Under some parameter combinations, preferential mating increased the heritability of the preferred trait, providing a possible resolution for the lek paradox. The Kirkpatrick–Barton approximation for rG proved to be biased downward, but the realized genetic correlations were also low, generally <0.2. Such low values of rG indicate that coevolution of the preference and preferred trait is likely to be very slow and subject to significant stochastic variation. Lande's model accurately predicted the incidence of runaway selection in the simulations, except where preferences were relative and the preferred trait was subject to natural selection. In these cases, runaways were over- or underestimated, depending on the number of males sampled. We conclude that rapid coevolution of preferences and preferred traits is unlikely in natural populations, but that the parameter combinations most conducive to it are most likely to occur in lekking species.This article extends and adds more realism to Lande's analytical model for evolution under mate choice by using individual-based simulations in which females sample a finite number of males and the genetic architecture of the preference and preferred trait evolves. The simulations show that the equilibrium heritabilities of the preference and preferred trait and the genetic correlation between them ( Prum  termed trG is the genetic correlation, rP is the phenotypic correlation between them. The Kirkpatrick and Barton estimate, hereafter designated rKB, sets an upper limit of 0.5 for the genetic correlation and in most cases the genetic correlation is likely to be much lower, suggesting that the coevolution of preference and preferred trait may be a very lengthy process.Lande  worked oA critical assumption of the null model as presented in Lande's analysis is that selection is sufficiently weak that the heritabilities of the two traits remain constant, with losses of additive genetic variance due to selection being replaced by mutation. This assumption is unlikely to be true under realistic scenarios of preferential mating because mate choice would be expected to exert significant selection on the preferred trait, potentially reducing trait heritability. In addition, as a form of assortative mating, preferential mating has the potential to either reduce or inflate the heritability of the preferred trait. Hayashi  showed tThe degree to which the heritabilities of the preference and preferred trait and the genetic correlation between them are affected by preferential mating will be influenced by the number of males each female can potentially survey before making her choice. Lande's model represents the extreme in which each female can survey the entire male population  and mates with a given male with a probability specified by the preference function. However, if females must chose their mates based on only a small sample of males, realized mating will more closely resemble random mating. The strength of selection through mate choice will therefore be low, the heritabilities should remain close to those expected under random mating, and little genetic correlation is likely to build up due to linkage disequilibrium.In this article, we extend and add more realism to Lande's model, and hence to the null model of evolution by sexual selection Prum , using iAre the equilibrium heritabilities and genetic correlation influenced by the initial model parameters?Does Lande's analytical model accurately predict the quantitative genetic combinations that lead to Fisher's runaway process?rKB approximation predict the equilibrium genetic correlation?How well does the x for parameters referring to preference and y for those referring to the preferred trait and, for simplicity we assume that females are the choosy sex. We assume a diploid organism in which the two traits are each equal to the sum of the effects of 100 unlinked loci with no loci affecting both traits  plus an environmental effect. The genes for both traits occur in both sexes but each is phenotypically expressed only in one sex. Genetic values at each locus of the preferred trait in the starting population were drawn from a normal distribution with a mean of zero and a variance of 1. Because the variance in mating preference relative to that of the preferred trait is predicted to affect the heritability of the latter trait, we varied the genetic variance at the preference loci from 0.1 to 4.0. The per locus ratio of additive genetic variance in preference to additive genetic variance in preferred trait is the genotypic ratio, which we designate as Gratio.Definitions and acronyms for all model parameters are given in Table r signifies that these are the heritabilities sustained under random mating) and the heritabilities resulting from preferential mating simply as To distinguish the initial heritabilities from the heritabilities that evolve during a simulation we designate the initial heritabilities as in Reeve  . As in Lande's model, stabilizing natural selection on males is determined by a Gaussian function. We considered two selection regimes, very weak and strong selection P (y|x), where y is the male trait value and x is the female preference trait value. However, it seems unlikely that a female in a large population actually has access to all the males in the population. A survey of studies in which the number of males surveyed has been estimated shows that on average females sample <5 males before making their choice (N), with a probability P (y|x) of mating with each male encountered. Each female mated with only one male and if no male was accepted after N males had been examined, the female chose the male with the highest probability of being accepted from within her set of N males. We call this mode of mate choice the “sequential/best male” (SE/BM) mode to indicate that the female samples males sequentially (SE) and that her default, if no males are chosen on first pass, is to choose the best male from those already sampled. It is important to note here that N is the maximum number of males a female can sample before making a choice, not the average number of males sampled before the choice is made  a given male with a probability N males prior to making her choice and then selects the male that most closely approximates her preference. We label this the “simultaneous/best male” (SI/BM) mode because the female compares all surveyed males before making her choice, which is equivalent to simultaneous sampling ) as a normally distributed function, using the absolute and relative preference functions  described by Lande. The AP function is simpler in having one less parameter, the probability of a female preferring a male whose trait value (y) matches her preference (x) being,We model female preference  so that we could examine the evolution of genetic architecture due to female preference alone rather than due to the combined effect of female preference and directional selection induced by stabilizing natural selection on the males. The initial values of these parameters have no effect on the genetic architecture at equilibrium  and high values of Gratio . The heritabilities of the preference and preferred trait  shows little change, remaining quite close to the initial value, Gratio (bottom row) and its behavior is complex in that it may be either depressed or elevated relative to that under random mating (Gratio > 1) and reduced when the reverse occurs.We first consider the AP model without natural selection and with the SE/BM mode of mate choice Fig. . Our simPratio was twice Gratio. To determine if the initial heritabilities influence the genetic correlation at equilibrium and whether Pratio has an effect independent of Gratio, we examined the results from simulation set 2. Stepwise regression with the equilibrium genetic correlation as the dependent variable and the parameters Gratio, Pratio, ν, N, and their interactions as independent variables produced a highly significant model  that accounted for 90.4% of the variance in the equilibrium genetic correlations. Neither the heritability of preference  and when separate regressions were done for each category of number of males , which suggests an overall positive relationship between the initial heritability for the preferred trait and the resulting equilibrium correlations. This second set of simulations also confirms that the genetic correlation increased overall with Gratio  and indicates that the Pratio does not have a significant independent effect.In the set 1 simulations, the initial heritabilities were set at To determine if stabilizing natural selection on males affects the equilibrium correlations and heritabilites, we plotted the equilibrium parameter values with selection against those without selection for each combination of initial parameter values in the AP model Fig. . StabiliFor most parameter combinations, stabilizing natural selection on males had little influence on the heritability of preference, which tended to remain at or close to its random mating value 0.2). However, a few parameter combinations did give rise to very high heritabilities in the absence of selection, and in these cases natural selection reduced the heritabilities to close to 0.2. The heritability of the preferred trait was more uniformly reduced in the presence of natural selection, with the greatest reduction occurring at intermediate heritabilities  function with the SE/BM mode of mate choice. To assess the impact of type of preference function, we compared the equilibrium parameter values generated by the two preference functions in the absence of natural selection on males Fig. . AnalogoN = 5 or 20, the break point occurs when the phenotypic correlations reach approximately 0.2, after which the correlations in the RP model decline and then plateau at much lower values than those from the AP model. With N = 100 the phenotypic correlations increase in step with each other until about 0.5, after which the phenotypic correlations in the RP plateau and become consistently less than those from the AP model. In all cases, the global tendency is for the maximum phenotypic correlations generated to be much lower for RP model than for the AP model.The two preference functions produced strikingly disparate results. In the RP model, the genetic correlation was uniformly at or close to zero. With respect to the phenotypic correlation there appears to be a break point, with correlations being the same for both models at lower values but becoming divergent thereafter Fig. . With N N = 20 and 100. The heritability of the preferred trait is uniformly low in the RP model with the values that rank inversely with N  causing an increased deviation in the SI/BM mode and a decreased deviation in the SE/LM mode  and the genetic