the implications and applications of polygenic scores derive from its power to predict behavioral traits without regard to explanation (Plomin and von Stumm A final milestone on the journey from behavioral genetics to behavioral genomics is a suite of new approaches that use GWA genotypes in causal models that attempt to dissect sources of genetic influence on behavioral traits (Pingault et al. Science on the topic of the nature of nurture (Kong et al. genetic nurture. GCTA has also been used to investigate genotype-environment correlation (Eilertsen et al. An explosion of research on genotype-environment correlation was ignited by a 2018 paper in This whistle-stop tour has highlighted some of the milestones in a century of research in behavioral genetics. The progress is unmatched in the behavioral sciences and its discoveries have been transformative. The most exciting development is the synthesis of quantitative genetics and molecular genetics into behavioral genomics. The energy from this fusion will propel the field far into the future.


Cebus capucinus imitator), with a multi-generational pedigree. We analyze two measures of spatial association, using repeat sampling of 376 individuals . Conditioned on the effects of age, sex, group size, seasonality, and El Niño–Southern Oscillation phases, we show low to moderate long-term repeatability (across years) of the proportion of time spent social  and of average number of partners  . Most of this long-term repeatability could be explained by modest heritability  with small long-term maternal effects . Our models capture the majority of variance in our behavioral traits, with much of the variance explained by temporally changing factors, such as group of residence, highlighting potential limits to the evolvability of our trait due to social and environmental constraints.Various aspects of sociality in mammals  are linked with measures of biological fitness . How within- and between-individual variation in relevant social traits arises in uncontrolled wild populations is challenging to determine but is crucial for understanding constraints on the evolution of sociality. We use an advanced statistical method, known as the ‘animal model’, which incorporates pedigree information, to look at social, genetic, and environmental influences on sociality in a long-lived wild primate. We leverage a longitudinal database spanning 20 years of observation on individually recognized white-faced capuchin monkeys ( The last two decades have shown a surge in research linking individual variation in different measures of sociality and variation in survival and/or reproductive success in social mammals  versus non-genetic  sources of variation? Measuring the relative contribution of additive genetic effects is of substantive evolutionary interest, because the heritability of a trait can indicate the potential for a population to respond to selection on it  is a statistic that estimates the proportion of total phenotypic variation in a trait in a population that is explained by additive genetic effects  in addition to alleles with their parents. Cross-fostering designs can help separate the common environmental versus genetic effects of parents on offspring, but such methods are not feasible with wild primates for both ethical and logistical reasons. Fortunately, in populations where parentage information can be confirmed, or reasonably deduced, alternative approaches are available  to disentangle genetic and non-genetic influences on sociality. White-faced capuchins are a particularly suitable species in which to attempt to partition environmental and genetic influences on a behavioral trait. As a result of long male alpha tenures and high reproductive skew toward alpha males, capuchins have complex social and genetic group structure, with multi-generational overlap and large numbers of close kin through both maternal and paternal lines (Perry r > =0.25) is not confined within groups or even matrilines, making it easier to separate out genetic versus non-genetic influences on phenotypic traits.We use 20 years of observational data and a multi-generational pedigree from a wild population of white-faced capuchin monkeys .Of the 376 individuals in our behavioral dataset, 280 (74.5%) were first seen within three months of their births, and we could confidently assign maternity to them based on demographic (pregnancies) and behavioral data (primary nursing) even prior to genotyping. Of the remaining individuals, 41 (10.9%) were males of unknown origin that immigrated into our study population, while the rest were natal to our study groups but were first seen as older infants (>3 months), juveniles, or (sub)adults (14.6%) and required genotyping to assign/confirm maternity. Paternity was assigned based on genetic information when possible  had two assigned parents, 37 had one assigned parent (9.8%), and 52 (13.8%) had no assigned parent based on demographic, behavioral, and/or genetic parentage information. Most individuals with no assigned parents were immigrant males (78.9%).n = 91, 2012–2020) (See SI File 1). Briefly, DNA was extracted primarily from non-invasively collected fecal samples, and occasionally from tissue samples obtained from deceased individuals, then amplified at up to 18 autosomal tetranucleotide microsatellite loci (Muniz and Vigilant Information on genetic parentage assignment (at up to 18 microsatellite loci) in our study population is available from previously published work . Genotypes at each of the loci were assigned to be heterozygous when each allele was seen at least twice in independent PCRs, and assigned as homozygous when the allele was seen in at least three independent PCRs in absence of a second allele.Amplicons were analyzed using an ABI PRISM3100 automated sequencer and GeneMapper Software . Likelihood-based parentage assignments were performed using CERVUS 2.0 or 3.0  were genotyped twice  following the procedures described above to guard against sample mix up. Known mother-offspring pairs were confirmed by ascertaining the absence of Mendelian mismatches across all loci for the pair, though one mismatch was allowed to account for null alleles, mutations, and genotyping