Dissecting indirect genetic effects from peers 1 in laboratory mice 2 3

The phenotype of one individual can be affected not only by the individual’s own genotypes (direct genetic effects, DGE) but also by genotypes of interacting partners (indirect genetic effects, IGE). IGE have been detected using polygenic models in multiple species, including laboratory mice and humans. However, the underlying mechanisms remain largely unknown. Genome-wide association studies of IGE (igeGWAS) can point to IGE genes, but have not yet been applied to non-familial IGE arising from “peers” and affecting biomedical phenotypes. In addition, the extent to which igeGWAS will identify loci not identified by dgeGWAS remains an open question. Finally, findings from igeGWAS have not been confirmed by experimental manipulation. We leveraged a dataset of 170 behavioural, physiological and morphological phenotypes measured in 1,812 genetically heterogeneous laboratory mice to study IGE arising between same-sex, adult, unrelated laboratory mice housed in the same cage. We developed methods for igeGWAS in this context and identified 24 significant IGE loci for 17 phenotypes (FDR < 10%). There was no overlap between IGE loci and DGE loci for the same phenotype, which was consistent with the moderate genetic correlations between DGE and IGE for the same phenotype estimated using polygenic models. Finally, we fine-mapped seven significant IGE loci to individual genes and confirmed, in an experiment with a knockout model, that Epha4 gives rise to IGE on stress-coping strategy and wound healing. Our results demonstrate the potential for igeGWAS to identify IGE genes and shed some light into the mechanisms of peer influence.


Abstract 21
The phenotype of one individual can be affected not only by the individual's own 22 genotypes (direct genetic effects, DGE) but also by genotypes of interacting partners 23 (indirect genetic effects, IGE). IGE have been detected using polygenic models in 24 multiple species, including laboratory mice and humans. However, the underlying 25 mechanisms remain largely unknown. Genome-wide association studies of IGE 26 (igeGWAS) can point to IGE genes, but have not yet been applied to non-familial IGE 27 arising from "peers" and affecting biomedical phenotypes. In addition, the extent to 28 which igeGWAS will identify loci not identified by dgeGWAS remains an open 29 question. Finally, findings from igeGWAS have not been confirmed by experimental 30

manipulation. 31
We leveraged a dataset of 170 behavioural, physiological and morphological 32 phenotypes measured in 1,812 genetically heterogeneous laboratory mice to study 33 IGE arising between same-sex, adult, unrelated laboratory mice housed in the same 34 cage. We developed methods for igeGWAS in this context and identified 24 significant 35 IGE loci for 17 phenotypes (FDR < 10%). There was no overlap between IGE loci and 36 DGE loci for the same phenotype, which was consistent with the moderate genetic 37 correlations between DGE and IGE for the same phenotype estimated using polygenic 38 models. Finally, we fine-mapped seven significant IGE loci to individual genes and 39 confirmed, in an experiment with a knockout model, that Epha4 gives rise to IGE on 40 stress-coping strategy and wound healing. 41 Our results demonstrate the potential for igeGWAS to identify IGE genes and shed 42 some light into the mechanisms of peer influence. heritable traits of interacting partners (Figure 1b), which can include behavioural and 54 non-behavioural traits of partners as well as modifications of the non-social 55 environment by partners(4). IGE have been detected in many laboratory systems(5-56 14), livestock(15-17), crops(18), wild animals(19-21), and humans (22)(23)(24)(25)(26)(27), 57 demonstrating that they are an important component of the genotype to phenotype 58 path and an aspect of the environment that can be studied using genetic approaches. 59 Most prior studies of IGE have used polygenic modelling approaches to study 60 aggregate genetic effects, either studying IGE mediated by specific traits of partners 61 using trait-based models(2, 28) or polygenic risk scores (22,25), or detecting IGE 62 mediated by unknown heritable traits of partners using variance components 63 models (9,15,29,30). More recently, the genome-wide association study of IGE 64 (igeGWAS) has been proposed as a strategy to identify individual genetic loci 65 underlying IGE associations (5,7,8,11,(31)(32)(33)(34)(35). 66 However, igeGWAS has only been applied in limited settings: in particular, it 67 has not been used to study non-familial IGE from peers affecting biomedical phenotypes, despite growing evidence from polygenic models in laboratory mice(9) 69 and in humans(25) that such effects are important. Moreover, the relationship between 70 DGE and IGE affecting the same phenotype has not been fully addressed, such that 71 the scope for igeGWAS to identify loci not detected by dgeGWAS is unknown. Finally, 72 the results of igeGWAS have not yet been translated into experimentally validated 73 genes causing IGE. 74 To address these issues, we leveraged a published dataset of 170 behavioural, 75 physiological and morphological phenotypes measured in 1,812 male and female, 76 genetically heterogeneous mice (Figure 1c), which we supplemented with previously 77 unreported cage information (Supplementary Table 1

