{"paper_id":"02e3511a-3370-4d60-a8eb-623fbeeb18b0","body_text":"Estimating cis and trans contributions to\ndifferences in gene regulation\nIngileif B. Hallgrímsdóttir 1, Maria Carilli 1, and Lior Pachter 1,2\n1Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, 91125, USA\n2Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, 91125, USA\nWe describe a coordinate system and associated hypothesis\ntesting framework for determining whether cis or trans regula-\ntion is responsible for differences in gene expression between\ntwo homozygous strains or species.\nCorrespondence: Ingileif Hallgrimsdottir (ingileif@caltech.edu)\nIntroduction\nIn 1961, Jacob and Monod developed a theory of gene reg-\nulation in which they distinguished local effects (cis) from\ndistal regulation (trans) (1). Their work immediately raised\nthe question of the relative contributions of these two regu-\nlation modalities (2, 3). One approach to assessing whether\ncis or trans regulation is responsible for differences in gene\nexpression between strains or species is to compare differ-\nences in expression of genes in parents to allele-specific dif-\nferences in F1 hybrids. This approach was explored in (4),\nwho used crosses of C57BL/6J and CAST/Ei mice to study\nregulatory mechanisms that could explain differences in gene\nexpression between parental strains. Their approach was de-\nveloped in (5, 6), who used pyrosequencing to study the reg-\nulation differences between D. melanogaster and D. simu-\nlans. With the advent of RNA-seq, genome-wide scans were\npossible, and (7) examined RNA-seq from F1 crosses of\nC57BL/6J and CAST/EiJ to tease apart cis and trans contri-\nbutions to gene expression differences between the parental\nstrains. Similarly, (8) performed such an RNA-seq analysis\nusing Drosophila lines.\nFormally, the idea of using crosses to study cis and\ntrans contributions to differences in gene expression between\nstrains or species is as follows: consider a gene with ex-\npressionXP 1 in a homozygous strain 1,XP 2 in a homozy-\ngous strain 2, and expression XH1 for the haplotype from\nstrain 1 in the F1 cross of 1 and 2, and expression XH2\nfor the haplotype from strain 2 in the F1 cross of 1 and 2.\nLet RP =log\n(\nXP 1\nXP 2\n)\nand RH =log\n(\nXH1\nXH2\n)\n. That is, RP\ncorresponds to the log fold-change difference in expression\nbetween the two parental strains, and RH to the log-fold-\nchange difference between the expression of the hybrid hap-\nlotypes in the F1 offspring. The connection between RP ,\nRH, and regulation is as follows: consider that a gene can\nbe regulated via cis, trans, or both (Fig. 1A). Gene expres-\nsion measurements in the parents and hybrid (Fig. 1B), can be\nused to infer the nature of regulations underlying the differ-\nence in expression in the parental strains (Fig. 1C). Specifi-\ncally, amending the classification of (6), we have:\n• conserved: No change in gene expression indicating\nthere has been no change in regulation, i.e. RP = 0\nandRH = 0, which impliesRP−RH = 0.\n• cis: The relative difference in gene expression between\nthe parents is the same as between the haplotypes in the\nhybrid indicating that the difference in parents is due to\nlocal cis effects, i.e.RH̸= 0,RP̸= 0andRP−RH =\n0, which impliesRP =RH, arises from changes only\nin cis-regulatory elements.\n• trans: Gene expression from the two haplotypes in the\nhybrid is the same, indicating that differences between\nthe parents resulted from non-local trans regulation,\ni.e.RH = 0andRP−RH̸= 0, which impliesRP̸= 0,\narises from a change only intrans-regulatory elements.\n• cis + trans: RH ̸= 0and RP−RH ̸= 0with\nsgn(RH) = sgn(RP−RH) arises as a result of\nchange in both cis- and trans-regulatory elements with\nchanges in cis and trans contributing to changes in\ngene expression between strains in the same direction.