Large molecular interaction networks are nowadays assembled in biomedical researches along with important technological advances. Diverse interaction measures, for which input solely consisting of the incidence of causal-factors, with the corresponding outcome of an inquired effect, are formulated without an obvious mathematical unity. Consequently, conceptual and practical ambivalences arise. We identify here a probabilistic requirement consistent with that input, and find, by the rules of probability theory, that it leads to a model multiplicative in the complement of the effect. Important practical properties are revealed along these theoretical derivations, that has not been noticed before. A combination of drugs can produce synergistic effects even when administered separately in time. The first can “prepare the field” for the later action of the second, without meeting in a direct physical contact. This meaning of interaction has been practical in toxicology for the discovery of dosage combinations that better perform on clinical parameters of interest. A similar notion is in usage in epidemiology and in the construction of gene interactions networks.2. These factors need not be in direct physical contact, while the observable effect, measured in terms of a particular biological outcome, laid far at the other end of the triggered process. The mechanisms and process structures operating in the way from factors and their effect are not observable at this experimental stage. The tacit assumption is that recurrent patterns of factor and effect provide information of the presence of cross-talk structures along the process perturbed by the factors , in their way to the outcome of some measurable parameter . The above loose meaning of interaction fits to the kind of inference permitted by this kind of data, the circumstance that we focus in this manuscript.Forefront high-throughput technologies are delivering interaction data relevant for the study of poorly known complex systems, like the cell. Factors and effects are often the sole kind of data released in large scale experiments by these technologies. For example, synthetic genetic arrays and gene-editing technologies, in both targeted and large-scale experiments, allows to knock out or selectively activate/repress target genes along the genome in various cell types and organisms, altering cellular process and functions3. Later enrichments with functional annotations and additional biological knowledge permit the systematic elucidation of higher-level principles of the cellular organization and function. The utility of theses mapping efforts has been shown across diverse prokaryotes and eukaryotes organisms including mammalian and human cells6. Therefore, inaccuracy at the interaction mapping stage propagates to the subsequence stages of enrichment and functional mapping7.The data in these large scale screening provide no cues of when, where and how the intermediate events interconnect8. Currently, diverse measures are advocated in the literature, and the concept of interaction await open for resolution.However, at the basic level, the definition of interaction remains conceptually ambivalent. The issue is not new, testimonies of everlasting debates can be traced back along more than a century12. Some epidemiologist proclaim that there is no biological rationale for calling interactions to the product terms in a regression model, arguing that they can disappear or even change sign by transforming the outcome scale (ex. logarithm)14. Others are more confident to cast sufficient-cause interactions method in complementary log regressions framework15. Another faction claim for broadening the scope of the casual inference school, and for a more pluralistic approach12.On one side, interaction models in epidemiology gravitates around risk, i.e. the probability of a disease (effect) given the exposure factors . Dominant theoretical and methodological streams advocate developments from causal inference , not without controversies among scholars and philosophers19. Based on "genetic" grounds20, the double-mutant fitness is expected to be the product of the single-mutant fitness, on absence of interaction, but fitness itself exhibit a plurality of meanings, or varied in scales. A phenotype can be consistently expressed in terms of any monotonic function  of the “original” phenotypic scale. But the product or the addition in one scale is not the same than in another. Evoking a “regression model” or a “multiplicative model” is just not enough. The concerns is not new, and the reaction should not be confined to comparisons between mathematically defined measures in term of ad hoc criteria of performance19. Of course, performance is the final goal, yet this path of assessment is limited to the already defined competitors, a useful but postmortem dictamen.On another side, ad hoc measures are adopted in the construction of large-scale genetic interaction networks. Often, regression model are written down directly in terms of the physical parameters measured in the experiment , with a hasty explanation for the rational of the choiceStriving to come out from this conceptual quandary in the direction of fundamental development, we undertake a pragmatic resolution of the concept of interaction that depart from precedent approach. In this endeavour, we do not write down in advance a mathematical definition of interaction, but advocate a concept that comply with the practical meaning and kind of input data stated above. We identify from a verbally stated definition, elementary but general probabilistic requirements for multivalued factors and dichotomous effect scenarios. Sticking to the rules of probability theory, we derive a model which is general and simple. Finally, we illustrate for a genetic interaction mapping case, how to cast the measured parameters into the language of factor and effect, so as to apply the framework just derived. Though we do not pose a causal inference approach, we detour briefly into association and causality in connection with our development.7.Genetic interactions underlie diverse aspects of biology, including the evolution of sex, speciation, and complex disease. Simple inbred systems, such as yeast, provide an experimental format for mapping the genetic interactions networks of a cell. Genome-scale interaction studies in isogenic yeast populations, collected growth measurements from four possible mutant states for each pair of genes mentclass2pt{minim7. So far, the mathematical definition of a neutrality function remain open to arbitrariness21. Mani et al7 examined properties of four reported definitions of interaction and show that the choice can dramatically alter the resulting set of genetic interactions with inconsistencies that propagates to the functional mapping. For a quick illustration of the magnitude of this impact, we compare two measures at the basic interaction networks level, of a more recent and extensive global genetic interaction studies in Saccharomyces Cerevisiae1. One of the measures, 1, while the other measure, 22.Mathematical functions delivering the expectation of the combined factor effect, from the individual factor’s effect, have been named neutrality functionFigure mentclass2pt{minimThe issue is not merely on how large the deviation is, but from what and how we measure the deviation. The question of “from what?” is quantitatively answered by choosing a neutrality function. The question of “how we measure the deviation?” is another source of plural inspiration. No fundamental agreement in the answers has been achieved for neither of these questions. The commonest choices are additivity and multiplicative for the neutrality function, and arithmetic difference and the ratio for the deviation. In both cases, one choice can be converted to the other by exponentiation or logarithm. But, asking instead, what conversion is appropriate for the parameters? introduce no progress at all.Modeling controversies can become endless not because the mathematics, but because disputants might not be talking about the same thing. To keep away from such ambiguities, we commence by stating explicitly the definition of interaction we advocate.3 quotation: “… the mutations must be interacting with one another, at least in the loose sense that they exist within pathways that both influence the same phenotype”, comply with the pragmatic meaning and the factor-effect kind of input data we aimed. Slightly re-stated for widening the context, we regard that:Before jumping to write down a quantitative definition, we aim to answer the pragmatic question: what we want from what we have? The inmediate output of the large scale experiment we are focusing, are not going to explain by themselves mechanistic bases from the analysis of each factor pair, but are delivering hypotheses from loose interactions networks, that can be tested by further stages of functional analysis. PhillipsTwo factors interact with one another, in the loose sense that they exist within pathways that cross or interconnect, altering their individual influence to the same effect.Figure entclass1pt{minimaentclass1pt{minimaWe will show how the definition, verbally stated above, become quantifiable in terms of probabilities rules.We are interested in classifying the interaction or non-interaction relationships between two multivalued factors with respect to a distant dichotomous effect. An unstated and unproven assumption in previous approaches is that it is possible to infer interaction from factor and effect data alone, without considering details of the internal machinery connecting factors and effect. To prove the validity of this assumption we introduce, by the symbol The effect due to the individual exposure to factors entclass1pt{minimaThe instances of factor entclass1pt{minimawhere  stands fTherefore, the equalities in  are quanThe product rule of probability theory, i.e. mentclass2pt{minimfor all mentclass2pt{minimmentclass2pt{minimis the sole necessary condition for non-interacting factors The factorization in the right side of  is the eractions  can be sThis path of reasoning departs from previous approaches appealing to neutrality functions or casual inference arguments. The factorization  is a conWe arrived to the neutral model  through The identity can be conveniently shown by substituting , 6) and and6) anIn the particular non-interaction case, the requirement  implies complement of the effect, and Hence, absence of interaction implies a log-linear form of the probability distribution in the Fixing δxy=0 in  implies If ted from  and 9)..\documenNotice that requirement  entails les from  by11\doc25. Lee15 provided instructions to perform such a regression using existing statistical software.where Faithful to the rules of probability theory, we derive now an equivalent expression of  in termswhere mentclass2pt{minimmentclass2pt{minimmentclasspt{minimairements  can be wExpanding the product of summations in the denominator and using  yields14Substituting  in the dAs noted from  and its We already shown, Eqs. –8), tha, tha8), The numerator in the right side of  becomes\The denominator in  becomes\The summation terms cancel in the numerator and denominator of (15), yielding Therefore, a log-linear function in terms of We show first how the conventional additive and multiplicative models in epidemiology can be related to the model multiplicative in the complement of the effect. Later we will see how to derive the additive model as an approximation.Equating to  the expot}δab in  , multipRearranging equality  yields:126:Assuming that 27.Thus, the model multiplicative in the complement of the effect justifies the additive model as an approximation valid for low risk regimes, as has been previously settledMultiplicative or additive models, advocated for long in the epidemiology literature, can be useful approximations in some domains, which might explain why they remain pervasive in the interaction field.complement of the effect convey an interaction meaning. Can we say the same for the probability on the effect? Nothing in mathematic forbid us to write the logarithm of We demonstrated that the cross-product term complement of the effect, and follows the analog of Eqs. –7), wit, wit7), g of Eq. , evaluatnalog to  supportiesult in  follows esult in , which imentclass2pt{minimmentclass2pt{minimA real-life scenario of an evident interaction case, where Let now see how disappointing is the strong condition Equality  is satis side of  become cTherefore, the cross-product term 22. Indeed, many of such functions can be defined. But as shown by Eqs. (Gene-interaction studies wrote down different “interaction” functions in terms of fitness by Eqs. –7), eve, eve22. In general, just because the log of a mathematical function complement of the effect, this function can be interpreted as an interaction term.Therefore, a criterium connected to reality precede the question of whether the cross-product term represent interaction; otherwise, the call for interactions remain ill posed. We got a criterium leading to , plainlyThe notation rivation –15) of  of \docuuirement  cannot htisfying , that mi1, millions of gene pairs are tested but only a small fraction interacts. This already daunting task would be impossible if the molecular mechanisms mediating each