98
We used the genome-wide genotypes (both LD-pruned and unpruned genotypes 99 derived from low-coverage (0.15×), Illumina sequencing, see Methods) and 200 100 phenotypes for 2,073 commercially available, outbred Crl:CFW(SW)-US_P08(36) 101 (herafter CFW) mice reported in Nicod et al. (37) and Davies et al. (38). In addition, 102 we used previously unreported cage information provided by the authors of the original 103 study upon request (Supplementary Table 1). Mice were housed in same-sex groups 104 of three and interacted for at least nine weeks before phenotyping. We excluded any 105 animal whose cage mates changed over the course of the experiment, as well as 106 suspected siblings to rule out confounding from parental and litter effects. These steps 107 resulted in a final sample size of 1,812 mice (927 females, 885 males) for analysis. 108 We normalised each phenotype and excluded 30 phenotypes that could not be 109 satisfactorily normalised (see Methods), yielding a total of 170 phenotypes measured 110 in between 844 and 1,729 mice. 111

Polygenic analysis of the correlation between DGE and IGE 112
Initially, we used polygenic models to assess the extent to which loci are shared 113 between DGE and IGE affecting the same phenotype. Briefly, for each trait, we 114 estimated the genetic correlation ρ between DGE and IGE. As this correlation is 115 equivalent to the correlation between DGE on the phenotype of interest and DGE on 116 the traits of partners mediating IGE (Figure 1b) Table 2). 122 We found that ρ was different from zero for ten out of twenty eight phenotypes (P < 123 0.05), indicating that, often, the traits mediating IGE on a phenotype of interest are 124 genetically correlated (in the classical sense) with the phenotype of interest. Evidence 125 that ρ was different from zero was strongest for mean weight of the adrenal glands, 126 which correlates with stress(39), mean platelet volume, LDL cholesterol levels, and 127 rate of healing from an ear punch. Second, ρ was different from plus or minus one for 128 ten phenotypes (P < 0.05), with the strongest evidence for a measure of stress-coping 129 strategy (immobility in the forced swim test) and rate of healing from an ear punch. 130 These results indicate that IGE on a phenotype of interest are often mediated by traits of partners other than the phenotype of interest. To uncover those traits, we turned to 132   Table 3). The 17 phenotypes with one or more IGE loci tended to 168 have a higher aggregate contribution of IGE (across the genome) than phenotypes 169 without significant IGE loci (averages of 3.8% and 2.8% respectively), a trend that was 170 not significant (one-sided t-test P = 0.14). 171 To enable a direct comparison between igeGWAS and dgeGWAS, we 172 performed dgeGWAS for each phenotype using the same approach as taken for 173 igeGWAS, including random effects for DGE and IGE polygenic effects and cage 174 effects and including a fixed effect covariate for IGE arising from the tested variant.