\n• cis ×trans: RH ̸= 0and RP−RH ̸= 0with\nsgn(RH)̸=sgn(RP−RH) arises as a result of com-\npensatory change in both cis- and trans-regulatory el-\nements with changes in cis and trans contributing to\nchanges in gene expression between strains in the op-\nposite direction.\nThis classification corrects (6), which fail to properly as-\nsign regulation differences to cis + trans when bothRH < 0\nandRP < 0. This issue, and the relationships between RP\nandRH in general, can be visualized as lines and regions in\na 2D plot (5), as illustrated in Fig. 1D(i). While this direct\nrepresentation of RP and RH is useful, a quantitative as-\nsessment of the gene regulatory modalities reflected in RP\nand RH requires a biologically meaningful notion of dis-\ntance between points in Fig. 1D(i). Consider, for example,\nthe situation where XP 1 = 2XP 2 andXH1 = 2XH2, i.e. a\n2-fold change in gene expression between the parents due to\nsolely to cis regulation which corresponds to the point (1,1)\nin Fig. 1D(i). The distance from this point to the origin (con-\nserved), is\n√\n2, whereas the same 2-fold difference in gene\nexpression in in the parents due solely to trans regulation\nwithRP = 1 andRH = 0 is distance 1 from the origin. This\nimbalance can be corrected via a linear transformation.\nHallgrimsdottir et al. | bioRχiv | July 14, 2024 | 1–6\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted July 16, 2024. ; https://doi.org/10.1101/2024.07.13.603403doi: bioRxiv preprint \n\nFig. 1. Geometry of parental and hybrid expression ratios. A) The cis, trans, cis + trans, and cis×trans types of regulation. B) Homozygous parents with haplotypesP1\nandP2, counts of RNA molecules for a genes (XP 1 andXP 2 respectively), and the haplotypes in anF1 hybrid along with counts for the gene (XH1 andXH2). C)\nDifferences in regulation between the parents is reflected in distinct ratios between countsXP 1,X P 2 andXH1,X H2. D.i) Illustration of how regulation differences\nemerge in log-fold changesRP andRH, D.ii) Linear transformation ofRP =log2\n(XP 1\nXP 2\n)\nandRH =log2\n(XH1\nXH2\n)\nto yield orthogonal cis and trans coordinates, D.iii)\nRepresentation of proportion cis in real projective space P1.\nResults\nGeometry. To decouple the effects of cis and trans regula-\ntion onRP andRH we begin by noting that if the difference\nin parental expression is solely due to cis regulation, then\nRP =RH, or equivalently RP−RH = 0 (orange vertical\nline in Fig. 1D(ii)). If the difference in parental expression\nis solely due to trans regulation, thenRH = 0 (blue horizon-\ntal line in Fig. 1D(ii)). Therefore, the transformation from\nFig. 1D(ii) to Fig. 1D(i) is obtained by\n(RP\nRH\n)\n=\n(1 1\n0 1\n) (RP−RH\nRH\n)\n. (1)\nThus, the inverse transformation from the coordinate system\nin Fig. 1D(i) to the coordinate system in Fig. 1D(ii) is given\nby\n[1 1\n0 1\n]−1\n=\n[1 −1\n0 1\n]\n, (2)\ni.e., the transformation inverts the mapping of the vertical\naxis to the diagonal cis line.\nThe determination of whether a difference in parental\ngene expression is due to cis or trans can now be understood\nto be an assessment of whether the line passing through the\norigin and a point (RP,RP−RH) is a perturbation (due to\nnoise) of the line ∆ trans, the line ∆ cis or sufficiently far\naway from the axes in Fig. 1D(ii) to merit a designation of∆\n2 | bioRχiv Hallgrimsdottir et al. |\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted July 16, 2024. ; https://doi.org/10.1101/2024.07.13.603403doi: bioRxiv preprint \n\nFig. 2. Contributions of cis and trans regulation to differences in gene expression between yeast strains. A) Results of (9) B) Comparison of the results of (9) to the\nassignment of genes based on hypothesis testing, C) Reanalysis of the data from (9).\ncis + trans or ∆ cis×trans (the designations are enumerated\nin Supp. Table 1). In other words, the sufficient statistic is a\npoint in real projective space P1 (Fig. 1D(iii)), and the pro-\nportion of the difference in gene expression between parents\nthat can be attributed to cis can be understood to be a scaling\nof the angle of the line through the origin correspond to the\npoint in P1, i.e.