errors. We detected one null allele in the population in 19 individuals and traced it back to a male who was either the father or grandfather of those individuals . In cases when conceptions occurred prior to the habituation of a study group, we used the identities of all adult males present when the group was first observed. Candidate mothers were similarly chosen for individuals that were first seen as older infants, juveniles, or (sub)adults. For individuals born post-group habituation, CERVUS has always assigned paternity from the pool of potential candidate fathers. Parent-offspring pairs and trios were allowed one mismatch .During stable tenures, alpha males in our population sire approximately 73% of infants born in their groups, including 90% of offspring born to unrelated females , we lacked parentage information  for 12 individuals first seen at the time of habituation. We had incomplete parentage on an additional 11 adults . We used the software program COLONY version 2.0.6.7 to look for evidence of whether these individuals were related to each other at the level of full sibling  whether an individual was seen in proximity of another monkey (within ~4 meters) during a scan , and (2) the number of partners an individual has nearby (within ~4 meters) during a scan. The former is measure of the propensity of an individual to be social versus alone, while the latter is more indicative of the gregariousness of an individual. These two phenotypes are not independent, as they are generated from the same data Fig. .Fig. 1DiWe compiled the scans of individuals by month  so that we had counts of (1) the total number of scans where an individual was social and (2) the total number of partners an individual had. With these counts we could look at the (1) proportion of time spent social  and (2) the average number of partners an individual had, while still preserving information about sampling density (number of scans).To be included in any month, subjects needed to have at least five scan samples in that period. As we are interested in the repeatability of our measures of social behavior, subjects had to have at least six months of data to be included.We excluded dependent infants (less than one year of age) as potential social partners of their mothers. We also excluded these dependent infants as subjects, since an infant is expected to be in close proximity of its mother, particularly during the first half of their first year of life Godoy . IncludiOn average, subjects spent just over half of their sampled time within approximately four meters of another monkey  and had approximately one social partner per scan  Fig. . Our datWe included age (as a cubic function) and sex in our models, as well as their interaction to account for differences in how male and female capuchins sexually mature and age. Age in our dataset was right-skewed with higher representation at younger ages  Fig. . To put Nomascus concolor), group averages of dyadic proximity have been documented to decrease from the dry season to wet season, with increased average group proximity during cold months and lowered proximity during warm months  to determine the different phases. MEI.v2 is a composite index of five different variables  used to create a time series of ENSO conditions from 1979 to present  has an impact on large scale patterns of temperature and precipitation  as a random factor, as well as subject identity nested within year , the identity of each subject’s mother , maternal identity nested within group of residence within year of data collection , and a special variable known as the animal term to account for additive genetic variance (VA). These components contribute to long- and/or short-term repeatability of individuals. All models also include year of data collection , month nested within year , and the identity of each subject’s group of residence both across years  and within years .All models include the identity of the subject  can be thought of as estimating the “permanent environment variance”  of an individual, which is the “individual-specific variation in environmental conditions that permanently affect the phenotype (e.g. early-life conditions)” . During such a relatively short period, individuals are more likely to be stable in important social traits such as kin availability, dominance rank for adults, and maternal dominance rank for infants and young juveniles.VM estimates the variance explained by maternal effects (m2), specifically similarity between maternal siblings. Maternal identities were not available for all subjects, namely 11 immigrant males of unknown origin who were not assigned by COLONY as having a full sibling. We created unique dummy codes for their maternal identities, so that no two of these individuals shared the same mother. We additionally nested maternal identities (VM:GroupAlpha:Year) to account for similarity between maternal siblings residing in the same group in the same year. Such a nested structure might capture potential upward biases on heritability due to maternal kin biases in spatial association among siblings residing in the same group.Vh2 in our models by fitting a random effects term (VA), referred to as the animal term, which in the R package MCMCglmm links to the identities of individuals in our population pedigree (Hadfield MCMCglmm). Inclusion of the animal term provides our models with an additive genetic variance component based on the estimated coefficients of relatedness between individuals in our pedigree. In short, if animals that share more alleles are also more like each other in their behavior, then variation in the behavior may well be due to genetic variation in the population .We estimate Year and VMonth:Year were included in order to account for temporal variation in sociality scores not captured by the fixed effects of seasonality or ENSO phase. These could arise from, for example, observer drift in coding  or prevailing environmental conditions  that could lead to changes to how individuals cluster near others. There were 218 unique observer combinations across the 224 months represented in the dataset, so VMonth:Year should also capture variance due to any differences between