Identification of putative causal genes for experimental evaluation 218
Linkage disequilibrium decays faster in the CFW population than in many other mouse 219 populations used for mapping, which facilitates identification of putative causal genes 220 at associated loci (36,37,45). To identify such genes, we fine-mapped the 24 221 significant IGE loci using the full set of variants (rather than the pruned set used for 222 igeGWAS) in the 1.5Mb window surrounding the most significant variant at the locus, 223 which corresponds, in this sample, to the average 95% confidence interval for the 224 association(37). We then identified, for each significant IGE locus, all of the genes that 225 either overlapped the associated plateau or were located in direct proximity (see 226 Supplementary Table 3 and local association plots in 227 locusZooms_SupplTable3.zip). At seven loci there was a single putative causal 228 gene: Abca12 at a locus for adult neurogenesis, Epha4 (stress-coping strategy), Pkn2, 229

Methods, genes listed in
Slit3 and Pgk1-rs7 (at three different loci for sleep), H60c (home cage activity), and 230 Adcy1 (osteopetrosis). 231 One example of a putative causal IGE gene identified via this strategy is Epha4, which 232 was identified at an IGE locus on chromosome 1 for immobility during the first two 233 minutes of the forced swim test (FST), a measure of stress-coping strategy (46)  was the only putative causal gene at a significant locus, the locus was in the top half 236 of the list in terms of significance, and a knockout mouse model was readily available 237 from a neighbouring institute. 238 Epha4 encodes a synaptic protein that plays an important role in synaptic 239 plasticity in the hippocampus(47, 48) and DGE of Epha4 on FST immobility have been 240 reported(49, 50). Therefore we evaluated the possibility that Epha4 directly influences 241 stress-coping strategy and that the stress-coping strategy of a mouse in the weeks 242 prior to or during the FST gets copied by the other mice in the cage (behavioural 243 contagion), thereby giving rise to IGE on stress-coping strategy. To investigate this 244 hypothesis, we tested whether Epha4 had direct effects on FST immobility in CFW 245 mice, using the full set of variants in the same 1.5Mb window including Epha4 as for 246 IGE analysis. We found little evidence that Epha4 directly affects FST immobility in 247 CFW mice (maximum -logP value at the locus: 2.14, Figure 4b), making it unlikely 248 that behavioural contagion explains the detected IGE in CFW mice. 249 In addition to the significant IGE association between Epha4 and FST 264 immobility, we found suggestive evidence for an IGE association between Epha4 and 265 rate of healing from an ear punch (igeGWAS -logP value = 4.1, FDR > 10%, Figure  266 4c). This finding was of particular interest because the Epha4 locus was among the 267 three most significant IGE loci for wound healing (all three loci with -logP=4.1) and 268 because IGE on wound healing seem to be ubiquitous in laboratory mice: indeed, we 269 have found a significant aggregate contribution of IGE to rate of healing from an ear 270 punch in all three mouse populations we have looked at to date (inbred C57BL/6J mice 271 and outbred Heterogeneous Stock mice in Baud et al.(9), and CFW mice in this study). 272 Thus, we were particularly interested in testing whether Epha4 was involved in IGE on 273 wound healing. 274 We found two additional significant IGE loci for FST immobility, more precisely 275 for immobility during the last four minutes of the test (Supplementary Table 3 (45), was significantly and highly correlated with that of Epha4 (Spearman 281 r = 0.868, Bonferroni-corrected P = 2,3.10 -19 , Supplementary Figure 6b). As was the 282 case for Epha4, we found no evidence of DGE arising from Dlgap1 and affecting FST 283 immobility in CFW mice (maximum -logP value at the locus 2.46). 284 Evaluating the role of Epha4 and Dlgap1 in IGE using knockout models 285 We tested the hypotheses that Epha4 can give rise to IGE on FST immobility and rate 286 of healing using a constitutive Epha4 knockout model on a mixed C56BL/6 & 287 C56BL/10 genetic background. In addition, we tested for IGE from Dlgap1 on FST 288 immobility using a constitutive Dlgap1 knockout model on a C57BL/6N background. 289 At weaning, one Epha4 mouse (heterozygote or wild-type, see Methods) or one 290 Dlgap1 mouse (homozygote knockout, heterozygote or wild-type) was co-housed with 291 one focal FVB/NJ (FVB) mouse of the same sex (male or female). The FVB strain was 292 chosen because it is the inbred strain whose genetic background is most similar to 293 that of the outbred CFW mice used in igeGWAS, contributing 38% of all alleles in CFW 294 mice(37). Focal FVB mice were ear punched prior to pairing, then the pairs of mice 295 were left to interact in their cages for two months before they were all tested in the 296 FST and the ears of FVB mice were analysed to measure the rate of healing (see 297