possible pair were required a priori to select the “appropriate” null model to detect interaction. Instead, the presence of interactions can be diagnosed by  into the probability framework of factor and effect concepts is not straightforward. The example in the domain of genetic interaction introduced in We derived a neutral model in terms of general abstract concepts of factors and effect, without explicit reference to physical parameters. In this sense, it is a unifying theoretical framework. But, to make practical application of this framework, it is required to land the model into actual data scenarios. The model obtained here from basic principles, though accepted in toxicology, is ignored or undervalued by the dominant genetic networks literatureSaccharomyces Cerevisiae). Even when addressing the same interaction question, and advocate the same null multiplicative model 7. The sub-indices correspond to wild-type . These authors defined fitness of each deletion strain directly by its duplication rate Onge et al.1 wired the most extensive global genetic interaction network in Saccharomyces Cerevisiae, with over 23 million double mutants involving 5 416 different genes, including the first large-scale interaction network comprising ~ 120 000 pairs of essential genes. This hallmark works revealed the first comprehensive global functional genetic landscape. These authors defined fitness proportional to colony growth rate relative to that of wild type, i.e. Costanzo et al.Can the measures used in these studies be casted in terms of the model derived here? To address this interrogation in a unified manner, the experimental problem originally contextualized in terms of genes and fitness, need to be reformulated here in terms of factors and effect.29 byLet In this case 22 denoted εA in By posing the genetic interaction problem in terms of probabilities of factors and effect, the equality  show thaWe take a glance on the functional mapping implications, to settle some ground on the application arena. It is not our purpose to dwell deeper on functional mapping, having others devised and championed. Further, diverse methods have been developed for discovering and visualization of functional and organizational features of the cell. Though ingenious and successful in their purpose, they are ad hoc devices in a large part, that preclude their use as standard-gold for performance assessment of others methods. We have no answer to … which one to choose for benchmark? In 30. Perturbations of genes-hubs are expected to have a major fitness impact, i.e. more essential33. These genes play prominent roles in the characteristics and development of diseases34.We will explore how the gene degrees (# of interactors) are distributed by the two measures, and the correspondence with biological evidence.Cellular process in an organism can accounts for the integrated and concerted activity of specific “gene constellations, forming a complex hierarchical web of molecular interactions. It is a well-known fact that most genes interact with a limited number of other genes, whereas only a smaller set of genes interacts with many other genes (network hubs)1. However, a preponderance of genes with larger positive interaction is apparent. The histograms in Fig. In Fig. Genes with ten or more interactors, obtained at least by any of the measures εM or εA, are plotted in Fig. With these preliminary evidences, we find relevant for the comparison of gene degrees, to be more restricting in regarding interactions when the magnitude of the measure is larger than two standard deviations of the values obtained for the complete library i.e. ε > 2 s.d.). This restriction is more conservative in assuming approximately that less than 5% of the pairs interact (with one standard deviation the number rise to about 33%). Then we apply a deliberate but simple criterium to select candidate gene-hubs obtained from one measure and missed by the other. It is a fair symmetric criterium, based on simple counting. We look for genes that according to one measure has less than 10% of the number of interactions captured by the other measure. The candidate hubs so captured from the Essential x Essential library are listed in Table  s.d.. ThThe measure εM does not deliver genes satisfying this tenfold criterium, neither even a twofold one. Supplementary Table Notably in contrast, 13 genes satisfied the tenfold criterium in favor of εA. Further, the measure εM predicted for these genes less than 3% of the interactors predicted by εA. The magnitudes of the interactions of the candidate hubs of Table The interaction networks in-between candidate hubs and interactors, obtained by εM and εA, are show in Fig. http://www.yeastgenome.org/). For instance, SGD listed more than 100 physical and genetic interactions (GI) for genes mpp10 (GI = 23), tif35 (GI = 44), noc4 (GI = 28), and rrp7 (GI = 41),   processome, required along with imp4 for early co-transcriptional events in ribosome biogenesis40. The SSU processome is completed by a centrally placed Rcl1-Bms1 heterodimer and an outer shell of ribosome assembly factors40. GTPase bms1 and the endonuclease rcl partake in ribosomal small subunit biogenesis and rRNA processing41, as well as the DEAD-box RNA helicase rok142.The 13 candidate hubs comprise diverse molecular functions and cellular components 47. Finally, six of the εA surfaced hubs  have been recently identified as structural key components of the same nucleolar superstructure, the S. cerevisiae SSU processome48.Overall, ribosomal biogenesis and rRNA associated processes prevail, with 9 of 13 GO-SlimAltogether, the candidate hubs surfaced by εA are convincingly supported as actual hubs on yeast biology. Therefore, the fact that a widely used measure like εM could underscores their interactions indicate there is still room for improvements on how we detect and quantify genetic interactions, specially in the framework of high-throughput data. Noteworthy, that most of the surfaced hubs are involved in ribosomal biogenesis further suggests that not only the overall number of scored genetic interactions may differ when using one or the other interaction measure; rather, that the study of a particular biological processes through the lens of genetic interactions might be significantly biased, just because the scored method used. The magnitude and direction of such bias, their distribution across fitness values, as well as the type of genetic interaction (suppression/masking), are worth of further research.3. The fact that for example, in a given genetic network background, a phenotype strongly depends on the combination of gene variants at two or more loci, suggests that this dependency would be causally and mechanistically implicated, and hence informative of the functional relationship between genes, and the genetic ordering of regulatory pathways. Therefore, a causal analysis require a holistic approach, that situate the interacting factors in its network background. Previous to this stage, the interaction network should be already wired, even in the loose sense permitted by the data. The model we derived provide the inference permitted by the data, of the interactions wiring such networks, without departing from the rules of probability theory.A central tenets of system biology is that properties of complex systems, not predicted from the individual components, can be essential for understanding the function of the system as a whole49. The high throughput screens that produce these data, deliver information of loose interactions networks, that constitute source of simple hypotheses that should be tested by further systematic analysis of mechanistic and functional relevance, complemented with additional knowledge annotated in databases and in the literature.The kind of interaction data we are focusing does not permit to ask whether two factors interact mechanistically, in the sense of a collection of causal mechanisms, that require component causes to operatesBecause of the very reasons just posed, it is worth to explicit out that what we have been calling “interaction” all around, is not necessarily a causal interaction. Further, we will see analytically why, by testing the interaction of two fully correlated factors, and of substituting one of the factors by a fully correlated partner see in . Besides50, has the same form of the multiplicative in the complement of the effect model (11). This index invokes the no redundancy assumption51, asserting that for every subject in the population, there can be at most one arrival event of the unknown components in a sufficiently short time interval. The correspondence of this index with the sufficient-component cause model  has been demonstrated by Lee15, under the assumptions that the exposure status is time-invariant, the follow-up is fully complete, and there is no confounding, selection bias, or measurement error in the study. Rothman’s model52 of sufficient and component causes, often described by pie-charts, is one of the most discussed causal models in epidemiology, aiming the elucidation of the possible mechanisms through which multiple exposures interact in causing an outcome. Lee15 show that in the complementary log regression, the coefficient of the cross-product term can be used to test for sufficient-cause mechanistic interactions, the same 15, the model multiplicative in the complement of the effect can also be used to mechanistic interaction inference, provided suitable causal assumptions are realized.Indices have been proposed for mechanistic interaction tests, for two binary factors and dichotomous effect, under some moderate assumptions. The peril ratio index of synergy based on multiplicativity’ (PRISM), recently proposedA factor 53) to a locus causally connected to a given disease, mimicking the frequencies and correlations of the nearby causal locus and their phenotypes.Such spurious association arises for example when a “non-causal” locus is in the close proximity  sat sat\docuolved in . Indeed,cause of , and thecause of , fully cFurther, whenever  is satisTherefore, all the Eqs. –13), sa, sa13), We finish this epigraph by assessing the neutral model with two fully correlated factors. Regarding our requirements for interactions, a partner-pair and thenHence, the necessary condition for no interaction fined by . AllowanThe full-correlation regime  is an exNow suppose the causal gene  us Fig. , constri}B, Fig. a, can no}B, Fig. b. No mod54. However, large-scale experiments nowadays are examples of mass-discoveries without a priori possession of such causal hypothesis at this preliminary stage of network wiring. It works because the association-to-A hypothesis (Fig. Simply, when a causal or mechanistic hypothesis is not there, and if we don’t put it in, no amount of sample data increase will provide it1, and the various technologies of genome wide editing, can provide such interventions for gathering relevant information, and, delivering and testing causal hypotheses. These technologies have revolutionized biomedical research with promising impact in the clinic. However, their extensive use has revealed much unpredictability. The variability in genome editing outcomes remain a challenge, and both on-target efficiency and off target effects are the major concern56. These large-scale editing tools can produce unpredicted correlation, that can resemble scenarios like the one in (Fig. Further experimental designs of interventions and/or alternative sources of information are required to inquire about the causal natures of phenomena. Synthetic genetic arraysBut there is another side of the story, inherent to modelling, that should be differentiated from the correlated situation of Figs. A measure of interaction was derived solely from a practical definition asserting that two factors interact when the events they trigger cross or interconnect somewhere in the pathways toward the inquired effect. This measure for multivalued factors and dichotomous effect leads to Finney’s independent action principle as a necessary condition for no interaction. This model obtained from basic principles, though accepted in toxicology, is ignored or undervalued by the dominant epidemiological and genetic networks literature. However, the application in epidemiology is straightforward in term of risk, while it needs to be casted into the parameter space of the application domain in other fields. We showed how to cast the model multiplicative in the complement of the effect into the domain of current genome-wide technologies for genetic interaction. The additive measure in growth rates derived from the model has been assessed with real data from large scale fitness experiments on yeast, and the results were supported by biological evidence validated in the literature and from systematically annotated databases. The theoretical properties revealed for the first time in our derivations, asseverate the advantages of this measure not proved in other alternatives. Further, the unity of arguments elaborated here illustrates how dissimilar interaction contexts can be accommodated into a common framework. We hope this unified view contributes towards relaxing the vivid controversy and coexistence of different models of interaction that plague the literature.Supplementary Information 1.Supplementary Information 2.