observer teams, though we cannot separate out the unique influence of observers.VGroupAlpha represents variance arising from the different alpha tenures within groups in our study population. VGroupAlpha captures both variance due to group of residence effects and the additional influence of alpha tenures within those groups. In capuchins, alpha males are ‘keystone’ individuals, whose influence is disproportionate relative to that of others in the population, and thus play important roles in establishing group dynamics (Jack and Fedigan GroupAlpha:Year) so as to separate the within-year and across-year influences of group of residence.VMCMCglmm version 2.32 , which was pooled into monthly units, we fit models with a binomial distribution and logit link function , with the number of scans each individual was documented social (‘successes’) versus the number of times alone (‘failures’).For our other response variable (number of partners), which was also pooled into monthly units, we fit models with a Poisson distribution (family = “poisson”), with the total number (sum) of partners per month. We included the natural log of the number of scans per month as a fixed effect to account for sampling effort. We set a strong prior for the log of sampling effort so that the rate at which events occurred was 1 .We used a parameter-expanded prior  and two inverse Wishart priors  for the G structures in our models . The prior on the residual variance component was set to one for both the binomial and Poisson models. Estimates for variance components were robust against the choice of prior SI Fig. . We therPilot runs  indicated that autocorrelation values would remain high for some variance components in models run with parameter-expanded priors, even with large thinning intervals. We therefore increased the number of iterations to guarantee effective sample sizes of at least 1000, but ideally closer to 4000. All models were run with a long burn-in period of at least 10,000 iterations.n = 4) of each model and assessed convergence of the chains visually (SI Files 2a-b), as well as through the Gelman-Rubin criterion implemented via the ‘gelman.diag’ function from the coda package in R (version 0.19-4)  is estimated (and partitioned among the different random effects) after conditioning on the fixed effects. Heritability estimates, for example, can be higher because the variance explained by the fixed effects structure (VFE) is not included in VP, thus making the relative contribution of VA to VP larger compared to the same model without fixed effects (Wilson A and associated heritability (h2).Inclusion of fixed effects can potentially have an impact on the estimates of variance components in models because total phenotypic variance , then built-up complexity by adding in versions with the properties of the individuals first , then properties of the group (group size), and subsequently environmental properties . Outputs for these reduced models are provided in the Supplementary Information (SI Table MCMCglmm package). DIC is a generalization for multi-level models of the Akaike Information Criterion (AIC); and as in AIC, lower DIC values indicate better fit.We provide the deviance information criterion (DIC) values for models  to additionally compute parameters of interest on the observed data scale  on the observed data scale. We implemented the ‘QGparams’ and ‘QGicc’ functions with parameters model = ‘binomN.logit’ and n.obs = 32 (the average number of scans per subject per month in our dataset) for the binomial model and model = ‘Poisson.log’ for the Poisson model. The choice of value for n.obs is somewhat arbitrary, and we show the consequences for changes in values of this parameter  in SI Fig. Outputs from our QGglmm are not available for integrating over posterior distributions generated from binomial models with logit link functions (de Villemereuil n = 1000 iterations).Closed form solutions in MCMCglmm outputs from the latent scale to the original data scale are available online (see DATA AVAILABILITY).The code used for transforming the P) was the sum of estimates from all variance components and residual variance in a model . The proportion of variance explained by each variance component was calculated by including its estimate in the numerator while including total phenotypic variance in the denominator. So, for example the proportion of variance explained by year of data collection was calculated as Total phenotypic variance  in the numerator to capture additional consistency in among-individual differences resulting from greater environmental similarity within a time series .Long-term repeatability was calculated with the sum of VFE) incorporated into VP. For completeness, estimates with VFE included in VP and transformations to the observed data scale are also provided in SI Table We report posterior modes and 95% Highest Posterior Density intervals . Unless mentioned otherwise, we present results on the unobserved latent scale, and without the variance from the fixed effects .The posterior distributions  for VEstimates for the proportions of variance explained by the random effects were similar in both models, but usually with higher estimates in the model for time spent social than for number of partners Fig. .Fig. 4UnRlong-term: 0.207 ) and the number of partners   and permanent environment effects There was modest >0.1) long-term repeatability 1]) Fig. . Repeata long-tersocial: 0.343 ), but less for number of partners  , explained modest variation in time spent social  and a larger proportion of variance in number of partners . A smaller additional amount of variation was explained by alpha tenures within groups within years (VGroupAlpha:Year) for both time spent social  and number of partners .Group of residence across years, as defined by alpha male tenures within groups  Month:Year explained modest variation in both time spent social  and number of partners . VYear explained modest variation in time spent social , but had lower estimates for number of partners . Estimates for VYear were more uncertain .VM, VGroupAlpha, and VMonth:Year  repeatability in sociality, which is largely explained by additive genetic sources of variation, and