Methods). 298
Although FVB mice are genetically similar to CFW mice, we observed that focal 299 FVB mice showed much less immobility during the first two minutes of the FST than 300 CFW mice (2.0 seconds on average across all FVB mice vs 12.2 seconds on average 301 across all CFW mice). Therefore, in our analysis of FVB focal mice we focused on 302 immobility during the last four minutes of the test, even though this measure showed 303 a lower association in igeGWAS than immobility during the first two minutes of the test 304 (-logP = 2.8 and 5.2 respectively). 305 When considering males and females together we found no effect of the 306 genotype of cage mates on either FST immobility (P = 0.52, ANOVA, N = 81) or wound 307 healing (P = 0.40, ANOVA, N = 85). However, model comparison using the Akaike 308 Information Criterion (AIC) suggested there was an interaction between sex and 309 genotype of the cage mate (i.e. IGE) for both FST immobility and wound healing, as 310 the model including an interaction term between sex and genotype of the cage mate 311 was favoured. Therefore, we considered the two sexes separately and observed, in 312 males but not in females, IGE on FST immobility (P = 0.054, ANOVA, N = 35) and 313 wound healing (P = 0.038, ANOVA, N = 38) (Figure 5). The detection of male-specific 314 IGE from Epha4 on wound healing is consistent with the observation of stronger IGE 315 at the Epha4 locus in male CFW mice compared to female CFW mice 316 (Supplementary Figure 7a). The detection of male-specific IGE on FST immobility, 317 on the other hand, was not expected from the analysis of CFW mice as similar effects 318 were observed in males and females (Supplementary Figures 7b and 7c). A 319 potential explanation for male-specific IGE on FST immobility in FVB focal mice is that 320 FVB females showed lower immobility than FVB males, hindering our ability to detect 321 genetic effects. Nevertheless, these experimental results support the hypothesis that 322 Epha4 can give rise to IGE on FST immobility and wound healing in laboratory mice. 323 As was the case in CFW mice, we did not observe a direct effect of Epha4 on 324 FST immobility whether all mice or males only were considered (P = 0.22 and 0.23 325 respectively, ANOVA, N = 81 and 35 respectively), indicating behavioural contagion is 326 unlikely to explain these IGE. 327 Finally, we found no evidence of IGE from Dlgap1 on FST immobility. 328 In this study, we leveraged a published dataset of 170 behavioural, physiological and 336 morphological phenotypes measured in 1,812 genetically heterogeneous mice housed 337 in same-sex groups of three to comprehensively assess the contribution of IGE to 338 phenotypic variation and characterise the relationship between DGE and IGE for the 339 same phenotype. Using polygenic models we showed that the genetic correlation r 340 between DGE and IGE for a given phenotype is often significantly different from one, 341 indicating IGE loci are different from DGE loci for the same phenotype. Consistently, 342 we found that none of the 24 significant IGE loci identified for 17 phenotypes using 343 igeGWAS overlapped with significant DGE loci identified using dgeGWAS. We fine-344 mapped seven significant IGE loci to a single putative causal gene and experimentally 345 validated IGE from one of them, Epha4, on stress-coping strategy and wound healing 346 using a knockout model. 