\nproportion cis =\n⏐⏐⏐⏐\n2\nπtan−1\n( RH\nRP−RH\n)⏐⏐\n⏐⏐. (3)\nStatistics. The determination of whether a measurement\n(RP,RH) reflects a difference in gene expression between\nparents due to cis or trans regulation, or both, requires a sta-\ntistical assessment (10). Specifically, hypothesis tests can be\nused to reject a null hypothesis of a difference in gene ex-\npression being due solely to trans or solely to cis. Geomet-\nrically, as evident from the linear transformation on log-fold\nchanges, these two tests correspond to testing whether one\ncan reject the null hypotheses that(RP,RP−RH) is located\non thex- andy- axes respectively.\nWe performed such hypothesis tests for data from (9),\nwhich consists of bulk RNA-seq performed on hybrid and\nparental strains of genetically divergentSaccharomyces cere-\nvisiae (see Methods, Supp. Figs. 1,2). Briefly, (9) generated\n323 hybrid crosses from 26 parental yeast isolates derived\nfrom diverse environmental conditions. In (9), genes were\nclassified according to the representation shown in Fig. 1D(i).\nFirst, both RP and RH were tested for statistically signifi-\ncant differences from 0 and assigned \"null\" (our conserved)\nif both tests failed to reject the null hypothesis; then, changes\nbetween parental and hybrid allelic ratios were tested for\nsignificance. For genes that passed significance thresholds,\nregulatory assignments were made by dividing the untrans-\nformed 2D plane into cones (Fig. 2A). We reassigned genes\nbased on our hypothesis tests as derived from the transformed\ncoordinate system (Fig. 2C), with one test with the null hy-\npothesis of cis regulation and one with the null hypothesis of\ntrans regulation, thereby putting the two regulation strategies\non equal footing. Compared to the original study, we found\nmajor differences in assignment (Fig 2B, Supp. Fig. 3A,3B,\nSupp. Table 2).\nInterestingly, whereas (9) conclude that \"the transcrip-\ntome is globally buffered at the genetic level mainly due to\ntrans-regulatory variation in the population\", we find that a\nconsiderable amount of difference in gene expression can\nbe attributed to cis (supp. Fig. 3C), with the difference\nHallgrimsdottir et al. | bioRχiv | 3\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted July 16, 2024. ; https://doi.org/10.1101/2024.07.13.603403doi: bioRxiv preprint \n\nFig. 3. Proportion cis. A) Comparison of slope vs. angle in determining proportion cis. B) Ratio between slope and angle. C) Examples of four genes displaying high\nvariance in proportion cis across cell types.\ndue to (9) deriving assignments in the untransformed coor-\ndinate system using a statistical testing procedure that treats\ncis and trans regulation asymmetrically. Specifically (9) re-\nport 57,253 cases where gene expression difference is due\nto trans regulation (Supp. Fig. 3A). We find 51,627 cases\nthat can be assigned to trans (Supp Fig. 3B). These numbers\nare similar; however, (9) report 2,804 cases assigned to cis\n(Supp. Fig. 3A), whereas we find 17,112 (Supp.‘Fig. 3B).\nFurthermore, we find 4,807 cases assigned to cis + trans\n(Supp. Fig. 3B) versus 1,727 in (9) (Supp. Fig. 3A). Overall,\nthere is a marked difference between our results and those of\n(9) (Supp. Fig. 3C).