to only a small extent by shared maternal environments between siblings. Much of the variance in our models is explained by temporally changing factors such as group of residence, month, and year of data collection.Our posterior mode estimates for repeatability (short-term) in time spent social (0.343) and number of partners (0.213) fall in the range reported in a meta-analysis by Bell and colleagues , where tm2social: 0.045; m2partners: 0.044) and heritability  are within the synthetic range  reported for behavioral traits . Similarly, maternal effects can be inflated when not accounting for shared genes between siblings . Likewise, in assessing both heritability and maternal effects it is useful to consider other common environment effects that may also bias estimates. One such potential source is paternal effects. In capuchins, such influences would best be captured by the identity of alpha males during an individual’s infancy. This is because alpha males are typically the adult male around whom infants spend the most time , reflecting short-term phenotypic plasticity in our behavioral measures, and environmental  influences. Group of residence  explained a modest proportion of variance in time spent social (0.163) and even more for number of partners (0.332). Groups thus vary consistently in their sociality, particularly regarding the average number of partners; or in other words, some groups are consistently more social and gregarious across years than other groups. These differences are not driven by differences in group sizes, which are already accounted for in the models (by including group size as a fixed effect). In fact, not including group size reduces estimates for group of residence. These stable group differences may be consequential if, for example, more social groups can outcompete less social groups. Future studies on sociality should therefore consider not just individual-level fitness consequences of sociality, but also group-level consequences which may well amplify or constrain selection for more social individuals.Month:Year)  may reflect the influence of shorter term temporal changes in clustering of food sources , while VYear  may reflect more long-lasting environmental changes , though both may also reflect observer bias or drift in coding . More direct methods for assessing environmental influences  while controlling for observer identities would be necessary to better understand what drives consistency in behavioral measures within years and months.The variance explained by the factor Month:Year  from a large group  was on average more social than an individual from a small group , both when sociality was measured as (a) proportion of time spent social  and (b) average number of partners  though the differences were not dramatic. El Niño (dry) and La Niña (wet) phases were both associated with reduced sociality scores. Drought conditions during El Niño phases likely drive individuals farther apart as they spend more time searching for scarcer resources. La Niña phases may also lead to changes in how individuals cluster near others. However, since heavy rainfall also affects visibility in the field, the effects captured by La Niña phases may also reflect underestimation of sociality due to reduced visibility in the canopy. Observers are less able to accurately count the number of conspecifics near a subject when visibility is poor.The inclusion of age and of group size had the largest impact on model fit and estimates for the relative contribution of variance components. However, estimates for variance components were largely robust to changes in the fixed effects structure of models, with little difference between reduced and full models once age, at least, was accounted for. Repeatability was higher in models lacking any fixed effects, driven by much larger maternal effects (which disappeared with inclusion of age as a fixed effect). In other words, the effect of individual age, if not accounted for, is associated with increased similarity between the social phenotypes of maternal siblings. Inclusion of age increased estimates for month of data collection for both phenotypes and also increased heritability estimates for time spent social, though there was little change across models for number of partners. Large maternal effects in the intercept-only models may reflect the age structure of our dataset, which is highly skewed toward younger individuals. Also, in the absence of controlling for the effects of age, individuals may appear more consistent in their behavior simply because they are observed more intensely over a shorter range of time. This may be compounded by higher maternal effects in younger age groups, since maternal effects are typically stronger in juvenile versus adult stages of development . Those estimates might be low because many maternal sibling pairs do not reside in the same group. We thus additionally nested maternal identities within group within year (VMother:GroupAlpha:Year), to capture potential biases that might arise from maternal siblings spending lots of time near each other (siblings living in the same group in the same year). Nesting maternal effects within group of residence and year of data collection captured only a small proportion of the total variance in our models, giving us more confidence that maternal kin biases in spatial association were not upwardly biasing our estimates for heritability.Another related limitation in our study, and in most studies on uncontrolled populations, is the non-independence of data points collected on social behavior. This issue is particularly problematic in capuchins, since they show strong maternal kin-biases in affiliation . Much of that variance was explained by temporally changing factors, which are in addition to additive genetic, long-term maternal, and permanent environmental effects. Our results highlight potential limits to the evolvability of our behavioral trait, because of constraints imposed by social  or other temporally changing factors . We provide one of the first longitudinal studies to disentangle genetic and non-genetic influences on social behavior in a long-lived primate, while thoroughly attempting to account for common environmental effects. Studies on primates are often more focused on social or environmental effects on sociality, in particular maternal effects given the extended period of maternal care. Our results indicate that genetic effects may be just as (or more) critical than social parental effects in determining long-term repeatability, at least in measures of spatial association. Extensive pedigree and longitudinal social phenotype data are available from several long-term primate studies. These data, in combination, are key for studying the evolution of sociality. Extensive pedigrees have been used to look at, as examples, the contribution of additive genetic effects to the gut microbiome (Grieneisen et al. Supplementary Information File 1Supplementary Table 3