347 The analysis of the genetic correlation r between DGE and IGE for the same 348 phenotype provides insights into the overlap between DGE and IGE loci for a given 349 phenotype and whether the traits mediating IGE on a phenotype of interest are 350 genetically correlated (in the classical sense) with that phenotype. The correlation r 351 was expected to be different from zero for many phenotypes, based on reports that 352 emotions(52-54), behaviours(25, 55, 56), pathogens, and components of the gut 353 microbiome(57) can "spread" between individuals and contribute to phenotypic 354 variation, both in mice and in humans. In our study we found that r is significantly 355 different from zero for a variety of phenotypes, which indicates some overlap between 356 DGE loci and IGE loci for the same trait and is consistent with a genetic correlation (in 357 the classical sense) between the phenotype of interest and the traits mediating IGE. 358 However, we also found that r is significantly different from ±1 for ten out of twenty 359 eight traits, reflecting differences between DGE and IGE loci and demonstrating that 360 IGE on a phenotype of interest often involve traits of cage mates other than the 361 phenotype of interest. This was true even for phenotypes that likely spread, namely 362 stress and stress-coping strategies. 363 Consistent with the estimates of r from polygenic models, we found no overlap 364 between the 24 loci identified by igeGWAS for 17 phenotypes and the loci identified 365 by dgeGWAS for the same phenotypes. Our survey of a large number of phenotypes 366 suggests that the loci identified by igeGWAS will, generally, be different from those 367 identified by dgeGWAS, meaning igeGWAS holds great potential to uncover new loci 368 underlying phenotypic variation and that these loci will point to traits of cage mates 369 different from the phenotype studied. 370 Identifying IGE genes using igeGWAS has been previously attempted (5, 7, 8, 371 11, 31-35), but there has been limited evidence that this approach can indeed identify 372 genes that are causally involved in IGE. The results of our igeGWAS and fine-mapping 373 analyses identified a single putative causal gene at seven IGE loci: Abca12 at a locus 374 for adult neurogenesis, Epha4 at a locus for stress-coping strategy, Pkn2, Slit3 and 375 Pgk1-rs7 at three different loci for sleep, H60c at a locus for home cage activity, and 376 Adcy1 at a locus for osteopetrosis. We tested one of these genes, Epha4, as well as 377 another gene, Dlgap1, in experiments with knockout models. Epha4 and Dlgap1 were 378 putative causal genes at two different IGE loci for stress-coping strategy and both 379 encode synaptic proteins. However, only Epha4 was at a locus with a single putative 380 causal gene, making it a stronger candidate than Dlgap1. We confirmed the role of 381 Epha4 in giving rise to IGE on stress-coping strategy and wound healing in laboratory 382 mice, but did not find evidence of IGE from Dlgap1. A limitation of our experiment is 383 that FVB focal mice showed little to no immobility during the first two minutes of the 384 FST, in contrast with the CFW mice used in igeGWAS. Hence, even though the 385 significant igeGWAS locus was for immobility during the first two minutes of the test, 386 we had to focus on immobility during the last four minutes when analysing the 387 behaviour of FVB mice. Similarly, immobility during the last four minutes was lower in 388 FVB female mice than it was in FVB male mice, which may explain why only observed 389 IGE from Epha4 in FVB male. Effects of the genetic background of knockout models 390 have been reported in studies of DGE(58); our results show that in studies of IGE both 391 the genetic background of the focal individuals matter too. In the future we will consider 392 a broader range of genetic backgrounds for focal mice. The seven genes listed above 393 as single putative causal genes at IGE loci as well as the experimental system we 394 have developed to test Epha4 and Dlgap1 will serve as valuable starting points to gain 395 further insights into the mechanisms of IGE in the future.  (59)) in R; phenotypes that could not be normalised 419 satisfactorily (transformation parameter lambda outside of -2 to 2 interval) were 420 excluded. Because data for some phenotypes were missing for some mice, the sample 421 size varied. The sample size for each phenotype after all filtering (see below) is 422