parameter values generated in the simulations each generation  into the predictive equations. We then determined if runaway selection was predicted for each generation from 100 through 10,000, scoring the result as 1.0 if yes and 0 if no. The scores were then averaged over all generations to estimate the probability of runaway selection, Prunaway, for that run.We derived the predicted line of equilibria and the conditions for runaway selection from Lande's analysis  and testPrunaway = 0.0 in all runs). To determine if this prediction was accurate, we computed the predicted equilibrium values of Runaway selection was not predicted for any of the simulations using the AP model . The regression approach used for the AP model could not be used to test this prediction because the predicted value of ω is infinitely large (For the relative preference (RP) model, the predicted outcome depended on whether or not the preferred trait was subject to natural selection. Without natural selection runaway selection was predicted for all generations in all runs , runaway was consistently predicted for 5.6% of combinations (Prunaway = 1.0), and 18.8% of combinations were indeterminate in that Prunaway varied from 0.01 to 0.99. If we assume that Prunaway > 0.5 predicts runaway, 16.7% of combinations were predicted to produce runaway selection. For N = 5, runaway selection was predicted when the females were most choosy , but we did not observe runaway selection for any combination; the average change in N = 5, the runaway process was less common than predicted. In contrast, when N = 20 or 100 runaway was much more common than predicted. A runaway process was predicted for only 15% of combinations, again mainly when females were very choosy (ν = 10 [eight cases] or 20 [two cases]), but runaway was observed in all cases. The value of x in the RP model is the female preference expressed as a deviation from the mean of the preferred trait in the sampled males [y*]. Thus, it is possible for y*] while When natural selection on the preferred trait was added to the RP model, the predictions were more mixed: stable equilibria were consistently predicted for 75.6% of the combinations  for low values but the two progressively deviate, with rGobs eventually exceeding rKB  as the response variable and rGobs as the predictor variable. Initially we included presence or absence of natural selection as a covariate, but the effect of selection was not significant  and so it was dropped from the model. The model with only rGobs as a predictor variable was highly significant  and indicates that rKB underestimates the genetic correlation from the AP model when rGobs exceeds 0.1 , indicating that the type of preference function does influence the probability that rGobs will exceed rKB. , but was slightly negative and not significant for the RP model . Thus, for the RP model, the probability that the rKB will underestimate the observed genetic correlation is independent of, or only weakly related to, rGobs, while for the AP model this relationship is strong and positive.We next tested if the type of preference function (AP or RP) was a significant predictor in addition to rGobs was again considerably underestimated at higher genetic correlations and overestimated at low genetic correlations  on log (rKB), with N, ν, Gratio, and their interactions as possible covariates. The final model was highly significant and included all these variables plus several interactions . Stepwise logistic regression retained rGobs,ν, Gratio, and a number of interaction terms but not N. The effect of Gratio is evident from the top four panels in Figure rGobs exceeded rKB on rGobs is highly significant  and indicates a switch from overestimation to underestimation of rGobs at around 0.1 predominantly due to the higher values of Gratio  the genetic correlation evolved to more extreme values in our simulations than predicted by the rKB estimator, but if the Gratio was <1, the theoretical prediction tended to overestimate the genetic correlation at equilibrium.In the set 2 simulations, which were based on the AP model, ons Fig. . Becauseatio Fig . OverallGratio), and the maximum number of males sampled (N), with maximum correlations evolving when males were not subject to natural selection , and females were very choosy (ν is low), had absolute rather than relative preferences, and were able to compare all of their potential mates before making their choice (the SI/BM mode of mate choice).Our simulations reveal that the genetic correlation between the preference and preferred trait is sensitive to most, but not all, of the model components. Although robust to changes in the initial ratio of phenotypic variances and the heritability of preference, the equilibrium correlation was strongly affected by all aspects of the mating system , by the presence or absence of natural selection on the preferred trait, and by several components of the initial genetic architecture (the ratio of genetic variances and heritability of the preferred trait). It tended to increase with the initial heritability of the preferred trait , the simulations produced much higher correlations. In the extreme, if individual females are very choosy (ν< 20), the genetic variance of the preference greatly exceeds that of the preferred trait (Gratio > 2), and females are each able to sample 100 males, the genetic correlation between preference and preferred trait can approach unity. However, this combination of variables is highly unlikely to occur. Much more modest genetic correlations prevail if females sample 20 or fewer males. The highest correlations were generated by the SI/BM mode of mate choice with the absolute preference function and no natural selection on males, but the vast majority (>87%) of combinations in those runs still produced genetic correlations <0.2.The maximum equilibrium genetic correlations were generally <0.20 and were much smaller than this over most of the parameter space. However, when Gratio), and by the presence or absence of natural selection on the preferred trait. As we predicted, the heritabilities of both the preferred trait and the preference could be inflated by preferential mating, the effect of preferential mating depending upon both Gratio and female choosiness. The latter parameter is important as it governs the width of the preference function and hence the extent to which females favor males in the tail of the distribution of the preferred trait. If the additive genetic variance in preference exceeds the additive genetic variance in the preferred trait  and females are very choosy  then females at the tails of the preference distribution will choose males that lie at the extremes of the distribution of the preferred trait, thereby increasing the additive genetic variance in the preferred trait and its heritability. While both heritabilities increase dramatically if females are very choosy and the genetic variance for the preference greatly exceeds that for the preferred trait, the heritability of the preferred trait is much more sensitive to these parameters than the heritability of preference. Whereas the latter increases only at very high values of Gratio and low values of ν, the heritability of the preferred trait varies over the full range of parameter values and is particularly sensitive to Gratio. If the initial genetic variance for preference exceeds that for the preferred trait (Gratio > 1), preferential mating tends to increase the heritability of the preferred trait, but if Gratio < 1, the heritability is reduced. These results lead to the conjecture that the effects of preferential mating on genetic architecture may provide a partial resolution for the lek paradox. Specifically, in populations where Gratio > 1, females are very choosy, and females are able to sample 20 or more males, preferential mating could maintain high heritabilities for preferred traits in spite of strong sexual selection on those traits.The equilibrium heritabilities for the preference and the preferred trait were also sensitive to many of the model components, both being affected by aspects of the mating system , and the initial genetic architecture (N = 200). Their analysis was based on the RP model and, as shown here, the equilibrium heritabilities and genetic correlations under this model may be very low even in a very large population. Thus, the effects of the preference function and population size on response to selection are confounded, since both will tend to decouple the preference and the preferred trait and reduce response to selection.The type of preference function  also plays a highly significant role in the evolution of the heritabilities and the genetic correlation. In the absence of stabilizing natural selection on the males, the genetic correlation under the RP model never increases beyond 0.02, whereas under the AP model it can approach unity. Similarly, the heritability of the preferred trait rarely rises above 0.1 under the RP model whereas under the AP model it spans the range from 0.1 to 1. The heritability of preference under the AP model remains close to its initial value but under the RP model it varies from this value down to zero. These results call into question the conclusion of Nichols and Butlin  that theN = 20 or 100), the RP model is unstable because the mean of the preferred trait is continually pushed farther from its natural selection optimum. In our simulations, this causes increasing mortality of males until none survive to mate with the females and the population goes extinct. This result likely reflects a deficiency in the classic model rather than biological reality. The model includes no cost to female choice in terms of inability to find a suitable male or the energetic, time and survival costs of mate searching. We would expect that in natural populations such costs  would increase as preferred males become increasingly rare, eventually stopping the runaway process and resulting in an equilibrium genetic architecture.If the preferred trait is under the stabilizing selection and females are able to sample large numbers of males before making their choice . These predictions were not confirmed by our simulation results. When females were able to sample only a small number of potential mates (N = 5), Lande's model overestimated the incidence of runaway selection, as we found stable equilibria for all parameter combinations. In contrast, the model greatly underestimated the incidence of runaway selection for N = 20 and 100. Runaway was never predicted for these parameter combinations but occurred in all of our simulations. This had the unfortunate consequence of causing rapid extinction of the populations because of high male mortality. Population extinction cannot occur in an infinite