Genome-wide variation in introgression rates across hybrid zones offers a powerful opportunity for studying population differentiation. One poorly understood pattern of introgression is the geographic displacement of a trait implicated in lineage divergence from genome-wide population boundaries. While difficult to interpret, this pattern can facilitate the dissection of trait genetic architecture because traits become uncoupled from their ancestral genomic background. We studied an example of trait displacement generated by the introgression of head plumage coloration from personata to alba subspecies of the white wagtail. A previous study of their hybrid zone in Siberia revealed that the geographic transition in this sexual signal that mediates assortative mating was offset from other traits and genetic markers. Here we show that head plumage is associated with two small genetic regions. Despite having a simple genetic architecture, head plumage inheritance is consistent with partial dominance and epistasis, which could contribute to its asymmetric introgression. Hybrid zones are windows into the evolutionary process. Semenov et al. find that the head plumage differences between white wagtail subspecies have a simple genetic basis involving two small genetic regions, in which partially dominant and epistatic interactions help to explain how this sexual signal has become decoupled from other plumage traits. If hybrids are not completely sterile, hybridization will often result in backcrossing and a flux of foreign alleles into parental populations, i.e. introgression. Introgression rates vary substantially across the genome due to local differences in the strength of selection, frequency of recombination, and the interplay between selection and recombination along chromosomes9. Loci directly targeted by divergent selection (or closely linked to its targets) will show particularly reduced introgression rates compared to the genome-wide average , aiding in the detection of loci associated with population divergence12.Hybrid zones have long been recognized as windows into the evolutionary process16. This pattern poses an evolutionary quandary. In a given hybrid zone, we expect loci underpinning traits under divergent selection to show narrower clines than those of neutral loci elsewhere in the genome. Yet, if these divergently selected loci act as “barriers” promoting incipient speciation, we also expect their cline centers to be co-located with the cline centers of neutral loci varying across species. Asymmetric sexual or natural selection is often invoked to explain this pattern. Indeed, simulation studies suggest that differences in allele fitness and selection strength18, as well as epistasis19, and deviation from codominant genetic inheritance of selected phenotypes17 can contribute to asymmetric introgression. However, there exist few empirical examples in the literature due to the difficulty of dissecting the genetic architecture of phenotypic traits in natural study systems—data crucial for distinguishing among these potential mechanisms. Furthermore, the connection between trait genetic architecture and asymmetric introgression under a scenario of positive assortative mating—commonly found in the hybrid zones—remains poorly understood19.An intriguing observation, now recorded in several study systems, is the geographic displacement of a trait under selection away from the majority of genetic markersMotacilla alba) is a small passerine bird with nine commonly recognized subspecies distributed across most of Eurasia, North Africa, and northwestern North America21. Historically, white wagtails likely bred on the banks of rivers and other water bodies22; now they are a common synanthropic species in many parts of their range23. The subspecies M. a. alba and M. a. personata differ in a suite of phenotypic traits that distinguish allopatric populations  and hybridize in two geographically isolated regions in Iran and central Siberia20  or personata (29%) head plumages, while the remaining individuals were 20% alba-like hybrids, 4% intermediates, and 14% personata-like hybrids (n = 104). Strong positive assortative mating by head plumage  and the observed predominance of parental phenotypes over hybrids are consistent with the maintenance of restricted introgression of head plumage by selection.The white wagtail  genomic regions on chromosomes 1A and 20, of which the latter contains the agouti signaling protein gene and appears to have the major phenotypic effect. Despite seemingly simple genetic architecture, head plumage inheritance patterns support a model of partial dominance and epistatic interactions between the two genomic regions. Our findings suggest that peculiarities of genetic architecture may contribute to asymmetric introgression of head plumage, therefore illuminating the connection between mechanisms of formation of reproductive barriers between nascent species and evolutionary dynamics of these barriers.In this study, we utilize whole genome analysis of many individuals to investigate the genetic architecture of alba (n = 10), allopatric personata (n = 10), and 62 individuals from the hybrid zone  at 5–7.5× depth of coverage . After applying stringent filters (see the “Methods” section), we obtained ~10.6M SNPs for downstream analyses.We sequenced whole genomes of allopatric alba n = 0, allopaalba n = 0, allopaalba and personata was low (weighted FST = 0.046), but sufficient to detect population structure , with only two strongly differentiated regions located on chromosomes 1A (~200 kb in size) and 20 (~150 kb in size)  Fig. , and no 10P = 22.5, Fig. 10P = 8.1). Further, an analysis of genetic architecture of head plumage using a Bayesian sparse linear mixed model (BSLMM) indicated that 96.4 ± 3.6% of the phenotypic variance was explained by the complete set of ~11M SNPs, of which sparse effect terms  accounted for 96.0 ± 4.0%. The average number of SNPs in the best model was 5.3 ± 2.6 loci, with up to 11.8% and 50.9% of variance explained by SNPs in divergent regions on chromosomes 1A and 20, respectively, all consistent with a simple genetic architecture of head plumage. To assess the predictive power of BSLMM, we used leave-one-out cross validation. Specifically, we iteratively excluded the phenotypic information from one individual and used the model fit for the remaining individuals to predict that phenotype based on its genotype  but rather moderate predictive power for hybrids (adjusted R2 = 0.54), suggesting that the relationship between phenotypic and genetic variation is non-linear to some extent and indicating potential deviations from additive and codominant inheritance models.We performed admixture mapping using whole genomes of 62 individuals sampled within the hybrid zone to test for an association between individual SNPs and variation in head plumage. The only genomic regions with strong plumage associations coincided with peaks of genomic differentiation on chromosomes 1A and 20, with the region on chromosome 20 exhibiting the strongest signal (maximum −logFST) and absolute (dXY) divergence in the regions on chromosomes 1A and 20 26 revealed a strong excess of shared ancestry between allopatric and sympatric personata in both regions  and coiled-coil domain-containing protein 91 (CCDC91) —a well-studied gene regulating melanogenesis—with highly homozygous non-coding regions  Fig. . The pea91) Fig.  and was To examine inheritance patterns of head plumage, we first assessed genotypic variation by extracting loci with the highest admixture mapping signal from the divergent regions on chromosome 1A (43 SNPs spanning ~138 kb) and on chromosome 20 (49 SNPs spanning 86 kb) Fig. . Within alba) or 1 (personata) and low heterozygosity. First-generation hybrid genotypes were expected to fall in the very top-center of each plot because they should have the highest heterozygosity and the most intermediate hybrid index possible, whereas more recombined genotypes of advanced-generation hybrids  should have lower heterozygosity and intermediate hybrid indices27. Backcrosses should have varying degrees of heterozygosity and hybrid indices closer to the respective parental genotypes27. To evaluate how distinct combinations of genotypic states match variation in head plumage, we categorized genotypes into “parental” states typical for allopatric populations and “intermediate” genotypes typical for hybrids and backcrosses.Parental genotypes were expected to have hybrid indices close to 0  were found among alba and intermediate head plumage phenotypes, but most commonly in alba-like hybrids. Supporting the idea of dominant expression of alba phenotype, the majority of individuals with both an intermediate hybrid index and high heterozygosity for both genomic regions—likely F1 hybrids—had phenotypes of alba-like hybrids and less commonly had strict intermediate phenotypes . Two personata-like hybrids  or heterozygotes (Ap) produce alba head plumage in combination with the alba-type 1A genotype (aa). These two ASIP genotypes produce alba-like hybrids or intermediate plumage types when combined with intermediate (aP) or personata-type (PP) genotypes on 1A. Most personata-like hybrids have alba-type (aa) or sometimes highly recombinant (aP) 1A genotypes combined with personata-type ASIP genotype (pp). The 1A heterozygotes (aP) typically have no phenotypic effect when combined with personata-type ASIP genotype (pp) and are commonly found in personata head phenotype. Interestingly, we did not observe any genotypes with personata-type genotype at 1A (PP) and the alba-type ASIP (AA), suggesting it is either a very rare direction of hybridization or that carriers of this genotype are inviable. To formally test the hypothesized mechanism of head plumage inheritance, we compared a series of models with additive/codominant, completely and partially dominant, and epistatic interactions. In these models, we followed an assumption of our working hypothesis that the regions on chromosomes 1A and 20 act as a two-locus bi-allelic system . The model with partially dominant inheritance of personata chromosome 1A alleles, partially dominant inheritance of alba chromosome 20 alleles and with epistatic interactions between the two loci best explained phenotypic variation . We simulated geographic clines for one or two-locus mating traits, varying the dominance coefficient and the degree of assortativity. These simulations revealed that cline centers for mating trait loci will often not stay stable in space .Given the partially dominant expression of the ace Fig. . Interesace Fig. . In 30% one Fig. . When thone Fig. . The aveASIP and appears to have the major phenotypic effect. Further, our results