Epistasis strongly affects the performance of superior maize hybrids. In this study, a multiple-hybrid population, consisting of three hybrid maize sets with varied interparental divergence, was generated by crossing 28 temperate and 23 tropical inbred lines with diverse genetic backgrounds. We obtained 1,154 tested hybrids. Among these tested hybrids, heterosis increased steadily as the heterotic genetic distance increased. Mid-parent heterosis was significantly higher in the temperate by tropical hybrids than in the temperate by temperate hybrids. Genome-wide prediction and association mapping was performed for grain weight per plant (GWPP) and days to silking (DTS) using 20K high-quality SNPs, showing that epistatic effects played a more prominent role than dominance effects in temperate by tropical maize hybrids. A total of 33 and 420 epistatic QTL were identified for GWPP and DTS, respectively, in the temperate by tropical hybrids. Protein–protein interaction network and gene-set enrichment analyses showed that epistatic genes were involved in protein interactions, which play an important role in photosynthesis, biological transcription pathways, and protein synthesis. We showed that the interaction of many minor-effect genes in the hybrids could activate the transcription activators of epistatic genes, resulting in a cascade of amplified yield heterosis. The multiple-hybrid population design enhanced our understanding of heterosis in maize, providing an insight into the acceleration of hybrid maize breeding by activating epistatic effects. The mechanism of heterosis can be determined according to three primary hypotheses based on classical genetics. The dominance hypothesis explains heterosis by the action of superior dominant alleles from both parents at multiple loci, which complement corresponding unfavorable alleles leading to the enhancement of hybrid vigor. Such complementation might allow hybrids to be similar to or better than the superior parent  network analysis and gene-set enrichment analysis (GSEA) demonstrated that many minor loci interacting with the gene networks might improve the performance of the hybrids.The multiple-hybrid population used in this study was derived from the cross between 23 tropical and 28 temperate inbred lines, representing high diversity in temperate and tropical regions. These lines were grouped into seven heterotic pools according to their pedigrees, original regions, and genetic population structure inferred from molecular markers . The tem2O kg–1.Days to silking (DTS) and days to anthesis (DTA) were recorded as the number of days from planting to when 50% of the plants in a plot had shed pollen and extruded silks, respectively; anthesis–silking interval (ASI) was defined as the time interval between DTS and DTA. After female flowering, the PH values were recorded as the averaged value of the five plants from the center of the plot. The grain yield per plant (GWPP) was estimated based on the mean value of 10 plants. The grain number per row (GNPR), the row number (RN), and the ear barren tips (TIP) were measured as the averaged value of 10 ears from each plot. Harvesting was performed manually, and the harvest was adjusted to a moisture content of 140 g HA two-stage method was adopted for phenotypic data analysis , where eyijk represents the phenotypic performance of the ijth genotype  within the lth incomplete block for the kth replication, gij represents the genetic effect of the ijth genotype, rk represents the effect of the kth replication, blk represents the effect of the lth incomplete block within the kth replication, and eijkl represents the residual. Except for the effect of gij, the remaining effects were random.where In the second step, to analyze the phenotypes in various environments, we used a linear mixed model based on the adjusted best linear unbiased estimates (BLUEs) of individual environments:gij and ln denote the genotypes and individual environments, respectively. Except for the effect of gij, all other effects were random.where MPH) of all hybrids by MPH = F1−MP, where, F1 represents the hybrid performance, and MP represents the mid-parent value for two parents, P1 and P2. Then, we determined the relative MPH(%) for all hybrids using the formula BPH) using the formula BPH = F1−PBetter, where PBetter represents the performance of the better-performing parental line. We measured relative BPH using the formula t-tests were performed to compare the BLUEs among diverse genotypes.The fixed genotypic effects were used to obtain the BLUEs for parental and hybrid genotypic values. Next, we used the BLUEs for calculating mid-parent heterosis  of female and male subjects, as well as the variance resulting from the specific combining ability (SCA) of the hybrids :yijkl represents the phenotypic performance of the ijth entry  in the nth environment, a represents hybrid and line group effects, ln indicates the effect of the nth environment, gi and gj indicate the genetic effects of the parental lines, gij represents the SCA effect of the crosses between i and j lines, gi:ln and gj:ln represents the interplay effect between the i/jth parental lines and the nth environment, gij:ln represents the interplay effect between the SCA and the environment, whereas, eijn represents the residual. Heritability was estimated by the genotypic-to-phenotypic variance ratio,E represents environment number, R represents the