Cage information 429
Mice were four to seven weeks old when they arrived at the phenotyping facility and 430 were housed in same-sex groups of three mice. They were left undisturbed for nine to 431 twelve weeks during their time in quarantine and spent another four weeks together 432 during phenotyping. 433 Cage assignments were not included in the publicly available dataset but were 434 provided by the authors upon request and are now provided in Supplementary Table  435 1. Cage assignments were recorded at eleven time points throughout the study and 436 showed that a few mice were taken out of their original cages and singly housed, 437 presumably because they were too aggressive. We only included in our analyses mice 438 that had the same two cage mates throughout the experiment. We further excluded a 439 subset of mice based on their genotype-based genetic similarity, as described below. 440 Finally, all mice were singly housed during the sleep test and until sacrifice a few days 441 later. Hence, we investigated "persistent" IGE on sleep and tissue phenotypes. 442 443

Genome-wide genotypes 444
From http://wp.cs.ucl.ac.uk/outbredmice/ we retrieved both allele dosages for 7 million 445 variants and allele dosages for a subset of 353,697 high quality, LD-pruned variants 446 (as described in Nicod et al.(37); genotyping based on sparse sequencing data). We 447 used LD-pruned variants for all analyses but the identification of putative causal genes 448 at IGE loci (see below), for which we used the full set of variants. 449 450

Genetic relatedness matrix (GRM) and exclusion of presumed siblings 451
The genetic relatedness matrix was calculated as the cross-product of the LD-pruned 452 dosage matrix after standardizing the dosages for each variant to mean 0 and variance 453 1. A few pairs of mice were outliers in the distribution of GRM values, which made us 454 suspect that siblings had been included in the sample even though they were not 455 supposed to be (siblings were excluded by design). To mitigate confounding of DGE 456 and IGE analyses by litter effects, we excluded 19 cages (57 mice) from all analyses. 457 458

Variance components model 459
The same model as described in detail in Baud et al.(9) was used. Briefly, the model 460 used is the following: 461 ! is the phenotypic value of the focal mouse , ! is a row of the matrix of covariate 463 values and a column vector of corresponding estimated coefficients. ",! is the 464 additive direct genetic effects (DGE) of . ! is a row of the matrix that indicates 465 cage mates (importantly %,% = 0) and $ the column vector of additive indirect (social) 466 genetic effects (IGE). " refers to direct environmental effects (DEE) and $ to indirect 467 (social) environmental effects (IEE). ! is a row of the matrix that indicates cage 468 assignment and the column vector of cage effects. 469 The joint distribution of all random effects is defined as: 470 where A is the GRM matrix and I the identity matrix. 472

473
The phenotypic covariance is: 474 When all cages have the same number of mice, as is the case in this study, the non-479 genetic random effects are not identifiable (15,60). An equivalent model can, in that 480 case, be defined as (60): 481 if ≠ and and share a cage 483 if and are in different cages 484 We checked that both model (0) and this alternative model yielded the same genetic 485 estimates and maximum likelihoods. The alternative model was fitted using the 486 SimplifNonIdableEnvs option in LIMIX(41, 61). 487 488

Aggregate contributions of DGE and IGE 489
The aggregate contributions of DGE and IGE were calculated, respectively, as 490 where is the sample variance of the corresponding covariance matrix: 492 suppose that we have a vector of random variables with covariance matrix , the 493 sample variance of is calculated as Significance of the IGE variance component was assessed using a two-degree 497 of freedom log likelihood ratio (LLR) test (for the variance component and the 498 covariance with DGE). Note that this testing procedure is conservative. The Q value 499 for the aggregate contribution of IGE was calculated for each phenotype using the R 500 package qvalue(62). Significant IGE contributions were reported at FDR < 10% 501 (corresponding to Q value < 0.1). 502 503

Correlation between DGE and IGE 504
The correlation between " and $ was calculated as: 505 We tested whether ρ was significantly different from 0 and whether |ρ| was significantly 507 different from 1 using a one-degree of freedom LLR test, which is conservative for the 508 latter test. variance, IEE explaining 16% of phenotypic variance, ) !" = -0.97, and cage effects 516 explaining 26% of phenotypic variance. These variances correspond to the median 517 value of estimates across traits with aggregate IGE and DGE > 5%. After building the 518 phenotypic covariance matrix, the sample variance of the simulations was calculated 519 and used to calculate "realised" simulation parameters from the "target" parameters 520 above. The realised parameters were used for comparison with the parameters 521 estimated from the simulations. 522 523