suggest partially dominant expression of ASIP alleles: the mostly black head plumage of one subspecies (personata) is a homozygous recessive trait, while a significant proportion of heterozygotes exhibit the mostly white plumage of the other subspecies . Our simulations suggest that this inheritance mechanism, in combination with plumage-mediated assortative mating, might contribute to asymmetric introgression of the personata plumage signal into the alba genomic background.Identifying the molecular basis of traits targeted by divergent selection is a key step towards understanding the evolution of phenotypic variation. Here we show that a distinct plumage signal in a pair of white wagtail subspecies is associated with two narrow autosomal genomic regions, one of which contains the gene encoding personata–alba hybrid zone corresponded to only two small genomic regions harboring a few genes. Importantly, our results suggest that non-coding genetic variation plays an important role in determining head plumage differences between wagtail subspecies, as has been found in other recent studies of plumage variation in birds31. Long runs of homozygosity upstream and downstream of ASIP in personata-type plumages likely overlap with promoters and enhancers of this gene. This finding adds to a growing collection of studies connecting genetic variation in ASIP and animal coloration37, and particularly highlights the role of regulatory genetic elements in evolutionary change40. Given that a few homozygous SNPs upstream and downstream of ASIP in highly recombinant phenotypes  also appears to contribute to determination of head plumage, although with a minor phenotypic effect. The peak on 1A mostly occurs within non-coding sequence and the functional importance of this locus remains unclear. The nearby gene Parathyroid hormone-related protein (PTHLH) is involved in hair follicle development in mice41, suggesting its regulation might similarly affect feather patterning in birds. Supporting this hypothesis, PTHLH has been associated with plumage diversification in munias33. Moreover, two other genes  and tyrosinase hydroxylase (TH)—are involved in melanogenesis43. Finally, the region on 1A could be a trans-acting regulatory element affecting expression of ASIP—a possibility that is hard to evaluate using sequence data alone.As we hypothesized, the simple segregation pattern of head plumage previously documented in the pes Fig.  are potenes Fig.  in the vpersonata-type plumage is largely determined by a recessive homozygous locus that includes ASIP. ASIP plays a critical role in pigment switching because it is an antagonist to the transmembrane receptor melanocortin 1 receptor (MC1R) that, when activated, promotes biochemical cascades of melanin production and darker coloration (reviewed in ref. 36). Expression of ASIP blocks MC1R signaling, resulting in reduced intensity of melanin pigmentation. The plausible explanation of head inheritance patterns observed in wagtails is that the regulatory effect of the alba allele increases expression of ASIP and thereby causes lighter coloration, and that a single gene dosage is sufficient to explain the partial dominance effect.Our results suggest that mostly black ASIP heterozygotes resemble alba head phenotype, it appears likely that first-generation hybrids between alba and personata wagtails have a much higher likelihood of mating with alba than personata. This particularly opens up an opportunity for sex-biased introgression, if females choose mates based on head plumage, and F1 males are more likely to attract female alba than personata. Our simulations suggest that such a mechanism could contribute to the observed head plumage cline displacement under certain degrees of assortative mating and dominance of phenotypic alleles .Given the strong positive assortative mating by head plumage and the fact that most les Fig. , even inCorvus (corone) corone) and Hooded (Corvus (corone) cornix) crows. In these taxa, plumage differences between darker and lighter melanin-based body coloration is governed by two genomic regions: one containing a major-effect gene norrin (NDP), the other harboring a cluster of genes with suppressed recombination that interact epistatically with NDP44. Moreover, simulations parameterized to crow plumage inheritance patterns suggest that assortative mating coupled with this epistatic genetic architecture can alone promote sexual trait introgression similar to results presented here19. Together, these results and our own findings support the long-standing hypothesis17, that peculiarities of barrier trait architecture governed by dominance, epistasis, or both, can drive asymmetric introgression. We stress, however, that the simulations alone do not rule out the possibility that the wagtail head plumage cline has moved as a consequence of other mechanisms. Although the displacement of the head plumage cline from the genomic background in wagtails was not associated with asymmetric mating preferences in social pairs16, selective advantage of one allele over another, social dominance, asymmetric aggressive behavior and skewed extra-pair mating all can promote asymmetric introgression46. Long-term monitoring of the alba and personata hybrid zone will be necessary to determine whether observed introgression patterns are due to whole zone movement  or asymmetric introgression of head plumage alone.The genetic architecture of the plumage trait we documented in white wagtails  share properties with the genetic architecture of plumage color in the Carrion  and Uzbekistan (personata). A female Motacilla samveasnae collected in Stung Treng, Cambodia  and a male M. citreola citreola collected in Bayan Ovoo, Hentiy Aymag, Mongolia (University of Washington Burke Museum: 59798/CSW 5764) were used as outgroups.We utilized 316 breeding individuals previously sampled along a 3000 km transect spanning the allopatric range of 49 to assess read quality and Trimmomatic v.0.3950 to trim poor-quality reads and Illumina adapters with default settings. Next, bwa mem51 v.0.7.17-r1188 was used to align reads to the draft eastern yellow wagtail (Motacilla tschutschensis tschutschensis) reference genome (see below). Bam files were sorted, duplicates were marked, and files were indexed using samtools v. 1.3.152 and picard-tools v.2.8.153. Variants were called using HaplotypeCaller from GATK54 v.4.2. The resulting gvcfs were merged using CombineGVCFs and genotyped with GenotypeGVCFs followed by VariantFiltration using GATK-recommended filters. Finally, we used VCFtools55 v.0.1.15 to remove indels, keep only biallelic SNP with minor allele frequency above 5%, minQ > 20, min-meanDP > 4, max-meanDP < 75 and max-missing = 0.75. This resulted in a final dataset of 10,634,326 SNPs used for downstream analysis. Examples of all scripts are available via GitHub: https://github.com/erikrfunk/whole_genome_bioinformatics/blob/master/rosyfinch_notes.md. Raw read data associated with this project are publicly available as NCBI BioProject PRJNA690099 https://www.ncbi.nlm.nih.gov/bioproject/PRJNA690099.Genomic DNA was extracted using DNeasy Blood & Tissue kit (Qiagen). Whole-genome libraries were prepared using Nextera XT (Illumina) v.2 kit, fragmented and 400–600 bp-long fragments were selected using BluePippin (Sage Science). Paired-end sequencing was performed on the NovaSEQ 6000 (Illumina) platform aiming to achieve ~10× coverage. Outgroup taxa were prepared separately using Illumina TruSeq PCR-free library preparations with a 350 bp insert size and sequenced on a NovaSEQ 6000 with a target sequencing coverage of 20×. We used FastQC v.0.11.756 using a fragment library (180 bp) and two jumping libraries (3000 and 6000 bp) sequenced on an Illumina HiSeq 2500. We used MUMmer v.4.0 to establish the synteny between the yellow wagtail reference genome and a high-quality chromosome-level assembly of the zebra finch (Taeniopygia guttata) (https://www.ncbi.nlm.nih.gov/assembly/GCA_009859065.1/). We ran MUMmer for each zebra finch chromosome separately using default setting except increasing—maxgap to 1000 to boost from default of 90 to account for structural rearrangements in a divergent reference https://github.com/elinck/syma_speciation/blob/master/scripts/wgs_align_mummer.sh.The reference genome file was generated using ALLPATH-LG 4.7.026)  to estimate the relative FST (Kst58 but with a modification to account for missing genotypes on a pair-by-pair basis) and the absolute dXY59 genomic divergence, and the nucleotide diversity59 in 25 kb sliding windows with 10 kb step. We used the default option (“coordinate”) to define the size of sliding windows. In this case, windows will cover a fixed range in the genome and if there are missing data, this can lead to variable numbers of sites used for each window. Per-site Weir-and-Cockerham FST60 was estimated with VCFtools55. To test a hypothesis about introgression of personata alleles into alba genomic background, we utilized a further functionality of the “genomics_general” scripts to estimate windowed ABBA–BABA (fd)26. Here, we used a topology where P1 = sympatric alba, P2 = sympatric personata, P3 = allopatric personata, and P4 was designated as the outgroup. To estimate ancestral and derived allelic states, we polarized sites based on the genomes of a species closely related to the white wagtail (M. samvesnae) and a more distantly related member of the genus (M. citreola)21. Because using a small number of SNPs per window can generate stochastic errors that may cause fd to have meaningless values even when D is positive, the “genomics_general” documentation suggests a minimum window size that allows at least 100 biallelic SNPs per window. To meet these criteria, we imposed a 50 kb sliding window with a 10 kb step. This resulted in an average of 505 loci per window (range: 176–1020). If shared variation between P3 and P2 (positive D) is of interest, then fd might not be the best approach. Therefore, we utilized an alternative statistic fdM26, to better fit this scenario. Both metrics revealed similar patterns. We used principal component analysis (PCA) to assess population structure, and to summarize genomic variation of regions of interest. For the analysis of whole genome population structure, we thinned the dataset to retain one SNP per 10 kb window to avoid using loci in physical linkage. All SNPs were used for PCA in divergent regions on chromosomes 1A and 20. We ran PCA on the mean-centered genetic covariance matrix of SNP genotypes using the R v.3.6.1 (RStudio v.1.1.453) function prcomp.We used Python scripts developed by Simon Martin  to annotate focal scaffolds in the yellow wagtail reference genome using zebra finch (http://useast.ensembl.org/Taeniopygia_guttata/Info/Index?redirect=no) protein and cDNA databases. Genes were predicted using SNAP (see MAKER documentation), which was trained iteratively until gene models converged. A few gene models had poor convergence between consecutive SNAP iterations. Therefore, as an alternative method we confirmed gene models within regions of divergence using the Flo lift over pipeline (https://github.com/wurmlab/flo) again using the Zebra Finch annotations (taeGut1: GCA_000151805.2).We used MAKER v.2.31.10 pipeline .Coloration of head and neck in white wagtails varies as a proportion of white unpigmented area on an otherwise black, melanin-based plumage. In des Fig. . Hybridsdes Fig. . We used62 to conduct admixture mapping for head plumage. To minimize the effects of isolation-by-distance and population structure we used only samples (n = 62) from the alba and personata hybrid zone. To estimate effects of isolated SNPs, we ran linear mixed-effects models . To account for potential relatedness between individuals, we estimated a relatedness matrix using the -gk 1 option of GEMMA, which then was supplied as a covariate for LMM and BSLMM analyses used to assess genetic architecture of head plumage. For BSLMM, we ran four chains with a burn-in of five million steps and a subsequent 20 million MCMC steps sampling every 1000 iterations. We assessed four BSLMM hyperparameters: PVE , PGE , posterior number of SNPs explaining trait variance in the model and gamma parameter assessing the proportion of variance explained by an individual locus of interest. We used a leave-one-out cross-validation approach to assess the posterior predictive power of BSLMM. More specifically, we excluded phenotypic information for one individual at a time and used the remaining dataset (n = 61) to predict its phenotype based on genotype by running BSLMM with the setting indicated above. Linear regression was then used to estimate the proportion of variance explained by predicted phenotypes as a measure of predictive performance57.We used GEMMA v.0.98 (genome-wide efficient mixed-model association)alba-type, heterozygotes, or personata-type based on hybrid index and heterozygosity  due to highly recombinant genotypes and missing data for some loci that made it their genotype classification ambiguous. We then used linear models to assess power and contribution of each term in predicting head plumage values63.Given an apparent non-linear relationship between genotypic and head plumage variation, we compared a series of inheritance models with additive/codominant, partially dominant and completely dominant inheritance modes for genomic regions on chromosomes 1A and 20, and with epistatic interactions between 1A and 20. In these models, we encoded genotypes in the two genomic regions as ity Fig. . We exclhttps://search.datacite.org/works/10.5061/dryad.fg49r) to construct geographic cines for head plumage and ancestry. We summarized genomic variation using PCA and used PC1 scores as a proxy for ancestry16. Quantitative estimates for head plumage were taken as described above. We fit empirical data to five geographic cline models as described in ref. 64 using Metropolis–Hastings MCMC algorithm implemented HZAR65 v.0.2–5 package in R.We re-analyzed published data for the wagtail hybrid zone  and minLengthBps = 9000, with the rest of parameters being as described in the manual (https://cran.r-project.org/web/packages/detectRUNS/vignettes/detectRUNS.vignette.html).We used the R package HZAM28 v.2.0.0, which models one-dimensional hybrid zone dynamics in the presence of assortative mating, underdominance, and other processes. Our modification extended HZAM’s base features to support partial dominance of mating trait loci, using a user-defined dominance coefficient indicating the proportion of the homozygous dominant phenotype expressed by heterozygotes. Full code and an interactive web app implementing it can be found at https://github.com/elinck/hzam_shiny. Given that available evidence suggests that two regions on chromosomes 1A and 20 effectively work as a two-locus system (with the locus on chromosome 20 having the major effect) in determining head plumage in wagtails, we focused our simulations on genetic architectures with one or two mating trait loci. We ran 50 replicate simulations of 500 generations each with one or two mate choice loci and three neutral loci, 0.5 and 0.75 ratios of heterospecific to homospecific matings, a dominance coefficient of 0.5 and 0.75, a per-species carrying capacity of 800, initial range limits of 0–0.48 and 0.52–1 , a population growth rate of 1.05, a density dependence effect standard deviation of 0.01, and no loss of hybrid fitness. We fit clines for mating trait and neutral loci every five generations using a general additive model (GAM) implemented in the R package mgcv67 v.1.8–31 with the gam function, using the formula allele_frequency ~ s(transect_location) and the "P-ML" method. We then used the predict_gam function in the R package tidymv v.2.2.0 (https://github.com/stefanocoretta/tidymv) to generate model predictions for evenly spaced transect values, and used these to calculate cline width and cline center. To calculate cline width and center, we used Irwin’s28 "eightieth percentile" approach, which defines hybrid zone width as the geographic area between the locations at which the GAM cline fit crosses HI (hybrid index) = 0.1 and HI = 0.9, and center as the region within half a dispersal distance from the location at which the cline fit crosses HI = 0.5. Using these data, we performed Wilcoxon paired one-sided signed rank tests to determine whether cline center differed between neutral and mating trait loci. To compare the degree of asymmetry between introgression patterns in our simulations and the wagtail hybrid zone, we scaled displacement between simulated cline centers via means of dispersal distance63.To evaluate whether partial dominance of a plumage trait involved in mate choice might lead to displacement between phenotypic and genomic background clines, we ran forward-time simulations using a modified version of the R program Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


Sclerotinia sclerotiorum is a necrotrophic fungus that causes Sclerotinia head rot (SHR) in sunflower, with epidemics leading to severe yield losses. In this work, we present an association mapping (AM) approach to investigate the genetic basis of natural resistance to SHR in cultivated sunflower, the fourth most widely grown oilseed crop in the world.Our association mapping population (AMP), which comprises 135 inbred breeding lines (ILs), was genotyped using 27 candidate genes, a panel of 9 Simple Sequence Repeat (SSR) markers previously associated with SHR resistance via bi-parental mapping, and a set of 384 SNPs located in genes with molecular functions related to stress responses. Moreover, given the complexity of the trait, we evaluated four disease descriptors . As a result, this work constitutes the most exhaustive AM study of disease resistance in sunflower performed to date.Mixed linear models accounting for population structure and kinship relatedness were used for the statistical analysis of phenotype-genotype associations, allowing the identification of 13 markers associated with disease reduction. The number of favourable alleles was negatively correlated to disease incidence, disease severity and area under the disease progress curve for disease incidence, whereas it was positevily correlated to the incubation period.Four of the markers identified here as associated with SHR resistance  validate previous research, while other four novel markers  were consistently associated with SHR resistance, emerging as promising candidates for marker-assisted breeding. From the germplasm point of view, the five ILs carrying the largest combination of resistance alleles provide a valuable resource for sunflower breeding programs worldwide. Helianthus annuus L.) is the fourth most widely grown oilseed crop in the world, with an annual production estimated at 36 million metric tons (www.sunflowernsa.com). Unlike other vegetable oils, about 90% of the total production of sunflower oil is used for human consumption, and only 10% is used for biodiesel and industrial applications [Sunflower (Sclerotinia sclerotiorum causes Sclerotinia head rot (SHR), which is one of the main diseases in sunflower growing areas of Europe, Argentina, and the USA, with epidemics resulting in severe yield losses [d losses . This neS. sclerotiorum in both SHR [SHR resistance is a complex trait because it is controlled by a polygenic architecture, (i.e. quantitative inheritance with predominance of additive gene action) and has moderate heritability, being greatly affected by different environmental conditions of temperature, humidity, and rainfall, among others –9. Durinboth SHR  and stemboth SHR . More reboth SHR –21, theiboth SHR , there iboth SHR , sunflowThe goal of the present work was to identify genetic variants associated with SHR resistance. For this purpose, we expanded our initial AM study  to incluCandidate genes (CGs) for SHR resistance were selected from four different data sources , two by enzymatic cleavage CEL1CH) (HeAn_315 and HaGLP5), seven by fluorescent capillary electrophoresis  and three were typified by direct sequencing  (Table SCH (HeAn_The 384-SNP Sunflower Oligo Pool Assay (SOPA) matrix retrieved from Filippi et al.  was filtFinally, nine SSR previously associated with SHR resistance were successfully amplified in the AMP, ranging from three to eight alleles and with a mean of five Table S.A filter of minor allele frequency (MAF) <0.05 was applied as a final step for CG and marker selection, rendering a total of 168 markers to be tested for association with disease incidence (DI), area under the disease progress curve for disease incidence (AUDPCI), disease severity 168 (DS) and incubation period (IP): 20 CGs, 139 bi-allelic SNPs from the 384-SNPs SOPA and nine SSR. The final data matrix is provided in Table SBayesian population structure and kinship analysis were based on the 42 SSR used by Filippi et al. . The estA genetic distance matrix D, estimated based on the number of shared alleles between all pairs of individuals is presented in Table SRegarding phenotypic data, the 135 AMP-ILs evaluated for (DI), (AUDPCI), (DS) and (IP) exhibited substantial variability in all disease descriptors, with rankings being similar to those reported by Filippi et al.  for the 2 = 0.028; Mantel test, p = 0.18). Additionally, no significant correlations were observed between ancestries inferred by STRUCTURE and the SHR-phenotypic variables .No significant correlation was observed between the genetic