mean replication number in each entry in one location, and where ironment .Fst statistic and SNP nucleotide divergence (π) between the temperate and tropical inbred lines were calculated using VCFtools (Fst statistics and sequence diversity statistics (π) with 100-kb steps in the maize genome. We also determined π values for temperate and tropical inbred lines, and the ratio of π  was used to detect the genetic-improvement sweeps. For parental lines and hybrids, the LD decomposition, based on the genetic map distance, was evaluated by fitting the natural smoothing splines to r2 values using the software package PLINK  matrix from the original trait vectors to the MPH vector, r indicates the hybrid number, and s represents the parental line number. Next, the F metric was used for calculating kinship matrices derived from the markers, resulting in model non-orthogonal parametrization  was denoted as the locus subset, where the male and female parents had the genotypes l and k, respectively.  For i, j ∈ Q and i ≠ j, di is assumed as the dominance effect of the ith QTL, while aaij, adij, and ddij represent the additive-by-additive, additive-by-dominance, and dominance-by-dominance epistatic effects between ith and jth QTL. For the ith locus, its heterotic effect is shown below:For a locus, its heterotic effect represents its genetic contribution to MPH and also the combination of the self-dominance effect and epistatic interaction effect with the entire genetic background . SpecifiAccording to the definition, the MPH value of the hybrid represents the summation of all heterotic effects among polymorphic loci.A three-step process proposed by y, gd, gaa, gad, gdd, and e represent the same parameters as those presented in Equation 5. Particularly, α represents the dominance effect of a marker or the epistatic interaction effect of a pair of markers, and m represents the relevant coefficient. We assumed α to be an unknown fixed parameter, while the rest were assumed to be the same as those in Equation 5. We converted this model into a standard linear regression model for calculating efficiency, where only the residual terms were random. The converted model was similar to the original one as long as the effect of different parameters on the estimation of the variance components was negligible ], where n denotes the tested number of SNPs ].In steps one and three, we examined the genome-wide threshold for the  of SNPs . The smar2 = 0.1  decay was 245 kb at r2 = 0.1 . In thisdatabase . A seed database , and theabase , followed by the groups of the tropical (0.36) and temperate lines (0.35). The genetic diversity in the intergroup was also determined, and a faster LD decay was found in the temperate by tropical hybrid set than in the other two hybrid sets. The PCA confirmed the differences among the three hybrid sets, with three final patterns being distributed in different spaces. Using an NJ phylogenetic tree, cluster analysis based on GD estimates identified 49 groups, and the hybrids derived from a parent were mostly clustered into the same group  with the other nine epistatic interaction loci were analyzed. A total of 40 candidate genes within 55 kb widows of their epistatic loci were analyzed; 12 core genes showed interactions . The 12 1 hybrids, however, such suppression was relieved due to the complementation of heterozygosity, which resulted in the activation of epistasis between Gene 1 and Gene 2. Thus, Gene 1 and Gene 2 might be considered to be epistatically controlled QTL , grain number per row (0.25), ASI (r = 0.17), and hundred-grain weight (0.34) for tropical parents, due to the negative correlation between mid-parent performance and heterosis (Hybrid breeding largely depends on heterosis, which can be determined by the genetic distance between parental lines . The leveterosis . Geneticeterosis . Thus, ieterosis .The complexity of the digenic epistatic network identified in this study suggests that many rare genes with minor effects were modulated by the core genes for yield heterosis. The signals of selection identified between the temperate and tropical hybrids indicated the presence of polygenic heterogeneity along the whole genome , and in Arabidopsis and positively regulates salicylic acid and abscisic acid biosynthesis (Our GWAS and haplotype analyses indicate that epistasis contributes to the greater heterosis identified in the tropical by temperate hybrids. Epistasis might be related to various molecular interactions, and single or combined alterations of hybrid biological networks might contribute to heterosis to different degrees . The comynthesis . Our resDesigning optimal genotypic combinations and increasing the favorable alleles among parental lines might further enhance hybrid performance. In this study, we found that increasing parental heterotic genetic distance is necessary for maximizing heterosis. The mid-parent values only contributed to a fraction of hybrid performance in maize, while the lines with high GCA for yield were more suitable as parents for hybrid breeding . ConversThe original contributions presented in this study are included in the article/YX and ZS conceived and designed the experiments and wrote the manuscript. ZS, HW, and ZZ performed the experiments. ZS, YY, XL, and ZL analyzed the data. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer KB declared a shared parent affiliation with the several authors ZS, HW, YY, XL, ZL, and YX to the handling editor at the time of review.