population, as assumed by Lande's model, but our results indicate that it would be a risk in finite populations.The line of stable equilibria generated under the AP model was well predicted by Lande's model , and theN = 5), but greatly underestimated if females can sample 20 or more males. In the latter case, the runaway process is likely to be of short duration and associated with rapid population decline because males suffer increasing mortality as the preferred trait moves ever further from its natural selection optimum.In summary, our simulations confirm Lande's predictions that runaway selection should not occur if females have absolute preferences, regardless of the strength of natural selection on the preferred trait, but is expected if female preferences are relative and the preferred trait is not subject to natural selection. However, the model fails when preferences are relative and the preferred trait is subject to natural selection. Under those parameter combinations, the incidence of runaway is overestimated if females can survey relative few males before making their choice . In addition, whereas the maximum value that can be taken by rKB is 0.5, our realized genetic correlations greatly exceeded this maximum when the Gratio was >4 and females were both very choosy and able to sample 100 males. These parameter values are probably unrealistic, but nevertheless the simulations reveal the potential for evolution of much higher genetic correlations than previously thought.The KB estimator deviated markedly from the genetic correlations generated by our simulations and, in particular, tended to underestimate the equilibrium genetic correlation when Our simulations also reveal that, contrary to expectations, the accuracy of the KB estimator does depend on the female preference function. In their 1997 paper, Kirpatrick and Barton state that the approximation x was normally distributed in the population. These are difficult assumptions to validate in real organisms. It is important to distinguish between the individual preference functions ))x was noGryllus texensis , but they also include much higher values and even negative values in the case of the collared flycatcher. Unfortunately, such imprecise estimates are not informative with respect to testing out our prediction that correlations >0.2 should be rare.Our simulations demonstrated that the magnitude of the genetic correlation that can be generated by preferential mating generally increases with the number of males sampled by each female. Empirical estimates Table  indicate(Gratio> 1) and females are choosy , the heritability of the preferred trait will be inflated relative to that maintained under random mating. Our results also indicate that the critical ratio is that between the additive genetic variances rather than the phenotypic variances. Unhappily, whereas we have estimates for the phenotypic variances ratios in four species (1.0–1.1 for the collared flycatcher (Qvarnstrom et al. Colias eurytheme (Sappington and Taylor Gratio = 0.11, which our simulations suggest would generate a very low genetic correlation. This is consistent with the estimated genetic correlation between mate choice and the preferred trait of −0.015 ± 0.169 in this species (Qvarnstrom et al. Gratio. Given these problems, it is not possible to truly evaluate whether or not the results of this study are consistent with our model predictions.As a prelude to our simulations, we advanced the hypothesis that preferential mating will increase the heritability of the preferred trait if the initial genetic variance of the preference exceeds that of the preferred trait. Under this hypothesis, preferential mating may at least partially explain the unexpectedly high heritabilities often observed for preferred traits in natural populations. The simulations support this hypothesis in showing that if the additive genetic variance of the preference trait exceeds that of the preferred trait Our review of the available empirical estimates has revealed the difficulties inherent in testing the null model of evolution by sexual selection Prum  as formu


In psychiatric genetics research, the volume of ambivalent findings on gene-environment interactions (G x E) is growing at an accelerating pace. In response to the surging suspicions of systematic distortion, we challenge the notion of chance capitalization as a possible contributor. Beyond qualifying multiple testing as a mere methodological issue that, if uncorrected, leads to chance capitalization, we advance towards illustrating the potential benefits of multiple tests in understanding equivocal evidence in genetics literature.HTTLPR) and childhood adversities with regard to depression. After testing 2160 interactions with all relevant measures available within the Dutch population study of adolescents TRAILS, we calculated percentages of significant (p < .05) effects for several subsets of regressions. Using chance capitalization  as a competing hypothesis, we expected more significant effects in the subsets of regressions involving: 1) interview-based instead of questionnaire-based measures; 2) abuse instead of milder childhood adversities; and 3) early instead of later adversities. Furthermore, we expected equal significance percentages across 4) male and female subsamples, and 5) various genotypic models of 5-HTTLPR.We focused on the interaction between the serotonin-transporter-linked promotor region (5-We found differences in the percentages of significant interactions among the subsets of analyses, including those regarding sex-specific subsamples and genetic modeling, but often in unexpected directions. Overall, the percentage of significant interactions was 7.9% which is only slightly above the 5% that might be expected based on chance.Taken together, multiple testing provides a novel approach to better understand equivocal evidence on G x E, showing that methodological differences across studies are a likely reason for heterogeneity in findings - but chance capitalization is at least equally plausible. In psychiatric genetics, the volume of studies examining gene-environment interactions (G x E) is increasing at an accelerating pace . Nonethe15 ≈ 0.54; see, for example: [Ideally, a hypothesis reflects an a priori expectation and the variables involved are operationalized in a single, best possible, way. Subsequently, the test result indicates whether or not the null hypothesis should be rejected. In practice, however, this process usually takes a different form ,8,9. In example: ).Consistent lines of evidence are essential for understanding G x E pathways to psychiatric disorders and advancing the field, but career benefits of reporting significant findings make it conceivable that published associations reflect a non-representative selection of all tests conducted ,9. Impor5-HTTLPR) and childhood adversities with regard to depression. After Caspi and colleagues [5-HTTLPR short allele, studies exploring this interplay rapidly accumulated. Similar to other genotypes in psychiatric genetics research, however, the original findings of Caspi and colleagues [This more transparent approach will be illustrated using the interaction between the serotonin-transporter-linked promotor region ..5-HTTLPR5-HTTLPR genotype encompasses a short (S) allele and a long (L) allele variant, which can be modeled in various ways, each based on a different assumption on the relative risk associated with the allelic combinations. Whereas the additive genetic model assumes that the risk increases linearly with the number of S alleles, the dominant model assumes that carriers of the S-alleles have equal risks, regardless of whether their genotype is hetero- or homozygous, and the co-dominant model allows any association pattern without a priori assumptions. Furthermore, in addition to the traditional, so-called biallelic approach of modeling, a triallelic approach has become increasingly popular. The triallelic approach is based on the notion that the L allele is functionally equivalent to the S allele in the presence of the g allele variant of the Single Nucleotide Polymorphisms (SNP) rs25531 . Whereadetails: ,28,30,31ications –34.In response to suspicions of publication bias among many, and inspiring findings by a few e.g. ,35–38), –38, 35–35-HTTLPR and childhood adversities in more than 5% of the analyses, and especially in the subsets involving: 1) measures based on structured interviews instead of self-report questionnaires; 2) measures of abuse instead of milder childhood adversities; and 3) measures of early adversities instead of those experienced at a later age. Furthermore, we expected the percentages of significant effects to be equal across 4) sex and 5) varying genetic models of 5-HTTLPR. Absence of meaningful association patterns, with randomly distributed significant effects in, on average, approximately 5% of the analyses, were considered support for publication bias in favor of false positive findings as an explanation for the inconsistent findings reported in the literature [Using chance capitalization as the competing hypothesis, we expected a significant interaction between terature .The data were collected as part of the TRacking Adolescents’ Individual Lives Survey (TRAILS), a prospective cohort study of Dutch adolescents ,40. FiveSD = 0.6, 51% girls) [N = 2149, mean age 13.6, SD = 0.5, 51% girls) participated at T2. The response rates at T3 and T4 were, respectively, 81%  and 83% . The data collection included, among many other things, self-report and parent-report questionnaires, a psychiatric diagnostic interview, and a life stress interview.At T1, 2230 (pre-)adolescents were enrolled in the study  , of whom1, α = .68; YSR1 α = .77), T2  and T3 . In addition to the scores for each assessment wave separately, we calculated the mean over these three time points, labeled as CBCLmean and YSRmean, respectively.Depressive symptoms were assessed using three different instruments, which yielded nine measures in total  was assPPRISKS) were assessed at T1 in an interview with one of the parents, usually the mother, and included questions about maternal prenatal smoking, maternal prenatal alcohol use, birth weight, gestational age, and pregnancy and delivery complications. Maternal prenatal smoking was coded as follows: 0 = no smoking; 1 = 10 cigarettes a day or less; 2 = more than 10 cigarettes a day. Maternal prenatal alcohol use was coded as follows: 0 = no alcohol use, 1 = up to three glasses per week, 2 = four glasses per week or more. Birth weight was coded as 0 = normal birth weight and 1 = either low  or high  birth weight. Gestational age was recoded into two groups: 0 = normal (between 34 and 42 weeks) and 1 = abnormal . Pregnancy and delivery complications were coded as 0 = no complications; 1 = between one and four complications; 2 = five or more complications. The index of pre- and perinatal risks was composed by adding the scores of these variables.Exposure to childhood adversities was operationalized in ten different ways  reflects stressful events that occurred before T1, and was also assessed at the T1 parent interview. The variable was created by summing the following events: severe  disease of father or mother; severe illness (life-threatening or threat of serious permanent effects) of a sibling; death of a household member; parental divorce; and absence from home for three months or longer.