Definition of "social genotype" for igeGWAS 524
We assumed additive effects across cage mates and calculated the "social genotype" 525 of a mouse as the sum of the reference allele dosages of its cage mates. The same 526 assumption was made by Biscarini et al.(40) and Brinker et al.(31) among others. 527 528

Models used for igeGWAS and dgeGWAS 529
To test IGE of a particular variant in igeGWAS, we compared the following two models: 530 (1, null) 531 Here, is the vector of direct genotypes at the tested variant; hence, ! is the 533 genotype of the individual that is phenotyped (f) and ! is the sum of the genotypes 534 of the two cage mates of f. " the estimated coefficient for local DGE and $ the 535 estimated coefficient for local IGE. Note that ! could be defined as the average of the 536 genotypes of the two cage mates of f, in which case $ would be doubled but the 537 igeGWAS P values would remain unchanged. In igeGWAS, we refer to the inclusion 538 of ! " in model (1, null) as "conditioning". 539 The models were fitted using LIMIX with the covariance of the model estimated 540 only once per phenotype, in the null model with no local genetic effect (model 0). 541 The significance of local IGE was calculated by comparing models (1) and (2)  542 with a 1-degree of freedom LLR test. 543 dgeGWAS was carried out by comparing model (2) above to the null model (3) 544 below: 545 In dgeGWAS, we refer to the inclusion of ! $ in model (3, null) as "conditioning". 547 548

Identification of significant associations 549
We used a genome-wide permutation strategy to control the FDR for each phenotype, 550 as done by Nicod et al.(37). This strategy takes into account the specific patterns of 551 linkage disequilibrium present in the sample and identifies significant associations for 552 each phenotype independently of the results for the other phenotypes in the dataset. 553 More precisely, for each phenotype and for each type of genetic effect (direct and 554 indirect), we performed 100 "permuted GWAS" by permuting the rows of the matrix of 555 social (respectively direct) genotypes, and testing each variant at a time using the 556 permuted genotypes together with the un-permuted phenotypes, un-permuted 557 covariates, un-permuted GRM and un-permuted matrix of direct (respectively social) 558 genotypes (for conditioning)(41, 42). For a given P value x, the per-phenotype FDR 559 can be calculated as: 560 We reported those loci with FDR < 10%. 562 563

Definition of putative causal genes at associated loci 564
At each significantly associated locus we defined a 1.5Mb window centred on the lead 565 variant corresponding, in this sample, to the 95% confidence interval for the 566 association(37). We identified all the variants that segregate in this window based on 567 the full set of 7M variants and reran igeGWAS and dgeGWAS locally using all the 568 variants at the locus. We defined "putative causal genes" as those genes that either 569 overlapped the associated plateau or were located in direct proximity, and whose MGI 570 symbol does not start by 'Gm', 'Rik', 'Mir', 'Fam', or 'Tmem' in Supplementary Table 3 are provided in 577 locusZooms_SupplTable3.zip. 578 579

Gene expression in the hippocampus of an independent sample of CFW mice 580
Gene expression in the hippocampus of an independent sample of 79 male CFW mice, 581 initially published in Parker et al.(45), was available from GeneNetwork 582 (http://gn2.genenetwork.org/)(64, 65). The data are accessible by selecting Mouse as 583 Species, CFW Outbred GWAS as Group, Hippocampus mRNA as Type, and UCSD 584 CFW Hippocampus (Jan17) RNA-Seq Log2 Z-score as Dataset. To retrieve the genes 585 whose expression is most highly correlated with that of Epha4, we entered "Epha4" in 586 the Get Any field. Following selection of the Epha4 record (click on 587 ENSMUSG00000026235), we used Calculate Correlations with Sample r as Method, 588 UCSD CFW Hippocampus (Jan17) RNA-Seq Log2 Z-score as Database, and 589 Spearman rank as correlation Type. Supplementary Figure 6b was obtained by 590 clicking on the value of the correlation between Epha4 and Dlgap1 expression levels 591 (column Sample rho). 592 593