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Rapid reductions in emissions from fossil fuel burning are needed to curb global climate change. Biofuel production from crop residues can contribute to reducing the energy crisis and environmental deterioration. Wheat is a renewable source for biofuels owing to the low cost and high availability of its residues. Thus, identifying candidate genes controlling these traits is pivotal for efficient biofuel production. Here, six multi-locus genome-wide association (ML-GWAS) models were applied using 185 tetraploid wheat accessions to detect quantitative trait nucleotides (QTNs) for fifteen traits associated with biomass composition.p.value < 0.05). Candidate genes survey carried out within 4 Mb flanking the QTNs, revealed putative biological functions associated with lipid transfer and metabolism, cell wall modifications, cell cycle, and photosynthesis. Four genes encoded as Cellulose Synthase (CeSa), Anaphase promoting complex (APC/C), Glucoronoxylan 4-O Methyltransferase (GXM) and HYPONASTIC LEAVES1 (HYL1) might be responsible for an increase in cellulose, and natural and acid detergent fiber (NDF and ADF) content in tetraploid wheat. In addition, the SNP marker RFL_Contig3228_2154 associated with the variation in stem solidness (Q.Scsb-3B) was validated through two molecular methods .Among the 470 QTNs, only 72 identified by at least two models were considered as reliable. Among these latter, 16 also showed a significant effect on the corresponding trait (The study provides new insights into the genetic basis of biomass composition traits on tetraploid wheat. The application of six ML-GWAS models on a panel of diverse wheat genotypes represents an efficient approach to dissect complex traits with low heritability such as wheat straw composition. The discovery of genes/genomic regions associated with biomass production and straw quality parameters is expected to accelerate the development of high-yielding wheat varieties useful for biofuel production.The online version contains supplementary material available at 10.1186/s12870-022-03900-6. Wheat yield has more than doubled over the last century because of genetic improvement mainly due to the effect produced by the breeding activity on plant height and floret fertility , 2. Stroi.e., wheat straw) are playing an increasingly important role as a source of renewable energy since modern technological processes aim at the use of inexpensive raw materials (second-generation biofuels) and are more suitable to produce bioethanol and biogas _ij are the genotype-trial interaction, and e corresponds to the residual effect considering as random and assuming to have a normal distribution r ~ N. The model was implemented using the function lmer in the R package lme4 . The norPutative candidate genes were searched in flanking regions of the significant QTNs. The linkage disequilibrium (LD) decay value was calculated using the LD Ajacent Pairs Analysis function (SVS) and then used to define the confidence interval.https://www.interomics.eu/durum-wheat-genome). Putative candidates were then used as baits for a BLASTn search against the NCBI database to assign gene names based on direct orthologs of Oryza sativa.Then, gene annotation was retrieved based on the Svevo durum wheat high-confidence gene models (http://primer3.ut.ee) was adopted to design primers. The HRM analyses were performed in 384 well plates on the QuantStudio 12 K Flex , following the procedure described by [Firstly, two different molecular methods  and rhAmp allelic discrimination assay) have been used to validate the SNP marker associated with basal stem solidness using a panel of 34 accessions with a contrasting behavior for SCSb and for allelic profiles. As far as HRM is concerning, primer3 software version 4.0.0  and second (PC2) principalcomponents showing the variation among individuals. Based on Triticum ssp.,genotypes are represented by different colored symbols indicated in the legend.Additional file 4: Supplementary  Fig. 4. Intra-chromosomal LD decaydistance (kb) evaluated considering (A) the whole genome, (B) A genome, (C) Bgenome. Dashed lines indicate the r2 threshold. The intersectionpoint between the decay LD curve and the LD threshold was shown. Additional file 5: Supplementary Fig. 5. Numbers of significant QTNs detected for 15 traits using six multi-locus GWASmethods Additional file 6: Supplementary Fig. 6. Singular QQ plots for associatedtraits. On X axis the expected –log10pvalues, whereas observed –log10pvalues are reported on Y axis. Additional file 7: Supplementary Table 1. BLUPs values for the traits under study.Additional file 8: Supplementary Table 2. Molecular validation of RFL_Contig3228_2154)associated with SCSb with HRM and rhAMP assays.Additional file 9: Supplementary Table  3. List of acronyms and their abbreviation used in this study. Additional file 10: Supplementary Table 4. QTNs comparison with QTL identified in the literature.


Alzheimer’s disease (AD) is a complex neurodegenerative disorder and the most common type of dementia. AD is characterized by a decline of cognitive function and brain atrophy, and is highly heritable with estimated heritability ranging from 60 to 80We propose a novel method to identify disease-related genetic variants enriched by imaging endophenotypes, which are the imaging traits associated with both genetic factors and disease status. Our analysis consists of three steps: (1) map the effects of a genetic variant  onto imaging traits across the brain using a linear regression model, (2) map the effects of a diagnosis phenotype onto imaging traits across the brain using a linear regression model, and (3) detect SNP-diagnosis association via correlating the SNP effects with the diagnostic effects on the brain-wide imaging traits. We demonstrate the promise of our approach by applying it to the Alzheimer’s Disease Neuroimaging Initiative database. Among 54 AD related susceptibility loci reported in prior large-scale AD GWAS, our approach identifies 41 of those from a much smaller study cohort while the standard association approaches identify only two of those. Clearly, the proposed imaging endophenotype enriched approach can reveal promising AD genetic variants undetectable using the traditional method.We have proposed a novel method to identify AD genetic variants enriched by brain-wide imaging endophenotypes. This approach can not only boost detection power, but also reveal interesting biological pathways from genetic determinants to intermediate brain traits and to phenotypic AD outcomes.The online version contains supplementary material available at 10.1186/s12920-022-01323-8. Alzheimer’s Disease (AD) is a complex neurodegenerative disorder, and the most common type of dementia . Today, cument}% . The mosmentclass2pt{minimcument}% , 5) haveTo address this challenge, imaging genetics  is emergTo bridge this gap, we propose an innovative