\nProportion cis. In addition to naturally revealing the ap-\npropriate hypothesis tests to conduct for attribution of gene\nexpression difference in parents to cis or trans, as previ-\nously discussed the linear transformation we propose leads\ndirectly to a meaningful measure of the proportion of dif-\nference in gene expression that can be attributed to cis reg-\nulation (or trans) (Equation 3). To illustrate this, we ex-\namined and re-analyzed a dataset of gene expression from\nhuman-chimpanzee hybrids (11), calculating the proportion\ncis according to Equation 3. In (11), the proportion cis was\ncalculated using slope, as is natural to do when working in\nthe untransformed coordinate framework, whereas the cor-\nrect calculation (Equation 4) uses angle in the transformed\ncoordinate system. While the absolute differences are small\n(Fig. 3A), with a maximum difference of 0.045 (see Meth-\nods), the relative difference is large when the proportion\ncis is small (Fig. 3B), and can be as high as 57% (see\nMethods). Moreover, our computation provides a biologi-\ncally interpretable measure of proportion cis. We found sev-\neral genes in (11) exhibiting high variance in proportion cis\n(Fig. 3C), and identified interesting differences between cell\ntypes (Supp. Fig. 4 – 7).\nDiscussion\nThe use of crosses between strains to identify the nature of\ndifferential regulation is a powerful tool for genetics stud-\nies that is particularly relevant now that single-cell RNA-seq\ncan be used for cell type resolution. Moreover, whereas orig-\ninal studies were limited by gene expression measurement\ntechnologies to a handful of genes, genome-wide single-cell\nRNA-seq assays can complement genome-wide eQTL stud-\nies.\nWe have shown that geometric considerations reveal\nthe need for applying a linear transformation prior to visu-\nalisation and data analysis. The linear transformation also\nhighlights independent axes that lead naturally to hypothesis\ntests for classifying genes according to the type of regulation\nunderlying differences in gene expression between parents.\nWhile we have focused on explaining differences between\n4 | bioRχiv Hallgrimsdottir et al. |\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted July 16, 2024. ; https://doi.org/10.1101/2024.07.13.603403doi: bioRxiv preprint \n\nparents that fall into five categories (conserved,cis, trans, cis\n+ trans, cis×trans), our approach can be extended to finer\nclassifications such as in (9). We note that in the hypothesis\ntesting framework, referring to a gene as having differences\nin expression explained by cis or trans is technically incor-\nrect. This is because the rejection of the cis null hypothesis\nonly shows that the difference in gene expression is not due\nsolely to cis regulation. It does not mean that the difference in\ngene expression can, or should be, attributed solely to trans.\nThe same is the case for rejecting the trans hypothesis. In\nFig. 2, our coloring of genes as cis or trans is therefore not\nprecise, but we have done so to facilitate comparisons to prior\nwork.\nOur statistical tests also depend on the assumption that\nread counts are binomially distributed. This assumption is\nstandard in the absence of biological replicates, however in\npractice biological replicates should be obtained, and they\ncan and should be used to better assess the extent of technical\nvariation. An extension of this work to that case is possible\nand can be based on modeling counts with negative binomial\ndistributions, as is done in methods such as W ASP (12).\nFinally, we note that our framework is general and can\nbe applied to phenotypes other than gene expression. For\nexample, with single-cell RNA-seq data it could be used to\nassess the regulation mechanisms underlying differences in\nvariance in gene expression. Such extensions will be partic-\nularly interesting to explore in conjunction with complemen-\ntary modalities (13).\nData and Code Availability\nAll code to download data and generate the\nmain and supplementary figures is available at\nhttps://github.com/pachterlab/HCP_2024, executable in\nGoogle Colaboratory notebooks.\nAcknowledgements\nIH and LP were funded, in part, by NIH 5UM1HG012077-\n02. MC was funded by a NSF graduate research fellowship\nunder Grant No. 2139433. This work was additionally sup-\nported by the Caltech Bioinformatics Resource Center.