Variance explained by a significant association 594
The variance explained by a significant IGE association was estimated in an extension 595 of model (0) with additional fixed effects for both direct and social effects of lead SNPs 596 at all significant IGE loci (the lead SNP being the SNP with the most significant P value 597 at the locus in the igeGWAS). After fitting the model, the variance was calculated as: 598 ( ) is the sample variance of the covariance matrix in this model. 601 The variance explained by a significant DGE association was estimated in a 602 similar model but considering all significant DGE associations and 603 calculated as: 604 Phenotypes were simulated based on the real genotypes but random cages. 617 Phenotypes were simulated as the sum of random and fixed effects using the following 618 models: 619 for local DGE 620 The following parameter values were used for the random effects: Local DGE and IGE were simulated at variants with low MAF (MAF < 0.05), medium 625 MAF (0.225<MAF<0.275) or high MAF (MAF>0.45). Local IGE were simulated using 626 two alternative generative models: an "additive" model by using as in model (2) (i.e. 627 filled with 0s and 1s) or an "average" model by using 5 = 6 7 , where = 2. In all cases 628 (DGE, additive IGE and average IGE) we simullated an allelic effect of 0.2, which is 629 similar to the average allelic effect estimated in the igeGWAS. Power was calculated 630 at a genome-wide significance threshold of negative log P 5, which is similar to the 631 significance of associations detected at FDR < 10%. were then left to interact for two months before all mice were phenotyped in the forced 653 swim test (FST), sacrificed and the ears of FVB/NJ mice were collected. The sample 654 size was 52 Epha4 Het mice and 33 Epha4 WT mice for wound healing; for FST, there 655 were only 48 Epha4 Het mice as one mouse died during the FST, two mice had to be 656 separated from their cage mate due to fighting in the days before the FST (but their 657 ears were still collected as this did not significantly change the healing time), and the 658 battery of the camera recording the FST ran out during the FST of the fourth mouse. 659 A small subset of mice were video recorded in a new enclosure for 24h a few days 660 before the FST but the data from this pilot project are not reported here. Throughout 661 the experiment all mice were housed on a 12h:12h light-dark cycle, with lights on at 662 06:00, and all behavioural testing occurred during the light phase of the light-dark 663 cycle. 664 665 Forced swim test 666 Following the same protocol as in the CFW study(37), mice were tested in the forced 667 swim test: they were placed for 6 minutes in 6'' wide x 12'' tall glass buckets filed with 668 water at 24-26°C. Mice were video recorded from the side and their immobility during 669 the first 2 and last 4 minutes of the test was scored by an observer blind to the 670 genotypes of the black (Epha4 and Dlgap1) mice. The analysis of IGE focused on 671 immobility of FVB mice in the last four minutes of the test as FVB mice are rarely 672 immobile during the first two minutes of the test. 673

674
Healing from an ear punch 675 Both ears of FVB/NJ mice were punched with a 2mm-diameter ear punch scissor just 676 before the mice were paired with an Epha4 or a Dlgap1 cage mate at weaning. 677 Following the same protocol as in the CFW study(37), the ears were collected two 678 months later after sacrifice, stored in 10% buffered formalin phosphate until analysis. 679 To measure the area of the hole, each ear was mounted on an histology slide and 680 photos were taken from a fixed distance. Images were analysed with the ImageJ 681 software(67) and the average across the two ears calculated.

Ethics approval 705
All animal procedures were approved by the Institutional Animal Care and Use 706 Committee of the University of California San Diego (UCSD) and were conducted in 707 accordance with the NIH Guide for the Care and Use of Laboratory Animals. 708 for generously providing mice from the EphA4 knockout line, which was produced 735 thanks to funding from NIH grant NS087070. 736