distance estimates and the Euclidean distances based on standardised SHR-phenotypic variables   between the observed and expected t) Fig. S.p < 0.05) , a total of 23 marker-trait associations were detected , encompassing 13 different genes .Under the QK model, which includes both the population (Q) and the kinship structures (K), eighty-six markers were associated with SHR resistance before multiple testing corrections  Table S. Considees Table . The marp ≤ 0.01, q-value < 0.2) were mapped against the sunflower reference genome and localised on chromosomes 2, 6, 7, 9, 10, 14, and 15. The GO-terms of the genes harbouring the associated markers are detailed in Table The 13 associated genes . The curves of observed vs. expected p-values (under the hypothesis of no marker effect) and the mean square difference between them [Q) did not contribute to a clear reduction in the number of significant marker-trait associations (p < 0.05). The same result was obtained by including the kinship structure (model K) and both sources of structure (model QK). These results are in accordance with the fact that none of the SHR-phenotypic variables showed association with the underlying population structure, thus minimising the risk of spurious associations derived from marker-trait covariance [To test for associations, we first applied a naïve approach that did not include any correction for the level of relatedness or structure between ILs . Moreover, each of these markers were associated with three of the four SHR phenotypic variables. Two of these associated markers validate a previous biparental mapping study of Sclerotinia resistance in sunflower [Sclerotinia stem rot resistance [Arabidopsis thaliana COI1 gene, which encodes a leucine-rich repeat (LRR) protein essential for the Jasmonic acid (JA) signaling pathway. The JA has a crucial role in plant defense against biotic and abiotic stresses [S. sclerotiorum, are known to act as primary activators of JA-dependent defenses through the COI1 receptor [A ery rate , 29. Thrsistance . The HaCstresses . Indeed,receptor .progesterone 5β-reductase (P5βR). In spite of being a family first described in animals, PRISEs  are ubiquitous in plants and are involved in cardenolide and iridoid biosynthesis in many species [The gene harbouring SNP117 was assigned to the GO category  species . The occ species . In agre species .p ≤ 0.01; 0.10 < q-value < 0.20), ten additional markers, distributed across eight different chromosomes were associated with resistance. The orthologs of two of these genes, G33 and G34, were previously identified as differentially expressed in response to Sclerotinia infection in Brassica napus [At a less stringent threshold  accumulation and enhance protection against S. sclerotiorum and Rhizoctonia solani [The remaining eight markers include a germin-like protein , a β-hexosaminidase (SNP136), a putative rho-associated protein kinase (SNP23), and five genes with diverse annotations . Germins and GLPs are encoded by gene families with multiple members, and a wealth of evidence supports their involvement in plant defense. Many germins possess oxalate oxidase (OXO) activity, i.e. can degrade oxalic acid to H and CO2 , 41, whe and CO2 . In partz et al.  reporteda solani .β-n-acetylglucosaminidase that catalyses the hydrolysis of chitin oligosaccharides. Chitin  is commonly present in fungal cell walls, and its fragments are known to act as potent elicitor signals in plant defense [The marker SNP136 is of particular interest since it falls within a  defense .Fusari et al.  found thThe causal polymorphism for a QTL can be distant from the marker under scrutiny, particularly in species with high levels of linkage disequilibrium, such as sunflower , 46, 47.S. sclerotiorum. In addition, H2O2 levels and ROS scavenger enzyme activities were also increased, as well as callose deposition on the cell wall and soluble protein content.Overall, we found that most of the genes associated with resistance to SHR have molecular functions involving the accumulation and degradation of ROS and JA-mediated signaling pathways, which are primary processes in plant-pathogen interactions. In agreement with these findings, Na et al.  reportedPhomopsis heliantii . In sum, our results highlight that the adoption and application of strategies combining a moderate number of markers with previuos genomic information, as CG-association mapping, allows the identification of strong genomic signals associated with traits of agronomic importance, even for low heritability traits, as SHR resistamce. In this regard, this work brings the first hints towards the characterization of sunflower resistant genes to SHR, while contributing to marker-assisted breeding for crop improvement.As genotyping costs continue to decrease, phenotyping efforts are becoming the most critical issue for AM approaches. Although high correlations were observed among the four examined phenotypic variables , there wFour of the SHR resistance-associated markers identified in this work, HA1848, HaCOI_1, G33 and G34, validate previous research and emerge as promising candidates for marker-assisted breeding. Moreover, our work allowed the identification of novel markers, i.e. SNP117, SNP136, SNP144 and SNP128, consistently associated with SHR resistance, as determined by using different disease descriptors. Further studies are currently under way to confirm their effect on resistance using mutagenised populations. From a germplasm perspective, the ILs with the largest combination of resistance alleles also provide a valuable resource for sunflower breeding programs worldwide.The development of the sunflower association mapping population (AMP) used here is described in Filippi et al. . BrieflyS. sclerotiorum was assessed by Filippi et al. [The susceptibility of the original 137 AMP ILs towards i et al.  in five A full description of the experimental field design, fungal isolation, inoculum preparation and statistical methods associated to adjusted mean estimation for all the SHR-phenotypic variables can be found in Filippi et al. .In the present study, the number of AMP ILs was reduced to 135 because two of them were contaminated, so both genetic and phenotypic statistical analyses were repeated in order to obtain specific values for this reduced IL population. Seeds were provided by the Active Germplasm Bank of INTA Manfredi.Total DNA was extracted from leaf tissue from three individuals of each IL using NucleoSpin Plant II kit , following manufacturer’s instructions. The quality and concentration of the genomic DNA were assessed using electrophoretic analysis and Picogreen® technology .Three types of molecular markers were used to test for association with SHR resistance: 1) PCR amplicons: a panel of 27 candidate genes (CGs) selected from Zhao et al. , EhrenboA. thaliana in response to S. sclerotiorum [Table rotiorum , we firsrotiorum  to identrotiorum   was modelled as a set of nested random effects. In this regard, a matrix (S) of proportion of shared alleles was generated from the above-mentioned 42 SSR and used as input for the estimation of the distance matrix ward. D agglomeration method. The resulting dendrogram was cut at different levels (nodes) and as a result, ILs were grouped into 2 to 134 clusters. The Akaike Information Criteria was used to determine the optimal number of grouping factors needed to model the kinship structure.The kinship structure , which only includes a fixed effect for the marker (Mi), under the assumption of independence of errors.A simple linear model Q model, which extends the Generalised Linear Model (GLM) by including the population structure as a set of regressor variables corresponding to the STRUCTURE ancestry assignment matrix Q.The 3)K model, which does not include population structure but a set of nested random factors represented by the term Zk, where Z is an incidence matrix and k is a random effects vector (see the representation of the kinship structure in the previous section).The 4)QK, which includes both the population and the kinship structures.The model Correlations among SHR-phenotypic variables and the number of favourable alleles were estimated using Spearman’s rank correlation.lme4 [hclust with method ward.D was applied for cluster analysis, while the function cutree was implemented to cut the dendrogram that generated the grouping factors used to model kinship. Complementary statistical analyses were performed by means of InfoStat [The R environment  was usedlme4  was usedInfoStat  and InfoInfoStat .q-value cut-off of 0.2, as suggested by Iquira et al. [The false discovery rate (FDR) thresholds were determined using the QVALUE package  and a q-a et al. .Helianthus annuus (available at http://www.heliagene.org). We also searched for the genes surrounding the associated markers. To ensure physical linkage [Given that most of our SNP markers were located within CGs, we retrieved the annotations of the genes harbouring the associated markers using BLASTN searches against the reference genome of  linkage , we scan linkage ).Additional file 1: Table S1. Diversity estimates of candidate genes (CGs) for Sclerotinia Head Rot resistance.Additional file 2: Table S2. SSR markers that co-localised with QTLs for Sclerotinia Head Rot resistance .Additional file 3: Table S3. Genotypic data used for association mapping.Additional file 4: Table S4. Adjusted means across five field trials for Sclerotinia Head Rot-related phenotypic variables, STRUCTURE ancestry coefficients (K = 3) and number of favourable alleles for the inbred lines of the Association Mapping Population (AMP).Additional file 5: Table S5. Phenotypic and genetic distance matrices for the 135 Inbred lines (ILs).Additional file 6: Table S6. Spearman correlations among Sclerotinia Head Rot (SHR)-phenotypic variables and the ancestry groups inferred by STRUCTURE.Additional file 7: Table S7. Mean squared differences (MSD) between observed and expected p-values for the four association models applied in the study.Additional file 8: Table S8. Results of the association mapping analysis. Statistical significance and mean ± SE (standard error) per Sclerotinia Head Rot (SHR)-related phenotypic variable and genotype.Additional file 9: Table S9. Putative genes in the vicinity of the associated markers.Additional file 10: Table S10. Spearman correlations among Sclerotinia Head Rot (SHR)-phenotypic variables and the number of favourable alleles in each inbred line.Additional file 11: Figure S1. Hierarchical clustering dendrogram based on genetic distance between the 135 sunflower inbred lines.Additional file 12: Figure S2. Plot of the observed vs expected p-values for the four association models studied for all traits.