‘Long term difficulties’ (LTD) were assessed with a questionnaire completed by parents at T2, and reflects the sum score of the following difficulties: chronic disease or handicap of the participant, chronic disease or handicap of a household member, being bullied, long-lasting conflicts with a household member, and long-lasting conflicts with someone else, all experienced before T1.parent0-5STRESS and self0-5STRESS) and from age six to age eleven (parent6-11STRESS and self6-11STRESS). Parents were asked ‘How stressful was your child’s life in this life phase?’, and the participants ‘How many stressful events did you experience in this period?’ The stressfulness was rated on an 11-point scale, ranging from 0 = not at all to 10 = very much.Four measures involved subjective ratings of the stressfulness of the participants’ lives during early and later childhood. These were assessed at T2 using parent- and self-reported ratings of the overall stressfulness of the child’s life before the age of five  was measured by five questions ranging from screaming to threatening and physical abuse  by six questions ranging from being hit to being beaten up; the occurrence of which could be rated as 1 = no, never; 2 = yes, one or two times; 3 = sometimes; 4 = often; 5 = very often. Sexual abuse (sexABUSE) was based on a list of five unwanted sexual acts by an adult family member, friend of the family or stranger, ranging from touching to sexual intercourse, the occurrence of which could be rated as 1 = never happened to me, 2 = happened once, or 3 = happened several times. The abuse measures reflect the mean of the ratings.Three measures represented traumatic youth experiences before the age of sixteen years, as reported retrospectively by the adolescents at T4, with questions based on the Childhood Trauma Questionnaire . Verbal5-HTTLPR) were genotyped as described by Nederhof and colleagues [DNA was obtained at T3 through a manual salting out procedure using either blood samples or buccal swabs, as delineated in detail by Miller, Dykes, and Polesky . The lenlleagues .5-HTTLPR polymorphism was modeled in an additive, dominant and co-dominant way, which, combined with the biallelic and triallelic approach, yielded six different ways to operationalize genetic risk. In the additive genetic model, the risk associated with the LS genotype was coded as being half the size as the risk associated with the SS genotype, as compared to the LL genotype . In the S dominant model, the risk associated with the of SL and SS genotype was modeled as being equal to each other . In the co-dominant model, the risk associated with SS and LS was estimated using separate dummies, with LL serving as the reference group for both . These three genetic models were constructed using both the biallelic approach and the triallelic approach. In the latter case, the L allele was recoded into an S allele in the presence of ag allele of SNP rs25531 (Lg = S). For an overview of 5-HTTLPR coding in regression models per genetic model, see  and logistic regression (for binary outcomes) in SPSS , and one of the depression measures as outcome variable. We were primarily interested in the interaction between the childhood adversity and the 5-HTTLPR measure.We tested a total of 2160 interaction effects between sion 21; ). The tep < .05) interaction effects by the total number of interaction effects tested, and multiplying this proportion by 100. Because the tests could be considered neither independent observations nor repeated observations, formal testing of the hypothesis that the percentage of significant interactions (in a given subset) exceeded chance level  was not possible. Nevertheless, to provide a guideline to determine which percentage can be considered indicative of a real interaction effect we calculated a confidence interval around 5%.In order to explore our hypotheses, we calculated the percentage of significant findings for subsets of regression analyses, by dividing the number of statistically significant , corresponding with a 7.9% overall significance rate. When ignoring the analyses regarding early versus late adversities (because these were nested within the subset of mild stressors), two subsets of analyses generated a percentage of significant interaction that exceeded the preset criterion for substantial elevation above chance level (8%), whereas two others yielded a percentage of significant interactions that was substantially below what might be expected on chance (< 2%). parent0-5STRESS; parent6-11STRESS), and parent-reported depressive symptoms (CBCL), seem to yield the highest number of significant interaction effects with 5-HTTLPR.Overall, from the 2160 number of interaction effects tested, 171 were significant . Ioannidis  postulatWith regard to the quality of assessments, we expected more significant interaction effects in analyses involving interview-based than in analyses involving questionnaire-based measures, but found the opposite pattern. Questionnaire-based measures, although assumed to be less reliable than structured face-to-face interviews assessed by trained interviewers , might tThe significance rates in analyses that differed with respect to the severity of the childhood adversities were also contrary to what we expected based on prior findings, which suggest a higher probability of significance in case of severe adversities such as abuse ,18. Our 5-HTTLPR.While it has been proposed that adversities experienced at an early age have more developmental impact than those experienced later in childhood ,20,24, t5-HTTLPR on serotonergic neurotransmission possibly explain differences between males and females [5-HTTLPR, childhood adversity and (pre)adolescent depression.We found differences in significance rates as a function of sex. Although effects of  females , only fe females ,25,28. G females . The absFinally, and again contrary to what we expected a priori, different genetic models yielded varying percentages of significance, and the biallelic approach seemed to yield more significant interactions than the triallelic approach. However, none of the genetic models yielded significance rates that substantially exceeded the a priori set criterion of 8%, so our study does not provide enough evidence to abolish the notion that the choice of genetic model does not influence the probability of significance ,28,31.5-HTTLPR with regard to depressive symptoms. The alternative hypothesis postulated chance capitalization to explain heterogeneity in findings [As described above, we explored the consequences of a number of methodological differences among studies that have been proposed to explain inconsistencies in the field of G x E research, in this case the interaction of childhood adversities and findings . In ordeIn some analyses, the percentage of significant interactions exceeded the threshold of 8%, but in others the significance rate found was lower than 5%. In other words, the percentages were somewhat randomly distributed around chance level. Moreover, the characteristics of the analyses that yielded relatively high significance rates did not correspond to what was expected in advance, which further support the idea of random fluctuations.In line with earlier findings , our resOur study has various strengths. First and foremost, we are among the first to provide a transparent overview of the many possible ways to operationalize a specific gene-environment interaction within a single cohort study and to actually test all these interactions in order to explore ways to deal with scientific threats like multiple testing and selective reporting. Beyond qualifying multiple testing as a mere methodological issue that can lead to chance capitalization, we illustrate the potential benefits of multiple tests in understanding ambivalence in the psychiatric genetics literature. A second strength is that our interaction tests were each based on a relatively large number of individuals, offering reasonable power and accuracy—at least for the total sample. That is, while part of the gender-specific regression analyses may have been underpowered because some outcome variables were dichotomous and main effects sizes for G and E depend on the variables used, the analyses using the total sample were sufficiently powered.5-HTTLPR. Although threats like multiple testing and selective reporting are likely equal within G x E research, the extent to which chance capitalization contributes to equivocal evidence may differ across genotypes. Second, we relied on a fairly large number of questionnaire-based measures and only few interview-based measures. Moreover, of the three interview-based measures, CIDI and CE may be less powered than continuous questionnaire-based measures. Therefore, replication of these findings in studies with other and preferably more (continuous) interview-based measures is needed.The study is also limited in a number of respects. First, we illustrated the possible role of chance capitalization by using Taken together, our results demonstrate the need for caution in interpreting findings from datasets with comparable measures of the same construct. Obvious career benefits of reporting significant findings over null findings and easy access to comparable measures within one dataset may lead to overpublication of false positive findings. Hence, it is likely that chance capitalization explains at least partly the large number of inconsistencies in G x E research.Large cohort studies could play a major role in paving ways towards more consistent G x E findings in future research. The availability of multiple operationalizations of single factors, now often disregarded or even suspected as source of selective reporting, could be turned into a major advantage if researchers reported all options tried, rather than a biased selection. This way, we can move beyond the statement that “most research findings are false”, towards a novel approach: critically discussing the range of available measures within each study to evaluate the plausibility of findings, given the likelihood of chance capitalization.S1 Table(DOCX)Click here for additional data file.