method to identify disease-related genetic variants enriched by imaging endophenotypes, which are the imaging traits associated with both genetic factors and disease status. We demonstrate the promise of our method by applying it to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database . Our majWe first report the results of our first experiment. In this experiment, to demonstrate the promise of our approach, we performed a comparative study with a few conventional genetic association methods. The benchmark algorithms used in this work include: 1) conventional GWAS analysis controlled for relevant covariates including age, sex and education (implemented in PLINK v1.90), (2) Pearson’s correlation analysis between each SNP and each diagnosis outcome, and (3) the partial correlation analysis between each SNP and each diagnosis outcome while controling for relevant covariates. We performed empirical comparison on the real imaging genetics data from the ADNI cohort. On the genetics side, we analyzed 54 AD SNPs identified in recent landmark AD GWAS studies  conventi, 11. ThrConventional GWAS analysis was applied to identify genetic variants for three diagnostic outcomes , respectively. APOE-rs429358  across the entire brain. To the best of our knowledge, this is the first approach to enrich genetic variants associated with AD via mapping their association patterns with imaging QTs in the brain. In our empirical study on the ADNI data, we confirmed multiple genetic variants estimated by conventional models, such as APOE  reported mixed signs of correlation coefficients . A previous study showed a bidirectional modulation of CD33 genotype associated cognitive performance . The CD3In our second experiment, we performed comparative studies through applying the proposed pipeline to random “non-AD” SNPs. It is promising that our pipeline has been able to to identify a lot more AD susceptibility loci than random SNPs that have not yet been linked to AD before. However, these random SNP analyses have also yielded some significant findings, which warrant further investigation towards a few interesting directions. First, some of these findings could be true signals missed by the existing studies . Thus, our findings could provide valuable guidance for subsequent replication studies in independent cohorts. Second, some of the findings may not have a direct effect on the diagnosis. However, by the design of our pipeline, these findings are indirectly connected to the diagnostic phenotype via being related to a same set of imaging endophenotypes. Such a mechanism warrants a more detailed further investigation. Third, some of these findings could be false discoveries. One potential limitation of our method is that we include all the ROIs in the brain while correlating the genetic map with the diagnostic map. It is likely that some ROIs are irrelevant to the pathway from genetics to phenotypical outcomes. They may introduce noises and biases, leading to possible false discoveries. Thus, an interesting future direction could be to identify only relevant ROIs for mapping genetic and diagnostic effects. Another interesting direction could be to explore different and improved mapping strategies. For example, the current pipeline employs a linear regression model in both Step 1 and Step 2. This simple modeling strategy coupled with the existence of irrelevant ROIs could lead to false positive or negative discoveries. Expanding to a nonlinear model, such as polynomial regression or a fully connected neural network model, has the potential to capture complex associations and improve biomarker identification. This remains as an interesting future topic to explore.We have proposed an innovative method to identify disease-related genetic variants enriched by imaging endophenotypes, which are the imaging quantitative traits (QTs) associated with both genetic factors and disease status. Our approach consists of three steps: (1) association analysis between imaging QTs and diagnosis, (2) association analysis between imaging QTs and each genetic variant, and (3) correlation analysis between two brain maps produced in Step 1  and Step 2 . We applied our method to the ADNI cohort to identify genetic markers enriched by amyloid imaging endophenotypes in AD. Among 54 AD related susceptibility loci reported in prior large-scale AD GWAS, our approach identified 41 of those from a much smaller study cohort  while the standard genetic assocation approaches identified only two of those. Our method yielded not only a lot more AD genetic variants undetectable using the traditional method but also a set of imaging QTs significantly associated with both the genetic variant and the diagnostic outcome. Such QTs have the potential to serve as imaging endophenotypes linking genetics with AD outcomes. These promising findings demonstrate that our approach can not only boost detection power, but also provide valuable information for revealing interesting biological pathways from genetics to brain traits and to AD outcomes. An interesting future topic is to perform an in-depth investigation to explore the detailed relationships between the identified genetic markers and brain imaging traits for different disease stages.Data used in the preparation of this article were obtained from the ADNI database (adni.loni.usc.edu) . The ADNtapir AV-5 PET scaPreprocessed AV-45 PET scans are collected and aligned to the Montreal Neurological Institute space as NK v1.90 . We perfThe proposed pipeline aims to identify genetic markers enriched by amyloid imaging endophenotypes in AD. The pipeline consists of three steps: (1) association analysis between imaging QTs and diagnosis, (2) association analysis between imaging QTs and each genetic variant, and (3) correlation analysis between two brain maps produced in Step 1  and Step 2 .x be a diagnostic outcome  and Y be a set of AV-45 imaging QTs. We perform the following simple linear regression model to examine the diagnostic effect on each imaging QT x has a significant effect , (b), (c) show the p-value significance of imaging-geneticsanalysis for all SNP-ROI pairs on three data sets , respectively. For each ROI-SNP pair, the p-value is shown.