ZmCKX5 was resequenced in 285 inbred lines, 68 landraces, and 32 teosintes to identify the significant variants associated with root traits in maize. Sequence polymorphisms and nucleotide diversity revealed that ZmCKX5 might be selected during domestication and improvement processes. Marker–trait association analysis in inbred lines identified 12 variants of ZmCKX5 that were significantly associated with six root traits, including seed root number (SRN), lateral root length (LRL), total root area (RA), root length in 0 to 0.5 mm diameter class (RL005), total root volume (RV), and total root length (TRL). SNP-1195 explained the most (6.01%) phenotypic variation of SRN, and the frequency of this allele G increased from 6.25% and 1.47% in teosintes and landraces, respectively, to 17.39% in inbred lines. Another significant variant, SNP-1406, with a pleiotropic effect, is strongly associated with five root traits, with the frequency of T allele increased from 25.00% and 23.73% in teosintes and landraces, respectively, to 35.00% in inbred lines. These results indicate that ZmCKX5 may be involved in the development of the maize root system and that the significant variants can be used to develop functional markers to accelerate the improvement in the maize root system.Root system architecture plays a crucial role in water and nutrient acquisition in maize. Cytokinins, which can be irreversibly degraded by the cytokinin oxidase/dehydrogenase (CKX), are important hormones that regulate root development in plants. In this study,  The root system architecture (RSA) is associated with plants’ ability to absorb water and nutrients from the soil and resist various abiotic stresses in many crops. Varieties with a larger root system are excellent candidates to obtain desired traits, such as faster growth, higher yield, and better abiotic stress tolerance . In the AtCKX1 to AtCKX7. Overexpressing AtCKX1 to AtCKX4 could increase root length [OsCKX1 to OsCKX11). Up to now, only OsCKX2 and OsCKX4 have been studied in detail. Downregulating OsCKX2 can increase the tiller number and grain weight, leading to enhanced growth and productivity in rice [OsCKX4 [ZmCKX genes in the maize genome, ZmCKX1 to ZmCKX12, and ZmCKX4b. Studies have been conducted on the subcellular localization [ZmCKX genes. However, the role of ZmCKX genes in maize root development has not yet been elucidated.The root system of maize is composed of the embryonic and postembryonic root system. The embryonic root system includes the primary root (radicle) that is formed at the basal pole of the embryo and a variable number of seminal roots (seed roots) that are laid down at the scutellar node. The postembryonic root system consists of shoot-borne roots  that are formed at consecutive shoot nodes and lateral roots that are initiated in the pericycle of all roots . These st length ,14. A to in rice . A rice  [OsCKX4 . There alization  and bioclization  of the ZZmCKX genes, single-nucleotide polymorphism (SNP) in ten CKX genes were filtered from a genotyping-by-sequencing (GBS) dataset in 285 inbred lines. A candidate gene-based association analysis was conducted between ZmCKX genes and root traits. Our results showed that ZmCKX5 were significantly associated with five root traits at the seedling stage  examine nucleotide diversity of ZmCKX5 in maize inbred lines, landraces, and teosintes, (2) identify favorable alleles and haplotypes within ZmCKX5 that are associated with root morphology, and (3) explore the role of ZmCKX5 in the domestication and improvement processes of maize. Association analysis is an effective way to analyze the genetic mechanism of complex traits. This research option has been applied to investigate root development in maize ,19,20,21ng stage . We, the2O2 solution for 20 min and then rinsed with distilled water twice. The seeds were soaked in saturated CaSO4 solution for 6 h, then germinated at 28 ℃ for two days in a dark environment at 80% relative humidity. Eight seeds of each line were selected and vertically rolled in a double layer of brown germination roll paper . A completely randomized design with two replicates was used. The paper rolls were placed in black incubators and cultured with nutrient solution. The maize seedlings were grown with natural lighting, at 30/26 °C (light/darkness), and 40–70% relative humidity. The composition of the nutrient solution was as follows: 2.0 mmol L−1 Ca(NO3)2∙4H2O, 0.75 mmol L−1 K2SO4, 0.65 mmol L−1 MgSO4∙7H2O, 0.25 mmol L−1 KH2PO4, 0.1 mmol L−1 KCl, 0.1 mmol L−1 EDTA-FeNa, 1 × 10−3 mmol L−1 ZnSO4∙7H2O, 1 × 10−3 mmol L−1 MnSO4∙H2O, 1 × 10−3 mmol L−1 H3BO3, 1 × 10−4 mmol L−1 CuSO4∙5H2O, 5 × 10−6 mmol L−1 (NH4)6Mo7O24∙4H2O, adjusted the pH of nutrient solution to 6.0 ± 0.05 with NaOH solution [In this study, a total of 385 lines, including 285 maize inbred lines, 68 landraces, and 32 teosintes  from a wsolution . The nutsolution . A totalZmCKX5, were captured on the NimbleGen platform and sequenced by BGI Life Tech Co. [ZmCKX5 (GRMZM2G325612) from the B73 inbred line (AGPv3.31) was used as a reference for target sequence capture following the manufacturer’s protocols (Roche/NimbleGen) [ZmCKX5 was performed using MAFFT software [r2 was used to measure the LD level.The cetyltrimethylammonium bromide (CTAB) method was used to extract genomic DNA from young leaves of inbred lines, landraces, and teosintes . A totalTech Co. . The gen GRMZM2G3612 from mbleGen) ; variantmbleGen) . Multiplsoftware . The alisoftware . The gensoftware  was usedne AGPv3. was used5 GRMZM2G5612 fromsoftware  in the Dsoftware , and r2 ZmCKX5 and root traits was performed by TASSEL5.0 with mixed linear models (MLM). To reduce the false positive error, the top five principal components (PCs) and kinship (K) were used to control for population structure and kinship. A total of 559 ZmCKX5-based markers with a minor allele frequency (MAF) ≥ 0.05 were selected for association analysis in 285 inbred lines. The p-value thresholds were 0.00179 using the bonferroni correction  > 2.75). The association between variants of ZmCKX5 from B73 (RefGen_v3) was used as a reference, and the multiple sequence alignment was performed on all ZmCKX5 sequences obtained from plant individuals. A total of 6574 bp genomic regions of ZmCKX5 were sequenced, covering 1562 bp of the upstream (promoter) region, 63 bp of the 5′ untranslated region (UTR), 1818 bp of 3 exons, 2217 bp of 2 introns, 368 bp of 3′UTR, and 544 bp of the downstream region  was observed on the first exon  and lower diversity  than teosintes. Nucleotide diversity was calculated in different regions of ZmCKX5 among the three populations. The most significant divergence was observed in the upstream region between inbred lines and teosintes, and the highest nucleotide diversity was observed on the second intron in teosintes  and nucleotide diversity (π × 1000) were compared among the three populations. The C and π × 1000 values were 0.729 and 12.40, respectively . Inbred eosintes a. Linkaged lines b. This red lines .ZmCKX5 in 285 inbred lines. A total of 559 variants with a minor allele frequency (MAF) > 0.05 were included for a trait–marker association analysis. A total of 12 markers (5 SNPs and 7 Indels) were significantly associated (−log10(P) > 2.75) with at least one root trait (ZmCKX5 and could explain 3.68–6.01% of the phenotypic variations (The mixed linear model (PCA + Kinship) was applied to identify the association of root traits with nucleotide polymorphism of ot trait , includiriations . P = 3.7 × 10−5) was observed. SNP-1195 contributed the most phenotypic variation (r2 = 6.01%) to SRN, and the lines carrying the G allele had a significantly greater SRN (P = 2.5 × 10−5) than those carrying the A allele  that is strongly correlated with flowering time. The individual carrying the early-flowering SNP-1245A allele showed higher ZCN8 expression than those carrying the late-flowering SNP-1245G allele. It is worth noting that the promoter sequences in this study were 1500 bp, and some important variations were located more than 2000 bp from the start codon, such as a CACTA-like transposable element ~2.5 kb upstream of ZmCCT [r = 0.47–0.65) [r = 0.50) [r = 0.19–0.97; Gene-based association analysis is a powerful tool to identify causal variants between gene and target traits . More thg et al.  identifiof ZmCCT  and a Hoof ZmCCT . There mof ZmCCT . Root enof ZmCCT . Taken t47–0.65) , and cro = 0.50) . Here, a0) r = 0.–0.97; 19In conclusion, ZmCKX5 was resequenced in 285 inbred lines, 68 landraces, and 32 teosintes to identify the significant variants associated with root traits in maize. Sequence polymorphisms and nucleotide diversity revealed that ZmCKX5 might be selected during domestication and improvement processes. Marker–trait association analysis in inbred lines identified 12 variants of ZmCKX5 that were significantly associated with six root traits. The frequency of the increased allele of significant SNP-1195 and SNP-1406 increased during the maize domestication and improvement processes. The identified significant variants and elite haplotype could be used to improve root traits by molecular breeding.


The ionome of the rice grain is crucial for the health of populations that consume rice as a staple food. However, the contribution of phenotypic plasticity to the variation of rice grain ionome and the genetic architecture of phenotypic plasticity are poorly understood. In this study, we investigated the rice grain ionome of a rice diversity panel in up to eight environments. A considerable proportion of phenotypic variance can be attributed to phenotypic plasticity. Then, phenotypic plasticity and mean phenotype were quantified using Bayesian Finlay-Wilkinson regression, and a significant correlation between them was observed. However, the genetic architecture of mean phenotype was distinct from that of phenotypic plasticity. Also, the correlation between them was mainly attributed to the phenotypic divergence between rice subspecies. Furthermore, the results of whole-genome regression analysis showed that the genetic loci related to phenotypic plasticity can explain a considerable proportion of the phenotypic variance in some environments, especially for Cd, Cu, Mn, and Zn. Our study not only sheds light on the genetic architecture of phenotypic plasticity of the rice grain ionome but also suggests that the genetic loci which related to phenotypic plasticity are valuable in rice grain ionome improvement breeding. The ability of one genotype to produce multiple phenotypes in response to environmental change has been termed “phenotypic plasticity” . VariatiPhenotypic plasticity has been investigated in several crop species such as maize, wheat, rye, oat, barley, and rice for different traits including morphology, yield, and resistance to abiotic stress . The varOsHMA2 for Cd and Zn  and the genetic correlation coefficient (gr). With significantly associated loci (SALs) identified by GWAS, the genetic architectures of the three phenotypic measures and the relationship among them were further investigated. In addition, the effect of phenotypic plasticity-related SALs was also estimated in each environment. Our study paves the way toward utilizing phenotypic plasticity of the rice grain ionome in diverse environments and will benefit the balance of the nutritional elements for human health.To understand the role of phenotypic plasticity in the rice grain ionome, the concentrations of 16 elements in rice grain of a rice diversity panel were measured in four to eight environments. The response of each accession to the macro-environment and micro-environment was measured as linear plasticity and non-linear plasticity, respectively. The relationships between mean phenotype and two plasticity measures were investigated using the Pearson correlation coefficient  were collected after harvest in each environment for analyzing the total elemental concentration and pH. These eight environments varied with respect to soil pH (from 5.2 to 7.8) and total element concentration; all of this information including sowing dates are detailed in https://www.r-project.org/) package ggplot2 hj + ϵij, on each element, where ijy is the element concentration of the ith accession measured in the jth environment, ig is the main genetic effect of the ith accession, jh is the mean effect of the jth environment, i) . The Bayasticity .1g) and kurtosis (2g) of the three phenotypic measures  were calculated using the R package EnvStats (r) among the three phenotypic measures for each element was calculated using the R function “cor.test.” The genetic correlation coefficient (gr) was estimated in the R function “mmer” from the package sommar, and the Kinship (K) used in this step was calculated from a set of 57,388 LD pruned SNPs. The same Kinship was also obtained in the R package heritability to calculate the marker-based heritability (2h) of each phenotypic measure. The phenotypic divergence (STP) of each phenotypic measure between indica and japonica subspecies was calculated in the R package Pstat. All other data manipulation and illustrations were performed in R.The skewness (EnvStats . The oveindica subspecies (294 accessions) and japonica subspecies (239 accessions) by the FarmCPU (https://github.com/XiaoleiLiuBio/rMVP). The first three principal components (PCs), which were calculated using all SNPs in EIGENSTART . The SALs for the three phenotypic measures were denoted as either mSALs (SALs for mean phenotype), lSALs (SALs for linear plasticity), or nlSALs (SALs for non-linear plasticity). Manhattan plots and quantile-quantile plots of the GWAS results were produced in the R package qqman  was performed in the entire diversity panel (575 accessions), the  FarmCPU  model whGENSTART  (versionge qqman  with few2r) between the SAL and the flanking variable loci was calculated with Plink  based procedure: First, the LD  calculated using all mSALs identified for this element, lSALg is the GRM calculated using all lSALs identified for this element, nlSALg is the GRM calculated using all nlSALs, and ijϵ is the residual error. The whole-genome-regression was not performed on phenotypic measures with SALs less than two.The phenotypic variances explained by three types of SAL  were estimated by the whole-genome-regression approach  which waIn order to confirm that the phenotypic variance explained by the lSALs was not caused by its genetic correlation to the mSAL or population structure, a permutation test was performed to generate the null-distribution of the percent of the variance explained (PVE). In each permutation test, the same model was used but the lSALs of each element were replaced by the same number of randomly selected genetic loci. The permutation test was performed 200 times for every element in each environment. All the permutation results were analyzed and illustrated in R.The concentrations of 16 elements  in rice grains which were harvested from 575 rice cultivars were measured in four to eight environments that varied in soil biochemical properties, elemental concentrations, and irrigation regimes Table S1Variation in phenotypic plasticity, termed “genotype-by-environment interaction” (G×E), was observed in the diversity panel. For example, the difference between the mean Cd concentrations measured in 2016Field-2 and 2017Field-1  was 2.39 mg/kg. For each accession in the diversity panel, the differences between Cd concentrations measured in these two environments showed large variations, ranging from 0.25 mg/kg to 4.6 mg/kg with an IQR (interquartile range) of 1.63 mg/kg. We then performed an analysis of variance (ANOVA) for each element to determine the phenotypic variance assigned to the genotype, environment, and G×E Table S22g, the fourth standardized moment of distribution) , and the kurtosis of linear plasticity was in between them. This observation indicates that the mean phenotype shows the greatest variation in these three phenotypic measures, followed by linear plasticity and non-linear plasticity. The dispersions of linear plasticity were greater than that of non-linear plasticity in the majority of elements , suggesting that responses to macro-environments (linear plasticity) show greater variation than responses to micro-environments (non-linear plasticity) in the diversity panel. Comparing the linear plasticity of these elements, As, Mg, S, Cd, and K, showed great dispersion (2g < 0.5), while P (2 = g 9.17) and Ca (2 =g 25.7) showed an apparently centralized distribution.In order to systematically investigate phenotypic plasticity in the diversity panel, we quantified phenotypic plasticity with the Bayesian Finlay-Wilkinson Regression (Bayesian-FWR). Three parameters including mean phenotype, slope, and residual were estimated from the Bayesian-FWR. Specifically, the mean phenotype refers to the main genetic effect of each accession in all environments. The slope was termed linear plasticity, which describes the response of each accession to the planting environment or the macro-environment. The variance of the fitted model's residuals was termed non-linear plasticity, which describes each accession's response to the micro-environment within the planting environment . All eleibution) Table S32h) (2h = 0.11). The 2h of linear plasticity was lower than that of mean phenotype but showed greater dispersion, which ranged from 0.02 (Ca) to 0.90 (Cd) with a mean of 0.43. However, the 2h of non-linear plasticity was low and ranged from 0.01 (Pb) to 0.64 (Cd) with a mean of 0.21, which might be explained by the random environmental error that was assigned to non-linear plasticity in the Bayesian-FWR. This indicates that phenotypic plasticity of rice grain ionome is also under genetic control, but shows lower heritability than mean phenotype.Next, we investigated the degree of phenotypic plasticity that resulted from genetic variation by calculating the marker-based heritability (r). It was found that mean phenotype and two measures of phenotypic plasticity tend to correlate in the diversity panel, especially between mean phenotype and linear plasticity (P <0.05) between mean phenotype and linear plasticity, followed by the correlation between mean phenotype and non-linear plasticity for 11 elements, and between linear plasticity and non-linear plasticity for 10 elements. Comparing their Pearson correlation coefficients, the highest correlation coefficients were observed between mean phenotype and linear plasticity , which ranged from 0.0014 (P) to 0.9077 (As) with a mean of 0.3742. The other two pairs  had lower Pearson correlation coefficients with means of 0.1823 and 0.1322, respectively. In addition, we also computed their genetic correlation (gr) with the genotype of the diversity panel, and a similar correlation situation was observed  were declared to be significantly associated loci (SALs). A total of 319 SALs were identified, containing 133 SALs related to mean phenotype (mSAL) of 13 elements , 116 SALs related to linear plasticity (lSAL) of 14 elements (except for As and Pb) and 70 SALs related to non-linear plasticity (nlSAL) of 12 elements  . The Cd transporter HMA3 located just near the major effect SAL for the mean phenotype of Cd concentration .A genome-wide association study (GWAS) was performed with the FarmCPU (Fixed and random model circulating probability unification) model using three phenotypic measures (transformed with the Box-Cox procedure) as input to identify their causal genetic loci. Loci with , and P) 54. The P > 0.05, We then compared the location of mSALs, lSALs, and nlSALs for the same element. Six chromosomal regions that were overlapped by different types of SALs for the same element were identified , tropical japonica (TRJ), and japonica intermediate . A simulation test showed that the Pearson correlation coefficients (r) between two phenotypes were positively correlated with the products of the two phenotypes' PST values in the whole panel and two subspecies (STP = 0.63), linear plasticity (mean STP = 0.55), and non-linear plasticity (mean STP = 0.27). For each element, significant correlations  were found between the products of any two phenotypic measures' PST and the Pearson correlation coefficients between them. Therefore, the population structure of the diversity panel, which leads to the phenotypic divergence, was at least in part responsible for the correlations among the three measures of elements.A correlation between phenotypic plasticity and mean phenotype was detected in this study Figure 2rmediate . The pheP > 0.05). Therefore, this possibility was excluded. Large variations were observed when comparing the PVE of the three types of SALs . These results confirmed that lSALs contributed a considerable proportion of the phenotypic variance in some environments. Thus, lSALs can also be used in breeding practice, especially for Cd, Cu, Mn, and Zn.To exclude the possibility that the PVE of lSALs estimated in the whole-genome regression was caused by similarities between the genetic correlation matrix (GRM) of lSALs and the GRM of the whole genome (population structure), a permutation test was performed to compare the PVE of lSALs with randomly selected loci . The permutation results indicated that the PVE of lSALs was significantly higher than the null-distribution in nearly half of the environments (39/84) for 13 elements  A considerable proportion (from 0 to 24.91%) of the rice grain ionome variation could be attributed to the variation of phenotypic plasticity; (2) The genetic architecture of phenotypic plasticity was quite different from that of mean phenotype; (3) The genetic loci involved in phenotypic plasticity of rice grain ionome can be utilized in breeding, especially for Cd, Cu, Mn, and Zn.2h) of phenotypic plasticity were relatively high, especially for linear plasticity of some elements such as Cd, K, Ni, and Zn. The result of our study shows that it is feasible to improve the rice grain ionome by harnessing linear phenotypic plasticity in rice breeding. However, we failed to obtain a convincing relationship between environmental factors and elemental accumulation because some environmental factors correlated in eight environments. In addition, environmental factors fluctuate over the duration of the crop growing season, and the temporal and spatial variation of different environmental factors and their effect on rice grain ionome also need to be investigated. These can be investigated by phenotyping cultivars in a series of environments in which more environmental factors are strictly controlled and systematically recorded, just as quantifying the sensitivities of wheat to water deficiency and high temperature  of phenotypic variance in the diversity panel. It was consistent with the result observed in the agronomic traits of a maize panel . We thenperature . All of indica and japonica subspecies, respectively)   hinders ctively)  and clasctively) . The relThe lSALs contributed to the phenotypic variance in certain environments. These loci can be further utilized in cultivating environment-specific accessions through marker-assisted selection (MAS) or genomic selection (GS). However, both of these strategies were hindered because the correspondence relationship between the genetic locus alleles and the detailed environmental factors were not dissected for the limited amount of data. Further studies that systematically investigate phenotypic plasticity of the rice grain ionome in response to various environmental factors are needed. Firstly, phenotypic plasticity needs to be investigated in a series of widespread planting environments such as the Global Rice Science Partnership (GRiSP) phenotyping network, which covers a broader range of variation on environmental factors. Limited environmental scenarios can be clustered from these planting environments based on their environmental factors. Thereafter, the correspondence relationships between plasticity-related genetic loci and environmental factors or scenarios can be investigated, and the favorable alleles of these genetic loci can be utilized in MAS to cultivate environmental-specific cultivars. In addition, the rice grain ionome recorded in these studies can also be used to perform GS across varied environments, just as the prediction of maize yield under G×E interaction .http://bigd.big.ac.cn/gsa.The raw sequence data used in this paper can be download from the Genome Sequence Archive in the BIG Data Center, Beijing Institute of Genomics (BIG), Chinese Academy of Sciences, under accession numbers CRA000778, CRA000779, and CRA000995 that are publicly accessible at The authors declare that the experiments comply with the current laws of the country in which they were performed.YT and LS designed the research. YT, JZ, LS, and JW performed the field experiments and elements concentration determination. YT analyzed the data. YT and LS wrote the paper. All the authors read and approved the manuscript.This work was jointly supported by the National Key Research and Development Plan (2017YFD0800901) and the National Natural Science Foundation of China (31470443 and 31501391), and the Key Research Program of the Chinese Academy of Sciences (KFZD-SW-111).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.