Extensive genetic studies have identified a large number of causal genetic variations in many human phenotypes; however, these could not completely explain heritability in complex diseases. Some researchers have proposed that the “missing heritability” may be attributable to gene–gene and gene–environment interactions. Because there are billions of potential interaction combinations, the statistical power of a single study is often ineffective in detecting these interactions. Meta-analysis is a common method of increasing detection power; however, accessing individual data could be difficult. This study presents a simple method that employs aggregated summary values from a “case” group to detect these specific interactions that based on rare disease and independence assumptions. However, these assumptions, particularly the rare disease assumption, may be violated in real situations; therefore, this study further investigated the robustness of our proposed method when it violates the assumptions. In conclusion, we observed that the rare disease assumption is relatively nonessential, whereas the independence assumption is an essential component. Because single nucleotide polymorphisms (SNPs) are often unrelated to environmental factors and SNPs on other chromosomes, researchers should use this method to investigate gene–gene and gene–environment interactions when they are unable to obtain detailed individual patient data. Extensive genetic studies have identified a large number of causal genetic variations in many phenotypes; however, these could not completely explain the phenomenon of heritability in complex phenotypes . PreviouMeta-analysis is a commonly used method for increasing detection power, and a subgroup analysis also could be used to detect the effects of interactions. Meta-analysis using individual patient data is considered the gold standard for investigating the moderator effect of participant-type variables ,6; howevWe hereby propose a simple method for detecting the effects of interactions in a meta-analysis of a case-control study. We have applied this method to an earlier study . HoweverMost genetic association studies utilize a case-control design, in which the association between the aggregated summary values of the factor and odd ratios was based on multiple factors. To better understand this principle, we hereby describe an example. In this example, the moderator can be not only factors of environment but also gene. That is a moderator implies any kind of covariates. This did not impact the results of derivation.E1, E2, E3, and E4 in the population are the minor allele frequencies among the case women, case men, control women, and control men, respectively; these were based on seven population parameters, and their relationships are presented in the When the independent variable is an allele encoded with values of “minor allele” or “major allele” and the moderator is gender-encoded with values of “male” or “female,” the variables k1) and control group (k2):Based on these definitions, when a researcher conducts a case-control study, the expectation of a simple combined OR is affected by the proportion of males in the case group  rare disease and (2) independence (there was no association between the factor of interest and the major independent variable), and ulations . TherefoORwomen ≠ ORmen), the proportion of males in the case group (k1) is the only factor that could affect the ORcombine. Researchers often perform a meta-regression to describe the association between the proportion of males and ORcombine.When moderator effects are present ], and we denote ηi as the residuals representing the unexplained errors of the reported yi] as follows:A typical single moderator equation of meta-regression (fixed-effect model) is shown in mi is an unknown vector witch let mi is calculated using mi, b0 is considered to be the log(ORwomen), and b1 is considered the logarithmic moderator effect of gender [log(ORmen) − log(ORwomen)]  is satisfied ], the proportion of moderator in the “case” group, residuals representing the unexplained errors of the reported yi from each study, respectively. Following above setting, the b0 and b1 are log(ORpeople without moderator), moderator effect, respectively. In this method, the coefficient of b1 can be represented the interaction between focus SNP and the moderator, such as gene-gene and gene-environment interactions. This could be employed to detect gene-gene interactions when k1i is the minor allele frequency of another SNP and detect gene-environment interactions when k1i is the proportion of environment exposure in the "case group."Where, the k1i) could be employed to build the meta-regression model, and the b0, b1 are log(ORpeople without moderator), moderator effect, respectively. The detailed calculated method of above coefficients and their variance were shown in Following k1i is the minor allele frequency of another SNP and detect gene–environment interactions when k1i is the proportion of environment exposure in the “case group.”This could be employed to detect gene–gene interactions when Individual patient data regression analysis is the gold standard in analyzing pooled data . HoweverP1, P2, P3, P4, P5, and P6 indicate the disease prevalence among people with homozygous major without moderator [p(D = 1|x1 = 0∩x2 = 0)], people with homozygous major with moderator [p(D = 1|x1 = 0∩x2 = 1)], people with heterozygous genotype without moderator [p(D = 1|x1 = 1∩x2 = 0)], people with heterozygous genotype with moderator [p(D = 1|x1 = 1∩x2 = 1)], people with homozygous minor without moderator [p(D = 1|x1 = 2∩x2 = 0)], and people with homozygous minor with moderator [p(D = 1|x1 = 2∩x2 = 1)], respectively. The symbol πi denotes the minor allele frequency in each study population, and P7, P8, and P9 are the proportions of moderator status in people with homozygous major [p(x2 = 1|x1 = 0)], people with heterozygous genotype [p(x2 = 1|x1 = 1)], and people with homozygous minor [p(x2 = 1|x1 = 2)], respectively. D = disease status . x1 = SNP . x2 = moderator .Ten population parameters could be employed to describe the association between a disease, single nucleotide polymorphism (SNP), and moderator. The symbols x2 can the genetic factor or environmental factor. The first step in generating simulation data is to set the parameters of the population. We assume that the moderator effect of the specific moderator is a fixed effect, and the association between SNP, the status of moderators, and the disease outcome in each study population is equal to following equation:p = prevalence of outcome diseaseIt is worth noting that β0 is the logit-transformation prevalence of the outcome disease in people with homozygous major and without the moderators in study population. β1 is the log-transformation odds ratio of allele effect in people without moderators, β2 is the log-transformation OR of moderators on disease in people with homozygous major, and β3 is the log-transformation moderator effect. Following this model, we could set β0, β1, β2, and β3 to calculate P1, P2, P3, P4, P5, and P6. In our simulation, we set the mean of the minor allele frequency with 50%  in each study will be randomly generated from a beta distribution (p(x1 = 0)i, q0i], heterozygous , and homozygous minor  in each study were (1 − πi)2, 2πi(1 − πi), and πi2, respectively.In this equation, ls model . Under t−5) in the Basic model; therefore, β0, the logit-transformation disease prevalence, is log[10−5/(1 − 10−5)]. Moreover, we set the odds ratios of allele effect and moderator effect as 1.5 and 2.0, respectively; therefore, β1 and β2 are log(1.5) and log(2.0), respectively. P7, P8, and P9 are the same in the Basic model and were set at 50%. Based on the Basic model, we set two kinds of models that violated the rare disease or independence assumptions, and there are two levels in each situation. The model Minor violation of rare disease assumption replaced β0 with log[10−2/(1 − 10−2)], and the model Serious violation of rare disease assumption replaced β0 with log[10−1/(1 − 10−1)]. The model Minor violation of independence assumption replaced P7, P8, and P9 with 0.4, 0.5, and 0.6, respectively, and the model Serious violation of rare disease assumption replaced P7, P8, and P9 with 0.3, 0.5, and 0.7, respectively.x2) was encoded with values the following values: people without moderator (x2 = 0) and with moderator (x2 = 1). There were 69 case-control studies that contained information regarding gender distribution as well as 14,692 cases and 13,414 controls. The genotype of each individual, which was encoded by values of 0, 1, or 2, was randomly generated from a multinomial distribution . G1i, G2i, G3i, and G4i were the vector of genotype frequencies in cases without moderator , cases with moderator , controls without moderator , and controls with moderator , respectively. G1i, G2i, G3i, and G4i were calculated based on P1, P2, P3, P4, P5, P6, P7, P8, P9, q0i, q1i, and q2i, respectively . The confidence interval coverage rate was the proportion of the 95% confidence interval, including the real parameter. The appropriate confidence interval coverage was 95%. In addition, type 1 errors were assessed in the null moderator effect model (β3 = 0). The secondary outcome was the power of moderator effect assessment because the nonsignificant result may often be ignored. In addition, researchers often reports the results of stratified analysis when the moderator effect was significance. We also presented the 95% confidence interval coverage rate of the allele effect in people without a moderator (β1) and people with a moderator (β1 + β3).The primary outcome was the 95% confidence interval coverage rate of the moderator effect (p = 0.05 significance threshold did not significantly differ from that observed using 5% in the null moderator effect model (β3 = 0). However, the power of our method was lower than the individual patient data regression analysis, indicating that the individual patient data regression analysis was more accurate. Fst is the difference in allele frequencies among various studies. Fst = 0, 0.01, and 0.1 indicated no differences, small difference, and large difference in allele frequency between the population and a specific ethnic group, respectively. The higher Fst may reduce the power of the analysis, although this may not impact the stability of the 95% confidence interval coverage rates.Tables β1) and people with a moderator (β1 + β3). The 95% confidence interval coverage rates of our method were close to 95% in any condition under the rare disease and independence assumptions. The individual patient data regression analysis was also robust in this situation.Figs Fst. However, we observed that the 95% confidence interval coverage rates of our method were lower in the higher moderator effect model (β3 = 0.25–1.0). The extent of reduction was impacted by disease prevalence and moderator effect; the simulation with higher disease prevalence and moderator effect showed lower 95% confidence interval coverage rates. Moreover, the analytical power was reduced because of higher disease prevalence. The individual patient data regression analysis remained robust regardless of the condition. The 95% confidence interval coverage rate of the allele effect in people without a moderator and people with a moderator was also lower in the Serious violation of rare disease assumption model, and the extent of reduction was impacted by the moderator effect.Two models, Minor violation of rare disease assumption and Serious violation of rare disease assumption, tested the robustness when the outcome disease is not a rare disease, and we set the 1% and 10% disease prevalence rates in people with homozygous major without moderator, respectively. In the null moderator effect model analysis, the false positive rate of our method did not significantly differ from the 5% in any model and P7,P8, and P9, which indicated a small and strong association between SNP and moderator. We observed that the 95% confidence interval coverage rates of our method were lower in the model with violation of independence assumptions, and the extent of reduction was impacted by the strength of association between SNP and moderator. Moreover, the false positive rates of our method were significantly different from 5%. Therefore, the power analysis in this scenario was insignificant. The association between SNP and moderator did not impact the robustness of individual patient data regression analysis. Its 95% confidence interval coverage rates remained close to 95%, and it had appropriate false positive rates and high powers in any condition. Similar to the moderator effect, the results of allele effect in people without a moderator and people with a moderator showed that our method was not robust in the model with the violation of independence assumptions. The individual patient data regression analysis was also robust in any situation.We tested the robustness of our method when the situation violated the independence assumption. We set the small difference (0.1) and large difference (0.2) between This work is trying to propose a new method for meta-analysis when researchers were unable to obtain the raw data of each individual sample. It is difficult for accessing the detailed individual data ,6. Meta-Previous papers generally present the stratified results of minority participant types such as smoking status, and researchers utilize such information to assess their moderator effects . HoweverIndividual patient data analysis had the higher confidence interval coverage rate and power, and this result was similar to that of previous simulation studies on meta-analyses of RCT . HoweverThe independence assumption is important because the relationship between summary values and odds ratios does not follow a linear correlation when it occurs as a Simpson’s paradox. The independence assumption could avoid the Simpson’s paradox to determine whether the robustness of our method was insufficient when the situation violated the independence assumption. The rare disease assumption was relatively unimportant because the association between the summary values and odds ratios continued to follow a linear correlation. Therefore, the false positive rate did not increase when the situation violated the rare disease assumption. However, with the increase in disease prevalence, the effect of the summary value from the “case” and “control” on odds ratio changed. When the actual disease prevalence approached 0%, the summary value from the “case” was the only factor that influenced the estimator of the combined odds ratio. When the true disease prevalence approached 100%, the summary value from the “control” was the only factor that influenced the estimator of the combined odds ratio. In fact, the impact of the summary value from the “case” and “control” were based on the actual disease prevalence. However, diseases with >50% prevalence rates may not be present; therefore, we considered that the impact of the summary value from the “case” was always larger than the summary value from the “control.” Because researchers often could not obtain actual disease prevalence rates, we considered that detecting the interactions using the summary value from a “case” was a suitable selection. In fact, the results of the meta-regression using the summary value from the case and control groups were similar because most of the studies had similar proportions of moderators in the case or control groups . However, using the summary value of a case group was apparently a better selection because the impact weight of the summary value from the “case” was higher than that of the summary value from the “control” unless the real disease prevalence was >50%.In conclusion, we considered that building the meta-regression using the summary value from a case group may be an effective approach when the information from every individual patient in insufficient. Furthermore, this approach is extremely easy to use and could assist in defining the biological significance. Several software programs can conduct meta-regression analysis such as R and STATA, and researchers can use these to investigate the interaction between the factor of interest, such as other SNPs or environment factor, and topic SNP. On the other hand, the rare disease assumption is relatively unimportant. However, when the actual disease prevalence is >10%, the estimators of meta-regression could be distorted, although the significant interactions may still possibly remain true. The independence assumption is important. The detection method for this interaction may largely deviate from the real situation, particularly when this violates the independence assumption. However, SNPs are often unrelated to environmental factors and SNPs of other chromosomes. Therefore, these results indicate that this method is useful in genetic studies. The meta-analysis of genetic association studies could also be effectively used in detecting gene–gene and gene–environment interactions, which may be accountable for the “missing heritability.”S1 Text(DOCX)Click here for additional data file.S2 Text(DOCX)Click here for additional data file.S3 Text(DOCX)Click here for additional data file.S4 Text(DOCX)Click here for additional data file.S5 Text(DOCX)Click here for additional data file.S6 Text(DOCX)Click here for additional data file.S7 Text(DOCX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.


The domestic dog is becoming an increasingly valuable model species in medical genetics, showing particular promise to advance our understanding of cancer and orthopaedic disease. Here we undertake the largest canine genome-wide association study to date, with a panel of over 4,200 dogs genotyped at 180,000 markers, to accelerate mapping efforts. For complex diseases, we identify loci significantly associated with hip dysplasia, elbow dysplasia, idiopathic epilepsy, lymphoma, mast cell tumour and granulomatous colitis; for morphological traits, we report three novel quantitative trait loci that influence body size and one that influences fur length and shedding. Using simulation studies, we show that modestly larger sample sizes and denser marker sets will be sufficient to identify most moderate- to large-effect complex disease loci. This proposed design will enable efficient mapping of canine complex diseases, most of which have human homologues, using far fewer samples than required in human studies. The domestic dog is an important model organism for our understanding of cancer and other diseases. Here the authors conduct a genome-wide association study across multiple breeds and identify novel loci significantly associated with several complex diseases and morphological traits. Canis lupus familiaris) is considered to be an excellent animal model for human disease, with over 350 diseases in common—from hip dysplasia to lymphoma—and similar pathways and genes often underlie these shared diseases24The domestic dog  with 100 cases and 100 controls from a single breedSignificantly larger sample sizes than those used for canine disease GWAS have been used to discover genes affecting morphological traits, where breed-average phenotypes can be used rather than individual case/control or quantitative data. Large-effect quantitative trait loci (QTLs) have been found for chondrodysplasia3121431112131718192021It is an unanswered question as to what sample sizes and study designs should be employed to improve the power of mapping efforts for complex canine phenotypes6N=2,072), canine hip dysplasia , elbow dysplasia , cranial cruciate ligament disease , mast cell tumour , lymphoma (N=337), portosystemic vascular anomalies  and mitral valve degeneration .Here we conduct the largest dog genotyping study, with 4,224 samples genotyped on a semicustom 180,000 single-nucleotide polymorphism (SNP) array, in an effort to improve canine mapping for complex traits. Furthermore, we use simulations to determine how different parameters  affect the power to detect causal loci of different effect sizes. Our samples are a heterogeneous mix of purebred dogs representing over 150 breeds, 170 mixed-breed dogs and 350 free-ranging village dogs. The village dogs were sampled from 32 countries worldwide. The samples were gathered by multiple researchers and deposited in the Cornell Veterinary Biobank. Over 65 clinical and morphological phenotypes were considered, although each trait was recorded for only a subset of the cohort. The most common recorded phenotypes were body weight  ≥5%) underlying a complex phenotype. These results not only validate the dog as a large animal model for the discovery of genes associated with multigenic traits of importance to human medicine, but also demonstrate how to improve canine association-mapping methods for future studies on the genetics underlying complex canine disease.Using GWAS on the 12 most common recorded phenotypes, we find loci associated with several canine complex diseases  and idiopathic epilepsy), as well as novel loci affecting morphological traits, namely body size, fur length and shedding. Furthermore, we use simulations to show that a denser array (SNP spacing of 2 kb) and larger sample sizes  would enable the identification of moderate- to large-effect loci  for all GWAS is 1.00 (range of 0.96–1.05), showing that the stratification correction worked well. After Bonferroni correction, we identified seven significant QTLs, and one suggestive QTL, that are associated with complex canine diseases  in the gene CTBP2 —in 921 dogs across 69 breeds and found an association reaching genome-wide significance on chromosome (CFA) 28  and CFA1 , within LD