\nReferences\n1. François Jacob and Jacques Monod. Genetic regulatory mechanisms in the synthesis of\nproteins. Journal of molecular biology, 3(3):318–356, 1961.\n2. Rita JS Phillips. A cis-trans position effect at the a locus of the house mouse. Genetics, 54\n(2):485, 1966.\n3. John S Kovach, Antonio O Ballesteros, Marilyn Meyers, Marco Soria, and Robert F Gold-\nberger. A cis/trans test of the effect of the first enzyme for histidine biosynthesis on regula-\ntion of the histidine operon. Journal of Bacteriology, 114(1):351–356, 1973.\n4. Christopher R Cowles, Joel N Hirschhorn, David Altshuler, and Eric S Lander. Detection of\nregulatory variation in mouse genes. Nature genetics, 32(3):432–437, 2002.\n5. Patricia J Wittkopp, Belinda K Haerum, and Andrew G Clark. Evolutionary changes in cis\nand trans gene regulation. Nature, 430(6995):85–88, 2004.\n6. Christian R Landry, Patricia J Wittkopp, Clifford H Taubes, Jose M Ranz, Andrew G Clark,\nand Daniel L Hartl. Compensatory cis-trans evolution and the dysregulation of gene expres-\nsion in interspecific hybrids of drosophila. Genetics, 171(4):1813–1822, 2005.\n7. Angela Goncalves, Sarah Leigh-Brown, David Thybert, Klara Stefflova, Ernest Turro, Paul\nFlicek, Alvis Brazma, Duncan T Odom, and John C Marioni. Extensive compensatory cis-\ntrans regulation in the evolution of mouse gene expression. Genome research, 22(12):\n2376–2384, 2012.\n8. Andreas Massouras, Sebastian M Waszak, Monica Albarca-Aguilera, Korneel Hens,\nWiebke Holcombe, Julien F Ayroles, Emmanouil T Dermitzakis, Eric A Stone, Jeffrey D\nJensen, Trudy FC Mackay, et al. Genomic variation and its impact on gene expression in\ndrosophila melanogaster. PLoS genetics, 8(11):e1003055, 2012.\n9. Andreas Tsouris, Gauthier Brach, Joseph Schacherer, and Jing Hou. Non-additive genetic\ncomponents contribute significantly to population-wide gene expression variation. Cell Ge-\nnomics, 4(1), 2024.\n10. C Joel McManus, Joseph D Coolon, Michael O Duff, Jodi Eipper-Mains, Brenton R Grav-\neley, and Patricia J Wittkopp. Regulatory divergence in drosophila revealed by mrna-seq.\nGenome research, 20(6):816–825, 2010.\n11. Kenneth A Barr, Katherine L Rhodes, and Y oav Gilad. The relationship between regulatory\nchanges in cis and trans and the evolution of gene expression in humans and chimpanzees.\nGenome Biology, 24(1):207, 2023.\n12. Bryce Van De Geijn, Graham McVicker, Y oav Gilad, and Jonathan K Pritchard. Wasp: allele-\nspecific software for robust molecular quantitative trait locus discovery.Nature methods, 12\n(11):1061–1063, 2015.\n13. Ibai Irastorza-Azcarate, Alexander Kukalev, Rieke Kempfer, Christoph J Thieme, Guido\nMastrobuoni, Julia Markowski, Gesa Loof, Thomas M Sparks, Emily Brookes, Kedar Nath\nNatarajan, et al. Extensive folding variability between homologous chromosomes in mam-\nmalian cells. bioRxiv, pages 2024–05, 2024.\n14. Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David\nCournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Sté-\nfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov,\nAndrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey,˙Ilhan Polat, Yu Feng,\nEric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Hen-\nriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian\nPedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fundamental Al-\ngorithms for Scientific Computing in Python. Nature Methods, 17:261–272, 2020. doi:\n10.1038/s41592-019-0686-2.\n15. Y oav Benjamini and Y osef Hochberg. Controlling the false discovery rate: a practical and\npowerful approach to multiple testing. Journal of the Royal statistical society: series B\n(Methodological), 57(1):289–300, 1995.\nHallgrimsdottir et al. | bioRχiv | 5\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted July 16, 2024. ; https://doi.org/10.1101/2024.07.13.603403doi: bioRxiv preprint \n\nMethods\nAcquisition and preprocessing of data from yeast crosses. Processed RNA-seq data from (9) were obtained from\nhttp://1002genomes.u-strasbg.fr/files/Diallel_RNAseq/ASE in the file ‘Datafile2_ase_sum_20230609.tab.’ This file included\nreported values for allelic expression in parents and expression per parental allele in hybrids for 323 unique parent-hybrid trios.\nDetails on the estimation of allelic expression are described in the original study (9). As integer value counts are required\nfor the binomial and the two sample binomial ratio statistical tests, reported values were rounded to the nearest integer before\nstatistical tests were performed.\nIn (9), 7 categories were considered (reverse, attenuating, reinforcing, compensatory, cis only, trans onlyand null). In order\nto maintain consistency with (6), we collapsed these into four categories: cis, trans, cis + trans, and cis×trans as follows:\nreverse→cis×trans, cis only→cis, trans only→trans, null→conserved, and attenuating, reinforcing and compensatory\n→cis×trans if sgn(RP−RH) = sgn(RH) and cis + trans otherwise.\nAcquisition of data from human-chimpanzee crosses. The reportedlog2 fold changes between human and chimpanzee\nparental cell lines (RP ) and hybrid alleliclog2 fold changes for human-chimpanzee hybrid cell lines (RH) were obtained from\n(11). The reportedlog2 fold changes were used without modification to recalculate proportion cis as\nproportion cis =\n⏐⏐\n⏐⏐\n2\nπtan−1\n( RH\nRP−RH\n)⏐⏐\n⏐⏐. (4)\nThe provided data also included reported proportion cis per gene per cell type, defined as\nproportion cis (11) = |RH|\n|RH|+|RP−RH|, (5)\nwhich were directly compared to Equation 4.\nThe maximum difference between x := |RH|\n|RH|+|RP−RH|and 2\nπtan−1\n(\nRH\nRP−RH\n)\nis 0.045atx = 0.239andx = 0.761.\nThe maximum of the ratio is 1.57and occurs atx≈0.00006.\nStatistical tests.\nBinomial test. To test the null hypothesis that there is no difference between expression of parental alleles in hybrids (or\nthat the difference in regulation is purely trans) was performed on rounded integer counts from (9) using the function\nscipy.stats.binomtest (14). This tests for the probability of having observed a value at least as extreme as k suc-\ncesses given probabilityp of success and a total ofN trials by summing over binomial probabilities:\nP(k;N,p ) =\n(N\nk\n)\npk(1−p)N−k. (6)\nIf XH1 is the allelic expression in the hybrid of one parental allele and XH2 is the allelic expression in the hybrid of the\nother parental allele, the binomial test was performed with k =XH1,N =XH1 +XH2,p = 0.5and a two-sided alternative\nhypothesis.\nTwo sample binomial ratio test. To test the null hypothesis that there is no difference in the ratio of expression of alleles in\nparents and allelic expression in hybrids (or that the difference in regulation between parents is purelycis), we performed a two\nsample binomial ratio test in which we assumed both XP 1 andXH1 are sampled from a binomial distribution with the same\nprobability of successps. Using\nps = XP 1 +XH1\nXP 1 +XP 2 +XH1 +XH2\n, (7)\nwe calculated the grid of probabilities over possibleP1 andH1 values:\nP(XP 1 =xP 1,XH1 =xH1;NP,NH,ps) =\n(NP\nxP 1\n)\npxP 1\ns (1−ps)NP−xP 1·\n(NH\nxH1\n)\npxH1\ns (1−ps)NH−xH1, (8)\nwhereNP =XP 1 +XP 2 is the total number of counts from parents andNH =XH1 +XH2 is the total number of counts from\nthe hybrid. We then calculated the probability of having observed values at least as extreme as the observedXP 1 andXH1.\nTo account for multiple testing, we corrected both binomial and two sample binomial significance values using the\nBenjamini-Hochberg correction for false discovery rates (15). We rejected the null hypothesis for tests with false discovery\nrates less than 0.05.\n6 | bioRχiv Hallgrimsdottir et al. |\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted July 16, 2024. ; https://doi.org/10.1101/2024.07.13.603403doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}