of the genes POP5 and TLE1, respectively  revealed a significant QTL on CFA36 , height (untransformed), fur length on a scale from 1 to 5, fur shedding on a scale from 0 to 1). We found 17 significant associations with male breed-average weight and/or height at a false discovery rate (FDR)<0.5% and <0.75%, respectively  in addition to the known fur genes FGF5  and RSPO2 MC5R that changes the ancestral alanine to the boxer reference threonine (A237T), and was included as a custom marker on the CanineHD array because it was observed to be segregating in village dog whole-genome sequencesMC5R protein sequence is evolutionarily conserved across mammals, and we find evidence that the A237T mutation causes a conformational change in the tertiary structure of the protein, with a change in binding sites  have the ancestral MC5R allele  to 5 (long hair) phenotypic scale and identified a novel locus on CFA1  have the derived MC5R allele in the presence of the ancestral RSPO2 allele , we confirm that dog body size has a simple underlying genetic architecture3σ that are identified using 200 cases and controls is 26–27% versus 5–7% for a within-breed versus across-breed design). However, using across-breed GWAS designs, we can more easily increase sample sizes up to at least 500 cases and controls, where the power to identify the same loci increases to 24% using the current CanineHD platform , 50% heritability and 20% liability, we find that the power to detect causal loci increases with an increase in number of cases and controls . For a gplatform . Furtherplatform . Increasplatform .P=1 × 10−7 and P=5 × 10−7 respectively, are appropriate.We examined the false discovery rate (FDR), calculated as the proportion of significant loci that are false positives, in our across-breed and within-breed simulation GWAS. For across-breed GWAS designs including more than 200 cases and controls, FDR plateaus around 5% . For theUsing an across-breed GWAS design, we see an increase in power with an increase in sample size, an increase in effect size, and increased SNP density, while the latter does not apply to a within-breed design , since LIn this study, we generate the largest canine genotyping data set so far, with 4,224 dogs genotyped at 180,000 markers. We expand the number of complex disease loci and morphological QTLs known in the dog and, importantly, demonstrate the efficacy of genetic mapping in heterogeneous populations of dogs. We identify significant associations using an across-breed mapping approach for CHD and ED, and a further four significant associations within breeds for lymphoma, GC, idiopathic epilepsy and MCT. The colitis association is particularly exciting because the region has also been identified in an inflammatory bowel disease (IBD) GWAS study in humans4647Despite large sample sizes, our scans failed to detect significant associations in across-breed GWAS for several complex diseases . While a larger genotyped cohort may be needed for some diseases due to genetic architecture and environmental effects, our simulations show that increased marker density is also needed to improve mapping power across breeds. A decrease in mean marker spacing from 13 kb (the current CanineHD array spacing) to 2 kb results in an increase in power for moderate-effect loci. Based on human complex disease studiesMC5R with fur length and shedding. Because these loci have undergone selective sweeps due to strong artificial selection for fur phenotype and size, relatively large haplotype blocks and high LD surrounding the causal variants facilitate genetic mapping by improving the likelihood that array markers accurately tag each causal variant. Nevertheless, improving marker density even at positively selected loci will improve power. If the MC5R A237T mutation had not been identified in resequencing data sets and included on this array, the association between CFA1 and fur length would not have reached Bonferroni significance and may have been missed. As resequencing data sets do not show other coding variants in this region in high LD with the A237T mutationIn contrast to disease traits, the mapping results for the morphological phenotypes of fur length and body size reveal highly significant associations that are consistent with earlier studies3111316P-values up to several orders of magnitude higher for most of the QTLs, compared to using the individual-size data. This difference is likely due to the extreme variation seen in dog body size across the different breeds and the greater role of environmental effects, such as diet, on individual weights compared to breed averages. For disease traits, multi-breed mapping using individual data is needed in order to capture both across-breed and within-breed genetic variation in association studies. Importantly, a balanced GWAS design is not necessary; using dogs that are randomly chosen across different breeds seems to be just as powerful as using a balanced number of cases and controls from each breed.Unlike previous canine body size studies, we used individual phenotypes as well as breed averages to detect genetic associations. Using breed-average size data resulted in a clear increase in GWAS power for detecting body size associations, with Our modelling indicates that future studies consisting of 500–1,000 cases and 500–1,000 controls from numerous purebred and mixed-breed populations, with denser marker spacing through denser genotyping arrays and/or imputation panels, will substantially increase the number of loci known to affect canine complex diseases, many of which are homologous to human disorders. This finding suggests that studies much smaller than those currently used in human GWAS designs will yield important genetic associations, making dogs an attractive model for studying and mapping complex phenotypes.Blood samples were collected in accordance with Cornell University animal care and use guidelines (IACUC #2005-0151 and #2011-0061). Genomic DNA was extracted using a standard salt precipitation from EDTA blood samples and stored in the Cornell Veterinary Biobank. Phenotypes were recorded at the time of blood collection, but disease phenotypes continued to be updated during subsequent veterinary examinations.http://omia.angis.org.au/home/), and markers that were designed to cover gaps in the existing array . In total, 4,224 samples were genotyped (44 plates) at 185,805 markers at the Cornell University core facility. All positions are listed in canFam3.1.Genotyping was done using the Illumina 173k CanineHD arrayPLINK data sets were generated in GenomeStudio using the PLINK report plugin. Genotypes were called using a GenCall threshold of 0.15 using cluster positions that were computed for the first 30 plates. In PLINK v1.07 ref. , SNPs wiSamples with >10% missing genotypes or with recorded sex not matching genotypic sex were excluded from further analysis. Genotypic sex was computed by calculating (1) the proportion of missing Y chromosome genotypes  and (2) the homozygosity across non-PAR X chromosome markers using the PLINK --check-sex option . In this manner, XXY samples were not misidentified as females and females with highly inbred X chromosomes were not misidentified as males. To check the recorded breed of our samples, we used the PLINK --genome option to check that each individual is most closely related to other individuals of the same breed, and we also ran a principal component analysis (PCA) on each breed using the program EIGENSTRAT in the EIGENSOFT v5.0.1 packagePhasing was performed on the data set to eliminate missing genotypes through imputation, allow for haplotype-based association, and to facilitate merging data from the custom chip to published and unpublished CanineHD data sets for meta-analysisP-values. To ensure sufficient correction for population stratification, we calculated inflation factors (λ) in R (ref. All GWAS were run using a linear-mixed model in GEMMA v.0.94 ref. . Unless n R ref.  for eachP=4 × 10−7 (Bonferroni cutoff of α=0.05) was used for across-breed GWAS; for within-breed GWAS, the significance threshold was based on the Bonferroni cutoff of SNPs that were not in complete or near-complete LD as calculated using the PLINK command --indep 100 10 10. For within-breed GWAS, PCA was first run to identify and remove outlier individuals.A significance threshold of Case/control or quantitative GWAS was performed on subsets of dogs using individual clinical phenotype data, as described below. Numbers of dogs in each breed included in each GWAS are listed in Orthopaedic traits: Dogs used in GWAS of orthopaedic traits were selected from the following four sources: Cornell University Hospital for Animals, The Baker Institute for Animal Health at Cornell University, Guiding Eyes for the Blind in Yorktown Heights, NY, and the Orthopedic Foundation for Animals.Hip dysplasia: CHD is the most common orthopaedic trait in medium- and large-breed dogs, with incidences ranging from less than 10% to over 70% across purebred dogs. The diagnosis of dysplasia was initially made on orthopaedic exam, but confirmed radiographically. The measure of CHD used was the NA, which is measured on a ventrodorsal extended-hip radiograph, and ranges from <20° (worst) to 120°. We ran a quantitative GWAS on the average NA score for the two hips of each dog across 69 breeds (and including 121 mixed-breed dogs) (N=921), where all dogs were over 5 months of age and the lowest NA was set to 75 to reduce outlier effects. Adjusting the NA score for the age of the dog at diagnosis did not affect the results.1. Elbow dysplasia: ED is a group of disorders that affect the articular surfaces of the elbow or elbow congruency. The three most common forms are fragmented medial coronoid process, osteochondritis dissecans and ununited anconeal process. Radiographs are useful for diagnosing ununited anconeal process and sometimes osteochondritis dissecans, but the best diagnostic method for the fragmented medial coronoid process is computed tomography. The Orthopedic Foundation for Animals uses a flexed lateral radiograph taken at ≥2 years of age, and radiologists look for signs of secondary osteoarthritis, which always occur with this condition. ED was diagnosed radiographically and, in a small number of cases, confirmed by computed tomography or arthroscopy. Control dogs were over 2 years of age and had a normal flexed lateral radiographic examination. GWAS was performed on 113 cases and 633 controls in 82 breeds (and including 20 mixed-breed dogs). In total, 476 of the ED dogs were also included in the hip dysplasia GWAS.2. Cranial cruciate ligament disease: CCLD is the most debilitating orthopaedic trait affecting the hind limb of dogs. Ruptures were diagnosed by palpation followed by stifle radiographs or by arthroscopy/arthrotomy during surgical correction. Control dogs were over 8 years of age and were subjected to careful orthopaedic examination, specifically feeling for stability on stifle palpation  and/or stifle radiography. GWAS was done using 271 cases and 399 controls across 68 breeds (and including 53 mixed-breed dogs).3. Mitral valve degeneration. MVD accounts for nearly three-quarters of all cardiovascular diseases in dogs, with small-breed dogs (<9 kg) more commonly affectedMast cell tumour: MCTs are the most common skin tumour in the dog, with a reported annual incidence of 126 cases per 100,000 dogset al.Phenotypic criteria included cytologic and/or histologic confirmation of the tumour at excisional biopsy and histologic grading. Control dogs (more than 8 years of age at presentation and not diagnosed with any other type of cancer) had all skin masses mapped and fine-needle aspirated by board-certified oncologists, and the cytology of all masses was reviewed to confirm the absence of mast cells. We performed a GWAS for MCT using 359 cases and 146 controls across 41 breeds, and another GWAS for Labrador Retrievers only, which included 152 cases and 106 controls after removal of PCA-identified outliers.Lymphoma: Lymphoma is the most common haematopoietic tumour of dogs, with a reported annual incidence of 79–103 cases per 100,000 dogs, with annual incidence rates in some breeds above 200 per 100,000 dogsGC in boxers and bulldogs: GC is a severe inflammatory bowel disease (IBD), typically diagnosed in Boxers and Bulldogs younger than 4 years of age. It is characterized by periodic acid-Schiff-positive macrophages and mucosally invasive E. coli30E. coli-positive, while unaffected dogs were non-GC with no invasive bacteria. Forty individuals were previously genotyped on the CanineHD array and merged with the current data set.Portosystemic vascular anomaly: PSVA is characterized by a severe malformation of the portal vein that carries splanchnic blood to the liver, and mainly afflicts small-breed dogs. Dogs with PSVA fail to detoxify substances in blood, resulting in high serum bile acid concentrations, seizures, lethargy and vomiting. Total serum bile acid (TSBA) values in young dogs (<4 years) were used to directly indicate phenotype status, whereas TSBA values in older dogs (>5 years) were interpreted in the light of that dog's health status  to rule out misinterpretation of acquired liver disorders as congenital vascular malformations. Control dogs had TSBA concentrations <25 μmol l−1, while cases had TSBA concentrations >25 μmol l−1. We conducted a PSVA GWAS using a balanced case/control design of eight small-sized breeds  and small-breed mixes, for a total of 160 cases and 155 controls. Our GWAS on Yorkshire Terriers included 57 cases and 101 controls, after removal of five dogs from the data set that were PCA outliers.Idiopathic epilepsy in Irish Wolfhounds: Idiopathic epilepsy was diagnosed by exclusion of other causes for seizures in all of the affected dogs. In a previous study of 796 Irish Wolfhounds, 146 dogs were diagnosed as having idiopathic epilepsyBreed mapping: Using a pruned data set of 1,873 unrelated individual dogs (maximum of 25 dogs per breed), from 158 breeds, we performed breed-average GWAS on several different morphological phenotypes: shedding, fur length, body weight and height at withers. Ancestral alleles for specific loci were determined by looking at the genotypes of a culpeo fox and wolf samplesBody size: Average male body weights were assigned to breeds based on American Kennel Club standards, CanMapwww.ncraoa.com) and compared to the averages of individual measurements from the Canine Behavioral Assessment and Research Questionnaireet al.0.38, as determined by Box–Cox transformation. Significance cutoff was set to P=5 × 10−6 . The raw breed-average male heights were used in the GWAS, also run as a quantitative trait. Breed-average values used in the GWAS are listed in N=2,072) measured in dogs over 1 year of age. Sex-corrected weights were computed by increasing female weights by 19% to account for the sexual dimorphism that we observed.Weight was run as a quantitative trait using the breed-average male weight0.38 and corrected height based on the 17 QTLs identified from the GWAS study to identify the additive effect of each locus. Observed weights and heights were corrected by first increasing female weights by 19% and female heights by 8% . After applying a 0.38-power transformation to the body weights, inbreeding correction based on the inbreeding coefficient, F, estimated by Germline v1.5.1  for all purebred dogs and setting F and breed as independent variables. These corrected weights and heights were used in linear models for each of the data sets: breed dogs  and village dogs.Using the function lm in R, we ran a linear additive model of corrected weight5.1 ref.  was doneTo determine the effect of the QTLs within breeds, we ran the original linear model, but with an independent variable, breed, as well as the 17 QTLs. To determine the effect of the QTLs among breeds, we ran the same linear model using  breed averages instead of individual heights and weights. For all linear models using individual phenotypes, QTL variables were encoded as 0/1/2 based on the derived allele count for each individual; for the linear models using breed averages, derived allele frequencies within each breed were used. No inbreeding correction was made for models using breed average phenotypes.N=2,072), we used GCTA67For individual body weight in dogs , medium–short , medium , medium–long  and long  ( breeds) .http://www.predictprotein.org) and the 3D structure was modelled in Swiss Model (http://swissmodel.expasy.org) using 3EML as the template.PolyPhen-2 ref.  was usedShedding: Phenotype information was collected from eight different websites: akc.org, dog-breeds.findthebest.com, www.1800petmeds.com, dogtime.com, www.dogbreedinfo.com, www.vetstreet.com, www.petstew.com and www.yourpurebredpuppy.com. Seasonal shedders  and hairless breeds  were excluded from the analysis. Shedding was mapped by assigning dog breeds into the categories of minimal , average  and heavy  shedders, assigned a value of 0, 0.5 and 1, respectively, to be used in quantitative GWAS  200 generations ago, which itself was founded from a ‘wolf' population with Ne=15,000, 4,000 generations earlier after a 150-generation bottleneck (Ne=600). We simulated 38 chromosomes (50 Mb per chromosome) with a mutation rate of 1e−8 and recombination rate of 1e−5. To ensure we could sample 500 diploid individuals  per population, we simulated larger population sizes  for the purebred populations for the final four generations , and selected segregating variants from those individuals either uniformly or based on the distribution of inter-SNP distances for the CanineHD array. For selecting uniform variants, we selected variants in order by selecting the subsequent ascertained variant in the simulation closest to 2 kb (or 10 kb) downstream. For selecting variants with CanineHD-like spacing, we permuted the inter-marker distances between consecutive markers on the CanineHD array, and then selected the subsequent simulated ascertained variants closest to this distance from the previous included variant.FST values and rates of LD substantially overlapped for the simulated and observed populations. Across all populations, weighted FST was 0.24 in the simulated populations versus 0.226 in the observed data (pairwise FST range was 0.12–0.51 versus 0.08–0.30). LD decay was somewhat faster within the simulated populations, with mean r2 being 0.247 (range 0.14–0.47) versus 0.235 (range 0.126–0.411) for autosomal markers 95–112.5 kb apart within simulated and observed populations, respectively. Thus, the simulation captures key aspects of dog population structure that influence mapping, but may somewhat underestimate the power to detect QTLs in real dog populations if LD is greater in those populations.To compare population genetic parameters between our simulation and the purebred populations in our study, we randomly selected 25 individuals from each simulated purebred population and compared these to the 31 breeds in the pruned data set containing exactly 25 individuals. We compared the CanineHD-like ascertained variants from our simulation to our array data, and found that the simulated σ, 0.5σ, 0.75σ, σ and 1.25σ, and we simulated a 20% disease liability (--simu-cc 2100 8400 --simu-hsq 0.5 --simu-k 0.2). As a control, we also simulated a sixth locus with 5–10% MAF and effect size of 0. We had 100 iterations in total.For simulating complex diseases, we used the GCTA --simu-qt option with five randomly selected causal variants  chosen from a list of all variants at 5–10% cumulative MAF across the 30 populations. Effect sizes were randomly assigned to the causal loci such that each iteration included effect sizes of 0.25Genotypes at ascertained markers for subsets of cases and controls were selected using PLINK, and case/control associations were run in GEMMA using a MAF filter of 5% and a kinship matrix as a random effect. Within-breed GWAS designs were done using 100 (or 200) cases and controls from within a single breed, and two breeds were used for each of the 100 iterations. We used four different across-breed GWAS designs: balanced, random, semibalanced and unbalanced. For each of these, we used 100, 200, 500, and 1,000 cases and controls. A balanced GWAS had an equal number of cases and controls from each breed. In a random GWAS design, the cases and controls were chosen randomly across any of the 30 breeds using the linux command shuf. A semibalanced design had the number of cases from each of 20 breeds proportional to the prevalence in that breed. In an unbalanced GWAS, we used an equal number of cases and controls from each of 20 breeds, but this number was proportional to the prevalence in each breed.P-value cutoff of ≤5 × 10−7 (current array and 10k array) and ≤1 × 10−7 (dense 2 k array). These cutoffs are approximately 5% Bonferroni cutoffs, and were therefore similar to the thresholds we set for our complex disease GWAS. False discovery rates were calculated as the number of false-positive loci over the total number of significant loci  for each GWAS design and array. Plots of results were generated in R and IPython notebook using Matplotlib library.The power of each GWAS was determined by counting the number of iterations (out of 100) that had detected the causal loci  with a Accession codes: Genotype and phenotype data have been deposited in Dryad .How to cite this article: Hayward, J. J. et al. Complex disease and phenotype mapping in the domestic dog. Nat. Commun. 7:10460 doi: 10.1038/ncomms10460 (2016).Supplementary Figures 1-7, Supplementary Tables 1-3, Supplementary Methods and Supplementary ReferencesNumbers of breeds used in each disease GWAS.Values used in average-breed GWAS for morphological phenotypes.